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Cation Adsorption in TiO2 Nanotubes: Implication for Water Decontamination

Cite this: ACS Appl. Nano Mater. 2023, 6, 14, 12711–12725
Publication Date (Web):July 11, 2023
https://doi.org/10.1021/acsanm.3c00916

Copyright © 2023 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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TiO2 nanotubes constitute very promising nanomaterials for water decontamination by the removal of cations. We combined a range of experimental techniques from structural analyses to measurements of the properties of aqueous suspensions of nanotubes, with (i) continuous solvent modeling and (ii) quantum DFT-based simulations to assess the adsorption of Cs+ on TiO2 nanotubes and to predict the separation of metal ions. The methodology is set to be operable under realistic conditions, which, in this case, include the presence of CO2 that needs to be treated as a substantial contaminant, both in experiments and in models. The mesoscopic model, based on the Poisson–Boltzmann equation and surface adsorption equilibrium, predicts that H+ ions are the charge-determining species, while Cs+ ions are in the diffuse layer of the outer surface with a significant contribution only at high concentrations and high pH. The effect of the size of nanotubes in terms of the polydispersity and the distribution of the inner and outer radii is shown to be a third-order effect that is very small when the nanotube layer is not very thick (ranging from 1 to 2 nm). Besides, DFT-based molecular dynamics simulations demonstrate that, for protonation, the one-site and successive association assumption is correct, while, for Cs+ adsorption, the size of the cation is important and the adsorption sites should be carefully defined.

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1. Introduction

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Human activities in industry, technology, and energy production generate various contaminants, such as organic compounds, dyes, radionuclides, or heavy metals, which entail a serious hazardous threat to life in general. Those emerging pollutants are difficult to remove, and therefore, finding new alternatives for water remediation is highly required. As instance, the presence of radionuclides in the aquatic ecosystem can lead to serious hazardous events in the environment due to their long half-life. The nuclear waste management process usually employs chemical methods, which involve chelator ligands that bind metal cations and remove them from wastewater. However, the undesired consequence is the production of waste, which has to be further processed. The new strategies for water remediation are based on carbon, (1) polymeric (2) and organic materials, (3) inorganic composites, (4) and hybrid inorganic–organic materials. (5−7) The aforementioned materials are employed as adsorbents, photocatalysts, and biocatalysts in water recovery processes. Although numerous methods are available for water remediation, adsorption has been recognized as a method of choice, due to its efficiency, simple design, and performance. The adsorption on porous nanomaterials (NMs) serves as a promising strategy for the selective removal of cations. In the context of water decontamination by selective removal of cations, especially in the framework of the nuclear industry, cesium (8) and strontium (9) are important target metal ions for which porous nanomaterials have a considerable potential. (10) Among all the existing metal–oxide nanotubes, very interesting are the titanium oxide nanotubes (TiO2 NTs) due to their nontoxicity, low-cost synthesis, high photocatalytic activity, and chemical stability, as well as their reusability for multiple decontaminations and stripping cycles. (11) Moreover, they present very good adsorption properties due to large specific surface areas and to the fact that both inner and outer surfaces are in contact with the interacting medium. Their amphoteric character enables tuning the solute adsorption with respect to ambient pH and composition of the colloidal suspension of nanotubes. (12) For all these reasons, TiO2 NTs are a very promising improvement from existing composite materials.
The fundamental knowledge of the adsorption properties of nanoporous nanomaterials is crucial for optimizing their applications such as metal decontamination, (13) photocatalysis, (14) organic molecules removal or decomposition, (15) etc. Numerous studies investigated the adsorption and decontamination efficiencies of loose nanotube materials. (13) From a fundamental point of view, it is still unclear whether the solute adsorption is equivalent between the inner and outer nanotube surfaces exposed to the liquid medium. Furthermore, it is not evident if solutes are chemi- or physisorbed on the nanotube surfaces at thermodynamic equilibrium. However, it is of paramount interest to understand these two questions before designing any practical process at the laboratory scale or at the pilot scale. To access the equilibrium properties, the classical approaches usually employ Langmuir-like models, in which all the surfaces are treated equally. (13,16) While this is a very good approximation for the gas adsorption by nanotubes or by other porous materials, (17) it is not sufficient when the objective is to assess the preferential adsorption of solutes on the nanotubular structures in a liquid medium. Moreover, in the case of a higher affinity for adsorption of solutes on either inner or outer nanotubes surface, it would impact process efficiencies beyond adsorption/decontamination, but including doping, photocatalysis, and contaminants degradation, etc. This is why further studies in this domain are required.
In the context of studying the efficiency of adsorption by nanomaterials, batch adsorption experiments are used in most cases. Nevertheless, the resulting adsorption efficiency from the batch experiment in the solid state should not be confused with the properties of the aqueous suspension, where the nanomaterial is in equilibrium with all ions and water. Apart from directly at the nanomaterial surface, ions reside in the electric double layer (EDL). (18) To assess the adsorption properties in the aqueous suspension, the activity of protons, also called the proton consumption, is measured during the titration experiments and can be directly compared to the mesoscopic models that take into account the local equilibria between the solution and the exposed surfaces of the adsorbent. (19,20) For the amphoteric nanomaterials, it was also shown that the size and curvature of the EDL are important. While a lot of work has been done on addressing the charge properties for variable sizes of TiO2 or SiO2 nanoparticles, (21,22) considerations are limited to the average size in terms of lengths and radius for nanotubular structures. Moreover, in the case of TiO2 NTs, the distributions of inner and outer radii and lengths can be severely polydisperse. (23) Overall, the usual route to probe the adsorption of solutes from the aqueous suspension is to combine potentiometric acid–base titration experiments with surface complexation (SC) models. (24) SC models are usually merged with classical density functional theory (cDFT), or simple Poisson–Boltzmann. (25) The idea is always the same: to connect analytical chemistry speciation by multiple equilibria (SC models) with the spatial distribution of ionic species in EDL in the presence of the nanomaterial. The general framework is very powerful since it has been applied consistently (with upgrades) for decades now, with applications in colloidal chemistry, geochemistry, nanopores, biophysics, and many other applied chemistry fields. (26,27)
While the technologies that use nanoporous materials are yet to ripen, pilot and larger scales processes will operate in air atmosphere conditions. (28) This means that CO2 is always present in separation processes and can therefore be considered as an impurity or as a contaminant. (20) Nevertheless, the effect of CO2 is seldom included or rationalized in most models. In the case of the TiO2 NTs, the study based on the SC-cDFT approach reported preferentially higher proton adsorption on the inner nanotubes surfaces at equilibrium, which led to a higher charge on the outer surfaces. (29) The predicted charging mechanism demonstrated a strong influence of the bulk pH and salt concentration. While, for these amphoteric materials, the adsorption is primarily governed by the electrostatic interactions between solute and adsorbent, the mesoscopic effects of the solutes confinement as well as the curvature of nanotubes also presented a significant effect. (23) Besides mean-field mesoscopic models, molecular dynamics simulations can bring useful insights into the adsorption mechanisms at a molecular level, (30−32) which are of uttermost importance to characterize the Cs+ adsorption on TiO2 NTs. Considering the significant reactivity of TiO2 surfaces in the presence of water, particularly in terms of acid–base reactions, density functional theory (DFT) based molecular dynamics (DFT-MD) simulations represent a very efficient compromise between the accuracy, including the description of the reactivity, and the computational costs. (33,34)
In this study, by a systemic experimental and theoretical work, we encompass different time and length scales to describe the charge inhomogeneities of TiO2 NTs in aqueous suspensions in terms of all relevant constituents and resulting chemical equilibria (ions and nanotubes). We used high-resolution transmission electron microscopy (HR-TEM) and atomic force microscopy (AFM) to assess the structural properties of TiO2 NTs and electrophoretic mobility measurements, potentiometric acid–base titrations, and batch adsorption experiments to probe the cation adsorption of TiO2 NTs in aqueous suspensions. The experiments are combined with two different scales of modeling to address the question of the preferential adsorption of Cs+ and similar solutes on the exposed nanotube surfaces: a mesoscopic Poisson–Boltzmann electrostatic description and DFT-based molecular dynamics simulations. The objective is to derive a feasible model and to compare it with macroscopic experiments such as potentiometric acid–base titrations, in which the total amount of ions is changed with the addition of the titrant. Meanwhile, we include the effects of dissolved CO2 that can act as a contaminant and can be a significant contributor to charge properties in both models and the experiments.

2. Experimental Section

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2.1. Materials

The synthesis of TiO2 NTs was based on TiO2 P25 (75% Anatase, 25% Rutile Degussa) and is depicted in Figure 1. The nitric acid (HNO3), sodium hydroxide (NaOH) and cesium hydroxide (CsOH) were provided by Riedel de Haën. Cesium nitrate (CsNO3) was purchased from Fluka. Potassium hydrogen phthalate (KHP) used for the NaOH standardization was obtained from Sigma-Aldrich. Five standard buffers, pH = 2, 4, 6, 8, and 10 that were purchased from Reidel-de Haën were used for the potentiometric measurements, i.e., electrode calibration. All solutions were prepared by dissolving them in CO2-free deionized water. All chemicals were used as-received without purification.

Figure 1

Figure 1. Synthesis of TiO2 nanotubes.

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2.2. Methods

TiO2 NTs were fabricated as reported in our previous studies. (23) The composition and structural properties of TiO2 NTs were determined with powder X-ray diffraction (PXRD) and attenuated total reflectance Fourier transform infrared spectroscopy (ATR FTIR). The morphological features were obtained via HR-TEM, SEM, and AFM. The specific surface area was determined with a multipoint Brunauer–Emmett–Teller method. The acid–base surface properties were elucidated by means of acid–base potentiometric titrations and electrokinetic measurements, for which all chemicals were used as-received without purification. To test the adsorption affinity of cesium ions for the TiO2 NTs surface, we performed adsorption measurements.
Due to the number of methods performed for this study, a detailed description of the experimental part is given in the Supporting Information.

3. Theory and Atomistic Simulations

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3.1. The Mesoscopic Model for Theoretical Description of TiO2 NTs Charge Properties and Cation Adsorption

We propose a mesoscopic method to simulate the behavior of ions around solid amphoteric nanotubes, in this case, TiO2 NTs, during the potentiometric acid–base titration experiment under an air atmosphere. The method is exhaustive, in the sense that all experimental quantities are simulated in a self-consistent way. These quantities are the pH, the total quantities of all ions and the surface sites of amphoteric nanotubes. Our method allows adjusting a small number of unknown parameters of the system, those which characterize the adsorption properties of the ions. An output of the results is also the determination of the ion spatial distributions between all locations of the system: inside the tubes, on the surfaces, and outside the tubes. We also handle CO2 “contamination”, inserting reference titration results, namely, TiO2 free titrations, into the titration simulations. To our knowledge, such a model has never been published.
To represent the CsNO3 aqueous suspension of TiO2 NTs, we consider an infinitely long tube immersed in an ideal gas of ions with dielectric properties of the medium being expressed by the dielectric constant ϵr,1. The experimental conditions of potentiometric acid–base titrations were (a) low suspension mass density (γ = 1 g dm–3) and (b) moderate CsNO3 concentrations (c(CsNO3) from 0.001 mol dm–3 to 0.01 mol dm–3). To simplify the mode, we neglected the interactions between TiO2 NTs based on the argument that these latter are sufficiently diluted, and electrostatic potentials for moderate salt concentrations are screened over a shorter distance compared with the average distance between NTs.
To represent the amphoteric character of TiO2 NTs, the model NTs surface charge was modulated via a charge regulation mechanism. (35) Figure S8 (see Supporting Information) shows the schematic representation of the charging processes that take place at both TiO2 NTs surfaces. Both surfaces have the same site density and the same type of sites and are in contact with the aqueous solution containing ions. The dielectric properties of the aqueous solution, ϵr,1, and of the TiO2 solid, ϵr,2, are considered as equal (ϵr,1 = ϵr,2 = 80.1). We considered anatase planes based on structural data (see Figure 2). By considering only anatase, we simplify the model. The heterogeneity of the TiO2 NTs samples (36) in terms of the presence of amorphous solid, different exposed atoms, the polydispersity of sizes, etc. mandates simplification of the model, which reduces the number of adjusted parameters. (37) We focused on the preferential cation adsorption between the exposed surfaces, for which we considered a single adsorption site along with multiple equilibria model for successive protonations and Cs+ associations onto the exposed oxygen atom. (38) We obtained the following set of equilibria, expressed as site-ion association constants:
≡TiO−4/3+H+⇌≡TiOH−1/3;⁣KH,1={≡TiOH−1/3}{≡TiO−4/3}[H+]loc,j
(1)
≡TiOH−1/3+H+⇌≡TiOH2+2/3;⁣KH,2={≡TiOH2+2/3}{≡TiOH−1/3}[H+]loc,j
(2)
≡TiO−4/3+Cs+⇌≡TiOCs−1/3;⁣KCs,1={≡TiOCs−1/3}{≡TiO−4/3}[Cs+]loc,j
(3)
≡TiOH−1/3+Cs+⇌≡TiOHCs+2/3;⁣KCs,2={≡TiOHCs+2/3}{≡TiOH−1/3}[Cs+]loc,j
(4)
where [H+]loc,j and [Cs+]loc,j are local (surface) ions concentrations. Index j depicts either the inner or outer nanotube surface. Local concentrations are functions of the electrostatic potential at the surfaces ψ(r = Rinner) or ψ(r = Router), (39) KH,1 and KH,2 are successive surface protonation reactions, and KCs,1 and KCs,2 correspond to Cs+ association constants. The interactions of the surface groups are taken into account indirectly through the mean field approximation. (40) The surface sites density Γ is defined as
Γ={≡TiO−4/3}+{≡TiOH−1/3}+{≡TiOH2+2/3}+{≡TiOCs−1/3}+{≡TiOHCs+2/3}
(5)
It follows that the surface charge densities are defined as σj = eΓ∑x=15zxfx,j., where e is the elementary charge, zx represents charges of sites x (eq 5), and fx,j are populations of the site x on the surface j. fx,j values are obtained by combining eq 1 to 4. Full expressions for fx,j are given in the Supporting Information.

Figure 2

Figure 2. Characterization of nanotubes sample. (a) Powder X-ray diffraction patterns of the TiO2 powders used in this study. (b) Topography (height) image of annealed TiO2 NTs sample.

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Besides, to represent the effect of the CO2 as a contaminant in acid–based titrations of nanomaterials suspension, we considered the following set of chemical equilibria:
CO2(g)⇌CO2(aq);⁣K°=[CO2]aqtotpCO2/p°
(6)
CO2(aq)+H2O⇌HCO3−+H+;⁣KA1
(7)
HCO3−⇌CO32−+H+;⁣KA2
(8)
where KA1 and KA2 are carbonates successive dissociation constants. The objective of the model is to calculate the total concentration of dissolved CO2 in the solution or suspension [CO2]aqtot, as a function of pH. Once the quantity [CO2]aqtot as a function of pH is known, HCO3– and CO32– speciation can be imported in the total proton balance calculation of the system. By considering this, we considered the contaminant at any point within the potentiometric titration experiments. This is the route toward applying mesoscopic models for real application systems of TiO2 NTs (and metal oxides in general) under an air atmosphere that have the potential for scaling to the pilot process. [CO2]aqtot is fitted from the blank titration and it is assumed that, for short time intervals, the dissolution rate of CO2 in the aqueous medium is the same for CsNO3 aqueous solution and for the dilute suspension containing TiO2 NTs. The full model derivation and the fitting of the blank titration procedure are given in detail in the Supporting Information.
To account for the electrostatic interactions in the system composed of a single, infinitely long TiO2 NT immersed in the aqueous solution containing the ions, we adopted the classical Density Functional Theory (c-DFT) of inhomogeneous Coulomb fluids. (41) We considered a cell model in which the infinitely long TiO2 NT is placed. (41,42) Ions were considered as an ideal gas under the influence of an external electric field arising from the TiO2 NT surface. Ions interacted with both the inner and outer surface of the nanotube and ion–ion interactions were Coulombic only. The minimization of the grand canonical potential functional yielded one-body ion densities ρα(r) = ρα0 exp(−zαΦ(r)), where ρα0 is the concentration of the ion α in the bulk (the reservoir), zα is the charge of that ion, and Φ(r) = eΨ(r)/kBT is the “dimensionless” potential. Ψ(r) is the electrostatic potential, e is the elementary charge, kB is the Boltzmann constant, and T is the thermodynamic temperature. (43) By introducing ion densities into the Poisson equation and considering only the radial component of the Laplace operator in the cylindrical coordinate system, one can derive the Poisson–Boltzmann level of description for the infinitely long nanotube:
d2Φ(r)dr2+1rdΦ(r)dr=−4πlB∑αzαρα0exp(−zαΦ(r))
(9)
where lB = e2/4πkBTϵ0ϵr,1 is the Bjerrum length and ϵ0 is the vacuum permittivity. Noteworthily, κ=(4πlB∑αzα2ρα0)1/2 is the inverse Debye length. We considered that dΦ(r)dr was 0 at r = 0 due to the symmetry (zero charge in the middle of the nanotube) and that the total charge was 0 at r = +∞. Using the continuity equation, we obtained the electrostatic potential through the TiO2 NTs layer in the following expression:
Φ(r)=Φ(Rinner)+e∫0Rinnerϱel,1rdrε0εr,2kBTln(Rinnerr)+eσinnerRinnerε0εr,2kBTln(Rinnerr)
(10)
The full model derivation is given in the Supporting Information.
To summarize, the model presented in this work is an extension of the theoretical framework first derived to qualitatively explain the results of colloidal polyelectrolyte titration of TiO2 NTs. (29) The three key differences here are (i) the inclusion of Cs+ association and competition reactions, (ii) the consideration of dissolved HCO3– and CO32– species, and (iii) the calculations that were made in the semigrand canonical ensemble, which means that we can reproduce the potentiometric acid–base experiments directly (only water molecules are considered as intensive quantity by high dilution).

3.2. Numerical Implementation of the Mesoscopic Model

We simulate the global adsorption system numerically. The simulation intends to mimic closely the experimental process: CsOH is added steadily to the initial CsNO3 aqueous suspension of TiO2 NTs. While the pH is measured for any addition of a volume of the base, Vd(CsOH), Cs+, NO3–, H+, and OH– concentrations are known from the experiment and simulated from the code. The simulation includes self-consistent potential and concentration profiles. Concentrations include Cs+, NO3–, H+, and OH– species, both in the aqueous medium and on the inner and the outer NTs surfaces. We proceed to iterations at two levels: (i) on the electric potential (inner loop) and (ii) on the concentrations (outer loop). Each guess for Cs+ and NO3– concentrations at a long distance from the nanotube generates a simulated pH through electroneutrality. The concentration of ions anywhere in space is the product of the bulk concentration and the Boltzmann factor. We proceeded to the inner iteration loop. Each iteration loop starts with a guess of the potential at the center of the tube and ends with the electric potential over a long distance (the bulk value). Inner iterations stop when the potential is negligibly small over a long distance. The total Cs+ and NO3– are then calculated and sent to the outer loop. The following iterations proceed with new guesses about Cs+ and NO3–. We resume outer loop iteration until the total concentrations match the experimental values. We underline that using electroneutrality for the determination of the pH is critical at neutral pH since the concentrations of both H+ and OH– ions can be small. Note that the total quantity of ions is the sum of the concentrations at a long distance, adsorbed ions at both surfaces, and in double layers both inside and outside of nanotubes. This is how we fulfill the criteria for the spontaneous adsorption of Cs+ and H+ through iterations. The details of the numerical implementation are given in detail in the Supporting Information.

3.3. Atomistic Simulations

All the calculations were conducted using the Vienna Ab Initio Simulation Package. (44) The semilocal exchange-correlation PBE functional in the generalized gradient approximation of Perdew and co-workers was used (45) along with the D2 method of Grimme to take into account the dispersion forces. (46) The electron–ion interactions were described using the projector augmented wave method (47,48) with a plane-wave cutoff kinetic energy of 400 eV. The following valence electrons were considered: 1s1 for H, 2s22p4 for O, 3s23p64s13d3 for Ti, 2s22p3 for N, and 5s25p66s1 for Cs. All the calculations were performed using the Γ-point only due to the large size of the cell and the significant disorder of atoms. The Kohn–Sham equations (49,50) were solved self-consistently (51) until the difference in energy between cycles was lower than 10–4 eV. For the relaxation of the first primitive cell and of the slab prior to the DFT-MD simulations, the calculations were conducted using a 4 × 4 × 4 k-points grid with a kinetic cutoff energy of 1,000 eV, an energy threshold of 10–8 eV, and the relaxation was stopped when all forces were lower than 10–3 eV· A–1. Since the semilocal DFT exchange-correlation functionals such as PBE are known to inaccurately describe the high-correlated nature of Ti 3d electrons, we used the DFT+U formalism of Dudarev, (52) as implemented in VASP. The on-site Coulomb repulsion of the Ti 3d electrons was described using U = 3.50 eV (and J = 0.00 eV), considering most values used in the literature. (53−56) The NVT DFT-MD simulations were conducted using a Nosé–Hoover thermostat (57−59) at a temperature of 300 K with a time step of 1 fs, allowed by replacing the mass of the proton by that of the tritium isotope. Each DFT-MD simulation was conducted during 80 ps, and a thermalization period of 10 ps was excluded at the beginning of the simulation.
A primitive cell of anatase was generated following the experimental cell parameters a = b = 3.7842 Å, c = 9.5146 Å, and α = β = γ = 90° given by Horn and co-workers. (60) This quadratic cell was relaxed in terms of ion positions, cell shape, and cell size, and the fully relaxed primitive cell exhibited a = b = 3.9344 Å, c = 9.7244 Å, and α = β = γ = 90°, which was in good accordance with the experimental parameters. Based on this relaxed primitive cell, we generated a supercell and created the (101) surface, which is known to be the most exposed surface of anatase. (53,61−63) The obtained slab was composed of three layers of 12 titanium atoms, which therefore represented a total number of 36 titanium atoms and 72 oxygen atoms (Figure S15a). On the (101) surface, among the 12 titanium atoms that constituted the surface plane, six were five-coordinated and located slightly above the average surface plane, while the six others were six-coordinated, like in the TiO2 bulk, and located slightly below the average surface plane. Besides, the in-plane surface oxygen atoms were three-coordinated, like in the TiO2 bulk, while six oxygen atoms were significantly above the average plane and were only two-coordinated. The ions positions of this slab was relaxed by a static DFT calculation that consisted in a series of wave function optimizations. To avoid any unwanted interaction between the two reciprocal surfaces (whose existence is due to the periodic boundary conditions), a vacuum of 20 Å was added above the uppermost atom of the TiO2 slab along the z-axis. Then, explicit water molecules were randomly added using the packmol software, (64) to completely fill in the aforementioned vacuum by meeting a density of 1 g cm–3 for the added liquid phase. The DFT-based molecular dynamics simulations were conducted on this system. For the simulations performed with CsNO3, the latter was added close to the surface by substituting four water molecules. All the molecular structures were visualized using VESTA software. (65)

4. Results

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4.1. Synthesis and Characterization

An alkaline hydrothermal synthesis route was applied to produce TiO2 NTs. TiO2 anatase in 10 mol dm–3 NaOH was treated for 65 h at 140 °C. The annealing post-treatment of the TiO2 NTs was performed in order to investigate the effect of the annealing temperature on the crystallinity of TiO2 NTs. PXRD was employed to determine the composition and crystal structure of the TiO2 NTs. The obtained PXRD diffraction pattern of the TiO2 NTs corresponds to protonated titanate, H2Ti3O7 (Figure 2a). Besides, the specific surface areas for raw and annealed TiO2 NTs were determined using BET, which showed a slight decrease in the specific surface area for the annealed TiO2 NTs at 200 °C and s = 238.35 m2 g–1. The calcination as a postsynthesis treatment was employed to increase the crystallinity of the TiO2 NTs. Besides crystallinity, the size of crystallites also increased, while the specific surface area decreased. The structural stability of TiO2 NTs was altered as the calcination temperature increased. The decrease in the peak intensities and peak disappearance started at 300 °C due to the collapse of the NT structure and the loss of tubular integrity. As the calcination temperature increased to 400 °C, a phase transition was observed and surface area significantly decreased due to growth of TiO2 crystallites and the complete loss of the tubular integrity. The small decrease in the specific surface area of the TiO2 NTs at 200 °C could be explained by sintering damage until the calcination temperature was elevated enough to cause structural changes. The composition of the TiO2 NTs was also confirmed using FTIR. On the FTIR spectra, the characteristic bands of protonated titanate were observed as well as a broad band that corresponds to coordinated water molecules (see Figure S1 in the Supporting Information). Meanwhile, the AFM image of the sample showed agglomerates of nanotubes that formed after spreading the solution with TiO2 NTs on top of the mica sheet (see Figure 2b). Sizes of the TiO2 NTs were determined from the line profile shown in Figure S2a,c in the Supporting Information. The height was in the range from 5 to 15 nm and the length was in the range from 50 to 250 nm.
The effect of the annealing process on the tubular morphology was also studied by using HR-TEM, where the powder sample was applied directly to a lacey carbon-coated Cu grid. The images of the nanoparticles show a characteristic tubular geometry contrast, in which the nanotubes walls display a higher intensity (darker in TEM and STEM-BF images and brighter in STEM-HAADF images, see Figure 3). During the annealing of the solid sample, the increase of the temperature from 200 to 500 °C resulted in the disappearance of the characteristic diffraction peaks of protonated titanate, while the anatase crystalline phase became dominant. To obtain the best crystallinity of TiO2 NTs, the temperature of 200 °C was chosen for the annealing process, to avoid any disruption of the tubular morphology (see Figure 2 in Supporting Information). TEM and STEM images are presented in Figure 3.

Figure 3

Figure 3. (a, b) TEM of TiO2 NTs sample. (c) Histogram of TiO2 NTs inner and outer diameter distribution. (d, f, i) STEM/HAADF micrograph of TiO2 NTs sample. (g, h) STEM/BF micrograph of TiO2 NTs sample.

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The length of the TiO2 NTs is around 200 nm on average; the histogram of inner and outer diameter distribution (Figure 3c) suggests that the inner radii Rinner range from 2 to 5.5 nm, with the most frequent value being Rinner = 3.5 nm while the outer radii Router range from 2.5 to 6 nm, with the most frequent value being Rinner = 4 nm. The thickness of the solid TiO2 layer (the thickness of the nanotube wall) is, on average, 1 nm. The contrasts in the TEM and STEM images in Figure 3 are characteristic of tubular geometry. The solid TiO2 NTs sample that was removed after the batch adsorption experiment was conducted (see the following section) was analyzed in order to identify the adsorbed Cs atoms. Since the intensity of the signal in STEM-HAADF images depends upon the atomic number, the bright spots in images f and i are individual Cs atoms.

4.2. Properties of TiO2 NTs Aqueous Suspensions

The properties of the aqueous suspensions of TiO2 NTs were probed by electrophoretic mobility measurements and by potentiometric acid–base titrations. The electrophoretic mobility measurements were conducted at two concentrations of CsNO3 in the system, namely, c(CsNO3) = 0.001 mol dm–3 and c(CsNO3) = 0.01 mol dm–3 (see Figure S4 in the Supporting Information). The results show the usual property of TiO2 NTs, which is a pronounced shift of the isoelectric point (pHiep) from pH = 3 at c(CsNO3) = 0.001 mol dm–3 to pH = 4 at c(CsNO3) = 0.01 mol dm–3. (23) For pH values below pHiep, the TiO2 NTs are positively charged, while, for pH values above pHiep, the TiO2 NTs are negatively charged. Qualitatively, the shift in pHiep with the increase of CsNO3 salt suggests specific cation partitioning in the vicinity of the nanotube (either adsorbed and/or in the EDL). (20) Furthermore, the magnitude of the ζ potential is globally smaller in absolute value in the case of a higher CsNO3 concentration for the entire pH range, suggesting further screening of the surface charge.
For further investigation concerning the ion partitioning in the TiO2 NTs system, we focused on the complementary potentiometric acid–base titrations. Those latter were systematically carried out from acid to base direction. The titration included the addition of the titrant (≈ 0.1 mol dm–3 CsOH) to the 0.01 mol dm–3 CsNO3 aqueous suspension of TiO2 NTs at γ = 1 g dm–3 or to the pure aqueous suspension. The analyzed potentiometric titration data are presented in Figure 4 along with the predictions of the theoretical mesoscopic model. The raw and treated data of measured pH of the suspension as a function of added CsOH base are presented in Figure S5 in the Supporting Information. Results of both c(CsNO3)tot=0.001 mol dm–3 and c(CsNO3)tot=0.01 mol dm–3 blank titrations show that there is not any clear inflection point, which suggests the presence of a contaminant that we identified as CO2. Titration curves of both TiO2 NTs suspensions overlap in the low and high additions of the CsOH base. The differences are visible in the intermediate region of the added base. At lower CsNO3 concentration (c(CsNO3)tot=0.001 mol dm–3), the measured pH of the suspension is systematically larger than for the higher CsNO3 concentration (c(CsNO3)tot=0.01 mol dm–3) in the intermediate region of the added base. This suggests the additional binding of Cs+ to the surface of TiO2 NTs and a related release of protons from the surfaces to the suspension (observed with lower pH). Note that the experimental values in the case of c(CsNO3)tot=0.01 mol dm–3 show lower standard error throughout the potentiometric acid–base titration experiment, compared to the c(CsNO3)tot=0.001 mol dm–3 case. This is due to the more efficient screening of the nanotube surface charge at higher salt concentrations.

Figure 4

Figure 4. Calculated and measured pH with standard deviations in error bars of the aqueous suspension as a function of the added volume Vd of the base CsOH for the total Cs+ concentration at the end-point of the titration: (a) c(Cs+)tot≈0.001 mol dm–3; (b) c(Cs+)tot≈0.01 mol dm–3. Calculations were performed for radii Rinner = 3.5 nm, Router = 4 nm, site density Γ = 2.2, and association constants log  KH,1 = 8.5, log  KH,2 = 4.8, log  KCs,1 = 1.2, and log  KCs,2 = −0.2.

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We have also performed the batch adsorption of Cs+ ions experiment to test other aspects of TiO2 NTs suspensions. Results are presented in Figure S6a–c. The obtained data confirm that the increase of c(CsNO3)tot concentration leads to a lower saturation of TiO2 NTs surface sites available for Cs+ ions adsorption.

4.3. Comparison of the Mesoscopic Model and Experimental Potentiometric Acid–Base Titration Data

The model was fitted versus the titration experiment. The output of the calculations is the full speciation of the system as a function of the volume of added CsOH base, in the presence of CO2 as “contaminant”. By speciation we consider namely the equilibrium concentrations of all ’mobile’ (e.g., H+, Cs+, OH–, NO3–, CO3–, and CO32–) and “interfacial” species (e.g., surface sites at both inner and outer surface).
The comparison between the model predictions with association constants that correspond to the best fit and the experimental data is presented in Figure 4. Calculations were performed for the most probable set of TiO2 NTs radii, namely, Rinner = 3.5 nm and Router = 4 nm, as determined by HR-TEM measurements (Figure 3). The best fit was obtained with the following set of association constants: log  KH,1 = 8.5, log  KH,2 = 4.8, log  KCs,1 = 1.2, and log  KCs,2 = −0.2 (see Figure S10 in the Supporting Information). The site density Γ was fitted to the value 2.2. The obtained set of parameters is in the range of the “usual” values for these kinds of materials. (38,39) To test the effect of the polydispersity of nanotube radii and the resulting effect of the curvature of the electric field onto ion-surface association phenomena, we performed the fitting with Rinner = 4 nm and Router = 6 nm. This radii set is far less represented (see Figure 3c) but corresponds to reduced curvature compared to the Rinner = 3.5 nm and Router = 4 nm case. Results are presented in Figure S13 in the Supporting Information. Again, the fitting of the experimental provided almost the same set of constants. We can conclude that the effect of the curvature of the electric field on ion-surface association phenomena is small compared to the effect of the chemistry and the Gibbs energy of ion-site association.
The model was tested for the two cases of CsNO3 concentrations in the aqueous suspension. The idea was to probe the physical conditions of the decontamination applications that range from dilute to moderately concentrated suspensions with salts. Figure 4a presents the c(CsNO3)tot≈0.001 mol dm–3 case. In the range from Vd(CsOH) = 1.5 to 0.3 mL, the model predicts a slightly lower pH of the aqueous suspension than the experimentally measured, but the discrepancy is within the range of the experimental error. In the same interval, the experiments show the largest discrepancy from the mean value. This can be attributed to the efficiency of screening of the metal–oxide surface by cations included in the charge regulation model, H+ and Cs+ in this case. Since the concentration of Cs+ in the acidic region is low, the charge of nanotubes is controlled by H+ from mineral acid. The model predicts the depletion of excess H+ into the solution from the nanotube surface, which acts as the apparent increase in the pH of the system. This is due to the overestimation of the repulsion of cation by Poisson–Boltzmann since it is an ideal model with no excluded volume of ions considered (ions are point-like charges). In the region between 0.3 and 0.4 mL, the model predicts a higher pH than the experimentally observed while, from 0.4 to 0.6 mL, the calculated pH is lower than the experimentally measured. For values larger than Vd(CsOH) = 0.6 mL, the model is in good agreement with the experiments.
Figure 4b presents the c(CsNO3)tot≈0.01 mol dm–3 case. The agreement with experiments is better for lower and higher Vd(CsOH) when compared to the c(CsNO3)tot≈0.001 mol dm–3 case. Nevertheless, in the region between 0.3 and 0.4 mL, the model predicts higher pH values than the experimental observed values. The origin of this discrepancy can be attributed to the overestimation of the amount of dissolved CO2 by our model. The calculated equilibrium concentrations of HCO3– and CO32– as a function of added CsOH are presented in Figure 5c.

Figure 5

Figure 5. Full speciation of charged species within the titration experiment at c(CsNO3) = 0.001 mol dm–3. The figure shows (a) site populations, (b) surface charge densities, (c) carbonate species in aqueous solution, (d) surface cation coverage of surface active Cs+ and H+ cations, (e) volume integrals of Cs+ and NO3– particle distribution functions normalized per unit length, and (f) ratio of surface cation coverage on both inner and outer interface, as a function of the volume of added base in the actual titration experiment. Calculations were performed for radii Rinner = 3.5 nm, Router = 4.0 nm, site density Γ = 2.2, and association constants log  KH,1 = 8.5, log  KH,2 = 4.8, log  KCs,1 = 1.2, and log  KCs,2 = −0.2.

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4.4. Insight into Nanoscale Distribution of Charge within TiO2 NTs Systems in Aqueous Solutions

To understand the charge properties of the system, in addition to monitoring the pH of the suspension, we can plot the full speciation (sites and ions) as a function of Vd(CsOH), for the whole titration experiment. The results are presented in Figure 5 for the c(CsNO3)tot≈0.001 mol dm–3 case while the results for the c(CsNO3)tot≈0.01 mol dm–3 case are presented in Figure S11 in the Supporting Information. The TiO2 NTs site populations (fraction of sites on the exposed surface fx,j; see eq 5) for the c(CsNO3)tot≈0.001 mol dm–3 case are plotted in Figure 5a. First, overall, the differences in terms of surface chemistry on the inner and outer surfaces are small, even in low CsNO3 concentrations. In the acidic medium, at the beginning of the titration, the dominant surface sites are {≡TiOH2+2/3} and {≡TiOH−1/3}. As CsOH is gradually added in the suspension, the Cs+ concentration increases and the medium becomes more basic, the {≡TiOHCs+2/3} site replaces {≡TiOH2+2/3}. This process of Cs+-H+ competition for adsorption to the TiO2 NTs surfaces can be seen in Figure 5d), where the surface cation coverage (number concentration per unit surface) is plotted as a function of Vd(CsOH). H+ dominates the inner and outer nanotube surfaces until there is a critical amount of Cs+ and OH– ions in the system (close to millimolar concentrations), after which its surface concentration is decreased. This is the anticipated view of the process since protonation constants (log  KH,1 = 8.5 and log  KH,2 = 4.8) are much larger than Cs+ association constants (log  KCs,1 = 1.2 and log  KCs,2 = −0.2). The population of {≡TiOCs−1/3} site becomes significant only at highly basic pH, at the end of titration, i.e., at large Vd(CsOH). Besides, in the case of a higher salt concentration in the system, i.e., for c(CsNO3)tot≈0.01 mol dm–3, the site populations are radically changed (see Figure S11a in Supporting Information). {≡TiOHCs+2/3} and {≡TiOCs−1/3} become more pronounced at lower Vd(CsOH) due to the larger initial Cs+ concentrations while {≡TiOH−1/3} populations are lowered.
The charge inhomogeneities in nanotube systems can be assessed by our model. With respect to the boundary conditions, we can divide the system into the interior of the nanotube, i.e. the inner surface, and the exterior of the nanotube, i.e. the outer surface. The average concentrations of Cs+ ⟨ρCs+,r⟩ and NO3−⟨ρNO3−,r⟩ are therefore the volume integrals of the ions distributions, normalized by the unit length (we avoid dealing with edge effects). In the case of a higher salt concentration in the system, i.e., c(CsNO3)tot≈0.01 mol dm–3, the NO3– average concentration is globally the same and the NO3– ions (pink full squares) are predominantly outside the nanotube, toward the bulk. This result is in good agreement with the DFT-MD simulations presented in the following section. During the titration experiment, the addition of CsOH resulted in an accumulation of Cs+ ions in the system. The calculations demonstrate that the majority of the Cs+ ions are, actually, also present at the exterior of the NTs (orange full squares), but are predominantly in the EDL, i.e., close to the solid/liquid interface. A small fraction of the ions is present inside the NTs and also adsorbed to the inner and outer surfaces. In the case of a higher salt concentration in the system, i.e., for c(CsNO3)tot≈0.01 mol dm–3, the significant observed changes include a higher Cs+ adsorption on the surface as well as Cs+ ions inside the NT and outside the outer surface (see Figure S11e in Supporting Information). Nevertheless, in both dilute c(CsNO3)tot≈0.001 mol dm–3 and more concentrated cases c(CsNO3)tot≈0.01 mol dm–3, the majority of the Cs+ cations in the system were not adsorbed to the surface.
Another important quantity that can be discussed is the surface charge density on the nanotube. During the titration experiment, the surface charge density is mostly affected by the pH and by the concentration of the ’surface active ions’, such as Cs+. In Figure 5b, the surface charge densities of the inner and outer surfaces σj are plotted as a function of Vd(CsOH). The magnitude (the absolute value) of σouter surface is larger than σinner surface for the entire range of Vd(CsOH), which is analogous for any pH. Both charge density curves present oscillations in the region between Vd(CsOH) = 0.3 and 0.4 mL, which are visible in all graphs (a–d). This is not in agreement with the expected monotonous change with respect to the pH of the medium at equilibrium. These oscillations are just the result of the model for CO2 dissolution within Poisson–Boltzmann calculations, and there is no physical relevance.
To answer the question of the preferential cation adsorption between the inner and outer surfaces, we can plot the fraction of the cation surface coverage (data from Figure 5d). Results plotted in Figure 5f show that depending upon the pH (or Vd(CsOH)), differences exist between the inner and outer NT surfaces. The ratio between the inner and outer radii (Router/Rinner = 4/3.5) is around 1.15, and the fraction of the surface coverage for both H+ and Cs+ deviates from this value in a complex pH-dependent fashion. Furthermore, the deviations are more pronounced for the Cs+ cations. The aforementioned asymmetry of the distribution of cations between the inner and outer surfaces comes from the continuity of the potential expressed by eq 10 within the model. In the model, the dampening of the electric field (lowering the absolute value) as a response to the dielectric properties of the solid TiO2 causes the difference in electrostatic potential at the interfaces and affects the Boltzmann distributions. This was already reported in the literature. (29) So far, this finding is purely based on theoretical grounds.

4.5. Molecular Level of Description of Cation Adsorption on TiO2: DFT-MD Simulations

4.5.1. Hydration of the (101) Surface of TiO2

The effect of water adsorption on the (101) surface of TiO2 (see Figure S15a in the Supporting Information for the bare surface) was first assessed by filling the vacuum above the surface with water molecules. Two different input configurations were investigated:

  • (1) All the water molecules were manually dissociated (on the two reciprocal surfaces), and the resulting hydroxy groups and protons were adsorbed on the five-coordinated surface titanium atoms and on the two-coordinated surface oxygen atoms, respectively;

  • (2) All the water molecules were put in their molecular form, i.e., nondissociated.

Those two simulations were let evolve spontaneously and monitored over time (see Figure S15b,c and Figure S16a,b in Supporting Information). For the hydroxylated surface, some water molecules spontaneously reformed during the simulation, while for the nonhydroxylated surface, some water molecules spontaneously dissociated during the simulation. When a water molecule dissociated on the surface, the hydroxy group adsorbed on a five-coordinated surface titanium atom while the proton adsorbed on a two-coordinated surface oxygen atom (see Figure S15 in Supporting Information). This was in accordance with the experimental (66,67) and theoretical works (53,68−70) that all demonstrated the coexistence of molecular and dissociated forms of water molecules on the (101) surface of anatase. During the whole simulations, regardless of the input configuration, 100% of the five-coordinated surface titanium atoms were occupied either by an adsorbed hydroxy group or by a water molecule, which is typical of a classical hydrophilic surface. (71) The average Ti–O bond length was (1.95 ± 0.05) Å in the case of hydroxy groups and (2.12 ± 0.05) Å in the case of nondissociated water molecules (see Figure S16c,d in Supporting Information). However, the two simulations did not converge to the same final configuration after 70 ps of simulation, which indicates that significant activation energy was probably required to attain the most stable configuration. This corresponded to an intermediate system between the two simulations, in which a part (20–50%) of the surface titanium atoms were occupied by hydroxy groups, i.e., by dissociated water molecules, and a part (50–80%) occupied by nondissociated water molecules. Consistently, the corresponding two-coordinated surface oxygen atoms were partly protonated. Overall, a dissociated water molecule corresponded to two ≡TiOH sites while a nondissociated water molecule corresponded to one ≡TiOH2 and one ≡TiO site, which is equivalent to the surface sites defined in eq 1 and 2. We can conclude that protonation equilibria can be safely modeled in a 2-pKH,x manner within our mesoscopic model for the titration experiment.

4.5.2. Adsorption of CsNO3 on the (101) Surface of TiO2

On a snapshot of the most stable hydrated system, i.e., with 30% of the surface Ti atoms hydroxylated, we added a CsNO3 molecule close to the surface by removing four water molecules in order to keep the volume constant. This avoided considering another thermalization period. Various input configurations for the orientation of the CsNO3 molecule regarding the surface plane were tested. We systematically observed the adsorption of the Cs+ ion on the TiO2 surface, while the nitrate ion did not adsorb and diffused to the water phase (see Figure S17 in Supporting Information), which was consistent with the assumptions we made in the Poisson–Boltzmann model. Besides, a first Bader charge analysis, performed on this system prior to the adsorption of Cs+, confirmed that the Cs atom was in the Cs+ form, while the nitrate group was in the NO3– form. During the simulation, the Cs+ ion adsorbed on the (101) surface of TiO2 by establishing several Cs–O bonds with surface oxygen atoms as well as with several water molecules from the water phase (Figure 6a and Figure S18 in the Supporting Information for more detailed analysis of the Cs–O bond lengths). It exhibited a total coordination number comprised between eight and ten (Figure 6b), which was in very good agreement with the experimental and theoretical reported values. (72,73) The number of water molecules comprised in the first coordination sphere and not adsorbed on the TiO2 surface (1 in Figure 6a) was comprised between 3 and 5, with an average value of 4. Besides, the nitrate ion, which was, at the beginning of the simulation, in the first coordination sphere of the Cs+ ion, progressively went away from the Cs+ ion and diffused to the water bulk (Figure 6b). The Cs+ ion established Cs–O bonds with two two-coordinated surface oxygen atoms (2 and 2’ in Figure 6a), i.e., the surface oxygen atoms that are undercoordinated, as well as with three surface hydroxy groups, which corresponded to dissociated water molecules adsorbed onto surface titanium atoms (3 in Figure 6a); see Figure 6c,d. The adsorption on two two-coordinated surface oxygen atoms and three adsorbed hydroxy groups is induced by the surface structure (Figure 6c,d): the three hydroxy groups are adsorbed on titanium surface atoms organized in layers in which they are separated by around 3.86 Å (Figure 6c). Two successive titanium atom layers are shifted of 1.93 Å from each other, which forms an adsorption cage composed of three adsorbed hydroxy groups and two two-coordinated surface oxygen atoms (represented in gray in Figure 6c,d). The two-coordinated surface oxygen atoms can be protonated or not, and the adsorbed hydroxy groups can also be nondissociated water molecules, considering the dynamic equilibrium of the surface in the presence of water. Therefore, the adsorption sites, represented by this five-coordinated cage, can exhibit a significant number of different chemical configurations. However, the adsorption of the Cs+ ion most probably induces the dissociation of the nondissociated water molecule on the three titanium atoms that surround the adsorption site and those are always in the ≡TiOH form. If we assume that no surface oxygen atoms are shared between adsorbed cesium ions when several Cs+ ions are added, the area of the effective adsorption site is around 80 Å2. This finding sets the requirement for the improvement of the mesoscopic model for definition of the surface site and complexation with larger monovalent ions such as Cs+.

Figure 6

Figure 6. Results of the DFT-MD simulations. (a) A representative snapshot of the (101) surface of TiO2 seen from the side, with water and adsorbed Cs+ ion, showing the first coordination sphere of Cs+ ion composed of (1) bulk water molecules, (2) two-coordinated surface oxygen atoms, (2′) protonated two-coordinated surface oxygen atoms, and (3) dissociated adsorbed water molecules. (b) Evolution of the coordination of the Cs+ ion over simulation time (moving average on 200 fs), showing the different components of the Cs+ total coordination number. (c) Cs+ ion adsorbed on the TiO2 surface seen from the top, without representing the nonadsorbed water molecules. (d) The Cs+ ion adsorbed on the TiO2 surface seen from the side, without representing the nonadsorbed water molecules. In parts c and d, the gray zone represents the pentagon-like adsorption site, and the numbers are the same as in part a. In parts a–d, the dashed lines represent hydrogen bonds.

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A second Bader charge analysis, performed after the adsorption of the Cs+ ion, demonstrated a slight change in its atomic charges of +0.05 electrons, which can be attributed to the deformation of the electron cloud by the adsorption. It could be concluded that the adsorption of Cs+ on the (101) surface of TiO2 was electrostatic and, therefore, reversible. This is agreement with magnitude of Cs+ association constants that were determined by a mesoscopic model.

5. Discussion

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In this study, we proposed a mesoscopic model to describe the charge properties and mass balance of the titration of metal–oxide nanomaterials that can be applied to different morphologies, such as spheres, rods, etc. There are a few key features that are increment to this study and need to be discussed in detail, such as the numerical stability of the code, the algorithm structure for solving highly nonlinear Poisson–Boltzmann equations, analytical description of chemical equilibria of all charged species in the system and their total balance, and spatial charge inhomogeneities for nanotubes system. From the aspect of the numerical implementation and solving the system of nonlinear Poisson–Boltzmann equations, the described algorithm showed numerical stability, i.e., generated reproducible results, for different salt concentrations and pH, ranging from dilute to more concentrated aqueous suspensions. Also, the results from the algorithm overcame the difficulty of evaluating the electrostatic potentials at the so-called ’high surface charge’ regime, for example, at high pH and salt concentration (see Figure 5b). Meanwhile, the algorithm satisfies the model condition of the Mass Action Law (semigrand canonical ensemble, where only water molecules are considered as the “reservoir”) for all the “mobile” ions and surface groups. This is, actually, a tool to probe and monitor concentrations of all ions, surface groups, and charge properties in a variety of system conditions involving metal–oxide nanomaterials. This is essential when describing experiments such as potentiometric acid–base titration where the ion concentrations change with every addition of the titrant. Additionally, by integrating a model for the estimation of the dissolution of CO2 and of the resulting carbonate protonation equilibria, it became clear that the pH of the dilute nanomaterials suspension is sensitive to time of the mixing or shaking time during the adsorption process.
From the analytical colloidal chemistry point of view, based on the practical example of potentiometric titration of TiO2 NTs with CsOH, the model predicted a moderate affinity of TiO2 NTs surface for Cs+ ions at acidic and neutral pH, due to the competition with H+. Even if the concentration of cesium (c(CsNO3)tot≈0.01 mol dm–3) is increased by an order of magnitude in the aqueous solution, the surface charge properties of nanotubes are dominated by the protonation equilibrium. From the nanoscale description point of view, the proposed mesoscopic model can be used to probe the spatial average positioning of Cs+ cations (or any other ion) within the titration experiment. The results presented in Figure 5e and Figure S11 show that Cs+ cations are predominantly located in the electric double layer in contact with the outer nanotube surface, rather than in the interior or adsorbed on the surfaces. This spatial distribution of cations appears to be irrespective of the total cation concentration in the aqueous solution. This radical view of the adsorption phenomenon for aqueous suspensions of nanoporous metal oxide materials in thermodynamic equilibrium is completely opposite when batch experiments are identified as “the adsorption” (see Figure S6a–c in Supporting Information) suggesting even up to 50% of the total amount of Cs+ is adsorbed. In this equilibrium state of the dilute aqueous suspension, the nanomaterial is not an efficient adsorbent, as might be concluded when the definition of adsorption is based only on the batch experiments. In contrast to our findings, most studies so far suggest high adsorption efficiency, but there is a trick: most studies fit the adsorption data based on the batch experiments in which the solid adsorbent is removed from the suspension after the sufficient time (with assumed equilibrium achieved). (74) It is worth emphasizing that the two states, the aqueous suspension at equilibrium and two-phase solid (adsorbent + adsorbate) and supernatant solution, correspond to completely different thermodynamic states. This is why the “adsorption efficiency” term should be used with great care.
The feature of the proposed model is a very important finding since it gives invaluable insight into the process at the nanoscale. When it comes to possible applications of nanotubes, most of which are aqueous suspensions (such as in catalysis or reversible decontamination), it is crucial to understand where ions are positioned in the system. This is not evident from batch adsorption experiments, which just show the “average” property of the system and, furthermore, reflect on the completely distinct thermodynamic states of two separated phases (solid and liquid).
Nevertheless, the model requires a few improvements. First, the prediction of the model that deviates from the monotonous change of suspension pH, site populations, and charging curves in the region between Vd(CsOH) = 0.3 and 0.4 mL can be traced to the drawback of the modeled dissolution of CO2. In Figure 5c the concentrations of carbonate species HCO3– and CO32– are plotted as a function of Vd(CsOH). Results show an increase in the HCO3– concentration after 0.3 mL of added CsOH, when the suspension approaches the neutral pH. CO32– species concentration increases under basic conditions, for which HCO3– deprotonates (7). It should be noted that the precision of calculated carbonate concentrations is crucial precisely around the inflection point in the titration curve.
The predicted abrupt increase of HCO3– in the region from 0.4 to 0.7 mL (pH from 6 to 8) is responsible for the increase of the proton concentration in the aqueous solution. As a consequence, our model which is in a canonical ensemble takes into account the additional proton concentration that evolves as HCO3– is introduced by the dissolution of CO2.
At near- and pH-neutral system conditions, numerical solutions show an unexpected decrease in suspension pH, which is a consequence of HCO3– deprotonation (eq 8). Note that this is not an error induced by the numerical noise of the code; rather, the results are reproducible with high confidence, where the absolute difference between iterative values of the Cs+, NO3–, H+, and OH– ions concentrations set to 1 × 10–8 mol dm–3. The overestimated HCO3– concentration is comparable to the site concentration. In the model, the deprotonation of HCO3– has the dominant effect on the proton balance in the range from pH = 6 to 8.
It is worth noting, in a general fashion, that difficulty of the electroneutrality (such as at neutral pH, where H+ and OH– concentrations are small) with the conjunction with any inaccurate estimate of the parameter (such as the dissolution of CO2 in our model) can lead to a significant discrepancy of the output of the calculation when compared to the experimental value.
Nevertheless, for practical applications, neutral pH is not often important, due to the reduced stability of metal oxide nanomaterials suspensions. Therefore, for practical use, the proposed model should already work sufficiently well, even for a quantitative estimate of ion adsorption.
Besides the inaccuracy caused by the estimate of CO2 dissolution within the model, we further explored the effect of the surface chemistry for the exposed (101) surface of TiO2 NTs. The aim was to test the approximation of the 1-site multiple association constants (pKx for Cs+ and H+ associations) that we used for charge regulation of nanotubes. Association (adsorption) of Cs+ and H+ to the TiO2 NTs surfaces and the description of the “actual surface site” were studied in greater detail by molecular simulations. While for protonation, 1-site multiple associations constants can be justified to some extent, (38) for Cs+ association, the approximation clearly does not hold. The size of the Cs+ ion and its first-sphere coordination shell cause binding to a few oxygen atoms on the titanate surface and in a complex structural modality. The generalization of the site model to account partitioning of multiple oxygen atoms in binding with Cs+ would be more adequate, and this is the area of our future work on the subject. Furthermore, in our mesoscopic model, we neglected co-ions (NO3– and OH– ions) specificity for the TiO2 NTs surfaces based on the argument of charge repulsion. The approximation was validated by simulations which showed that nitrate anion NO3–, even placed in the first coordination sphere of associated Cs+, diffuses toward the bulk aqueous solution. An important aspect of materials for water decontamination is their ability to be specific. In this study, we mainly looked at the competition between H+ and Cs+. There is a pH domain in which decontamination is possible in pure water for cesium ions, but this does not mean that it will be the case in any situation in real practical solutions, which can contain numerous metal ions. Nevertheless, the fact that adsorption of cesium appears to be reversible and that the Cs+ ion is adsorbed in well-defined surface states provides two interesting properties of the material. First, decontamination is based on weak interactions so that reversibility, which is important to regenerate the NTs, is possible with cesium. Second, the specific nature of adsorption sites for cesium ions makes the possibility of specific decontamination likely, but such a conclusion will need further developments.

6. Conclusions and Outlook

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In this work, the integrative study based on experimental and theoretical approaches was applied to gain understanding in the adsorption of Cs+ on TiO2 NTs, which represented a case study for porous nanomaterials. TiO2 NTs were obtained by alkaline hydrothermal synthesis and underwent a postsynthesis calcination at 200 °C to improve their crystallinity. The morphological features of TiO2 NTs were characterized in detail via HR-TEM and AFM, which confirmed the tubular morphology. Most NTs presented a length of 200 nm, an inner radius of 3.5 nm, and outer radius of 4 nm. Acid–base surface properties of TiO2 were elucidated by electrophoretic measurements and potentiometric titrations. The results revealed that the isoelectric and point of zero charge shift, which suggests the adsorption of Cs+ cations onto TiO2 NTs. To gain insights into the distribution of the adsorbed Cs+ cation within TiO2 NTs (and nanoporous materials in general), we derived a mesoscopic model that can be used to quantitatively describe the full speciation of the system during the spam of the potentiometric acid–base titration of the metal-oxide nanomaterials. Furthermore, the model is derived such that it includes CO2 dissolved in the aqueous suspension. The goal was to propose a model that can predict the separation of metal ions, ranging from dilute to moderately concentrated 1:1 salt aqueous suspensions. (75)
The key findings state that H+ dominates in TiO2 NTs charging process, while Cs+ becomes important only at high concentrations and in basic pH region. Furthermore, CO2 is an important contributor to the equilibrium in the system and thus cannot be neglected. In the case of shorter nanotube radii (Rinner = 3.5 nm, Router = 4 nm), the inner and the outer surfaces of the nanotube present similar surface sites populations and ion–surface association equilibrium states. The curvature of the nanotube has a very small effect as long as the TiO2 NT solid layer is thin. The comparison between model predictions and results of the potentiometric acid–base titrations showed the discrepancy around neutral pH, which originates from the overestimation of the dissolved CO2 by our model. When used to deduce spatial distribution of ions and charges in the system, the model proposed the radical explanation that in the aqueous suspension the majority of the target solute Cs+ is in the electric double layer around the outer surface, rather than adsorbed at the surface of nanotubes. This finding is especially important to stress in the context of possible application in terms of catalysis or reversible separations, where it is essential to understand the spatial partitioning or more simply said: “where the target species are located”. Besides, atomistic ab initio MD simulations were performed to test the 1-site multiple ion association approximation within the mesoscopic model. The simulations showed that for protons and co-ions the model works sufficiently well, but for larger Cs+ cations, the definition of surface site is inadequate due to the size of the cation.
The authors are currently working on the extension of this study in terms of improvements of the charge regulation model of surface sites as well as integration of the kinetic estimate of CO2 from the ambient atmosphere. In parallel, we are trying to perform a stereological estimation of the surface coverage of Cs+ onto TiO2 NTs by counting bright dots within HAADF images after the adsorbent is removed from the mixture in batch experiments. We plan to “follow” the adsorption isotherm from very dilute to concentrated aqueous solutions. At the same time, the use of a derived mesoscopic model can give insight into adsorption efficiency before the adsorbent is removed from the mixture.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsanm.3c00916.

  • Synthesis of TiO2 NTs, annealing of TiO2 NTs sample, structural characterization of TiO2 NTs, properties of the aqueous suspension of TiO2 nanotubes, batch experiments of Cs+ adsorption on TiO2 NTs, full model derivation: Poisson–Boltzmann theory to reproduce acid–base titration curve of TiO2 NTs aqueous suspension in dilute regime with CO2 as a contaminant, fitting of the model to the experimental data, model predictions for different sets of inner and outer nanotubes radii, first-principles Molecular Dynamics Simulations (PDF)

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Author Information

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  • Corresponding Authors
  • Authors
    • Atiđa Selmani - Pharmaceutical Technology & Biopharmacy, Institute of Pharmaceutical Sciences, University of Graz, A-8010, Graz, Austria;  Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
    • Bertrand Siboulet - ICSM, Université Montpellier, CEA, CNRS, ENSCM, 30207 Bagnols-sur-Ceze, France;  Orcidhttps://orcid.org/0000-0002-6895-202X
    • Yann Foucaud - ICSM, Université Montpellier, CEA, CNRS, ENSCM, 30207 Bagnols-sur-Ceze, France;  Orcidhttps://orcid.org/0000-0002-8846-4218
    • Goran Dražić - Laboratory for Materials Chemistry, National Institute of Chemistry, Hajdrihova ulica 19, SI-1000 Ljubljana, Slovenia;  Orcidhttps://orcid.org/0000-0001-7809-8050
    • Borna Radatović - Institute of Physics, Bijenicka 46, 10 000 Zagreb, Croatia;  Orcidhttps://orcid.org/0000-0001-5012-6005
    • Karla Korade - Faculty of Science, University of Zagreb, Horvatovac 102A, 10 000 Zagreb, Croatia
    • Ivan Nemet - Faculty of Science, University of Zagreb, Horvatovac 102A, 10 000 Zagreb, Croatia
    • Davor Kovačević - Faculty of Science, University of Zagreb, Horvatovac 102A, 10 000 Zagreb, Croatia
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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K.B. thanks the Research Agency for funding through Program P3-0388. K.B. thanks COST CA 18234. M.Š., J.-F.D. and K.B. acknowledge the Slovenia Research Agency and the French Alternative Energies and Atomic Energy Commission for support through Project CEA NC-0020. B.R. gratefully acknowledges financial support from the European Regional Development Fund for the “Center of Excellence for Advanced Materials and Sensing Devices” (Grant No. KK.01.1.1.01.0001). D.K. thanks the Croatian Science Foundation for the financial support through Project IPS-2020-01-6126. This work was granted access to the HPC resources of TGCC under the allocation 2020-A0090912068 made by GENCI. Y.F. acknowledges the RCHIM structure for its financial support. The authors would like to express great thanks to Dr. Sc. Krunoslav Užarević (Laboratory for Green Synthesis, Division of Physical Chemistry, Ruđer Bošković Institute, Zagreb, Croatia) for enabling XRD measurements and Dr. Sc. Jasminka Kontrec and Dr. Sc. Damir Kralj (Laboratory for precipitation processes, Division of Material Chemistry, Institute Ruđer Bošković, Zagreb, Croatia) for providing the BET measurements.

References

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    A review. This review outlines the potential of nanomaterials as nanoadsorbents and the many advances they have afforded in the sepn. and preconcn. of a variety of analytes. Over the past decade, nanomaterials have been the subject of great interest. These materials, notable for their extremely small size, have the potential for wide-ranging applications. In this review, the authors have explained the classification, properties, applications, and several procedures to prep. nanoadsorbents including (a) nanoparticles, such as metallic-oxide nanoparticles (Al2O3, ZnO, and TiO Ups), metallic nanoparticles (Au NPs), nanostructure mixed oxides (Fe-Ti mixed oxide), and magnetic nanoparticles; (b) carbonaceous nanomaterials, such as carbon nanotubes; (c) silicon nanomaterials, such as silicon dioxide nanoparticles and silicon nanotubes;(c)nanofibers;(d) nanoclays; (e) polymer-based nanoadsorbents; (f) xerogels and aerogels; and (g) destructive nanoadsorbents. This review systematically highlights the use of nanoadsorbents for the purpose of characterization and application. The demands of chem. anal. in modern biol.,environmental science, chem., medicine, and industry need very high sample throughput and parallel anal. strategies.
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  14. 14
    He, B.; Li, Z.; Zhao, D.; Liu, H.; Zhong, Y.; Ning, J.; Zhang, Z.; Wang, Y.; Hu, Y. Fabrication of Porous Cu-Doped BiVO4 Nanotubes as Efficient Oxygen-Evolving Photocatalysts. ACS Appl. Nano Mater. 2018, 1, 2589– 2599,  DOI: 10.1021/acsanm.8b00281
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    14
    Fabrication of Porous Cu-Doped BiVO4 Nanotubes as Efficient Oxygen-Evolving Photocatalysts
    He, Bin; Li, Zhipeng; Zhao, Dian; Liu, Huanhuan; Zhong, Yijun; Ning, Jiqiang; Zhang, Ziyang; Wang, Yongjiang; Hu, Yong
    ACS Applied Nano Materials (2018), 1 (6), 2589-2599CODEN: AANMF6; ISSN:2574-0970. (American Chemical Society)
    We introduce a facile route to fabricate one-dimensional (1D) porous Cu2+-doped BiVO4 (Cu-BVO) nanotubes with uniform size distribution and high structural stability. First, an electrospinning technique was developed to prep. the sacrificial template of polyacrylonitrile (PAN) nanofibers with a smooth surface. Second, a conformal layer of Cu-BVO nanoparticles was coated onto the PAN template through a solvothermal method to obtain the solid core-shell precursor which was finally converted into the product of porous Cu-BVO nanotubes with thermal treatment. Both exptl. characterizations and theor. calcns. based on the d. functional theory (DFT) calcns. have revealed the crucial functionality of the appropriate band structure of the Cu2+-doped nanostructure and introduced beneficial defect states by Cu doping, which boosts light absorption and promotes charge migration and sepn. and therefore results in highly efficient photocatalytic O2 evolution with visible-light irradn. As a result, the porous nanotube photocatalyst with an optimal Cu2+ doping of 5.0% exhibits an av. O2 evolution rate of 350.2 μmol h-1 g-1, about 2.4 times more than that of pristine BVO nanotubes.
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  15. 15
    Shiraishi, Y.; Saito, N.; Hirai, T. Adsorption-Driven Photocatalytic Activity of Mesoporous Titanium Dioxide. J. Am. Chem. Soc. 2005, 127, 12820– 12822,  DOI: 10.1021/ja053265s
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    Adsorption-Driven Photocatalytic Activity of Mesoporous Titanium Dioxide
    Shiraishi, Yasuhiro; Saito, Naoya; Hirai, Takayuki
    Journal of the American Chemical Society (2005), 127 (37), 12820-12822CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Unprecedented photocatalytic activity of mesoporous TiO2 driven by an adsorption degree of mols. on the catalyst surface which promotes a preferential conversion of a well-adsorbed mols. is reported. This property is applied to a selective transformation of a well-adsorbed mol. into a less-adsorbed mol., labeled as "stick-and-leave" transformation, which enables a direct transformation of benzene to phenol, one of the most difficult synthetic reactions, with very high selectivity (> 80%) and using water as a source of oxidant.
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  16. 16
    Abdel-Ghani, N. T.; El-Chaghaby, G. A.; Helal, F. S. Individual and competitive adsorption of phenol and nickel onto multiwalled carbon nanotubes. J. Adv. Res. 2015, 6, 405– 415,  DOI: 10.1016/j.jare.2014.06.001
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    Individual and competitive adsorption of phenol and nickel onto multiwalled carbon nanotubes
    Abdel-Ghani, Nour T.; El-Chaghaby, Ghadir A.; Helal, Farag S.
    Journal of Advanced Research (2015), 6 (3), 405-415CODEN: JAROES; ISSN:2090-1224. (Elsevier B.V.)
    Individual and competitive adsorption studies were carried out to investigate the removal of phenol and nickel ions by adsorption onto multiwalled carbon nanotubes (MWCNTs). The carbon nanotubes were characterized by different techniques such as X-ray diffraction, SEM, thermal anal. and Fourier transformation IR spectroscopy. The different exptl. conditions affecting the adsorption process were investigated. Kinetics and equil. models were tested for fitting the adsorption exptl. data. The characterization exptl. results proved that the studied adsorbent possess different surface functional groups as well as typical morphol. features. The batch expts. revealed that 300 min of contact time was enough to achieve equil. for the adsorption of both phenol and nickel at an initial adsorbate concn. of 25 mg/l, an adsorbent dosage of 5 g/l, and a soln. pH of 7. The adsorption of phenol and nickel by MWCNTs followed the pseudo-second order kinetic model and the intraparticle diffusion model was quite good in describing the adsorption mechanism. The Langmuir equil. model fitted well the exptl. data indicating the homogeneity of the adsorbent surface sites. The max. Langmuir adsorption capacities were found to be 32.23 and 6.09 mg/g, for phenol and Ni ions, resp. The removal efficiency of MWCNTs for nickel ions or phenol in real wastewater samples at the optimum conditions reached up to 60% and 70%, resp.
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    Editors and International Board Member collection.

  17. 17
    Swenson, H.; Stadie, N. P. Langmuir’s Theory of Adsorption: A Centennial Review. Langmuir 2019, 35, 5409– 5426,  DOI: 10.1021/acs.langmuir.9b00154
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    Langmuir's Theory of Adsorption: A Centennial Review
    Swenson, Hans; Stadie, Nicholas P.
    Langmuir (2019), 35 (16), 5409-5426CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    A review. The 100th anniversary of Langmuir's theory of adsorption is a significant landmark for the phys. chem. and chem. engineering communities. Despite its simplicity, the Langmuir adsorption model captures the key physics of mol. interactions at interfaces and laid the foundation for further progress in understanding interfacial phenomena, developing new adsorbent materials, and designing engineering processes. The Langmuir model has had an exceptional impact on diverse fields within the chem. sciences (ranging from chem. biol. to materials science), an impact that became clearer with the development of modified adsorption theories and continues to be relevant today.
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  18. 18
    Bohinc, K.; Bossa, G. V.; May, S. Incorporation of ion and solvent structure into mean-field modeling of the electric double layer. Adv. Colloid Interface Sci. 2017, 249, 220– 233,  DOI: 10.1016/j.cis.2017.05.001
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    Incorporation of ion and solvent structure into mean-field modeling of the electric double layer
    Bohinc, Klemen; Bossa, Guilherme Volpe; May, Sylvio
    Advances in Colloid and Interface Science (2017), 249 (), 220-233CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)
    A review. An elec. double layer forms when the small mobile ions of an electrolyte interact with an extended charged object, a macroion. The competition between electrostatic attraction and translational entropy loss of the small ions results in a diffuse layer of partially immobilized ions in the vicinity of the macroion. Modeling structure and energy of the elec. double layer has a long history that has lead to the classical Poisson-Boltzmann theory and numerous extensions that account for ion-ion correlations and structural ion and solvent properties. The present review focuses on approaches that instead of going beyond the mean-field character of Poisson-Boltzmann theory introduce structural details of the ions and the solvent into the Poisson-Boltzmann modeling framework. The former include not only excluded vol. effects but also the presence of charge distributions on individual ions, spatially extended ions, and internal ionic degrees of freedom. The latter treat the solvent either explicitly as interacting Langevin dipoles or in the form of effective non-electrostatic interactions, in particular Yukawa interactions, that are added to the Coulomb potential. We discuss how various theor. models predict structural properties of the elec. double layer such as the differential capacitance and compare some of these predictions with computer simulations.
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    Recent nanotechnology and colloid science development for biomedical applications.

  19. 19
    Kallay, N.; Preocanin, T.; Kovacevic, D.; Lutzenkirchen, J.; Chibowski, E. Electrostatic Potentials at Solid/Liquid Interfaces. Croat. Chem. Acta 2010, 83, 357– 370
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    19
    Electrostatic potentials at solid/liquid interfaces
    Kallay, Nikola; Preocanin, Tajana; Kovacevic, Davor; Lutzenkirchen, Johannes; Chibowski, Emil
    Croatica Chemica Acta (2010), 83 (3), 357-370CODEN: CCACAA; ISSN:0011-1643. (Croatian Chemical Society)
    This review deals with electrostatic potentials within solid/electrolyte interfaces. The electrostatic potentials of several planes are defined and discussed: the inner surface potential affecting the state of charged surface species due to interactions with potential detg. ions (Ψ0), the potential affecting the state of assocd. counterions (Ψβ), the potential at the onset of diffuse layer (Ψd) and the electrokinetic potential (ζ). The relevance of zero values of these potentials is also discussed and the corresponding points of zero charge are defined. Exptl. methods for the measurement of the interfacial potentials are presented. The relations between potentials and surface charges are given on the basis of the Surface Complexation model. Some exptl. findings are provided.
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  20. 20
    Lützenkirchen, J.; Preocanin, T.; Kovačević, D.; Tomišić, V.; Lövgren, L.; Kallay, N. Potentiometric Titrations as a Tool for Surface Charge Determination. Croatica Chemica Acta 2012, 85, 391– 417,  DOI: 10.5562/cca2062
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    20
    Potentiometric titrations as a tool for surface charge determination
    Luetzenkirchen, Johannes; Preocanin, Tajana; Kovacevic, Davor; Tomisic, Vladislav; Loevgren, Lars; Kallay, Nikola
    Croatica Chemica Acta (2012), 85 (4), 391-417CODEN: CCACAA; ISSN:0011-1643. (Croatian Chemical Society)
    A review. This article summarizes methods for detg. proton surface charge at mineral/water interfaces. It covers conventional exptl. procedures and discusses problems with the techniques. Also it involves recommendations for obtaining reasonable and comparable results. The term "comparable results" refers to comparison between results for the same solid as obtained in different labs. The most important parameters for the surface titrns. are discussed. We also propose a ref. titrn. procedure that would allow direct, unbiased comparisons of exptl. data. The article finally includes a check-list for researchers and reviewers which should allow limiting the amt. of titrn. data that are not useful for future uses.
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  21. 21
    Abbas, Z.; Labbez, C.; Nordholm, S.; Ahlberg, E. Size-dependent surface charging of nanoparticles. J. Phys. Chem. C 2008, 112, 5715– 5723,  DOI: 10.1021/jp709667u
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    Size-Dependent Surface Charging of Nanoparticles
    Abbas, Zareen; Labbez, Christophe; Nordholm, Sture; Ahlberg, Elisabet
    Journal of Physical Chemistry C (2008), 112 (15), 5715-5723CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Exptl. interest in the possible curvature dependence of particle charging in electrolyte solns. is subjected to theor. anal. The cor. Debye-Hueckel theory of surface complexation (CDH-SC) and Monte Carlo (MC) simulation are applied to investigate the dependence of surface charging of metal oxide nanoparticles on their size. Surface charge d. vs. pH curves for spherical metal oxide nanoparticles in the size range of 1-100 nm are calcd. at various concns. of a background electrolyte. The surface charge d. of a nanoparticle is found to be highly size-dependent. As the particle diam. drops to below 10 nm there is considerable increase in the surface charge d. as compared with the limiting values seen for particles larger than 20 nm. This increase in the surface charge d. is due to the enhanced screening efficiency of the electrolyte soln. around small nanoparticles, which is most prominent for particles of diams. less than 5 nm. For example, the surface charge densities calcd. for 2 nm particles at 0.1 M concn. are very close to the values obtained for 100 nm particles at 1 M concn. These predictions of the dependence of surface charge d. on particle size by the CDH-SC theory are in very good agreement with the corresponding results obtained by the MC simulations. A shift in the pH value of the point of zero charge toward higher pH values is also seen with a decreasing particle size.
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  22. 22
    Bareigts, G.; Labbez, C. Jellium and cell model for titratable colloids with continuous size distribution. J. Chem. Phys. 2018, 149, 244903,  DOI: 10.1063/1.5066074
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    Jellium and cell model for titratable colloids with continuous size distribution
    Bareigts, Guillaume; Labbez, Christophe
    Journal of Chemical Physics (2018), 149 (24), 244903/1-244903/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A good understanding and detn. of colloidal interactions is paramount to comprehend and model the thermodn. and structural properties of colloidal suspensions. In concd. aq. suspensions of colloids with a titratable surface charge, this detn. is, however, complicated by the d. dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addn., colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper, we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided. The methods, inspired by the seminal work of Torres et al., [J. Chem. Phys. 128, 154906 (2008)] are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various com. available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calcd. The importance of size and charge polydispersity as well as the validity of these two models is discussed in light of the results. (c) 2018 American Institute of Physics.
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  23. 23
    Selmani, A.; Špadina, M.; Plodinec, M.; Delač Marion, I.; Willinger, M. G.; Lützenkirchen, J.; Gafney, H. D.; Redel, E. An Experimental and Theoretical Approach to Understanding the Surface Properties of One-Dimensional TiO2 Nanomaterials. J. Phys. Chem. C 2016, 120, 4150,  DOI: 10.1021/acs.jpcc.6b01240
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    An Experimental and Theoretical Approach to Understanding the Surface Properties of One-Dimensional TiO2 Nanomaterials [Erratum to document cited in CA163:323607]
    Selmani, Atidja; Spadina, Mario; Plodinec, Milivoj; Delac Marion, Ida; Willinger, Marc Georg; Lutzenkirchen, Johannes; Gafney, Harry D.; Redel, Engelbert
    Journal of Physical Chemistry C (2016), 120 (7), 4150CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    On page 19735, Figure 5 contained an incorrect scale bar; the cor. figure is given.
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    Lützenkirchen, J. Comparison of 1-pK and 2-pK Versions of Surface Complexation Theory by the Goodness of Fit in Describing Surface Charge Data of (Hydr)oxides. Environ. Sci. Technol. 1998, 32, 3149– 3154,  DOI: 10.1021/es980125s
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    24
    Comparison of 1-pK and 2-pK Versions of Surface Complexation Theory by the Goodness of Fit in Describing Surface Charge Data of (Hydr)oxides
    Luetzenkirchen, Johannes
    Environmental Science and Technology (1998), 32 (20), 3149-3154CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
    1-PK and 2-pK formulations exist in surface complexation theory with respect to the description of basic charging behavior of (hydr)oxide electrolyte interfaces. The 2-pK approach has been commonly used with at least four different electrostatic models, whereas the 1-pK model has been primarily used with only one of those electrostatic models. In this paper the 1-pK approach is combined with three more electrostatic models. The eight resulting possible combinations have been tested on several sets of data. Applying the 2-pK basic Stern model (BSM) and the triple-layer model (TLM) was not satisfactory: due to the high no. of adjustable parameters involved in these model variations the optimization procedure of the applied computer codes did not converge. This was taken as an a priori justification to exclude even more complicated (four-layer) models. For the remaining six models which could be successfully applied in the present paper, the goodness of fit parameter given by a computer code was used to compare the quality of the description of the chosen exptl. data by the resp. models. A purely diffuse layer model (DLM) generally gave the poorest fit to exptl. data when combined with the 1-pK approach and was only slightly better when combined with the 2-pK formalism. Either the 1-pK BSM or the 2-pK const. capacitance model (CCM) gave the best fit to the data in all the examples. However, it was found in two cases that some arbitrary constraint was necessary to define a unique (and thus meaningful) parameter set for the 2-pK CCM. The 1-pK TLM version allowed in more than half of the examples to det. a unique parameter set, which is impossible with the 2-pK TLM. It is concluded that the 1-pK BSM should be considered as the first choice model with respect to the goodness of fit and the uniqueness of the estd. parameters. The 2-pK CCM is still a good choice for a const. ionic strength case when the exptl. data allow a detn. of unique parameters and if only goodness of fit is used as a criterion.
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    Parsons, D. F.; Carucci, C.; Salis, A. Buffer-specific effects arise from ionic dispersion forces. Phys. Chem. Chem. Phys. 2022, 24, 6544– 6551,  DOI: 10.1039/D2CP00223J
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    Buffer-specific effects arise from ionic dispersion forces
    Parsons, Drew F.; Carucci, Cristina; Salis, Andrea
    Physical Chemistry Chemical Physics (2022), 24 (11), 6544-6551CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Buffer solns. do not simply regulate pH, but also change the properties of protein mols. The zeta potential of lysozyme varies significantly at the same buffer concn., in the order Tris > phosphate > citrate, with citrate even inverting the zeta potential, usually pos. at pH 7.15, to a neg. value. This buffer-specific effect is a special case of the Hofmeister effect. Here the authors present a theor. model of these buffer-specific effects using a Poisson-Boltzmann description of the buffer soln., modified to include dispersion forces of all ions interacting with the lysozyme surface. Dispersion coeffs. are detd. from quantum chem. polarizabilites calcd. for each ion for tris, phosphate, and citrate buffer solns. The lysozyme surface charge is controlled by charge regulation of carboxylate and amine sites of the component amino acids. The theor. model satisfactorily reproduces exptl. zeta potentials, including change of sign with citrate, when hydration of small cosmotropic ions (Na+, H+, OH-) is included.
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    Yang, J.; Su, H.; Lian, C.; Shang, Y.; Liu, H.; Wu, J. Understanding surface charge regulation in silica nanopores. Phys. Chem. Chem. Phys. 2020, 22, 15373– 15380,  DOI: 10.1039/D0CP02152K
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    Understanding surface charge regulation in silica nanopores
    Yang, Jie; Su, Haiping; Lian, Cheng; Shang, Yazhuo; Liu, Honglai; Wu, Jianzhong
    Physical Chemistry Chemical Physics (2020), 22 (27), 15373-15380CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Nanoporous silica is used in a wide variety of applications, ranging from bioanal. tools and materials for energy storage and conversion as well as sepn. devices. The surface charge d. of nanopores is not easily measured by expt. yet plays a vital role in the performance and functioning of silica nanopores. Herein, we report a theor. model to describe charge regulation in silica nanopores by combining the surface-reaction model and the classical d. functional theory (CDFT). The theor. predictions provide quant. insights into the effects of pH, electrolyte concn., and pore size on the surface charge d. and elec. double layer structure. With a fixed pore size, the surface charge d. increases with both pH and the bulk salt concn. similar to that for an open surface. At fixed pH and salt concn., the surface charge d. rises with the pore size until it reaches the bulk asymptotic value when the surface interactions become negligible. At high pH, the surface charge d. is mainly detd. by the ratio of the Debye screening length to the pore size (λD/D).
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    Bohinc, K.; Špadina, M.; Reščič, J.; Shimokawa, N.; Spada, S. Influence of Charge Lipid Head Group Structures on Electric Double Layer Properties. J. Chem. Theory Comput. 2022, 18, 448– 460,  DOI: 10.1021/acs.jctc.1c00800
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    Influence of Charge Lipid Head Group Structures on Electric Double Layer Properties
    Bohinc, Klemen; Spadina, Mario; Rescic, Jurij; Shimokawa, Naofumi; Spada, Simone
    Journal of Chemical Theory and Computation (2022), 18 (1), 448-460CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    In this study we derived a model for a multicomponent lipid monolayer in contact with an aq. soln. by means of a generalized classical d. functional theory and Monte Carlo simulations. Some of the important biol. lipid systems were studied as monolayers composed of head groups with different shapes and charge distributions. Starting from the free energy of the system, which includes the electrostatic interactions, addnl. internal degrees of freedom are included as positional and orientational entropic contributions to the free energy functional. The calculus of variation was used to derive Euler-Lagrange equations, which were solved numerically by the finite element method. The theory and Monte Carlo simulations predict that there are mainly two distinct regions of the elec. double layer: (1) the interfacial region, with thickness less than or equal to the length of the fully stretched conformation of the lipid head group, and (2) the outside region, which follows the usual screening of the interface. In the interfacial region, the elec. double layer is strongly perturbed, and electrostatic profiles and ion distributions have functionality distinct to classical mean-field theories. Based purely on Coulomb interactions, the theory suggests that the dominant effect on the lipid head group conformation is from the charge d. of the interface and the structured lipid mole fraction in the monolayer, rather than the salt concn. in the system.
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    Sholl, D. S.; Lively, R. P. Exemplar Mixtures for Studying Complex Mixture Effects in Practical Chemical Separations. JACS Au 2022, 2, 322– 327,  DOI: 10.1021/jacsau.1c00490
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    Exemplar Mixtures For Studying Complex Mixture Effects in Practical Chemical Separations
    Sholl, David S.; Lively, Ryan P.
    JACS Au (2022), 2 (2), 322-327CODEN: JAAUCR; ISSN:2691-3704. (American Chemical Society)
    Materials and processes for chem. sepns. must be used in complex environments to have impact in many practical settings. Despite these complexities, much research on chem. sepns. focuses on idealized chem. mixts. In this paper, we suggest that research communities for specific chem. sepns. should develop well-defined exemplar mixts. to bridge the gap between fundamental studies and practical applications and we provide a hierarchical framework of chem. mixts. for this purpose. We illustrate this hierarchy with examples including CO2 capture, capture of uranium from seawater, and sepns. of mixts. from electrocatalytic CO2 reactions, among others. We conclude with four recommendations for the research community to accelerate development of innovative sepns. strategies for pressing real-world challenges.
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    Špadina, M.; Gourdin-Bertin, S.; Dražić, G.; Selmani, A.; Dufrêche, J.-F.; Bohinc, K. Charge Properties of TiO2 Nanotubes in NaNO3 Aqueous Solution. ACS Appl. Mater. Interfaces 2018, 10, 13130– 13142,  DOI: 10.1021/acsami.7b18737
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    Charge properties of TiO2 nanotubes in NaNO3 aqueous solution
    Spadina, Mario; Gourdin-Bertin, Simon; Drazic, Goran; Selmani, Atidja; Dufreche, Jean-Francois; Bohinc, Klemen
    ACS Applied Materials & Interfaces (2018), 10 (15), 13130-13142CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
    Charging of material surfaces in aq. electrolyte solns. is one of the most important processes in the interactions between biomaterials and surrounding tissue. Other than a biomaterial, titania nanotubes (TiO2 NTs) represent a versatile material for numerous applications such as heavy metal adsorption or photocatalysis. In this article, the surface charge properties of titania NTs in NaNO3 soln. were investigated through electrophoretic mobility and polyelectrolyte colloid titrn. measuring techniques. In addn., we used high-resoln. transmission electron microscopy imaging to det. the morphol. of TiO2 NTs. A theor. model based on the classical d. functional theory coupled with the charge regulation method in terms of mass action law was developed to understand the exptl. data and to provide insights into charge properties at different phys. conditions, namely, pH and NaNO3 concn. Two intrinsic protonation consts. and surface site d. have been obtained. The electrostatic properties of the system in terms of electrostatic potentials and ion distributions were calcd. and discussed for various pH values. The model can quant. describe the titrn. curve as a function of pH for higher bulk salt concns. and the difference in the equil. amt. of charges between the inner and outer surfaces of TiO2 NTs. Calcd. counterion (NO3-) distributions show a pronounced decrease of NO3- ions for high bulk pH (both inside and outside TiO2 NT) because of the strong elec. field. With the decrease of bulk pH or the increase of the salt concn., NO3- is able to accumulate near the TiO2 NTs surfaces.
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  30. 30
    Foucaud, Y.; Badawi, M.; Filippov, L. O.; Barres, O.; Filippova, I. V.; Lebègue, S. Synergistic adsorptions of Na2CO3 and Na2SiO3 on calcium minerals revealed by spectroscopic and ab initio molecular dynamics studies. Chem. Sci. 2019, 10, 9928– 9940,  DOI: 10.1039/C9SC03366A
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    Synergistic adsorptions of Na2CO3 and Na2SiO3 on calcium minerals revealed by spectroscopic and ab initio molecular dynamics studies
    Foucaud, Yann; Badawi, Michael; Filippov, Lev O.; Barres, Odile; Filippova, Inna V.; Lebegue, Sebastien
    Chemical Science (2019), 10 (43), 9928-9940CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    The synergistic effects between sodium silicate (Na2SiO3) and sodium carbonate (Na2CO3) adsorbed on mineral surfaces are not yet understood, making it impossible to finely tune their resp. amts. in various industrial processes. In order to unravel this phenomenon, diffuse reflectance IR Fourier transform and X-ray photoelectron spectroscopies were combined with ab initio mol. dynamics to investigate the adsorption of Na2SiO3 onto bare and carbonated fluorite (CaF2), an archetypal calcium mineral. Both exptl. and theor. results proved that Na2CO3 adsorbs onto CaF2 with a high affinity and forms a layer of Na2CO3 on the surface. Besides, at low Na2SiO3 concn., silica mainly physisorbs in a monomeric protonated form, Si(OH)4, while at larger concn., significant amts. of polymd. and deprotonated forms are identified. Prior surface carbonation induces an acid-base reaction on the surface, which results in the formation of the basic forms of the monomers and the dimers, i.e. SiO(OH)3- and Si2O3(OH)42-, even at low coverage. Their adsorption is highly favored compared to the acid forms, which explains the synergistic effects obsd. when Na2SiO3 is used after Na2CO3. The formation of the basic form on the bare surface is obsd. only by increasing the surface coverage to 100%. Hence, when Na2CO3 is used during a sepn. process, lower Na2SiO3 concns. are needed to obtain the same effect as with lone Na2SiO3 in the sepn. process.
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  31. 31
    Eskanlou, A.; Huang, Q.; Foucaud, Y.; Badawi, M.; Romero, A. H. Effect of Al3+ and Mg2+ on the flotation of fluorapatite using fatty- and hydroxamic-acid collectors – A multiscale investigation. Appl. Surf. Sci. 2022, 572, 151499,  DOI: 10.1016/j.apsusc.2021.151499
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    Effect of Al3+ and Mg2+ on the flotation of fluorapatite using fatty- and hydroxamic-acid collectors - A multiscale investigation
    Eskanlou, Amir; Huang, Qingqing; Foucaud, Yann; Badawi, Michael; Romero, Aldo H.
    Applied Surface Science (2022), 572 (), 151499CODEN: ASUSEE; ISSN:0169-4332. (Elsevier B.V.)
    Fluorapatite flotation is influenced by the dissolved lattice metal ions. Al3+ and Mg2+ from the assocg. gangue minerals influence the adsorption of collector mols. onto the fluorapatite surface during flotation. Hence, unveiling new insights on such interactions in the context of froth flotation at an at. level paves the way for improving flotation selectivity. An original multiscale approach has been developed involving flotation expts., electro-kinetic and adsorption d. measurements, XPS studies, and d. functional theory simulations. Fatty acid establishes an enhanced interaction with the bare apatite surface compared to the hydroxamates. Na+ counter-ion contributes to the adsorption of fatty acid on bare apatite. Both Al3+ and Mg2+ ions are beneficial for the adsorption of fatty acid, thereby the fluorapatite flotation. For octanohydroxamic acid, the presence of Al3+ results in a stronger collector-apatite interaction, and therefore an enhanced flotation. For fatty acid and hydroxamates, adsorption of Mg2+ leads to an improved collector-apatite interaction. Benzohydroxamic acid is more vigorously adsorbed than octanohydroxamic acid in the presence of Mg2+. Fatty acid establishes a stronger interaction with bare and Al3+ and Mg2+-treated fluorapatite, as opposed to hydroxamates. Mg2+ is more favorable than Al3+ in fluorapatite flotation using both fatty acid and hydroxamates.
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    Foucaud, Y.; Lainé, J.; Filippov, L. O.; Barrès, O.; Kim, W. J.; Filippova, I. V.; Pastore, M.; Lebègue, S.; Badawi, M. Adsorption mechanisms of fatty acids on fluorite unraveled by infrared spectroscopy and first-principles calculations. J. Colloid Interface Sci. 2021, 583, 692– 703,  DOI: 10.1016/j.jcis.2020.09.062
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    Adsorption mechanisms of fatty acids on fluorite unraveled by infrared spectroscopy and first-principles calculations
    Foucaud, Yann; Laine, Juliette; Filippov, Lev O.; Barres, Odile; Kim, Won June; Filippova, Inna V.; Pastore, Mariachiara; Lebegue, Sebastien; Badawi, Michael
    Journal of Colloid and Interface Science (2021), 583 (), 692-703CODEN: JCISA5; ISSN:0021-9797. (Elsevier B.V.)
    The adsorption mechanisms of fatty acids on minerals are largely debated from years, and their understanding is now required to improve flotation processing in the crit. context of raw materials. Three wavenumbers have been obsd. in the literature for the asym. stretching vibration of COO- after the adsorption of fatty acids on mineral surfaces. They have been interpreted as different adsorbed forms, such as a ppt. formation, an adsorption of sole or bridged carboxylates, an anion exchange, or adsorbed modes, such as monodentate or bidentate configurations. Diffuse reflectance IR Fourier transform spectroscopy was combined with ab initio mol. dynamics simulations and simulation of IR spectra. Fluorite and sodium octanoate - or longer-chain fatty acids - were used as prototypical materials for all the investigations. At low fatty acids concn., the asym. stretching vibration of COO- peaks at 1560 cm-1 while, at higher concn., this IR band converts into a doublet peaking at 1535 and 1575 cm-1. Using simulations, we assign the band at 1560 cm-1 to the adsorption of a carboxylate mol. bridged on a sodium counter-cation and the doublet at 1535 and 1575 cm-1 to the adsorption of the sole carboxylate anion under a monodentate or a bidentate binuclear configuration, resp. The formation of an adsorbed layer on the mineral surface is initiated by the adsorption of a sodium carboxylate and followed by the adsorption of mixed sole anionic forms. The role of the carboxylate counter-cation is highlighted for the first time, which was totally ignored in the literature beforehand. This particularly opens the path to the development of innovative strategies to enhance the sepn. contrast between minerals, which is of uttermost importance for the recovery of crit. raw materials.
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    Evans, J. D.; Fraux, G.; Gaillac, R.; Kohen, D.; Trousselet, F.; Vanson, J.-M.; Coudert, F.-X. Computational Chemistry Methods for Nanoporous Materials. Chem. Mater. 2017, 29, 199– 212,  DOI: 10.1021/acs.chemmater.6b02994
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    Computational Chemistry Methods for Nanoporous Materials
    Evans, Jack D.; Fraux, Guillaume; Gaillac, Romain; Kohen, Daniela; Trousselet, Fabien; Vanson, Jean-Mathieu; Coudert, Francois-Xavier
    Chemistry of Materials (2017), 29 (1), 199-212CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    We present here the computational chem. methods our group uses to investigate the phys. and chem. properties of nanoporous materials and adsorbed fluids. We highlight the multiple time and length scales at which these properties can be examd. and discuss the computational tools relevant to each scale. Furthermore, we include the key points to consider-upsides, downsides, and possible pitfalls-for these methods.
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    Foucaud, Y.; Badawi, M.; Filippov, L.; Filippova, I.; Lebègue, S. A review of atomistic simulation methods for surface physical-chemistry phenomena applied to froth flotation. Minerals Engineering 2019, 143, 106020,  DOI: 10.1016/j.mineng.2019.106020
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    A review of atomistic simulation methods for surface physical-chemistry phenomena applied to froth flotation
    Foucaud, Y.; Badawi, M.; Filippov, L.; Filippova, I.; Lebegue, S.
    Minerals Engineering (2019), 143 (), 106020CODEN: MENGEB; ISSN:0892-6875. (Elsevier Ltd.)
    A review. The froth flotation method, which is used for the processing of most non-ferrous ores, involves the adsorption of both org. and inorg. reagents at the mineral/water interface. Understanding the adsorption mechanisms of flotation reagents is a key step to enhance the flotation. New depressants and collectors formulations, more efficient, selective, and environmental friendly can be suggested. At the moment, few exptl. methods can show surface mol. mechanisms with accuracy and confidence. Therefore, atomistic simulations allow to gain understanding in the mechanisms involved in the reagents adsorption. Nowadays, atomistic simulations can be applied to describe the solid/liq. interface and the adsorption mechanisms. Depending on the method, the interactions between atoms are described on the basis of d. functional theory (DFT) or force-fields. They give access to various levels of accuracy, parameters consideration, sampling times, system sizes, and reactivity description, depending on the method used. In particular, ab initio mol. dynamics allows to investigate adsorption processes at liq.-solid interfaces at finite temp. with accuracy.
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    Podgornik, R. General theory of charge regulation and surface differential capacitance. J. Chem. Phys. 2018, 149, 104701,  DOI: 10.1063/1.5045237
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    General theory of charge regulation and surface differential capacitance
    Podgornik, Rudolf
    Journal of Chemical Physics (2018), 149 (10), 104701/1-104701/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A generalization of the mean-field approach will be derived that will take into account the ion-ion as well as ion-surface non-electrostatic effects on an equal footing, being based on the bulk and surface equations of state in the absence of electrostatic interactions. This approach will be applied to the anal. of a single planar surface with dissociable sites with several models of the specific ion-surface non-electrostatic interactions, providing a general thermodn. insight into the characteristics of the surface differential capacitance. The ion-surface interactions and ion-ion packing considerations at the surface will be shown to be more relevant than the bulk packing constraints for ions vicinal to the surface, as well as to set in prior to the conditions where the bulk packing constraints would become relevant. (c) 2018 American Institute of Physics.
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    Roy, P.; Berger, S.; Schmuki, P. TiO2 nanotubes: Synthesis and applications. Angew. Chemie - Int. Ed. 2011, 50, 2904– 2939,  DOI: 10.1002/anie.201001374
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    TiO2 Nanotubes: Synthesis and Applications
    Roy, Poulomi; Berger, Steffen; Schmuki, Patrik
    Angewandte Chemie, International Edition (2011), 50 (13), 2904-2939CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. TiO2 is one of the most studied compds. in materials science. Owing to some outstanding properties it is used for instance in photocatalysis, dye-sensitized solar cells, and biomedical devices. In 1999, first reports showed the feasibility to grow highly ordered arrays of TiO2 nanotubes by a simple but optimized electrochem. anodization of a titanium metal sheet. This finding stimulated intense research activities that focused on growth, modification, properties, and applications of these one-dimensional nanostructures. This review attempts to cover all these aspects, including underlying principles and key functional features of TiO2, in a comprehensive way and also indicates potential future directions of the field.
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    García, D.; Lützenkirchen, J.; Huguenel, M.; Calmels, L.; Petrov, V.; Finck, N.; Schild, D. Adsorption of Strontium onto Synthetic Iron(III) Oxide up to High Ionic Strength Systems. Minerals 2021, 11, 1093,  DOI: 10.3390/min11101093
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    Adsorption of Strontium onto Synthetic Iron(III) Oxide up to High Ionic Strength Systems
    Garcia, David; Lutzenkirchen, Johannes; Huguenel, Maximilien; Calmels, Lea; Petrov, Vladimir; Finck, Nicolas; Schild, Dieter
    Minerals (Basel, Switzerland) (2021), 11 (10), 1093CODEN: MBSIBI; ISSN:2075-163X. (MDPI AG)
    In this work, the adsorption behavior of Sr onto a synthetic iron(III) oxide (hematite with traces of goethite) has been studied. This solid, which might be considered a representative of Fe3+ solid phases (iron corrosion products), was characterized by X-Ray Diffraction (XRD) and XPS, and its sp. surface area was detd. Both XRD and XPS data are consistent with a mixed solid contg. more than 90% hematite and 10% goethite. The solid was further characterized by fast acid-base titrns. at different NaCl concns. (from 0.1 to 5 M). Subsequently, for each background NaCl concn. used for the acid-base titrns., Sr-uptake expts. were carried out involving two different levels of Sr concn. (1 x 10-5 and 5 x 10-5 M, resp.) at const. solid concn. (7.3 g/L) as a function of -log([H+]/M). A Surface Complexation Model (SCM) was fitted to the exptl. data, following a coupled Pitzer/surface complexation approach. The Pitzer model was applied to aq. species. A Basic Stern Model was used for interfacial electrostatics of the system, which includes ion-specific effects via ion-specific pair-formation consts., whereas the Pitzer-approach involves ion-interaction parameters that enter the model through activity coeffs. for aq. species. A simple 1-pK model was applied (generic surface species, denoted as >XOH-1/2). Parameter fitting was carried out using the general parameter estn. software UCODE, coupled to a modified version of FITEQL2. The combined approach describes the full set of data reasonably well and involves two Sr-surface complexes, one of them including chloride. Monodentate and bidentate models were tested and were found to perform equally well. The SCM is particularly able to account for the incomplete uptake of Sr at higher salt levels, supporting the idea that adsorption models conventionally used in salt concns. below 1 M are applicable to high salt concns. if the correct activity corrections for the aq. species are applied. This generates a self-consistent model framework involving a practical approach for semi-mechanistic SCMs. The model framework of coupling conventional electrostatic double layer models for the surface with a Pitzer approach for the bulk soln. earlier tested with strongly adsorbing solutes is here shown to be successful for more weakly adsorbing solutes.
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    Panagiotou, G. D.; Petsi, T.; Bourikas, K.; Garoufalis, C. S.; Tsevis, A.; Spanos, N.; Kordulis, C.; Lycourghiotis, A. Mapping the surface (hydr)oxo-groups of titanium oxide and its interface with an aqueous solution: The state of the art and a new approach. Adv. Colloid Interface Sci. 2008, 142, 20– 42,  DOI: 10.1016/j.cis.2008.04.003
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    Mapping the surface (hydr)oxo-groups of titanium oxide and its interface with an aqueous solution: The state of the art and a new approach
    Panagiotou, George D.; Petsi, Theano; Bourikas, Kyriakos; Garoufalis, Christos S.; Tsevis, Athanassios; Spanos, Nikos; Kordulis, Christos; Lycourghiotis, Alexis
    Advances in Colloid and Interface Science (2008), 142 (1-2), 20-42CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)
    The titanium oxide/electrolyte soln. interface is studied by taking advantage of recent developments in the field of surface and interface chem. relevant to this oxide. Ab-initio calcns. were performed in the frame of the DFT theory for estg. the charge of the titanium and oxygen atoms exposed on the anatase (101), (100), (001), (103)f and rutile (110) crystal faces. These orientations have smaller surface energy with respect to other ones and thus it is more probable to be the real terminations of the anatase and rutile nanocrystallites in the titania polycryst. powders. Potentiometric titrns. for obtaining fine structured titrn. curves as well as microelectrophoresis and streaming potential measurements have been performed. On the basis of ab-initio calcns., and taking into account the relative contribution of each crystal face to the whole surface of the nanocrystals involved in the titania aggregates of a suspension, the three most probable surface ionization models have been derived. These models and the Music model are then tested in conjunction with the Stern-Gouy-Chapman and Basic Stern electrostatic models. The finally selected surface ionization model (model A) in combination with each of the two electrostatic models describes very well the protonation/deprotonation behavior of titania. The description is also very good if this model is combined with the Three Plane (TP) model. The application of the A/(TP) model allowed mapping the surface (hydr)oxo-groups [TiO(H) and Ti2O(H)] of titania exposed in aq. solns. At pH > pzc almost all terminal oxygens [TiO] are non-protonated, whereas even at low pH values the non-protonated terminal oxygens predominate. The acid-base behavior of the bridging oxygens [Ti2O] is different. Thus, even at pH = 10 the greater portion of them is protonated. The application of the A/TP model in conjunction with potentiometric titrns., microelectrophoresis, and streaming potential expts. allowed mapping the titania/electrolyte soln. interface. The first (second) charged plane is located on the oxygen atoms of the first (second) water overlayer at a distance of 1.7 (3.4) Å from the surface. The region between the surface and the second plane is the compact layer. The region between the second plane and the shear plane is the stagnant diffuse part of the interface, with an ionic strength (I) dependent width, ranging from 20 (0.01 M) up to 4 Å (0.3 M). The region between the shear plane and the bulk soln. is the mobile diffuse part, with an ionic strength dependent width, ranging from 10 (0.01 M) up to 2 Å (0.3 M). At I > 0.017 M the mean concn. of the counter ions is higher in the stagnant than in the mobile part of the diffuse layer. For a given I, moving pH from pzc brings about an increase of the mean concn. in the interfacial region and a displacement of the counter ions from the mobile to the stagnant part of the diffuse layer. The mean concn. of the counter ions in the compact layer is generally lower than the corresponding ones in the stagnant and mobile diffuse layers. The mobility of the counter ions in the stagnant layer decreases as pH draws away from pzc or ionic strength increases.
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    Bourikas, K.; Hiemstra, T.; Van Riemsdijk, W. H. Ion pair formation and primary charging behavior of titanium oxide (anatase and rutile). Langmuir 2001, 17, 749– 756,  DOI: 10.1021/la000806c
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    Ion Pair Formation and Primary Charging Behavior of Titanium Oxide (Anatase and Rutile)
    Bourikas, K.; Hiemstra, T.; Van Riemsdijk, W. H.
    Langmuir (2001), 17 (3), 749-756CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    The primary charging behavior of Ti oxide (anatase, rutile, and P25) and the ion pair formation of the electrolyte ions with the surface groups were extensively studied. A large no. of titrn. and electrokinetic data sets available in the literature were successfully described, using the MUSIC (MultiSite Complexation) model with a basic Stern double-layer option and applying the ion pair formation concept. The systematic anal. of the data, over a large no. of different monovalent electrolytes and various ionic strength values, allowed the detn. of a no. of best estd. values for the ion pair formation consts. The values suggest that the interaction of the cations with the TiO2 surface is stronger than that of the anions. This is in accordance with the obsd. shift of the IEP of Ti oxide to higher pH values, at high electrolyte concns. The binding of the cations follows the sequence Cs+ < K+ < Na+ < Li+ and that of the anions follows the sequence Cl- > NO3- > ClO4- > I-. Ti oxide can be divided in 2 classes of materials, having a low (C = 0.9 F m-2) and a high (C = 1.6 F m-2) capacitance value, resp. The low capacitance value corresponds with the low values found for well-crystd. gibbsite and goethite. From the low capacitance value and the absence of correlation with the dielec. properties of the solids, it is hypothesized that the 1st layer of phys. adsorbed H2O has a unique relative dielec. const. ε of ∼40 on well-crystd. oxides. The high capacitance may correspond to a situation with a distorted H2O layer, which has bulk H2O properties (ε = 78). No other significant differences between the interfacial charging parameters of anatase and rutile were found.
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    Adžić, N. c. v.; Podgornik, R. Charge regulation in ionic solutions: Thermal fluctuations and Kirkwood-Schumaker interactions. Phys. Rev. E 2015, 91, 022715,  DOI: 10.1103/PhysRevE.91.022715
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    Charge regulation in ionic solutions: thermal fluctuations and Kirkwood-Schumaker interactions
    Adzic, Natasa; Podgornik, Rudolf
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2015), 91 (2-A), 022715/1-022715/13CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
    We study the behavior of two macroions with dissociable charge groups, regulated by local variables such as pH and electrostatic potential, immersed in a monovalent salt soln., considering cases where the net charge can either change sign or remain of the same sign depending on these local parameters. The charge regulation in both cases is described by the proper free-energy function for each of the macroions, while the coupling between the charges is evaluated on the approx. Debye-Huckel level. The charge correlation functions and the ensuing charge fluctuation forces are calcd. anal. and numerically. Strong attraction between like-charged macroions is found close to the point of zero charge, specifically due to asym., anticorrelated charge fluctuations of the macroion charges. The general theory is then implemented for a system of two proteinlike macroions, generalizing the form and magnitude of the Kirkwood-Schumaker interaction.
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    Trizac, E.; Hansen, J.-P. Wigner-Seitz model of charged lamellar colloidal dispersions. Phys. Rev. E 1997, 56, 3137,  DOI: 10.1103/PhysRevE.56.3137
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    Wigner-Seitz model of charged lamellar colloidal dispersions
    Trizac, Emmanuel; Hansen, Jean-Pierre
    Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics (1997), 56 (3-B), 3137-3149CODEN: PLEEE8; ISSN:1063-651X. (American Physical Society)
    A concd. suspension of lamellar colloidal particles (e.g., clay) is modeled by considering a single, uniformly charged, finite platelet confined with co- and counterions to a Wigner-Seitz (WS) cell. The system is treated within Poisson-Boltzmann theory, with appropriate boundary conditions on the surface of the WS cell, supposed to account for the confinement effect of neighboring platelets. Expressions are obtained for the free energy, osmotic, and disjoining pressures and the capacitance in terms of the local electrostatic potential and the co- and counterion d. profiles. Explicit solns. of the linearized Poisson-Boltzmann equation are obtained for circular and square platelets placed at the center of a cylindrical or parallelepipedic cell. The resulting free energy is found to go through a min. as a function of the aspect ratio of the cell, for any given vol. (detd. by the macroscopic concn. of platelets), platelet surface charge, and salt concn. The optimum aspect ratio is found to be nearly independent of the two latter phys. parameters. The osmotic and disjoining pressures are found to coincide at the free energy min., while the total quadrupole moment of the elec. double layer formed by the platelet and the surrounding co- and counterions vanishes simultaneously. The osmotic equation of state is calcd. for a variety of phys. conditions. The limit of vanishing platelet concn. is considered in some detail, and the force acting between two coaxial platelets is calcd. in that limit as a function of their sepn.
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    Hallez, Y.; Diatta, J.; Meireles, M. Quantitative Assessment of the Accuracy of the Poisson–Boltzmann Cell Model for Salty Suspensions. Langmuir 2014, 30, 6721– 6729,  DOI: 10.1021/la501265k
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    Quantitative Assessment of the Accuracy of the Poisson-Boltzmann Cell Model for Salty Suspensions
    Hallez, Yannick; Diatta, Joseph; Meireles, Martine
    Langmuir (2014), 30 (23), 6721-6729CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    The cell model is a ubiquitous, fast, and relatively easily implemented model used to est. the osmotic pressure of a colloidal dispersion. It has been shown to yield accurate approxns. of the pressure in dispersions with a low salt content. It is generally accepted that it performs well when long-ranged interactions are involved and the structure of the dispersion is solidlike. The aim of the present work is to det. quant. the error committed by assuming the pressure computed with the cell model is the real osmotic pressure of a dispersion. To this end, cell model pressures are compared to a correct estn. of the actual pressures obtained from Poisson-Boltzmann Brownian dynamics simulations including many-body electrostatics and the thermal motion of the colloids. The comparison is performed for various colloidal sizes and charges, salt contents, and vol. fractions. It is demonstrated that the accuracy of the cell model predictions is a function of only the av. intercolloid distance scaled by Debye's length κ‾d and the normalized colloidal charge. The cell model is accurate for κ‾d < 1 and not reliable for κ‾d > 5 independently of the colloidal charge. In the 1 < κ‾d < 5 range, covering a wide set of exptl. conditions, the colloidal surface charge has a large influence on the error assocd. with the cell approxn. The results presented in this article should provide a useful ref. to det. a priori if the cell model can be expected to predict accurately an equation of state for a given set of physicochem. parameters.
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    Effective interactions between electric double layers
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    Annual Review of Physical Chemistry (2000), 51 (), 209-242CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews Inc.)
    A review with 196 refs. that summarizes and assesses recent theor. and exptl. advances, with special emphasis on the effective interaction between charge-stabilized colloids, in the bulk or in confined geometries, and on the ambiguities of defining an effective charge of the colloidal particles. Some consideration is given to the often neglected discrete solvent effects.
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    The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
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    Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
    Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    Grimme, Stefan
    Journal of Computational Chemistry (2006), 27 (15), 1787-1799CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    A new d. functional (DF) of the generalized gradient approxn. (GGA) type for general chem. applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6·R-6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common d. functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on std. thermochem. benchmark sets, for 40 noncovalently bound complexes, including large stacked arom. mols. and group II element clusters, and for the computation of mol. geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for std. functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean abs. deviation of only 3.8 kcal mol-1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the av. CCSD(T) accuracy. The basic strategy in the development to restrict the d. functional description to shorter electron correlation lengths scales and to describe situations with medium to large interat. distances by damped C6·R-6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chem. method for large systems where dispersion forces are of general importance.
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    There is no expanded citation for this reference.
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    From ultrasoft pseudopotentials to the projector augmented-wave method
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    The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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    Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169,  DOI: 10.1103/PhysRevB.54.11169
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    Kresse, G.; Furthmueller, J.
    Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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    Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 1998, 57, 1505– 1509,  DOI: 10.1103/PhysRevB.57.1505
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    Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P.
    Physical Review B: Condensed Matter and Materials Physics (1998), 57 (3), 1505-1509CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    By taking better account of electron correlations in the 3d shell of metal ions in Ni oxide it is possible to improve the description of both electron energy loss spectra and parameters characterizing the structural stability of the material compared with local spin d. functional theory.
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    Aschauer, U.; He, Y.; Cheng, H.; Li, S.-C.; Diebold, U.; Selloni, A. Influence of Subsurface Defects on the Surface Reactivity of TiO2: Water on Anatase (101). J. Phys. Chem. C 2010, 114, 1278– 1284,  DOI: 10.1021/jp910492b
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    Influence of Subsurface Defects on the Surface Reactivity of TiO2: Water on Anatase (101)
    Aschauer, Ulrich; He, Yunbin; Cheng, Hongzhi; Li, Shao-Chun; Diebold, Ulrike; Selloni, Annabella
    Journal of Physical Chemistry C (2010), 114 (2), 1278-1284CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    The adsorption of water on a reduced TiO2 anatase (101) surface is investigated with scanning tunneling microscopy and d. functional theory calcns. The presence of subsurface defects, which are prevalent on reduced anatase (101), leads to a higher desorption temp. of adsorbed water, indicating an enhanced binding due to the defects. Theor. calcns. of water adsorption on anatase (101) surfaces contg. subsurface oxygen vacancies or titanium interstitials show a strong selectivity for water binding to sites in the vicinity of the subsurface defects. Moreover, the water adsorption energy at these sites is considerably higher than that on the stoichiometric surface, thus giving an explanation for the exptl. observations. The calcns. also predict facile water dissocn. at these sites, confirming the important role of defects in the surface chem. of TiO2.
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    Mattioli, G.; Filippone, F.; Alippi, P.; Amore Bonapasta, A. Ab initio study of the electronic states induced by oxygen vacancies in rutile and anatase TiO2. Phys. Rev. B 2008, 78, 241201,  DOI: 10.1103/PhysRevB.78.241201
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    Ab initio study of the electronic states induced by oxygen vacancies in rutile and anatase TiO2
    Mattioli, G.; Filippone, F.; Alippi, P.; Amore Bonapasta, A.
    Physical Review B: Condensed Matter and Materials Physics (2008), 78 (24), 241201/1-241201/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    We studied the origin of the differences between the anatase and rutile properties and show that they can be related to a remarkable difference in nature between the electronic levels induced by bulk oxygen vacancies (VOx) in the two TiO2 polymorphs using the DFT LSD and GGA+U methods. These levels have indeed different locations in the energy gap and give rise to different localizations of the electronic charge in real space, thus indicating the VOx's as important candidates to elucidate the different properties of the two TiO2 phases. The present results, achieved by applying a U correction to local spin-d. (LSD)-generalized gradient approxn. (GGA) methods, stress also the importance of beyond-LSD methods when investigating metal oxides. They show indeed that only such methods permit to reveal the different nature of the VOx electronic states in the two TiO2 phases.
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    Finazzi, E.; Di Valentin, C.; Pacchioni, G.; Selloni, A. Excess electron states in reduced bulk anatase TiO2: Comparison of standard GGA, GGA+U, and hybrid DFT calculations. J. Chem. Phys. 2008, 129, 154113,  DOI: 10.1063/1.2996362
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    Excess electron states in reduced bulk anatase TiO2: Comparison of standard GGA, GGA+U, and hybrid DFT calculations
    Finazzi, Emanuele; Di Valentin, Cristiana; Pacchioni, Gianfranco; Selloni, Annabella
    Journal of Chemical Physics (2008), 129 (15), 154113/1-154113/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The removal of lattice O atoms, as well as the addn. of interstitial H atoms, in TiO2 is known to cause the redn. in the material and the formation of "Ti3+" ions. By means of electronic structure calcns. we have studied the nature of such oxygen vacancy and hydrogen impurity states in the bulk of the anatase polymorph of TiO2. The spin polarized nature of these centers, the localized or delocalized character of the extra electrons, the presence of defect-induced states in the gap, and the polaronic distortion around the defect have been investigated with different theor. methods: std. d. functional theory (DFT) in the generalized-gradient approxn. (GGA), GGA+U methods as a function of the U parameter, and two hybrid functionals with different admixts. of Hartree-Fock exchange. The results are found to be strongly dependent on the method used. Only GGA+U or hybrid functionals are able to reproduce the presence of states at about 1 eV below the conduction band, which are exptl. obsd. in reduced titania. The corresponding electronic states are localized on Ti 3d levels, but partly delocalized solns. are very close in energy. These findings show the limited predictive power of these theor. methods to describe the electronic structure of reduced titania in the absence of accurate exptl. data. (c) 2008 American Institute of Physics.
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    Morgan, B.; Watson, G. W. A DFT+U description of oxygen vacancies at the TiO2 rutile (110) surface. Surf. Sci. 2007, 601, 5034– 5041,  DOI: 10.1016/j.susc.2007.08.025
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    A DFT+ U description of oxygen vacancies at the TiO2 rutile (110) surface
    Morgan, Benjamin J.; Watson, Graeme W.
    Surface Science (2007), 601 (21), 5034-5041CODEN: SUSCAS; ISSN:0039-6028. (Elsevier B.V.)
    Exptl. observations indicate that removing bridging oxygen atoms from the TiO2 rutile (1 1 0) surface produces a localized state approx. 0.7 eV below the conduction band. The corresponding excess electron d. is thought to localize on the pair of Ti atoms neighboring the vacancy; formally giving two Ti3+ sites. We consider the electronic structure and geometry of the oxygen deficient TiO2 rutile (1 1 0) surface using both gradient-cor. d. functional theory (GGA DFT) and DFT cor. for on-site Coulomb interactions (GGA + U) to allow a direct comparison of the two methods. We show that GGA fails to predict the exptl. obsd. electronic structure, in agreement with previous uncorrected DFT calcns. on this system. Introducing the +U term encourages localization of the excess electronic charge, with the qual. distribution depending on the value of U. For low values of U (≤4.0 eV) the charge localizes in the sub-surface layers occupied in the GGA soln. at arbitrary Ti sites, whereas higher values of U (≥4.2 eV) predict strong localization with the excess electronic charge mainly on the two Ti atoms neighboring the vacancy. The precise charge distribution for these larger U values is found to differ from that predicted by previous hybrid-DFT calcns.
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    A molecular dynamics method for simulations in the canonical ensemble
    Nose, Shuichi
    Molecular Physics (1984), 52 (2), 255-68CODEN: MOPHAM; ISSN:0026-8976.
    A mol. dynamics simulation method is proposed which can generate configurations belonging to the canonical (T, V, N) ensemble or the const. temp. const. pressure (T, P, N) ensemble. The phys. system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added. This device allows the total energy of the phys. system to fluctuate. The equil. distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space. The method is tested for an at. fluid (Ar) and works well.
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    A unified formulation of the constant-temperature molecular-dynamics methods
    Nose, Shuichi
    Journal of Chemical Physics (1984), 81 (1), 511-19CODEN: JCPSA6; ISSN:0021-9606.
    Three recently proposed const. temp. mol. dynamics methods [N., (1984) (1); W. G. Hoover et al., (1982) (2); D. J. Evans and G. P. Morris, (1983) (2); and J. M. Haile and S. Gupta, 1983) (3)] are examd. anal. via calcg. the equil. distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N-1/2 from the canonical distribution (N the no. of particles). The results for the const. temp.-const. pressure ensemble are similar to the canonical ensemble case.
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    Physical review. A, General physics (1985), 31 (3), 1695-1697 ISSN:0556-2791.
    There is no expanded citation for this reference.
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    Horn, M.; Schwerdtfeger, C. F.; Meagher, E. P. Refinement of the structure of anatase at several temperatures. Zeitschrift fur Kristallographie 1972, 136, 273– 281,  DOI: 10.1524/zkri.1972.136.3-4.273
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    Refinement of the structure of anatase at several temperatures
    Horn, M.; Schwerdtfeger, C. F.; Meagher, E. P.
    (1972), 136 (3-4), 273-81CODEN: ZEKGAX ISSN:.
    The crystal structure of anatase was refined by single-crystal x-ray diffraction at 25-800°. The only structural parameter, the z coordinate of O, changed regularly from 0.2081(2) at 25° to 0.2076(3) at 800°. This change was ∼1 order of magnitude smaller than that expected by M. Horn and C. F. Schwerdtfeger (1971) to explain the temp. dependence of EPR spectra of Fe impurities in anatase. The change was in the direction of increasing distortion of the TiO6 octahedra with increasing temp.
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    Vittadini, A.; Selloni, A.; Rotzinger, F. P.; Grätzel, M. Formic Acid Adsorption on Dry and Hydrated TiO2 Anatase (101) Surfaces by DFT Calculations. J. Phys. Chem. B 2000, 104, 1300– 1306,  DOI: 10.1021/jp993583b
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    Formic acid adsorption on dry and hydrated TiO2 anatase (101) surfaces by DFT calculations
    Vittadini, A.; Selloni, A.; Rotzinger, F. P.; Graetzel, M.
    Journal of Physical Chemistry B (2000), 104 (6), 1300-1306CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
    The adsorption of formic acid and sodium formate on the stoichiometric anatase (101) surface was studied by d. functional calcns. with a slab geometry. On the clean surface, the most stable adsorption structure for HCOOH is a mol. monodentate configuration, hydrogen-bonded to a surface bridging oxygen, while for HCOONa a dissocd. bridging bidentate geometry is preferred. The bidentate chelating structure is energetically unstable for both the acid and the salt. On the hydrated surface, both HCOOH and HCOONa preferentially form an inner-sphere adsorption complex. HCOOH maintains a monodentate coordination, but, due to the interaction with a nearby water mol., it becomes dissocd., while HCOONa again prefers a bridging bidentate structure. The energies for adsorption from an aq. soln. are estd. to be 0.30 and 0.79 eV for HCOOH and HCOONa, resp.
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    Oliver, P. M.; Watson, G. W.; Kelsey, E. T.; Parker, S. C. Atomistic simulation of the surface structure of the TiO2 polymorphs rutileand anatase. J. Mater. Chem. 1997, 7, 563– 568,  DOI: 10.1039/a606353e
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    Atomistic simulation of the surface structure of the TiO2 polymorphs rutile and anatase
    Oliver, Peter M.; Watson, Graeme W.; Kelsey, E. Toby; Parker, Stephen C.
    Journal of Materials Chemistry (1997), 7 (3), 563-568CODEN: JMACEP; ISSN:0959-9428. (Royal Society of Chemistry)
    Atomistic simulation has been used to calc. the surface structures and stability of the rutile and anatase polymorphs of TiO2. The surface and attachment energies were used to evaluate the equil. and pseudo-kinetic morphologies. The surfaces expressed in rutile were {011}, {110}, {100} and {221} with surface energies of 1.85, 1.78, 2.08 and 2.02 J m-2, resp. For anatase the {011} and {001} surfaces were dominant in the morphol. with relaxed surface energies of 1.40 and 1.28 J m-2. The predicted equil. forms were largely in good agreement with the reported exptl. morphologies of rutile and anatase and showed the importance of surface relaxation.
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    Agosta, L.; Gala, F.; Zollo, G. Water diffusion on TiO2 anatase surface. AIP Conf. Proc. 2015, 1667, 020006,  DOI: 10.1063/1.4922562
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    Water diffusion on TiO2 anatase surface
    Agosta, L.; Gala, F.; Zollo, G.
    AIP Conference Proceedings (2015), 1667 (1, NANOFORUM 2014), 020006/1-020006/9CODEN: APCPCS; ISSN:0094-243X. (American Institute of Physics)
    Compatibility between biol. mols. and inorg. materials, such as cryst. metal oxides, is strongly dependent on the selectivity properties and the adhesion processes at the interface between the two systems. Among the many different aspects that affect the adsorption processes of peptides or proteins onto inorg. surfaces, such as the charge state of the amino acids, the peptide 3D structure, the surface roughness, the presence of vacancies or defects on and below the surface, a key role is certainly played by the water solvent whose mols. mediate the interaction. Then the surface hydration pattern may strongly affect the adsorption behavior of biol. mols. For the particular case of (101) anatase TiO2 surface that has a fundamental importance in the interaction of biocompatible nano-devices with biol. environment, it was shown, both theor. and exptl., that various hydration patterns are close in energy and that the water mols. are mobile at as low temp. values as 190 K. Then it is important to understand the dynamical behavior of first hydration layer of the (101) anatase surface. As a first approach to this problem, d. functional calcns. are used to investigate water diffusion on the (101) anatase TiO2 surface by sampling the potential energy surface of water mols. of the first hydration layer thus calcg. the water mol. migration energy along some relevant diffusion paths on the (101) surface. The measured activation energy of water migration seems in contrast with the obsd. surface mobility of the water mols. that, as a consequence could be explained invoking a strong role of the entropic term in the context of the transition state theory. (c) 2015 American Institute of Physics.
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    PACKMOL: A package for building initial configurations for molecular dynamics simulations
    Martinez, L.; Andrade, R.; Birgin, E. G.; Martinez, J. M.
    Journal of Computational Chemistry (2009), 30 (13), 2157-2164CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    Adequate initial configurations for mol. dynamics simulations consist of arrangements of mols. distributed in space in such a way to approx. represent the system's overall structure. In order that the simulations are not disrupted by large van der Waals repulsive interactions, atoms from different mols. must keep safe pairwise distances. Obtaining such a mol. arrangement can be considered a packing problem: Each type mol. must satisfy spatial constraints related to the geometry of the system, and the distance between atoms of different mols. must be greater than some specified tolerance. We have developed a code able to pack millions of atoms, grouped in arbitrarily complex mols., inside a variety of three-dimensional regions. The regions may be intersections of spheres, ellipses, cylinders, planes, or boxes. The user must provide only the structure of one mol. of each type and the geometrical constraints that each type of mol. must satisfy. Building complex mixts., interfaces, solvating biomols. in water, other solvents, or mixts. of solvents, is straightforward. In addn., different atoms belonging to the same mol. may also be restricted to different spatial regions, in such a way that more ordered mol. arrangements can be built, as micelles, lipid double-layers, etc. The packing time for state-of-the-art mol. dynamics systems varies from a few seconds to a few minutes in a personal computer. The input files are simple and currently compatible with PDB, Tinker, Molden, or Moldy coordinate files. The package is distributed as free software and can be downloaded from . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009.
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    Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. Journal of applied crystallography 2011, 44, 1272– 1276,  DOI: 10.1107/S0021889811038970
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    VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
    Momma, Koichi; Izumi, Fujio
    Journal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
    VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.
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    Walle, L. E.; Borg, A.; Johansson, E. M. J.; Plogmaker, S.; Rensmo, H.; Uvdal, P.; Sandell, A. Mixed Dissociative and Molecular Water Adsorption on Anatase TiO2(101). J. Phys. Chem. C 2011, 115, 9545– 9550,  DOI: 10.1021/jp111335w
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    Mixed dissociative and molecular water adsorption on anatase TiO2(101)
    Walle, L. E.; Borg, A.; Johansson, E. M. J.; Plogmaker, S.; Rensmo, H.; Uvdal, P.; Sandell, A.
    Journal of Physical Chemistry C (2011), 115 (19), 9545-9550CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    The adsorption properties of water on the stoichiometric (101) surface of anatase TiO2 in the temp. range 160-400 K was studied by synchrotron radiation core level photoelectron spectroscopy. O 1s spectra give clear evidence for the formation of a first layer of water that comprises both H2O and OH. The compn. is 0.77 ± 0.05 ML H2O and 0.47 ± 0.05 ML OH. Decreasing the coverage by heating leads to a decreased H2O/OH ratio. The results are very similar to those recently reported for water on rutile TiO2(110) and show that the previously proposed model of mol. adsorption only on anatase TiO2(101) must be revised.
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    Nadeem, I. M.; Treacy, J. P. W.; Selcuk, S.; Torrelles, X.; Hussain, H.; Wilson, A.; Grinter, D. C.; Cabailh, G.; Bikondoa, O.; Nicklin, C.; Selloni, A.; Zegenhagen, J.; Lindsay, R.; Thornton, G. Water Dissociates at the Aqueous Interface with Reduced Anatase TiO2 (101). J. Phys. Chem. Lett. 2018, 9, 3131– 3136,  DOI: 10.1021/acs.jpclett.8b01182
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    Water dissociates at aqueous interface with reduced anatase TiO2 (101)
    Nadeem, Immad M.; Treacy, Jon P. W.; Selcuk, Sencer; Torrelles, Xavier; Hussain, Hadeel; Wilson, Axel; Grinter, David C.; Cabailh, Gregory; Bikondoa, Oier; Nicklin, Christopher; Selloni, Annabella; Zegenhagen, Jorg; Lindsay, Robert; Thornton, Geoff
    Journal of Physical Chemistry Letters (2018), 9 (11), 3131-3136CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Elucidating the structure of the interface between natural (reduced) anatase TiO2 (101) and water is an essential step toward understanding the assocd. photoassisted water splitting mechanism. Here we present surface X-ray diffraction results for the room temp. interface with ultrathin and bulk water, which we explain by ref. to d. functional theory calcns. We find that both interfaces contain a 25:75 mixt. of mol. H2O and terminal OH bound to titanium atoms along with bridging OH species in the contact layer. This is in complete contrast to the inert character of room temp. anatase TiO2 (101) in ultrahigh vacuum. A key difference between the ultrathin and bulk water interfaces is that in the latter water in the second layer is also ordered. These mols. are hydrogen bonded to the contact layer, modifying the bond angles.
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    Martinez-Casado, R.; Mallia, G.; Harrison, N. M.; Pérez, R. First-Principles Study of the Water Adsorption on Anatase(101) as a Function of the Coverage. J. Phys. Chem. C 2018, 122, 20736– 20744,  DOI: 10.1021/acs.jpcc.8b05081
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    First-Principles Study of the Water Adsorption on Anatase(101) as a Function of the Coverage
    Martinez-Casado, Ruth; Mallia, Giuseppe; Harrison, Nicholas M.; Perez, Ruben
    Journal of Physical Chemistry C (2018), 122 (36), 20736-20744CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    An understanding of the interaction of water with the anatase(101) surface is crucial for developing strategies to improve the efficiency of the photocatalytic reaction involved in solar water splitting. Despite a no. of previous investigations, it is still not clear if water preferentially adsorbs in its mol. or dissocd. form on anatase(101). With the aim of shedding some light on this controversial issue, we report the results of periodic screened-exchange d. functional theory calcns. of the dissociative, mol., and mixed adsorption modes on the anatase(101) surface at various coverages. Our calcns. support the suggestion that surface-adsorbed OH groups are present, which has been made on the basis of recently measured XPS, temp.-programmed desorption, and scanning tunneling microscopy data. It is also shown that the relative stability of water adsorption on anatase(101), at different configurations, can be understood in terms of a simple model based on the no. and nature of the hydrogen bonds formed as well as the adsorbate-induced at. displacements in the surface layers. These general conclusions are found to be insensitive to the specific choice of approxn. for electronic exchange and correlation within the d. functional theory. The simple model of water-anatase interactions presented here may be of wider validity in detg. the geometry of water-oxide interfaces.
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    Patrick, C. E.; Giustino, F. Structure of a Water Monolayer on the Anatase TiO2(101) Surface. Phys. Rev. Applied 2014, 2, 014001,  DOI: 10.1103/PhysRevApplied.2.014001
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    Structure of a water monolayer on the anatase TiO2(101) surface
    Patrick, Christopher E.; Giustino, Feliciano
    Physical Review Applied (2014), 2 (1), 014001CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)
    Titanium dioxide (TiO2) plays a central role in the study of artificial photosynthesis, owing to its ability to perform photocatalytic water splitting. Despite over four decades of intense research efforts in this area, there is still some debate over the nature of the first water monolayer on the technol. relevant anatase TiO2(101) surface. In this work, we use first-principles calcns. to reverse engineer the exptl. high-resoln. x-ray photoelectron spectra measured for this surface by Walle et al. and find evidence supporting the existence of a mix of dissocd. and mol. water in the first monolayer. Using both semilocal and hybrid functional calcns., we revise the current understanding of the adsorption energetics by showing that the energetic cost of water dissocn. is reduced via the formation of a hydrogen-bonded hydroxyl-water complex. We also show that such a complex can provide an explanation of an unusual superstructure obsd. in high-resoln. scanning tunneling microscopy expts.
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    Soria, F. A.; Di Valentin, C. Reactive molecular dynamics simulations of hydration shells surrounding spherical TiO2 nanoparticles: implications for proton-transfer reactions. Nanoscale 2021, 13, 4151– 4166,  DOI: 10.1039/D0NR07503E
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    Reactive molecular dynamics simulations of hydration shells surrounding spherical TiO2 nanoparticles: implications for proton-transfer reactions
    Soria, Federico A.; Di Valentin, Cristiana
    Nanoscale (2021), 13 (7), 4151-4166CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
    In many potential applications, nanoparticles are typically in an aq. medium. This has strong influence on the stability, optical properties and reactivity, in particular for their functionalization. Therefore, the understanding of the chem. at the interface between the solvent and the nanoparticle is of utmost importance. In this work, we present a comparative ReaxFF reactive mol. dynamics investigation on spherical TiO2 nanoparticles (NSs) of realistic size, with diams. from 2.2 to 4.4 nm, immersed in a large drop of bulk water. After force field validation for its use for a curved anatase TiO2 surface/water interface, we performed several simulations of the TiO2 nanoparticles of increasing size in a water drop. We found that water can be adsorbed jointly in a mol. and dissociative way on the surface. A Langmuir isotherm indicating an adsorption/desorption mechanism of water on the NS is obsd. Regarding the dissociative adsorption, atomistic details reveal two different mechanisms, depending on the water concn. around the NS. At low coverage, the first mechanism involves direct dissocn. of a single water mol., whereas, at higher water coverage, the second mechanism is a proton transfer reaction involving two water mols., also known as Grotthuss-like mechanism. Thermal annealing simulations show that several water mols. remain on the surface in agreement with the exptl. reports. The capacity of adsorption is higher for the 2.2 and 3.0 nm NSs than for the 4.4 nm NS. Finally, a comparative investigation with flat surfaces indicates that NSs present a higher water adsorption capacity (undissociated and dissocd.) than flat surfaces, which can be rationalized considering that NSs present many more low-coordinated Ti atoms available for water adsorption.
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    Foucaud, Y.; Canevesi, R.; Celzard, A.; Fierro, V.; Badawi, M. Hydration mechanisms of scheelite from adsorption isotherms and ab initio molecular dynamics simulations. Appl. Surf. Sci. 2021, 562, 150137,  DOI: 10.1016/j.apsusc.2021.150137
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    Hydration mechanisms of scheelite from adsorption isotherms and ab initio molecular dynamics simulations
    Foucaud, Y.; Canevesi, R. L. S.; Celzard, A.; Fierro, V.; Badawi, M.
    Applied Surface Science (2021), 562 (), 150137CODEN: ASUSEE; ISSN:0169-4332. (Elsevier B.V.)
    Apart from its interesting optical properties, scheelite is one of the main tungsten-bearing minerals, widely processed by the froth flotation method. A precise and comprehensive description of the hydration state of scheelite is required to achieve satisfactory flotation performance. The hydration mechanisms of scheelite have been poorly studied, using only theor. methods. Manometric gas sorption expts. were combined with ab initio mol. dynamics simulations, including correction for dispersive interactions. The isosteric enthalpy of adsorption was used as the value to link exptl. and theor. results, since it can be detd. by both methods. We have found that water adsorbs more favorably in its mol. form, with two adsorbed water mols. per calcium atom on the (0 0 1) surface, and with three adsorbed water mols. for two calcium atoms on the (1 1 2) surface. The very first water mols. adsorb with an isosteric enthalpy of adsorption of -80 kJ·mol-1 on the (0 0 1) surface, and of -117 kJ·mol-1 on the (1 1 2) surface, at 300 K. This is in very good agreement with the value of -90 kJ·mol-1 calcd. using the Clausius-Clapeyron approach on three exptl. isotherms, accurately fitted with a dual-site Freundlich-Langmuir model.
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    A study of the hydration of the alkali metal ions in aqueous solution
    Mahler Johan; Persson Ingmar
    Inorganic chemistry (2012), 51 (1), 425-38 ISSN:.
    The hydration of the alkali metal ions in aqueous solution has been studied by large angle X-ray scattering (LAXS) and double difference infrared spectroscopy (DDIR). The structures of the dimethyl sulfoxide solvated alkali metal ions in solution have been determined to support the studies in aqueous solution. The results of the LAXS and DDIR measurements show that the sodium, potassium, rubidium and cesium ions all are weakly hydrated with only a single shell of water molecules. The smaller lithium ion is more strongly hydrated, most probably with a second hydration shell present. The influence of the rubidium and cesium ions on the water structure was found to be very weak, and it was not possible to quantify this effect in a reliable way due to insufficient separation of the O-D stretching bands of partially deuterated water bound to these metal ions and the O-D stretching bands of the bulk water. Aqueous solutions of sodium, potassium and cesium iodide and cesium and lithium hydroxide have been studied by LAXS and M-O bond distances have been determined fairly accurately except for lithium. However, the number of water molecules binding to the alkali metal ions is very difficult to determine from the LAXS measurements as the number of distances and the temperature factor are strongly correlated. A thorough analysis of M-O bond distances in solid alkali metal compounds with ligands binding through oxygen has been made from available structure databases. There is relatively strong correlation between M-O bond distances and coordination numbers also for the alkali metal ions even though the M-O interactions are weak and the number of complexes of potassium, rubidium and cesium with well-defined coordination geometry is very small. The mean M-O bond distance in the hydrated sodium, potassium, rubidium and cesium ions in aqueous solution have been determined to be 2.43(2), 2.81(1), 2.98(1) and 3.07(1) ÅA, which corresponds to six-, seven-, eight- and eight-coordination. These coordination numbers are supported by the linear relationship of the hydration enthalpies and the M-O bond distances. This correlation indicates that the hydrated lithium ion is four-coordinate in aqueous solution. New ionic radii are proposed for four- and six-coordinate lithium(I), 0.60 and 0.79 ÅA, respectively, as well as for five- and six-coordinate sodium(I), 1.02 and 1.07 ÅA, respectively. The ionic radii for six- and seven-coordinate K(+), 1.38 and 1.46 ÅA, respectively, and eight-coordinate Rb(+) and Cs(+), 1.64 and 1.73 ÅA, respectively, are confirmed from previous studies. The M-O bond distances in dimethyl sulfoxide solvated sodium, potassium, rubidium and cesium ions in solution are very similar to those observed in aqueous solution.
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    Understanding the Structure of Aqueous Cesium Chloride Solutions by Combining Diffraction Experiments, Molecular Dynamics Simulations, and Reverse Monte Carlo Modeling
    Mile, Viktoria; Pusztai, Laszlo; Dominguez, Hector; Pizio, Orest
    Journal of Physical Chemistry B (2009), 113 (31), 10760-10769CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    A detailed study of the microscopic structure of an electrolyte soln., CsCl in water, is presented. For revealing the influence of salt concn. on the structure, CsCl solns. at concns. of 1.5, 7.5, and 15 mol % are investigated. For each concn., we combine total scattering structure factors from neutron and X-ray diffraction and 10 partial radial distribution functions from mol. dynamics simulations in one single structural model, generated by reverse Monte Carlo modeling. This combination of computer modeling methods is capable of (a) showing the extent to which simulation results are consistent with exptl. diffraction data and (b) tracking down distribution functions in computer simulation that are the least comfortable with diffraction data. For the present solns., we show that the level of consistency between simulations that use simple pair potentials and exptl. structure factors is nearly quant. Remaining inconsistencies seem to be caused by water-water distribution functions. Changing the pair potentials of water-water interactions from SPC/E to TIP4P-2005 has not had any effect in this respect. As a final result, we obtained particle configurations from reverse Monte Carlo modeling that were in quant. agreement with both diffraction data and most of the mol. dynamics (MD) simulated partial radial distribution functions (prdf's). From the particle coordinates, the distribution of the no. of first neighbors, as well as angular correlation functions, were calcd. The av. no. of water mols. around cations decreases from about 8 to about 6.5 as concn. increases from 1.5 to 15 mol %, whereas the same quantity for the anions changes from about 7 to about 5. The av. angle of Cl···H-O particle arrangements, characteristic of anion-water hydrogen bonds, is closer to 180° than that found for O···H-O arrangements (water-water hydrogen bonds). The present combination of exptl. and computer simulation methods appears to be promising for the study of other electrolyte solns.
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    Zhang, K.; Li, Z.; Qi, S.; Chen, W.; Xie, J.; Wu, H.; Zhao, H.; Li, D.; Wang, S. Adsorption behavior of Cs(I) on natural soils: Batch experiments and model-based quantification of different adsorption sites. Chemosphere 2022, 290, 132636,  DOI: 10.1016/j.chemosphere.2021.132636
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    Adsorption behavior of Cs(I) on natural soils: Batch experiments and model-based quantification of different adsorption sites
    Zhang, Kun; Li, Zhanguo; Qi, Sheng; Chen, Wenzhuo; Xie, Jianming; Wu, Hanyu; Zhao, Hongjie; Li, Daxue; Wang, Shanqiang
    Chemosphere (2022), 290 (), 132636CODEN: CMSHAF; ISSN:0045-6535. (Elsevier Ltd.)
    Understanding the adsorption behavior of radiocesium (RCs) in natural soils is crucial for remediation and evaluation of radioactive contaminated sites. In this study, we investigated the adsorption behavior of Cs(I) onto natural soils collected in Beijing by batch adsorption expts. and sequential extn. A multi-site adsorption model was built to quant. analyze the adsorption capacities of soil clay minerals and predict of Cs(I) adsorption ratio of different adsorption sites. Linear programming calcns. show that illite/smectite (I/S) mixt. and illite(I) are the mainly clay mineral compn. Batch adsorption expt. results show that soils adsorption of Cesium ions is an exothermic process, and the order of influence of competitive cations on the competitive adsorption strength of Cs(I) is:K+>Mg2+≈Ca2+>Na+. HA (Humic Acid)has little effect on soil adsorption. SEM-EDS anal. shows that Cs+ is mainly distributed on the surface (PS) of soil particles. Based on the above results, the adsorption of Cs(I) onto clay minerals in soils is well predicts in both linear programming calcns. and a multi-site adsorption model. The multi-site adsorption model can quant. describe and predict the adsorption behavior of Cs(I) on different clay sites in the soils. Frayed edge sites (FES) in the soil can effectively fix trace RCs. The higher concn. of cesium ions is mainly adsorbed on the PS and TIIS. Sequential extn. expt. further proved the adsorption form of cesium in soil under trace and high concn. conditions.
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    Seven chemical separations to change the world
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    Nature (2016), 532 (7600), 435-7 ISSN:.
    There is no expanded citation for this reference.
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  1. Kunyu Wang, Bertrand Siboulet, Jean-François Dufrêche. Collective Ion Adsorption on Silica Surfaces Driven by Ion Pairs. The Journal of Physical Chemistry C 2023, 127 (45) , 22315-22335. https://doi.org/10.1021/acs.jpcc.3c05113
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    Figure 1

    Figure 1. Synthesis of TiO2 nanotubes.

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    Figure 2

    Figure 2. Characterization of nanotubes sample. (a) Powder X-ray diffraction patterns of the TiO2 powders used in this study. (b) Topography (height) image of annealed TiO2 NTs sample.

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    Figure 3

    Figure 3. (a, b) TEM of TiO2 NTs sample. (c) Histogram of TiO2 NTs inner and outer diameter distribution. (d, f, i) STEM/HAADF micrograph of TiO2 NTs sample. (g, h) STEM/BF micrograph of TiO2 NTs sample.

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    Figure 4. Calculated and measured pH with standard deviations in error bars of the aqueous suspension as a function of the added volume Vd of the base CsOH for the total Cs+ concentration at the end-point of the titration: (a) c(Cs+)tot≈0.001 mol dm–3; (b) c(Cs+)tot≈0.01 mol dm–3. Calculations were performed for radii Rinner = 3.5 nm, Router = 4 nm, site density Γ = 2.2, and association constants log  KH,1 = 8.5, log  KH,2 = 4.8, log  KCs,1 = 1.2, and log  KCs,2 = −0.2.

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    Figure 5

    Figure 5. Full speciation of charged species within the titration experiment at c(CsNO3) = 0.001 mol dm–3. The figure shows (a) site populations, (b) surface charge densities, (c) carbonate species in aqueous solution, (d) surface cation coverage of surface active Cs+ and H+ cations, (e) volume integrals of Cs+ and NO3– particle distribution functions normalized per unit length, and (f) ratio of surface cation coverage on both inner and outer interface, as a function of the volume of added base in the actual titration experiment. Calculations were performed for radii Rinner = 3.5 nm, Router = 4.0 nm, site density Γ = 2.2, and association constants log  KH,1 = 8.5, log  KH,2 = 4.8, log  KCs,1 = 1.2, and log  KCs,2 = −0.2.

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    Figure 6

    Figure 6. Results of the DFT-MD simulations. (a) A representative snapshot of the (101) surface of TiO2 seen from the side, with water and adsorbed Cs+ ion, showing the first coordination sphere of Cs+ ion composed of (1) bulk water molecules, (2) two-coordinated surface oxygen atoms, (2′) protonated two-coordinated surface oxygen atoms, and (3) dissociated adsorbed water molecules. (b) Evolution of the coordination of the Cs+ ion over simulation time (moving average on 200 fs), showing the different components of the Cs+ total coordination number. (c) Cs+ ion adsorbed on the TiO2 surface seen from the top, without representing the nonadsorbed water molecules. (d) The Cs+ ion adsorbed on the TiO2 surface seen from the side, without representing the nonadsorbed water molecules. In parts c and d, the gray zone represents the pentagon-like adsorption site, and the numbers are the same as in part a. In parts a–d, the dashed lines represent hydrogen bonds.

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      Fabrication of Porous Cu-Doped BiVO4 Nanotubes as Efficient Oxygen-Evolving Photocatalysts
      He, Bin; Li, Zhipeng; Zhao, Dian; Liu, Huanhuan; Zhong, Yijun; Ning, Jiqiang; Zhang, Ziyang; Wang, Yongjiang; Hu, Yong
      ACS Applied Nano Materials (2018), 1 (6), 2589-2599CODEN: AANMF6; ISSN:2574-0970. (American Chemical Society)
      We introduce a facile route to fabricate one-dimensional (1D) porous Cu2+-doped BiVO4 (Cu-BVO) nanotubes with uniform size distribution and high structural stability. First, an electrospinning technique was developed to prep. the sacrificial template of polyacrylonitrile (PAN) nanofibers with a smooth surface. Second, a conformal layer of Cu-BVO nanoparticles was coated onto the PAN template through a solvothermal method to obtain the solid core-shell precursor which was finally converted into the product of porous Cu-BVO nanotubes with thermal treatment. Both exptl. characterizations and theor. calcns. based on the d. functional theory (DFT) calcns. have revealed the crucial functionality of the appropriate band structure of the Cu2+-doped nanostructure and introduced beneficial defect states by Cu doping, which boosts light absorption and promotes charge migration and sepn. and therefore results in highly efficient photocatalytic O2 evolution with visible-light irradn. As a result, the porous nanotube photocatalyst with an optimal Cu2+ doping of 5.0% exhibits an av. O2 evolution rate of 350.2 μmol h-1 g-1, about 2.4 times more than that of pristine BVO nanotubes.
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    15. 15
      Shiraishi, Y.; Saito, N.; Hirai, T. Adsorption-Driven Photocatalytic Activity of Mesoporous Titanium Dioxide. J. Am. Chem. Soc. 2005, 127, 12820– 12822,  DOI: 10.1021/ja053265s
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      Adsorption-Driven Photocatalytic Activity of Mesoporous Titanium Dioxide
      Shiraishi, Yasuhiro; Saito, Naoya; Hirai, Takayuki
      Journal of the American Chemical Society (2005), 127 (37), 12820-12822CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Unprecedented photocatalytic activity of mesoporous TiO2 driven by an adsorption degree of mols. on the catalyst surface which promotes a preferential conversion of a well-adsorbed mols. is reported. This property is applied to a selective transformation of a well-adsorbed mol. into a less-adsorbed mol., labeled as "stick-and-leave" transformation, which enables a direct transformation of benzene to phenol, one of the most difficult synthetic reactions, with very high selectivity (> 80%) and using water as a source of oxidant.
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    16. 16
      Abdel-Ghani, N. T.; El-Chaghaby, G. A.; Helal, F. S. Individual and competitive adsorption of phenol and nickel onto multiwalled carbon nanotubes. J. Adv. Res. 2015, 6, 405– 415,  DOI: 10.1016/j.jare.2014.06.001
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      16
      Individual and competitive adsorption of phenol and nickel onto multiwalled carbon nanotubes
      Abdel-Ghani, Nour T.; El-Chaghaby, Ghadir A.; Helal, Farag S.
      Journal of Advanced Research (2015), 6 (3), 405-415CODEN: JAROES; ISSN:2090-1224. (Elsevier B.V.)
      Individual and competitive adsorption studies were carried out to investigate the removal of phenol and nickel ions by adsorption onto multiwalled carbon nanotubes (MWCNTs). The carbon nanotubes were characterized by different techniques such as X-ray diffraction, SEM, thermal anal. and Fourier transformation IR spectroscopy. The different exptl. conditions affecting the adsorption process were investigated. Kinetics and equil. models were tested for fitting the adsorption exptl. data. The characterization exptl. results proved that the studied adsorbent possess different surface functional groups as well as typical morphol. features. The batch expts. revealed that 300 min of contact time was enough to achieve equil. for the adsorption of both phenol and nickel at an initial adsorbate concn. of 25 mg/l, an adsorbent dosage of 5 g/l, and a soln. pH of 7. The adsorption of phenol and nickel by MWCNTs followed the pseudo-second order kinetic model and the intraparticle diffusion model was quite good in describing the adsorption mechanism. The Langmuir equil. model fitted well the exptl. data indicating the homogeneity of the adsorbent surface sites. The max. Langmuir adsorption capacities were found to be 32.23 and 6.09 mg/g, for phenol and Ni ions, resp. The removal efficiency of MWCNTs for nickel ions or phenol in real wastewater samples at the optimum conditions reached up to 60% and 70%, resp.
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      Editors and International Board Member collection.

    17. 17
      Swenson, H.; Stadie, N. P. Langmuir’s Theory of Adsorption: A Centennial Review. Langmuir 2019, 35, 5409– 5426,  DOI: 10.1021/acs.langmuir.9b00154
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      17
      Langmuir's Theory of Adsorption: A Centennial Review
      Swenson, Hans; Stadie, Nicholas P.
      Langmuir (2019), 35 (16), 5409-5426CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      A review. The 100th anniversary of Langmuir's theory of adsorption is a significant landmark for the phys. chem. and chem. engineering communities. Despite its simplicity, the Langmuir adsorption model captures the key physics of mol. interactions at interfaces and laid the foundation for further progress in understanding interfacial phenomena, developing new adsorbent materials, and designing engineering processes. The Langmuir model has had an exceptional impact on diverse fields within the chem. sciences (ranging from chem. biol. to materials science), an impact that became clearer with the development of modified adsorption theories and continues to be relevant today.
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    18. 18
      Bohinc, K.; Bossa, G. V.; May, S. Incorporation of ion and solvent structure into mean-field modeling of the electric double layer. Adv. Colloid Interface Sci. 2017, 249, 220– 233,  DOI: 10.1016/j.cis.2017.05.001
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      18
      Incorporation of ion and solvent structure into mean-field modeling of the electric double layer
      Bohinc, Klemen; Bossa, Guilherme Volpe; May, Sylvio
      Advances in Colloid and Interface Science (2017), 249 (), 220-233CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)
      A review. An elec. double layer forms when the small mobile ions of an electrolyte interact with an extended charged object, a macroion. The competition between electrostatic attraction and translational entropy loss of the small ions results in a diffuse layer of partially immobilized ions in the vicinity of the macroion. Modeling structure and energy of the elec. double layer has a long history that has lead to the classical Poisson-Boltzmann theory and numerous extensions that account for ion-ion correlations and structural ion and solvent properties. The present review focuses on approaches that instead of going beyond the mean-field character of Poisson-Boltzmann theory introduce structural details of the ions and the solvent into the Poisson-Boltzmann modeling framework. The former include not only excluded vol. effects but also the presence of charge distributions on individual ions, spatially extended ions, and internal ionic degrees of freedom. The latter treat the solvent either explicitly as interacting Langevin dipoles or in the form of effective non-electrostatic interactions, in particular Yukawa interactions, that are added to the Coulomb potential. We discuss how various theor. models predict structural properties of the elec. double layer such as the differential capacitance and compare some of these predictions with computer simulations.
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      Recent nanotechnology and colloid science development for biomedical applications.

    19. 19
      Kallay, N.; Preocanin, T.; Kovacevic, D.; Lutzenkirchen, J.; Chibowski, E. Electrostatic Potentials at Solid/Liquid Interfaces. Croat. Chem. Acta 2010, 83, 357– 370
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      19
      Electrostatic potentials at solid/liquid interfaces
      Kallay, Nikola; Preocanin, Tajana; Kovacevic, Davor; Lutzenkirchen, Johannes; Chibowski, Emil
      Croatica Chemica Acta (2010), 83 (3), 357-370CODEN: CCACAA; ISSN:0011-1643. (Croatian Chemical Society)
      This review deals with electrostatic potentials within solid/electrolyte interfaces. The electrostatic potentials of several planes are defined and discussed: the inner surface potential affecting the state of charged surface species due to interactions with potential detg. ions (Ψ0), the potential affecting the state of assocd. counterions (Ψβ), the potential at the onset of diffuse layer (Ψd) and the electrokinetic potential (ζ). The relevance of zero values of these potentials is also discussed and the corresponding points of zero charge are defined. Exptl. methods for the measurement of the interfacial potentials are presented. The relations between potentials and surface charges are given on the basis of the Surface Complexation model. Some exptl. findings are provided.
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    20. 20
      Lützenkirchen, J.; Preocanin, T.; Kovačević, D.; Tomišić, V.; Lövgren, L.; Kallay, N. Potentiometric Titrations as a Tool for Surface Charge Determination. Croatica Chemica Acta 2012, 85, 391– 417,  DOI: 10.5562/cca2062
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      20
      Potentiometric titrations as a tool for surface charge determination
      Luetzenkirchen, Johannes; Preocanin, Tajana; Kovacevic, Davor; Tomisic, Vladislav; Loevgren, Lars; Kallay, Nikola
      Croatica Chemica Acta (2012), 85 (4), 391-417CODEN: CCACAA; ISSN:0011-1643. (Croatian Chemical Society)
      A review. This article summarizes methods for detg. proton surface charge at mineral/water interfaces. It covers conventional exptl. procedures and discusses problems with the techniques. Also it involves recommendations for obtaining reasonable and comparable results. The term "comparable results" refers to comparison between results for the same solid as obtained in different labs. The most important parameters for the surface titrns. are discussed. We also propose a ref. titrn. procedure that would allow direct, unbiased comparisons of exptl. data. The article finally includes a check-list for researchers and reviewers which should allow limiting the amt. of titrn. data that are not useful for future uses.
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    21. 21
      Abbas, Z.; Labbez, C.; Nordholm, S.; Ahlberg, E. Size-dependent surface charging of nanoparticles. J. Phys. Chem. C 2008, 112, 5715– 5723,  DOI: 10.1021/jp709667u
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      Size-Dependent Surface Charging of Nanoparticles
      Abbas, Zareen; Labbez, Christophe; Nordholm, Sture; Ahlberg, Elisabet
      Journal of Physical Chemistry C (2008), 112 (15), 5715-5723CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Exptl. interest in the possible curvature dependence of particle charging in electrolyte solns. is subjected to theor. anal. The cor. Debye-Hueckel theory of surface complexation (CDH-SC) and Monte Carlo (MC) simulation are applied to investigate the dependence of surface charging of metal oxide nanoparticles on their size. Surface charge d. vs. pH curves for spherical metal oxide nanoparticles in the size range of 1-100 nm are calcd. at various concns. of a background electrolyte. The surface charge d. of a nanoparticle is found to be highly size-dependent. As the particle diam. drops to below 10 nm there is considerable increase in the surface charge d. as compared with the limiting values seen for particles larger than 20 nm. This increase in the surface charge d. is due to the enhanced screening efficiency of the electrolyte soln. around small nanoparticles, which is most prominent for particles of diams. less than 5 nm. For example, the surface charge densities calcd. for 2 nm particles at 0.1 M concn. are very close to the values obtained for 100 nm particles at 1 M concn. These predictions of the dependence of surface charge d. on particle size by the CDH-SC theory are in very good agreement with the corresponding results obtained by the MC simulations. A shift in the pH value of the point of zero charge toward higher pH values is also seen with a decreasing particle size.
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    22. 22
      Bareigts, G.; Labbez, C. Jellium and cell model for titratable colloids with continuous size distribution. J. Chem. Phys. 2018, 149, 244903,  DOI: 10.1063/1.5066074
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      Jellium and cell model for titratable colloids with continuous size distribution
      Bareigts, Guillaume; Labbez, Christophe
      Journal of Chemical Physics (2018), 149 (24), 244903/1-244903/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A good understanding and detn. of colloidal interactions is paramount to comprehend and model the thermodn. and structural properties of colloidal suspensions. In concd. aq. suspensions of colloids with a titratable surface charge, this detn. is, however, complicated by the d. dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addn., colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper, we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided. The methods, inspired by the seminal work of Torres et al., [J. Chem. Phys. 128, 154906 (2008)] are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various com. available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calcd. The importance of size and charge polydispersity as well as the validity of these two models is discussed in light of the results. (c) 2018 American Institute of Physics.
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    23. 23
      Selmani, A.; Špadina, M.; Plodinec, M.; Delač Marion, I.; Willinger, M. G.; Lützenkirchen, J.; Gafney, H. D.; Redel, E. An Experimental and Theoretical Approach to Understanding the Surface Properties of One-Dimensional TiO2 Nanomaterials. J. Phys. Chem. C 2016, 120, 4150,  DOI: 10.1021/acs.jpcc.6b01240
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      An Experimental and Theoretical Approach to Understanding the Surface Properties of One-Dimensional TiO2 Nanomaterials [Erratum to document cited in CA163:323607]
      Selmani, Atidja; Spadina, Mario; Plodinec, Milivoj; Delac Marion, Ida; Willinger, Marc Georg; Lutzenkirchen, Johannes; Gafney, Harry D.; Redel, Engelbert
      Journal of Physical Chemistry C (2016), 120 (7), 4150CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      On page 19735, Figure 5 contained an incorrect scale bar; the cor. figure is given.
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    24. 24
      Lützenkirchen, J. Comparison of 1-pK and 2-pK Versions of Surface Complexation Theory by the Goodness of Fit in Describing Surface Charge Data of (Hydr)oxides. Environ. Sci. Technol. 1998, 32, 3149– 3154,  DOI: 10.1021/es980125s
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      24
      Comparison of 1-pK and 2-pK Versions of Surface Complexation Theory by the Goodness of Fit in Describing Surface Charge Data of (Hydr)oxides
      Luetzenkirchen, Johannes
      Environmental Science and Technology (1998), 32 (20), 3149-3154CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
      1-PK and 2-pK formulations exist in surface complexation theory with respect to the description of basic charging behavior of (hydr)oxide electrolyte interfaces. The 2-pK approach has been commonly used with at least four different electrostatic models, whereas the 1-pK model has been primarily used with only one of those electrostatic models. In this paper the 1-pK approach is combined with three more electrostatic models. The eight resulting possible combinations have been tested on several sets of data. Applying the 2-pK basic Stern model (BSM) and the triple-layer model (TLM) was not satisfactory: due to the high no. of adjustable parameters involved in these model variations the optimization procedure of the applied computer codes did not converge. This was taken as an a priori justification to exclude even more complicated (four-layer) models. For the remaining six models which could be successfully applied in the present paper, the goodness of fit parameter given by a computer code was used to compare the quality of the description of the chosen exptl. data by the resp. models. A purely diffuse layer model (DLM) generally gave the poorest fit to exptl. data when combined with the 1-pK approach and was only slightly better when combined with the 2-pK formalism. Either the 1-pK BSM or the 2-pK const. capacitance model (CCM) gave the best fit to the data in all the examples. However, it was found in two cases that some arbitrary constraint was necessary to define a unique (and thus meaningful) parameter set for the 2-pK CCM. The 1-pK TLM version allowed in more than half of the examples to det. a unique parameter set, which is impossible with the 2-pK TLM. It is concluded that the 1-pK BSM should be considered as the first choice model with respect to the goodness of fit and the uniqueness of the estd. parameters. The 2-pK CCM is still a good choice for a const. ionic strength case when the exptl. data allow a detn. of unique parameters and if only goodness of fit is used as a criterion.
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    25. 25
      Parsons, D. F.; Carucci, C.; Salis, A. Buffer-specific effects arise from ionic dispersion forces. Phys. Chem. Chem. Phys. 2022, 24, 6544– 6551,  DOI: 10.1039/D2CP00223J
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      Buffer-specific effects arise from ionic dispersion forces
      Parsons, Drew F.; Carucci, Cristina; Salis, Andrea
      Physical Chemistry Chemical Physics (2022), 24 (11), 6544-6551CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Buffer solns. do not simply regulate pH, but also change the properties of protein mols. The zeta potential of lysozyme varies significantly at the same buffer concn., in the order Tris > phosphate > citrate, with citrate even inverting the zeta potential, usually pos. at pH 7.15, to a neg. value. This buffer-specific effect is a special case of the Hofmeister effect. Here the authors present a theor. model of these buffer-specific effects using a Poisson-Boltzmann description of the buffer soln., modified to include dispersion forces of all ions interacting with the lysozyme surface. Dispersion coeffs. are detd. from quantum chem. polarizabilites calcd. for each ion for tris, phosphate, and citrate buffer solns. The lysozyme surface charge is controlled by charge regulation of carboxylate and amine sites of the component amino acids. The theor. model satisfactorily reproduces exptl. zeta potentials, including change of sign with citrate, when hydration of small cosmotropic ions (Na+, H+, OH-) is included.
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    26. 26
      Yang, J.; Su, H.; Lian, C.; Shang, Y.; Liu, H.; Wu, J. Understanding surface charge regulation in silica nanopores. Phys. Chem. Chem. Phys. 2020, 22, 15373– 15380,  DOI: 10.1039/D0CP02152K
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      Understanding surface charge regulation in silica nanopores
      Yang, Jie; Su, Haiping; Lian, Cheng; Shang, Yazhuo; Liu, Honglai; Wu, Jianzhong
      Physical Chemistry Chemical Physics (2020), 22 (27), 15373-15380CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Nanoporous silica is used in a wide variety of applications, ranging from bioanal. tools and materials for energy storage and conversion as well as sepn. devices. The surface charge d. of nanopores is not easily measured by expt. yet plays a vital role in the performance and functioning of silica nanopores. Herein, we report a theor. model to describe charge regulation in silica nanopores by combining the surface-reaction model and the classical d. functional theory (CDFT). The theor. predictions provide quant. insights into the effects of pH, electrolyte concn., and pore size on the surface charge d. and elec. double layer structure. With a fixed pore size, the surface charge d. increases with both pH and the bulk salt concn. similar to that for an open surface. At fixed pH and salt concn., the surface charge d. rises with the pore size until it reaches the bulk asymptotic value when the surface interactions become negligible. At high pH, the surface charge d. is mainly detd. by the ratio of the Debye screening length to the pore size (λD/D).
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      Bohinc, K.; Špadina, M.; Reščič, J.; Shimokawa, N.; Spada, S. Influence of Charge Lipid Head Group Structures on Electric Double Layer Properties. J. Chem. Theory Comput. 2022, 18, 448– 460,  DOI: 10.1021/acs.jctc.1c00800
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      Influence of Charge Lipid Head Group Structures on Electric Double Layer Properties
      Bohinc, Klemen; Spadina, Mario; Rescic, Jurij; Shimokawa, Naofumi; Spada, Simone
      Journal of Chemical Theory and Computation (2022), 18 (1), 448-460CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      In this study we derived a model for a multicomponent lipid monolayer in contact with an aq. soln. by means of a generalized classical d. functional theory and Monte Carlo simulations. Some of the important biol. lipid systems were studied as monolayers composed of head groups with different shapes and charge distributions. Starting from the free energy of the system, which includes the electrostatic interactions, addnl. internal degrees of freedom are included as positional and orientational entropic contributions to the free energy functional. The calculus of variation was used to derive Euler-Lagrange equations, which were solved numerically by the finite element method. The theory and Monte Carlo simulations predict that there are mainly two distinct regions of the elec. double layer: (1) the interfacial region, with thickness less than or equal to the length of the fully stretched conformation of the lipid head group, and (2) the outside region, which follows the usual screening of the interface. In the interfacial region, the elec. double layer is strongly perturbed, and electrostatic profiles and ion distributions have functionality distinct to classical mean-field theories. Based purely on Coulomb interactions, the theory suggests that the dominant effect on the lipid head group conformation is from the charge d. of the interface and the structured lipid mole fraction in the monolayer, rather than the salt concn. in the system.
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    28. 28
      Sholl, D. S.; Lively, R. P. Exemplar Mixtures for Studying Complex Mixture Effects in Practical Chemical Separations. JACS Au 2022, 2, 322– 327,  DOI: 10.1021/jacsau.1c00490
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      Exemplar Mixtures For Studying Complex Mixture Effects in Practical Chemical Separations
      Sholl, David S.; Lively, Ryan P.
      JACS Au (2022), 2 (2), 322-327CODEN: JAAUCR; ISSN:2691-3704. (American Chemical Society)
      Materials and processes for chem. sepns. must be used in complex environments to have impact in many practical settings. Despite these complexities, much research on chem. sepns. focuses on idealized chem. mixts. In this paper, we suggest that research communities for specific chem. sepns. should develop well-defined exemplar mixts. to bridge the gap between fundamental studies and practical applications and we provide a hierarchical framework of chem. mixts. for this purpose. We illustrate this hierarchy with examples including CO2 capture, capture of uranium from seawater, and sepns. of mixts. from electrocatalytic CO2 reactions, among others. We conclude with four recommendations for the research community to accelerate development of innovative sepns. strategies for pressing real-world challenges.
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    29. 29
      Špadina, M.; Gourdin-Bertin, S.; Dražić, G.; Selmani, A.; Dufrêche, J.-F.; Bohinc, K. Charge Properties of TiO2 Nanotubes in NaNO3 Aqueous Solution. ACS Appl. Mater. Interfaces 2018, 10, 13130– 13142,  DOI: 10.1021/acsami.7b18737
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      Charge properties of TiO2 nanotubes in NaNO3 aqueous solution
      Spadina, Mario; Gourdin-Bertin, Simon; Drazic, Goran; Selmani, Atidja; Dufreche, Jean-Francois; Bohinc, Klemen
      ACS Applied Materials & Interfaces (2018), 10 (15), 13130-13142CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
      Charging of material surfaces in aq. electrolyte solns. is one of the most important processes in the interactions between biomaterials and surrounding tissue. Other than a biomaterial, titania nanotubes (TiO2 NTs) represent a versatile material for numerous applications such as heavy metal adsorption or photocatalysis. In this article, the surface charge properties of titania NTs in NaNO3 soln. were investigated through electrophoretic mobility and polyelectrolyte colloid titrn. measuring techniques. In addn., we used high-resoln. transmission electron microscopy imaging to det. the morphol. of TiO2 NTs. A theor. model based on the classical d. functional theory coupled with the charge regulation method in terms of mass action law was developed to understand the exptl. data and to provide insights into charge properties at different phys. conditions, namely, pH and NaNO3 concn. Two intrinsic protonation consts. and surface site d. have been obtained. The electrostatic properties of the system in terms of electrostatic potentials and ion distributions were calcd. and discussed for various pH values. The model can quant. describe the titrn. curve as a function of pH for higher bulk salt concns. and the difference in the equil. amt. of charges between the inner and outer surfaces of TiO2 NTs. Calcd. counterion (NO3-) distributions show a pronounced decrease of NO3- ions for high bulk pH (both inside and outside TiO2 NT) because of the strong elec. field. With the decrease of bulk pH or the increase of the salt concn., NO3- is able to accumulate near the TiO2 NTs surfaces.
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    30. 30
      Foucaud, Y.; Badawi, M.; Filippov, L. O.; Barres, O.; Filippova, I. V.; Lebègue, S. Synergistic adsorptions of Na2CO3 and Na2SiO3 on calcium minerals revealed by spectroscopic and ab initio molecular dynamics studies. Chem. Sci. 2019, 10, 9928– 9940,  DOI: 10.1039/C9SC03366A
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      Synergistic adsorptions of Na2CO3 and Na2SiO3 on calcium minerals revealed by spectroscopic and ab initio molecular dynamics studies
      Foucaud, Yann; Badawi, Michael; Filippov, Lev O.; Barres, Odile; Filippova, Inna V.; Lebegue, Sebastien
      Chemical Science (2019), 10 (43), 9928-9940CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      The synergistic effects between sodium silicate (Na2SiO3) and sodium carbonate (Na2CO3) adsorbed on mineral surfaces are not yet understood, making it impossible to finely tune their resp. amts. in various industrial processes. In order to unravel this phenomenon, diffuse reflectance IR Fourier transform and X-ray photoelectron spectroscopies were combined with ab initio mol. dynamics to investigate the adsorption of Na2SiO3 onto bare and carbonated fluorite (CaF2), an archetypal calcium mineral. Both exptl. and theor. results proved that Na2CO3 adsorbs onto CaF2 with a high affinity and forms a layer of Na2CO3 on the surface. Besides, at low Na2SiO3 concn., silica mainly physisorbs in a monomeric protonated form, Si(OH)4, while at larger concn., significant amts. of polymd. and deprotonated forms are identified. Prior surface carbonation induces an acid-base reaction on the surface, which results in the formation of the basic forms of the monomers and the dimers, i.e. SiO(OH)3- and Si2O3(OH)42-, even at low coverage. Their adsorption is highly favored compared to the acid forms, which explains the synergistic effects obsd. when Na2SiO3 is used after Na2CO3. The formation of the basic form on the bare surface is obsd. only by increasing the surface coverage to 100%. Hence, when Na2CO3 is used during a sepn. process, lower Na2SiO3 concns. are needed to obtain the same effect as with lone Na2SiO3 in the sepn. process.
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    31. 31
      Eskanlou, A.; Huang, Q.; Foucaud, Y.; Badawi, M.; Romero, A. H. Effect of Al3+ and Mg2+ on the flotation of fluorapatite using fatty- and hydroxamic-acid collectors – A multiscale investigation. Appl. Surf. Sci. 2022, 572, 151499,  DOI: 10.1016/j.apsusc.2021.151499
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      Effect of Al3+ and Mg2+ on the flotation of fluorapatite using fatty- and hydroxamic-acid collectors - A multiscale investigation
      Eskanlou, Amir; Huang, Qingqing; Foucaud, Yann; Badawi, Michael; Romero, Aldo H.
      Applied Surface Science (2022), 572 (), 151499CODEN: ASUSEE; ISSN:0169-4332. (Elsevier B.V.)
      Fluorapatite flotation is influenced by the dissolved lattice metal ions. Al3+ and Mg2+ from the assocg. gangue minerals influence the adsorption of collector mols. onto the fluorapatite surface during flotation. Hence, unveiling new insights on such interactions in the context of froth flotation at an at. level paves the way for improving flotation selectivity. An original multiscale approach has been developed involving flotation expts., electro-kinetic and adsorption d. measurements, XPS studies, and d. functional theory simulations. Fatty acid establishes an enhanced interaction with the bare apatite surface compared to the hydroxamates. Na+ counter-ion contributes to the adsorption of fatty acid on bare apatite. Both Al3+ and Mg2+ ions are beneficial for the adsorption of fatty acid, thereby the fluorapatite flotation. For octanohydroxamic acid, the presence of Al3+ results in a stronger collector-apatite interaction, and therefore an enhanced flotation. For fatty acid and hydroxamates, adsorption of Mg2+ leads to an improved collector-apatite interaction. Benzohydroxamic acid is more vigorously adsorbed than octanohydroxamic acid in the presence of Mg2+. Fatty acid establishes a stronger interaction with bare and Al3+ and Mg2+-treated fluorapatite, as opposed to hydroxamates. Mg2+ is more favorable than Al3+ in fluorapatite flotation using both fatty acid and hydroxamates.
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    32. 32
      Foucaud, Y.; Lainé, J.; Filippov, L. O.; Barrès, O.; Kim, W. J.; Filippova, I. V.; Pastore, M.; Lebègue, S.; Badawi, M. Adsorption mechanisms of fatty acids on fluorite unraveled by infrared spectroscopy and first-principles calculations. J. Colloid Interface Sci. 2021, 583, 692– 703,  DOI: 10.1016/j.jcis.2020.09.062
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      Adsorption mechanisms of fatty acids on fluorite unraveled by infrared spectroscopy and first-principles calculations
      Foucaud, Yann; Laine, Juliette; Filippov, Lev O.; Barres, Odile; Kim, Won June; Filippova, Inna V.; Pastore, Mariachiara; Lebegue, Sebastien; Badawi, Michael
      Journal of Colloid and Interface Science (2021), 583 (), 692-703CODEN: JCISA5; ISSN:0021-9797. (Elsevier B.V.)
      The adsorption mechanisms of fatty acids on minerals are largely debated from years, and their understanding is now required to improve flotation processing in the crit. context of raw materials. Three wavenumbers have been obsd. in the literature for the asym. stretching vibration of COO- after the adsorption of fatty acids on mineral surfaces. They have been interpreted as different adsorbed forms, such as a ppt. formation, an adsorption of sole or bridged carboxylates, an anion exchange, or adsorbed modes, such as monodentate or bidentate configurations. Diffuse reflectance IR Fourier transform spectroscopy was combined with ab initio mol. dynamics simulations and simulation of IR spectra. Fluorite and sodium octanoate - or longer-chain fatty acids - were used as prototypical materials for all the investigations. At low fatty acids concn., the asym. stretching vibration of COO- peaks at 1560 cm-1 while, at higher concn., this IR band converts into a doublet peaking at 1535 and 1575 cm-1. Using simulations, we assign the band at 1560 cm-1 to the adsorption of a carboxylate mol. bridged on a sodium counter-cation and the doublet at 1535 and 1575 cm-1 to the adsorption of the sole carboxylate anion under a monodentate or a bidentate binuclear configuration, resp. The formation of an adsorbed layer on the mineral surface is initiated by the adsorption of a sodium carboxylate and followed by the adsorption of mixed sole anionic forms. The role of the carboxylate counter-cation is highlighted for the first time, which was totally ignored in the literature beforehand. This particularly opens the path to the development of innovative strategies to enhance the sepn. contrast between minerals, which is of uttermost importance for the recovery of crit. raw materials.
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      Evans, J. D.; Fraux, G.; Gaillac, R.; Kohen, D.; Trousselet, F.; Vanson, J.-M.; Coudert, F.-X. Computational Chemistry Methods for Nanoporous Materials. Chem. Mater. 2017, 29, 199– 212,  DOI: 10.1021/acs.chemmater.6b02994
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      Computational Chemistry Methods for Nanoporous Materials
      Evans, Jack D.; Fraux, Guillaume; Gaillac, Romain; Kohen, Daniela; Trousselet, Fabien; Vanson, Jean-Mathieu; Coudert, Francois-Xavier
      Chemistry of Materials (2017), 29 (1), 199-212CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      We present here the computational chem. methods our group uses to investigate the phys. and chem. properties of nanoporous materials and adsorbed fluids. We highlight the multiple time and length scales at which these properties can be examd. and discuss the computational tools relevant to each scale. Furthermore, we include the key points to consider-upsides, downsides, and possible pitfalls-for these methods.
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      Foucaud, Y.; Badawi, M.; Filippov, L.; Filippova, I.; Lebègue, S. A review of atomistic simulation methods for surface physical-chemistry phenomena applied to froth flotation. Minerals Engineering 2019, 143, 106020,  DOI: 10.1016/j.mineng.2019.106020
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      A review of atomistic simulation methods for surface physical-chemistry phenomena applied to froth flotation
      Foucaud, Y.; Badawi, M.; Filippov, L.; Filippova, I.; Lebegue, S.
      Minerals Engineering (2019), 143 (), 106020CODEN: MENGEB; ISSN:0892-6875. (Elsevier Ltd.)
      A review. The froth flotation method, which is used for the processing of most non-ferrous ores, involves the adsorption of both org. and inorg. reagents at the mineral/water interface. Understanding the adsorption mechanisms of flotation reagents is a key step to enhance the flotation. New depressants and collectors formulations, more efficient, selective, and environmental friendly can be suggested. At the moment, few exptl. methods can show surface mol. mechanisms with accuracy and confidence. Therefore, atomistic simulations allow to gain understanding in the mechanisms involved in the reagents adsorption. Nowadays, atomistic simulations can be applied to describe the solid/liq. interface and the adsorption mechanisms. Depending on the method, the interactions between atoms are described on the basis of d. functional theory (DFT) or force-fields. They give access to various levels of accuracy, parameters consideration, sampling times, system sizes, and reactivity description, depending on the method used. In particular, ab initio mol. dynamics allows to investigate adsorption processes at liq.-solid interfaces at finite temp. with accuracy.
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      Podgornik, R. General theory of charge regulation and surface differential capacitance. J. Chem. Phys. 2018, 149, 104701,  DOI: 10.1063/1.5045237
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      General theory of charge regulation and surface differential capacitance
      Podgornik, Rudolf
      Journal of Chemical Physics (2018), 149 (10), 104701/1-104701/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A generalization of the mean-field approach will be derived that will take into account the ion-ion as well as ion-surface non-electrostatic effects on an equal footing, being based on the bulk and surface equations of state in the absence of electrostatic interactions. This approach will be applied to the anal. of a single planar surface with dissociable sites with several models of the specific ion-surface non-electrostatic interactions, providing a general thermodn. insight into the characteristics of the surface differential capacitance. The ion-surface interactions and ion-ion packing considerations at the surface will be shown to be more relevant than the bulk packing constraints for ions vicinal to the surface, as well as to set in prior to the conditions where the bulk packing constraints would become relevant. (c) 2018 American Institute of Physics.
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      Roy, P.; Berger, S.; Schmuki, P. TiO2 nanotubes: Synthesis and applications. Angew. Chemie - Int. Ed. 2011, 50, 2904– 2939,  DOI: 10.1002/anie.201001374
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      TiO2 Nanotubes: Synthesis and Applications
      Roy, Poulomi; Berger, Steffen; Schmuki, Patrik
      Angewandte Chemie, International Edition (2011), 50 (13), 2904-2939CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. TiO2 is one of the most studied compds. in materials science. Owing to some outstanding properties it is used for instance in photocatalysis, dye-sensitized solar cells, and biomedical devices. In 1999, first reports showed the feasibility to grow highly ordered arrays of TiO2 nanotubes by a simple but optimized electrochem. anodization of a titanium metal sheet. This finding stimulated intense research activities that focused on growth, modification, properties, and applications of these one-dimensional nanostructures. This review attempts to cover all these aspects, including underlying principles and key functional features of TiO2, in a comprehensive way and also indicates potential future directions of the field.
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      García, D.; Lützenkirchen, J.; Huguenel, M.; Calmels, L.; Petrov, V.; Finck, N.; Schild, D. Adsorption of Strontium onto Synthetic Iron(III) Oxide up to High Ionic Strength Systems. Minerals 2021, 11, 1093,  DOI: 10.3390/min11101093
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      Adsorption of Strontium onto Synthetic Iron(III) Oxide up to High Ionic Strength Systems
      Garcia, David; Lutzenkirchen, Johannes; Huguenel, Maximilien; Calmels, Lea; Petrov, Vladimir; Finck, Nicolas; Schild, Dieter
      Minerals (Basel, Switzerland) (2021), 11 (10), 1093CODEN: MBSIBI; ISSN:2075-163X. (MDPI AG)
      In this work, the adsorption behavior of Sr onto a synthetic iron(III) oxide (hematite with traces of goethite) has been studied. This solid, which might be considered a representative of Fe3+ solid phases (iron corrosion products), was characterized by X-Ray Diffraction (XRD) and XPS, and its sp. surface area was detd. Both XRD and XPS data are consistent with a mixed solid contg. more than 90% hematite and 10% goethite. The solid was further characterized by fast acid-base titrns. at different NaCl concns. (from 0.1 to 5 M). Subsequently, for each background NaCl concn. used for the acid-base titrns., Sr-uptake expts. were carried out involving two different levels of Sr concn. (1 x 10-5 and 5 x 10-5 M, resp.) at const. solid concn. (7.3 g/L) as a function of -log([H+]/M). A Surface Complexation Model (SCM) was fitted to the exptl. data, following a coupled Pitzer/surface complexation approach. The Pitzer model was applied to aq. species. A Basic Stern Model was used for interfacial electrostatics of the system, which includes ion-specific effects via ion-specific pair-formation consts., whereas the Pitzer-approach involves ion-interaction parameters that enter the model through activity coeffs. for aq. species. A simple 1-pK model was applied (generic surface species, denoted as >XOH-1/2). Parameter fitting was carried out using the general parameter estn. software UCODE, coupled to a modified version of FITEQL2. The combined approach describes the full set of data reasonably well and involves two Sr-surface complexes, one of them including chloride. Monodentate and bidentate models were tested and were found to perform equally well. The SCM is particularly able to account for the incomplete uptake of Sr at higher salt levels, supporting the idea that adsorption models conventionally used in salt concns. below 1 M are applicable to high salt concns. if the correct activity corrections for the aq. species are applied. This generates a self-consistent model framework involving a practical approach for semi-mechanistic SCMs. The model framework of coupling conventional electrostatic double layer models for the surface with a Pitzer approach for the bulk soln. earlier tested with strongly adsorbing solutes is here shown to be successful for more weakly adsorbing solutes.
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    38. 38
      Panagiotou, G. D.; Petsi, T.; Bourikas, K.; Garoufalis, C. S.; Tsevis, A.; Spanos, N.; Kordulis, C.; Lycourghiotis, A. Mapping the surface (hydr)oxo-groups of titanium oxide and its interface with an aqueous solution: The state of the art and a new approach. Adv. Colloid Interface Sci. 2008, 142, 20– 42,  DOI: 10.1016/j.cis.2008.04.003
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      Mapping the surface (hydr)oxo-groups of titanium oxide and its interface with an aqueous solution: The state of the art and a new approach
      Panagiotou, George D.; Petsi, Theano; Bourikas, Kyriakos; Garoufalis, Christos S.; Tsevis, Athanassios; Spanos, Nikos; Kordulis, Christos; Lycourghiotis, Alexis
      Advances in Colloid and Interface Science (2008), 142 (1-2), 20-42CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)
      The titanium oxide/electrolyte soln. interface is studied by taking advantage of recent developments in the field of surface and interface chem. relevant to this oxide. Ab-initio calcns. were performed in the frame of the DFT theory for estg. the charge of the titanium and oxygen atoms exposed on the anatase (101), (100), (001), (103)f and rutile (110) crystal faces. These orientations have smaller surface energy with respect to other ones and thus it is more probable to be the real terminations of the anatase and rutile nanocrystallites in the titania polycryst. powders. Potentiometric titrns. for obtaining fine structured titrn. curves as well as microelectrophoresis and streaming potential measurements have been performed. On the basis of ab-initio calcns., and taking into account the relative contribution of each crystal face to the whole surface of the nanocrystals involved in the titania aggregates of a suspension, the three most probable surface ionization models have been derived. These models and the Music model are then tested in conjunction with the Stern-Gouy-Chapman and Basic Stern electrostatic models. The finally selected surface ionization model (model A) in combination with each of the two electrostatic models describes very well the protonation/deprotonation behavior of titania. The description is also very good if this model is combined with the Three Plane (TP) model. The application of the A/(TP) model allowed mapping the surface (hydr)oxo-groups [TiO(H) and Ti2O(H)] of titania exposed in aq. solns. At pH > pzc almost all terminal oxygens [TiO] are non-protonated, whereas even at low pH values the non-protonated terminal oxygens predominate. The acid-base behavior of the bridging oxygens [Ti2O] is different. Thus, even at pH = 10 the greater portion of them is protonated. The application of the A/TP model in conjunction with potentiometric titrns., microelectrophoresis, and streaming potential expts. allowed mapping the titania/electrolyte soln. interface. The first (second) charged plane is located on the oxygen atoms of the first (second) water overlayer at a distance of 1.7 (3.4) Å from the surface. The region between the surface and the second plane is the compact layer. The region between the second plane and the shear plane is the stagnant diffuse part of the interface, with an ionic strength (I) dependent width, ranging from 20 (0.01 M) up to 4 Å (0.3 M). The region between the shear plane and the bulk soln. is the mobile diffuse part, with an ionic strength dependent width, ranging from 10 (0.01 M) up to 2 Å (0.3 M). At I > 0.017 M the mean concn. of the counter ions is higher in the stagnant than in the mobile part of the diffuse layer. For a given I, moving pH from pzc brings about an increase of the mean concn. in the interfacial region and a displacement of the counter ions from the mobile to the stagnant part of the diffuse layer. The mean concn. of the counter ions in the compact layer is generally lower than the corresponding ones in the stagnant and mobile diffuse layers. The mobility of the counter ions in the stagnant layer decreases as pH draws away from pzc or ionic strength increases.
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      Bourikas, K.; Hiemstra, T.; Van Riemsdijk, W. H. Ion pair formation and primary charging behavior of titanium oxide (anatase and rutile). Langmuir 2001, 17, 749– 756,  DOI: 10.1021/la000806c
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      Ion Pair Formation and Primary Charging Behavior of Titanium Oxide (Anatase and Rutile)
      Bourikas, K.; Hiemstra, T.; Van Riemsdijk, W. H.
      Langmuir (2001), 17 (3), 749-756CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      The primary charging behavior of Ti oxide (anatase, rutile, and P25) and the ion pair formation of the electrolyte ions with the surface groups were extensively studied. A large no. of titrn. and electrokinetic data sets available in the literature were successfully described, using the MUSIC (MultiSite Complexation) model with a basic Stern double-layer option and applying the ion pair formation concept. The systematic anal. of the data, over a large no. of different monovalent electrolytes and various ionic strength values, allowed the detn. of a no. of best estd. values for the ion pair formation consts. The values suggest that the interaction of the cations with the TiO2 surface is stronger than that of the anions. This is in accordance with the obsd. shift of the IEP of Ti oxide to higher pH values, at high electrolyte concns. The binding of the cations follows the sequence Cs+ < K+ < Na+ < Li+ and that of the anions follows the sequence Cl- > NO3- > ClO4- > I-. Ti oxide can be divided in 2 classes of materials, having a low (C = 0.9 F m-2) and a high (C = 1.6 F m-2) capacitance value, resp. The low capacitance value corresponds with the low values found for well-crystd. gibbsite and goethite. From the low capacitance value and the absence of correlation with the dielec. properties of the solids, it is hypothesized that the 1st layer of phys. adsorbed H2O has a unique relative dielec. const. ε of ∼40 on well-crystd. oxides. The high capacitance may correspond to a situation with a distorted H2O layer, which has bulk H2O properties (ε = 78). No other significant differences between the interfacial charging parameters of anatase and rutile were found.
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      Adžić, N. c. v.; Podgornik, R. Charge regulation in ionic solutions: Thermal fluctuations and Kirkwood-Schumaker interactions. Phys. Rev. E 2015, 91, 022715,  DOI: 10.1103/PhysRevE.91.022715
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      Charge regulation in ionic solutions: thermal fluctuations and Kirkwood-Schumaker interactions
      Adzic, Natasa; Podgornik, Rudolf
      Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2015), 91 (2-A), 022715/1-022715/13CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
      We study the behavior of two macroions with dissociable charge groups, regulated by local variables such as pH and electrostatic potential, immersed in a monovalent salt soln., considering cases where the net charge can either change sign or remain of the same sign depending on these local parameters. The charge regulation in both cases is described by the proper free-energy function for each of the macroions, while the coupling between the charges is evaluated on the approx. Debye-Huckel level. The charge correlation functions and the ensuing charge fluctuation forces are calcd. anal. and numerically. Strong attraction between like-charged macroions is found close to the point of zero charge, specifically due to asym., anticorrelated charge fluctuations of the macroion charges. The general theory is then implemented for a system of two proteinlike macroions, generalizing the form and magnitude of the Kirkwood-Schumaker interaction.
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      Trizac, E.; Hansen, J.-P. Wigner-Seitz model of charged lamellar colloidal dispersions. Phys. Rev. E 1997, 56, 3137,  DOI: 10.1103/PhysRevE.56.3137
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      Wigner-Seitz model of charged lamellar colloidal dispersions
      Trizac, Emmanuel; Hansen, Jean-Pierre
      Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics (1997), 56 (3-B), 3137-3149CODEN: PLEEE8; ISSN:1063-651X. (American Physical Society)
      A concd. suspension of lamellar colloidal particles (e.g., clay) is modeled by considering a single, uniformly charged, finite platelet confined with co- and counterions to a Wigner-Seitz (WS) cell. The system is treated within Poisson-Boltzmann theory, with appropriate boundary conditions on the surface of the WS cell, supposed to account for the confinement effect of neighboring platelets. Expressions are obtained for the free energy, osmotic, and disjoining pressures and the capacitance in terms of the local electrostatic potential and the co- and counterion d. profiles. Explicit solns. of the linearized Poisson-Boltzmann equation are obtained for circular and square platelets placed at the center of a cylindrical or parallelepipedic cell. The resulting free energy is found to go through a min. as a function of the aspect ratio of the cell, for any given vol. (detd. by the macroscopic concn. of platelets), platelet surface charge, and salt concn. The optimum aspect ratio is found to be nearly independent of the two latter phys. parameters. The osmotic and disjoining pressures are found to coincide at the free energy min., while the total quadrupole moment of the elec. double layer formed by the platelet and the surrounding co- and counterions vanishes simultaneously. The osmotic equation of state is calcd. for a variety of phys. conditions. The limit of vanishing platelet concn. is considered in some detail, and the force acting between two coaxial platelets is calcd. in that limit as a function of their sepn.
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      Hallez, Y.; Diatta, J.; Meireles, M. Quantitative Assessment of the Accuracy of the Poisson–Boltzmann Cell Model for Salty Suspensions. Langmuir 2014, 30, 6721– 6729,  DOI: 10.1021/la501265k
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      Quantitative Assessment of the Accuracy of the Poisson-Boltzmann Cell Model for Salty Suspensions
      Hallez, Yannick; Diatta, Joseph; Meireles, Martine
      Langmuir (2014), 30 (23), 6721-6729CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      The cell model is a ubiquitous, fast, and relatively easily implemented model used to est. the osmotic pressure of a colloidal dispersion. It has been shown to yield accurate approxns. of the pressure in dispersions with a low salt content. It is generally accepted that it performs well when long-ranged interactions are involved and the structure of the dispersion is solidlike. The aim of the present work is to det. quant. the error committed by assuming the pressure computed with the cell model is the real osmotic pressure of a dispersion. To this end, cell model pressures are compared to a correct estn. of the actual pressures obtained from Poisson-Boltzmann Brownian dynamics simulations including many-body electrostatics and the thermal motion of the colloids. The comparison is performed for various colloidal sizes and charges, salt contents, and vol. fractions. It is demonstrated that the accuracy of the cell model predictions is a function of only the av. intercolloid distance scaled by Debye's length κ‾d and the normalized colloidal charge. The cell model is accurate for κ‾d < 1 and not reliable for κ‾d > 5 independently of the colloidal charge. In the 1 < κ‾d < 5 range, covering a wide set of exptl. conditions, the colloidal surface charge has a large influence on the error assocd. with the cell approxn. The results presented in this article should provide a useful ref. to det. a priori if the cell model can be expected to predict accurately an equation of state for a given set of physicochem. parameters.
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      Hansen, J.-P.; Löwen, H. Effective interaction between electric double-layers. Annu. Rev. Phys. Chem. 2000, 51, 209– 242,  DOI: 10.1146/annurev.physchem.51.1.209
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      Effective interactions between electric double layers
      Hansen, Jean-Pierre; Lowen, Hartmut
      Annual Review of Physical Chemistry (2000), 51 (), 209-242CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews Inc.)
      A review with 196 refs. that summarizes and assesses recent theor. and exptl. advances, with special emphasis on the effective interaction between charge-stabilized colloids, in the bulk or in confined geometries, and on the ambiguities of defining an effective charge of the colloidal particles. Some consideration is given to the often neglected discrete solvent effects.
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      Ab initio molecular dynamics of liquid metals
      Kresse, G.; Hafner, J.
      Physical Review B: Condensed Matter and Materials Physics (1993), 47 (1), 558-61CODEN: PRBMDO; ISSN:0163-1829.
      The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
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      Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Physical review letters 1996, 77, 3865,  DOI: 10.1103/PhysRevLett.77.3865
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      Generalized gradient approximation made simple
      Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
      Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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      Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of computational chemistry 2006, 27, 1787– 1799,  DOI: 10.1002/jcc.20495
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      Semiempirical GGA-type density functional constructed with a long-range dispersion correction
      Grimme, Stefan
      Journal of Computational Chemistry (2006), 27 (15), 1787-1799CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      A new d. functional (DF) of the generalized gradient approxn. (GGA) type for general chem. applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6·R-6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common d. functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on std. thermochem. benchmark sets, for 40 noncovalently bound complexes, including large stacked arom. mols. and group II element clusters, and for the computation of mol. geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for std. functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean abs. deviation of only 3.8 kcal mol-1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the av. CCSD(T) accuracy. The basic strategy in the development to restrict the d. functional description to shorter electron correlation lengths scales and to describe situations with medium to large interat. distances by damped C6·R-6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chem. method for large systems where dispersion forces are of general importance.
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      There is no expanded citation for this reference.
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      Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Physical review b 1999, 59, 1758,  DOI: 10.1103/PhysRevB.59.1758
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      From ultrasoft pseudopotentials to the projector augmented-wave method
      Kresse, G.; Joubert, D.
      Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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      Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169,  DOI: 10.1103/PhysRevB.54.11169
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      Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
      Kresse, G.; Furthmueller, J.
      Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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      Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 1998, 57, 1505– 1509,  DOI: 10.1103/PhysRevB.57.1505
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      Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
      Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P.
      Physical Review B: Condensed Matter and Materials Physics (1998), 57 (3), 1505-1509CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      By taking better account of electron correlations in the 3d shell of metal ions in Ni oxide it is possible to improve the description of both electron energy loss spectra and parameters characterizing the structural stability of the material compared with local spin d. functional theory.
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      Aschauer, U.; He, Y.; Cheng, H.; Li, S.-C.; Diebold, U.; Selloni, A. Influence of Subsurface Defects on the Surface Reactivity of TiO2: Water on Anatase (101). J. Phys. Chem. C 2010, 114, 1278– 1284,  DOI: 10.1021/jp910492b
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      Influence of Subsurface Defects on the Surface Reactivity of TiO2: Water on Anatase (101)
      Aschauer, Ulrich; He, Yunbin; Cheng, Hongzhi; Li, Shao-Chun; Diebold, Ulrike; Selloni, Annabella
      Journal of Physical Chemistry C (2010), 114 (2), 1278-1284CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      The adsorption of water on a reduced TiO2 anatase (101) surface is investigated with scanning tunneling microscopy and d. functional theory calcns. The presence of subsurface defects, which are prevalent on reduced anatase (101), leads to a higher desorption temp. of adsorbed water, indicating an enhanced binding due to the defects. Theor. calcns. of water adsorption on anatase (101) surfaces contg. subsurface oxygen vacancies or titanium interstitials show a strong selectivity for water binding to sites in the vicinity of the subsurface defects. Moreover, the water adsorption energy at these sites is considerably higher than that on the stoichiometric surface, thus giving an explanation for the exptl. observations. The calcns. also predict facile water dissocn. at these sites, confirming the important role of defects in the surface chem. of TiO2.
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    54. 54
      Mattioli, G.; Filippone, F.; Alippi, P.; Amore Bonapasta, A. Ab initio study of the electronic states induced by oxygen vacancies in rutile and anatase TiO2. Phys. Rev. B 2008, 78, 241201,  DOI: 10.1103/PhysRevB.78.241201
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      Ab initio study of the electronic states induced by oxygen vacancies in rutile and anatase TiO2
      Mattioli, G.; Filippone, F.; Alippi, P.; Amore Bonapasta, A.
      Physical Review B: Condensed Matter and Materials Physics (2008), 78 (24), 241201/1-241201/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      We studied the origin of the differences between the anatase and rutile properties and show that they can be related to a remarkable difference in nature between the electronic levels induced by bulk oxygen vacancies (VOx) in the two TiO2 polymorphs using the DFT LSD and GGA+U methods. These levels have indeed different locations in the energy gap and give rise to different localizations of the electronic charge in real space, thus indicating the VOx's as important candidates to elucidate the different properties of the two TiO2 phases. The present results, achieved by applying a U correction to local spin-d. (LSD)-generalized gradient approxn. (GGA) methods, stress also the importance of beyond-LSD methods when investigating metal oxides. They show indeed that only such methods permit to reveal the different nature of the VOx electronic states in the two TiO2 phases.
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      Finazzi, E.; Di Valentin, C.; Pacchioni, G.; Selloni, A. Excess electron states in reduced bulk anatase TiO2: Comparison of standard GGA, GGA+U, and hybrid DFT calculations. J. Chem. Phys. 2008, 129, 154113,  DOI: 10.1063/1.2996362
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      Excess electron states in reduced bulk anatase TiO2: Comparison of standard GGA, GGA+U, and hybrid DFT calculations
      Finazzi, Emanuele; Di Valentin, Cristiana; Pacchioni, Gianfranco; Selloni, Annabella
      Journal of Chemical Physics (2008), 129 (15), 154113/1-154113/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The removal of lattice O atoms, as well as the addn. of interstitial H atoms, in TiO2 is known to cause the redn. in the material and the formation of "Ti3+" ions. By means of electronic structure calcns. we have studied the nature of such oxygen vacancy and hydrogen impurity states in the bulk of the anatase polymorph of TiO2. The spin polarized nature of these centers, the localized or delocalized character of the extra electrons, the presence of defect-induced states in the gap, and the polaronic distortion around the defect have been investigated with different theor. methods: std. d. functional theory (DFT) in the generalized-gradient approxn. (GGA), GGA+U methods as a function of the U parameter, and two hybrid functionals with different admixts. of Hartree-Fock exchange. The results are found to be strongly dependent on the method used. Only GGA+U or hybrid functionals are able to reproduce the presence of states at about 1 eV below the conduction band, which are exptl. obsd. in reduced titania. The corresponding electronic states are localized on Ti 3d levels, but partly delocalized solns. are very close in energy. These findings show the limited predictive power of these theor. methods to describe the electronic structure of reduced titania in the absence of accurate exptl. data. (c) 2008 American Institute of Physics.
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      Morgan, B.; Watson, G. W. A DFT+U description of oxygen vacancies at the TiO2 rutile (110) surface. Surf. Sci. 2007, 601, 5034– 5041,  DOI: 10.1016/j.susc.2007.08.025
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      A DFT+ U description of oxygen vacancies at the TiO2 rutile (110) surface
      Morgan, Benjamin J.; Watson, Graeme W.
      Surface Science (2007), 601 (21), 5034-5041CODEN: SUSCAS; ISSN:0039-6028. (Elsevier B.V.)
      Exptl. observations indicate that removing bridging oxygen atoms from the TiO2 rutile (1 1 0) surface produces a localized state approx. 0.7 eV below the conduction band. The corresponding excess electron d. is thought to localize on the pair of Ti atoms neighboring the vacancy; formally giving two Ti3+ sites. We consider the electronic structure and geometry of the oxygen deficient TiO2 rutile (1 1 0) surface using both gradient-cor. d. functional theory (GGA DFT) and DFT cor. for on-site Coulomb interactions (GGA + U) to allow a direct comparison of the two methods. We show that GGA fails to predict the exptl. obsd. electronic structure, in agreement with previous uncorrected DFT calcns. on this system. Introducing the +U term encourages localization of the excess electronic charge, with the qual. distribution depending on the value of U. For low values of U (≤4.0 eV) the charge localizes in the sub-surface layers occupied in the GGA soln. at arbitrary Ti sites, whereas higher values of U (≥4.2 eV) predict strong localization with the excess electronic charge mainly on the two Ti atoms neighboring the vacancy. The precise charge distribution for these larger U values is found to differ from that predicted by previous hybrid-DFT calcns.
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      Nosé, S. A molecular dynamics method for simulations in the canonical ensemble. Molecular physics 1984, 52, 255– 268,  DOI: 10.1080/00268978400101201
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      A molecular dynamics method for simulations in the canonical ensemble
      Nose, Shuichi
      Molecular Physics (1984), 52 (2), 255-68CODEN: MOPHAM; ISSN:0026-8976.
      A mol. dynamics simulation method is proposed which can generate configurations belonging to the canonical (T, V, N) ensemble or the const. temp. const. pressure (T, P, N) ensemble. The phys. system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added. This device allows the total energy of the phys. system to fluctuate. The equil. distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space. The method is tested for an at. fluid (Ar) and works well.
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      Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81, 511– 519,  DOI: 10.1063/1.447334
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      A unified formulation of the constant-temperature molecular-dynamics methods
      Nose, Shuichi
      Journal of Chemical Physics (1984), 81 (1), 511-19CODEN: JCPSA6; ISSN:0021-9606.
      Three recently proposed const. temp. mol. dynamics methods [N., (1984) (1); W. G. Hoover et al., (1982) (2); D. J. Evans and G. P. Morris, (1983) (2); and J. M. Haile and S. Gupta, 1983) (3)] are examd. anal. via calcg. the equil. distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N-1/2 from the canonical distribution (N the no. of particles). The results for the const. temp.-const. pressure ensemble are similar to the canonical ensemble case.
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      Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 1985, 31, 1695,  DOI: 10.1103/PhysRevA.31.1695
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      Canonical dynamics: Equilibrium phase-space distributions
      Hoover
      Physical review. A, General physics (1985), 31 (3), 1695-1697 ISSN:0556-2791.
      There is no expanded citation for this reference.
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      Horn, M.; Schwerdtfeger, C. F.; Meagher, E. P. Refinement of the structure of anatase at several temperatures. Zeitschrift fur Kristallographie 1972, 136, 273– 281,  DOI: 10.1524/zkri.1972.136.3-4.273
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      Refinement of the structure of anatase at several temperatures
      Horn, M.; Schwerdtfeger, C. F.; Meagher, E. P.
      (1972), 136 (3-4), 273-81CODEN: ZEKGAX ISSN:.
      The crystal structure of anatase was refined by single-crystal x-ray diffraction at 25-800°. The only structural parameter, the z coordinate of O, changed regularly from 0.2081(2) at 25° to 0.2076(3) at 800°. This change was ∼1 order of magnitude smaller than that expected by M. Horn and C. F. Schwerdtfeger (1971) to explain the temp. dependence of EPR spectra of Fe impurities in anatase. The change was in the direction of increasing distortion of the TiO6 octahedra with increasing temp.
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      Vittadini, A.; Selloni, A.; Rotzinger, F. P.; Grätzel, M. Formic Acid Adsorption on Dry and Hydrated TiO2 Anatase (101) Surfaces by DFT Calculations. J. Phys. Chem. B 2000, 104, 1300– 1306,  DOI: 10.1021/jp993583b
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      Formic acid adsorption on dry and hydrated TiO2 anatase (101) surfaces by DFT calculations
      Vittadini, A.; Selloni, A.; Rotzinger, F. P.; Graetzel, M.
      Journal of Physical Chemistry B (2000), 104 (6), 1300-1306CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
      The adsorption of formic acid and sodium formate on the stoichiometric anatase (101) surface was studied by d. functional calcns. with a slab geometry. On the clean surface, the most stable adsorption structure for HCOOH is a mol. monodentate configuration, hydrogen-bonded to a surface bridging oxygen, while for HCOONa a dissocd. bridging bidentate geometry is preferred. The bidentate chelating structure is energetically unstable for both the acid and the salt. On the hydrated surface, both HCOOH and HCOONa preferentially form an inner-sphere adsorption complex. HCOOH maintains a monodentate coordination, but, due to the interaction with a nearby water mol., it becomes dissocd., while HCOONa again prefers a bridging bidentate structure. The energies for adsorption from an aq. soln. are estd. to be 0.30 and 0.79 eV for HCOOH and HCOONa, resp.
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      Oliver, P. M.; Watson, G. W.; Kelsey, E. T.; Parker, S. C. Atomistic simulation of the surface structure of the TiO2 polymorphs rutileand anatase. J. Mater. Chem. 1997, 7, 563– 568,  DOI: 10.1039/a606353e
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      Atomistic simulation of the surface structure of the TiO2 polymorphs rutile and anatase
      Oliver, Peter M.; Watson, Graeme W.; Kelsey, E. Toby; Parker, Stephen C.
      Journal of Materials Chemistry (1997), 7 (3), 563-568CODEN: JMACEP; ISSN:0959-9428. (Royal Society of Chemistry)
      Atomistic simulation has been used to calc. the surface structures and stability of the rutile and anatase polymorphs of TiO2. The surface and attachment energies were used to evaluate the equil. and pseudo-kinetic morphologies. The surfaces expressed in rutile were {011}, {110}, {100} and {221} with surface energies of 1.85, 1.78, 2.08 and 2.02 J m-2, resp. For anatase the {011} and {001} surfaces were dominant in the morphol. with relaxed surface energies of 1.40 and 1.28 J m-2. The predicted equil. forms were largely in good agreement with the reported exptl. morphologies of rutile and anatase and showed the importance of surface relaxation.
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      Agosta, L.; Gala, F.; Zollo, G. Water diffusion on TiO2 anatase surface. AIP Conf. Proc. 2015, 1667, 020006,  DOI: 10.1063/1.4922562
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      Water diffusion on TiO2 anatase surface
      Agosta, L.; Gala, F.; Zollo, G.
      AIP Conference Proceedings (2015), 1667 (1, NANOFORUM 2014), 020006/1-020006/9CODEN: APCPCS; ISSN:0094-243X. (American Institute of Physics)
      Compatibility between biol. mols. and inorg. materials, such as cryst. metal oxides, is strongly dependent on the selectivity properties and the adhesion processes at the interface between the two systems. Among the many different aspects that affect the adsorption processes of peptides or proteins onto inorg. surfaces, such as the charge state of the amino acids, the peptide 3D structure, the surface roughness, the presence of vacancies or defects on and below the surface, a key role is certainly played by the water solvent whose mols. mediate the interaction. Then the surface hydration pattern may strongly affect the adsorption behavior of biol. mols. For the particular case of (101) anatase TiO2 surface that has a fundamental importance in the interaction of biocompatible nano-devices with biol. environment, it was shown, both theor. and exptl., that various hydration patterns are close in energy and that the water mols. are mobile at as low temp. values as 190 K. Then it is important to understand the dynamical behavior of first hydration layer of the (101) anatase surface. As a first approach to this problem, d. functional calcns. are used to investigate water diffusion on the (101) anatase TiO2 surface by sampling the potential energy surface of water mols. of the first hydration layer thus calcg. the water mol. migration energy along some relevant diffusion paths on the (101) surface. The measured activation energy of water migration seems in contrast with the obsd. surface mobility of the water mols. that, as a consequence could be explained invoking a strong role of the entropic term in the context of the transition state theory. (c) 2015 American Institute of Physics.
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    64. 64
      Martínez, L.; Andrade, R.; Birgin, E. G.; Martínez, J. M. PACKMOL: a package for building initial configurations for molecular dynamics simulations. Journal of computational chemistry 2009, 30, 2157– 2164,  DOI: 10.1002/jcc.21224
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      PACKMOL: A package for building initial configurations for molecular dynamics simulations
      Martinez, L.; Andrade, R.; Birgin, E. G.; Martinez, J. M.
      Journal of Computational Chemistry (2009), 30 (13), 2157-2164CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      Adequate initial configurations for mol. dynamics simulations consist of arrangements of mols. distributed in space in such a way to approx. represent the system's overall structure. In order that the simulations are not disrupted by large van der Waals repulsive interactions, atoms from different mols. must keep safe pairwise distances. Obtaining such a mol. arrangement can be considered a packing problem: Each type mol. must satisfy spatial constraints related to the geometry of the system, and the distance between atoms of different mols. must be greater than some specified tolerance. We have developed a code able to pack millions of atoms, grouped in arbitrarily complex mols., inside a variety of three-dimensional regions. The regions may be intersections of spheres, ellipses, cylinders, planes, or boxes. The user must provide only the structure of one mol. of each type and the geometrical constraints that each type of mol. must satisfy. Building complex mixts., interfaces, solvating biomols. in water, other solvents, or mixts. of solvents, is straightforward. In addn., different atoms belonging to the same mol. may also be restricted to different spatial regions, in such a way that more ordered mol. arrangements can be built, as micelles, lipid double-layers, etc. The packing time for state-of-the-art mol. dynamics systems varies from a few seconds to a few minutes in a personal computer. The input files are simple and currently compatible with PDB, Tinker, Molden, or Moldy coordinate files. The package is distributed as free software and can be downloaded from . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009.
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      Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. Journal of applied crystallography 2011, 44, 1272– 1276,  DOI: 10.1107/S0021889811038970
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      VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
      Momma, Koichi; Izumi, Fujio
      Journal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
      VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.
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    66. 66
      Walle, L. E.; Borg, A.; Johansson, E. M. J.; Plogmaker, S.; Rensmo, H.; Uvdal, P.; Sandell, A. Mixed Dissociative and Molecular Water Adsorption on Anatase TiO2(101). J. Phys. Chem. C 2011, 115, 9545– 9550,  DOI: 10.1021/jp111335w
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      Mixed dissociative and molecular water adsorption on anatase TiO2(101)
      Walle, L. E.; Borg, A.; Johansson, E. M. J.; Plogmaker, S.; Rensmo, H.; Uvdal, P.; Sandell, A.
      Journal of Physical Chemistry C (2011), 115 (19), 9545-9550CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      The adsorption properties of water on the stoichiometric (101) surface of anatase TiO2 in the temp. range 160-400 K was studied by synchrotron radiation core level photoelectron spectroscopy. O 1s spectra give clear evidence for the formation of a first layer of water that comprises both H2O and OH. The compn. is 0.77 ± 0.05 ML H2O and 0.47 ± 0.05 ML OH. Decreasing the coverage by heating leads to a decreased H2O/OH ratio. The results are very similar to those recently reported for water on rutile TiO2(110) and show that the previously proposed model of mol. adsorption only on anatase TiO2(101) must be revised.
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    67. 67
      Nadeem, I. M.; Treacy, J. P. W.; Selcuk, S.; Torrelles, X.; Hussain, H.; Wilson, A.; Grinter, D. C.; Cabailh, G.; Bikondoa, O.; Nicklin, C.; Selloni, A.; Zegenhagen, J.; Lindsay, R.; Thornton, G. Water Dissociates at the Aqueous Interface with Reduced Anatase TiO2 (101). J. Phys. Chem. Lett. 2018, 9, 3131– 3136,  DOI: 10.1021/acs.jpclett.8b01182
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      Water dissociates at aqueous interface with reduced anatase TiO2 (101)
      Nadeem, Immad M.; Treacy, Jon P. W.; Selcuk, Sencer; Torrelles, Xavier; Hussain, Hadeel; Wilson, Axel; Grinter, David C.; Cabailh, Gregory; Bikondoa, Oier; Nicklin, Christopher; Selloni, Annabella; Zegenhagen, Jorg; Lindsay, Robert; Thornton, Geoff
      Journal of Physical Chemistry Letters (2018), 9 (11), 3131-3136CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Elucidating the structure of the interface between natural (reduced) anatase TiO2 (101) and water is an essential step toward understanding the assocd. photoassisted water splitting mechanism. Here we present surface X-ray diffraction results for the room temp. interface with ultrathin and bulk water, which we explain by ref. to d. functional theory calcns. We find that both interfaces contain a 25:75 mixt. of mol. H2O and terminal OH bound to titanium atoms along with bridging OH species in the contact layer. This is in complete contrast to the inert character of room temp. anatase TiO2 (101) in ultrahigh vacuum. A key difference between the ultrathin and bulk water interfaces is that in the latter water in the second layer is also ordered. These mols. are hydrogen bonded to the contact layer, modifying the bond angles.
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    68. 68
      Martinez-Casado, R.; Mallia, G.; Harrison, N. M.; Pérez, R. First-Principles Study of the Water Adsorption on Anatase(101) as a Function of the Coverage. J. Phys. Chem. C 2018, 122, 20736– 20744,  DOI: 10.1021/acs.jpcc.8b05081
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      68
      First-Principles Study of the Water Adsorption on Anatase(101) as a Function of the Coverage
      Martinez-Casado, Ruth; Mallia, Giuseppe; Harrison, Nicholas M.; Perez, Ruben
      Journal of Physical Chemistry C (2018), 122 (36), 20736-20744CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      An understanding of the interaction of water with the anatase(101) surface is crucial for developing strategies to improve the efficiency of the photocatalytic reaction involved in solar water splitting. Despite a no. of previous investigations, it is still not clear if water preferentially adsorbs in its mol. or dissocd. form on anatase(101). With the aim of shedding some light on this controversial issue, we report the results of periodic screened-exchange d. functional theory calcns. of the dissociative, mol., and mixed adsorption modes on the anatase(101) surface at various coverages. Our calcns. support the suggestion that surface-adsorbed OH groups are present, which has been made on the basis of recently measured XPS, temp.-programmed desorption, and scanning tunneling microscopy data. It is also shown that the relative stability of water adsorption on anatase(101), at different configurations, can be understood in terms of a simple model based on the no. and nature of the hydrogen bonds formed as well as the adsorbate-induced at. displacements in the surface layers. These general conclusions are found to be insensitive to the specific choice of approxn. for electronic exchange and correlation within the d. functional theory. The simple model of water-anatase interactions presented here may be of wider validity in detg. the geometry of water-oxide interfaces.
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    69. 69
      Patrick, C. E.; Giustino, F. Structure of a Water Monolayer on the Anatase TiO2(101) Surface. Phys. Rev. Applied 2014, 2, 014001,  DOI: 10.1103/PhysRevApplied.2.014001
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      Structure of a water monolayer on the anatase TiO2(101) surface
      Patrick, Christopher E.; Giustino, Feliciano
      Physical Review Applied (2014), 2 (1), 014001CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)
      Titanium dioxide (TiO2) plays a central role in the study of artificial photosynthesis, owing to its ability to perform photocatalytic water splitting. Despite over four decades of intense research efforts in this area, there is still some debate over the nature of the first water monolayer on the technol. relevant anatase TiO2(101) surface. In this work, we use first-principles calcns. to reverse engineer the exptl. high-resoln. x-ray photoelectron spectra measured for this surface by Walle et al. and find evidence supporting the existence of a mix of dissocd. and mol. water in the first monolayer. Using both semilocal and hybrid functional calcns., we revise the current understanding of the adsorption energetics by showing that the energetic cost of water dissocn. is reduced via the formation of a hydrogen-bonded hydroxyl-water complex. We also show that such a complex can provide an explanation of an unusual superstructure obsd. in high-resoln. scanning tunneling microscopy expts.
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      Soria, F. A.; Di Valentin, C. Reactive molecular dynamics simulations of hydration shells surrounding spherical TiO2 nanoparticles: implications for proton-transfer reactions. Nanoscale 2021, 13, 4151– 4166,  DOI: 10.1039/D0NR07503E
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      Reactive molecular dynamics simulations of hydration shells surrounding spherical TiO2 nanoparticles: implications for proton-transfer reactions
      Soria, Federico A.; Di Valentin, Cristiana
      Nanoscale (2021), 13 (7), 4151-4166CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
      In many potential applications, nanoparticles are typically in an aq. medium. This has strong influence on the stability, optical properties and reactivity, in particular for their functionalization. Therefore, the understanding of the chem. at the interface between the solvent and the nanoparticle is of utmost importance. In this work, we present a comparative ReaxFF reactive mol. dynamics investigation on spherical TiO2 nanoparticles (NSs) of realistic size, with diams. from 2.2 to 4.4 nm, immersed in a large drop of bulk water. After force field validation for its use for a curved anatase TiO2 surface/water interface, we performed several simulations of the TiO2 nanoparticles of increasing size in a water drop. We found that water can be adsorbed jointly in a mol. and dissociative way on the surface. A Langmuir isotherm indicating an adsorption/desorption mechanism of water on the NS is obsd. Regarding the dissociative adsorption, atomistic details reveal two different mechanisms, depending on the water concn. around the NS. At low coverage, the first mechanism involves direct dissocn. of a single water mol., whereas, at higher water coverage, the second mechanism is a proton transfer reaction involving two water mols., also known as Grotthuss-like mechanism. Thermal annealing simulations show that several water mols. remain on the surface in agreement with the exptl. reports. The capacity of adsorption is higher for the 2.2 and 3.0 nm NSs than for the 4.4 nm NS. Finally, a comparative investigation with flat surfaces indicates that NSs present a higher water adsorption capacity (undissociated and dissocd.) than flat surfaces, which can be rationalized considering that NSs present many more low-coordinated Ti atoms available for water adsorption.
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    71. 71
      Foucaud, Y.; Canevesi, R.; Celzard, A.; Fierro, V.; Badawi, M. Hydration mechanisms of scheelite from adsorption isotherms and ab initio molecular dynamics simulations. Appl. Surf. Sci. 2021, 562, 150137,  DOI: 10.1016/j.apsusc.2021.150137
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      Hydration mechanisms of scheelite from adsorption isotherms and ab initio molecular dynamics simulations
      Foucaud, Y.; Canevesi, R. L. S.; Celzard, A.; Fierro, V.; Badawi, M.
      Applied Surface Science (2021), 562 (), 150137CODEN: ASUSEE; ISSN:0169-4332. (Elsevier B.V.)
      Apart from its interesting optical properties, scheelite is one of the main tungsten-bearing minerals, widely processed by the froth flotation method. A precise and comprehensive description of the hydration state of scheelite is required to achieve satisfactory flotation performance. The hydration mechanisms of scheelite have been poorly studied, using only theor. methods. Manometric gas sorption expts. were combined with ab initio mol. dynamics simulations, including correction for dispersive interactions. The isosteric enthalpy of adsorption was used as the value to link exptl. and theor. results, since it can be detd. by both methods. We have found that water adsorbs more favorably in its mol. form, with two adsorbed water mols. per calcium atom on the (0 0 1) surface, and with three adsorbed water mols. for two calcium atoms on the (1 1 2) surface. The very first water mols. adsorb with an isosteric enthalpy of adsorption of -80 kJ·mol-1 on the (0 0 1) surface, and of -117 kJ·mol-1 on the (1 1 2) surface, at 300 K. This is in very good agreement with the value of -90 kJ·mol-1 calcd. using the Clausius-Clapeyron approach on three exptl. isotherms, accurately fitted with a dual-site Freundlich-Langmuir model.
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    72. 72
      Mähler, J.; Persson, I. A Study of the Hydration of the Alkali Metal Ions in Aqueous Solution. Inorg. Chem. 2012, 51, 425– 438,  DOI: 10.1021/ic2018693
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      A study of the hydration of the alkali metal ions in aqueous solution
      Mahler Johan; Persson Ingmar
      Inorganic chemistry (2012), 51 (1), 425-38 ISSN:.
      The hydration of the alkali metal ions in aqueous solution has been studied by large angle X-ray scattering (LAXS) and double difference infrared spectroscopy (DDIR). The structures of the dimethyl sulfoxide solvated alkali metal ions in solution have been determined to support the studies in aqueous solution. The results of the LAXS and DDIR measurements show that the sodium, potassium, rubidium and cesium ions all are weakly hydrated with only a single shell of water molecules. The smaller lithium ion is more strongly hydrated, most probably with a second hydration shell present. The influence of the rubidium and cesium ions on the water structure was found to be very weak, and it was not possible to quantify this effect in a reliable way due to insufficient separation of the O-D stretching bands of partially deuterated water bound to these metal ions and the O-D stretching bands of the bulk water. Aqueous solutions of sodium, potassium and cesium iodide and cesium and lithium hydroxide have been studied by LAXS and M-O bond distances have been determined fairly accurately except for lithium. However, the number of water molecules binding to the alkali metal ions is very difficult to determine from the LAXS measurements as the number of distances and the temperature factor are strongly correlated. A thorough analysis of M-O bond distances in solid alkali metal compounds with ligands binding through oxygen has been made from available structure databases. There is relatively strong correlation between M-O bond distances and coordination numbers also for the alkali metal ions even though the M-O interactions are weak and the number of complexes of potassium, rubidium and cesium with well-defined coordination geometry is very small. The mean M-O bond distance in the hydrated sodium, potassium, rubidium and cesium ions in aqueous solution have been determined to be 2.43(2), 2.81(1), 2.98(1) and 3.07(1) ÅA, which corresponds to six-, seven-, eight- and eight-coordination. These coordination numbers are supported by the linear relationship of the hydration enthalpies and the M-O bond distances. This correlation indicates that the hydrated lithium ion is four-coordinate in aqueous solution. New ionic radii are proposed for four- and six-coordinate lithium(I), 0.60 and 0.79 ÅA, respectively, as well as for five- and six-coordinate sodium(I), 1.02 and 1.07 ÅA, respectively. The ionic radii for six- and seven-coordinate K(+), 1.38 and 1.46 ÅA, respectively, and eight-coordinate Rb(+) and Cs(+), 1.64 and 1.73 ÅA, respectively, are confirmed from previous studies. The M-O bond distances in dimethyl sulfoxide solvated sodium, potassium, rubidium and cesium ions in solution are very similar to those observed in aqueous solution.
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      Mile, V.; Pusztai, L.; Dominguez, H.; Pizio, O. Understanding the Structure of Aqueous Cesium Chloride Solutions by Combining Diffraction Experiments, Molecular Dynamics Simulations, and Reverse Monte Carlo Modeling. J. Phys. Chem. B 2009, 113, 10760– 10769,  DOI: 10.1021/jp900092g
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      Understanding the Structure of Aqueous Cesium Chloride Solutions by Combining Diffraction Experiments, Molecular Dynamics Simulations, and Reverse Monte Carlo Modeling
      Mile, Viktoria; Pusztai, Laszlo; Dominguez, Hector; Pizio, Orest
      Journal of Physical Chemistry B (2009), 113 (31), 10760-10769CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      A detailed study of the microscopic structure of an electrolyte soln., CsCl in water, is presented. For revealing the influence of salt concn. on the structure, CsCl solns. at concns. of 1.5, 7.5, and 15 mol % are investigated. For each concn., we combine total scattering structure factors from neutron and X-ray diffraction and 10 partial radial distribution functions from mol. dynamics simulations in one single structural model, generated by reverse Monte Carlo modeling. This combination of computer modeling methods is capable of (a) showing the extent to which simulation results are consistent with exptl. diffraction data and (b) tracking down distribution functions in computer simulation that are the least comfortable with diffraction data. For the present solns., we show that the level of consistency between simulations that use simple pair potentials and exptl. structure factors is nearly quant. Remaining inconsistencies seem to be caused by water-water distribution functions. Changing the pair potentials of water-water interactions from SPC/E to TIP4P-2005 has not had any effect in this respect. As a final result, we obtained particle configurations from reverse Monte Carlo modeling that were in quant. agreement with both diffraction data and most of the mol. dynamics (MD) simulated partial radial distribution functions (prdf's). From the particle coordinates, the distribution of the no. of first neighbors, as well as angular correlation functions, were calcd. The av. no. of water mols. around cations decreases from about 8 to about 6.5 as concn. increases from 1.5 to 15 mol %, whereas the same quantity for the anions changes from about 7 to about 5. The av. angle of Cl···H-O particle arrangements, characteristic of anion-water hydrogen bonds, is closer to 180° than that found for O···H-O arrangements (water-water hydrogen bonds). The present combination of exptl. and computer simulation methods appears to be promising for the study of other electrolyte solns.
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      Zhang, K.; Li, Z.; Qi, S.; Chen, W.; Xie, J.; Wu, H.; Zhao, H.; Li, D.; Wang, S. Adsorption behavior of Cs(I) on natural soils: Batch experiments and model-based quantification of different adsorption sites. Chemosphere 2022, 290, 132636,  DOI: 10.1016/j.chemosphere.2021.132636
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      Adsorption behavior of Cs(I) on natural soils: Batch experiments and model-based quantification of different adsorption sites
      Zhang, Kun; Li, Zhanguo; Qi, Sheng; Chen, Wenzhuo; Xie, Jianming; Wu, Hanyu; Zhao, Hongjie; Li, Daxue; Wang, Shanqiang
      Chemosphere (2022), 290 (), 132636CODEN: CMSHAF; ISSN:0045-6535. (Elsevier Ltd.)
      Understanding the adsorption behavior of radiocesium (RCs) in natural soils is crucial for remediation and evaluation of radioactive contaminated sites. In this study, we investigated the adsorption behavior of Cs(I) onto natural soils collected in Beijing by batch adsorption expts. and sequential extn. A multi-site adsorption model was built to quant. analyze the adsorption capacities of soil clay minerals and predict of Cs(I) adsorption ratio of different adsorption sites. Linear programming calcns. show that illite/smectite (I/S) mixt. and illite(I) are the mainly clay mineral compn. Batch adsorption expt. results show that soils adsorption of Cesium ions is an exothermic process, and the order of influence of competitive cations on the competitive adsorption strength of Cs(I) is:K+>Mg2+≈Ca2+>Na+. HA (Humic Acid)has little effect on soil adsorption. SEM-EDS anal. shows that Cs+ is mainly distributed on the surface (PS) of soil particles. Based on the above results, the adsorption of Cs(I) onto clay minerals in soils is well predicts in both linear programming calcns. and a multi-site adsorption model. The multi-site adsorption model can quant. describe and predict the adsorption behavior of Cs(I) on different clay sites in the soils. Frayed edge sites (FES) in the soil can effectively fix trace RCs. The higher concn. of cesium ions is mainly adsorbed on the PS and TIIS. Sequential extn. expt. further proved the adsorption form of cesium in soil under trace and high concn. conditions.
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      Sholl, D. S.; Lively, R. P. Seven chemical separations to change the world. Nature 2016, 532, 435– 437,  DOI: 10.1038/532435a
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      Seven chemical separations to change the world
      Sholl David S; Lively Ryan P
      Nature (2016), 532 (7600), 435-7 ISSN:.
      There is no expanded citation for this reference.
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    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsanm.3c00916.

    • Synthesis of TiO2 NTs, annealing of TiO2 NTs sample, structural characterization of TiO2 NTs, properties of the aqueous suspension of TiO2 nanotubes, batch experiments of Cs+ adsorption on TiO2 NTs, full model derivation: Poisson–Boltzmann theory to reproduce acid–base titration curve of TiO2 NTs aqueous suspension in dilute regime with CO2 as a contaminant, fitting of the model to the experimental data, model predictions for different sets of inner and outer nanotubes radii, first-principles Molecular Dynamics Simulations (PDF)


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