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Zeta Potentials of Cotton Membranes in Acetonitrile Solutions
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  • Yuki Uematsu*
    Yuki Uematsu
    Department of Physics and Information Technology, Kyushu Institute of Technolohy, Iizuka 820-8502, Japan
    PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
    *Email: [email protected]
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    Orcidhttps://orcid.org/0000-0002-4970-4696
  • Suguru Iwai
    Suguru Iwai
    Department of Chemical Science and Engineering, School of Materials and Chemical Technology, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
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  • Mariko Konishi
    Mariko Konishi
    Department of Chemical Science and Engineering, School of Materials and Chemical Technology, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
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  • Shinsuke Inagi
    Shinsuke Inagi
    Department of Chemical Science and Engineering, School of Materials and Chemical Technology, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
    More by Shinsuke Inagi
    Orcidhttps://orcid.org/0000-0002-9867-1210
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Cite this: Langmuir 2024, 40, 38, 20294–20301
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https://doi.org/10.1021/acs.langmuir.4c02798
Published September 16, 2024

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Abstract

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Solid surfaces in contact with nonaqueous solvents play a key role in electrochemistry, analytical chemistry, and industrial chemistry. In this work, the zeta potentials of cotton membranes in acetonitrile solutions were determined by streaming potential and bulk conductivity measurements. By applying the Gouy–Chapman theory and the Langmuir adsorption isotherm of ions to the experimental data, the mechanism of the electrification at the cotton/acetonitrile interface is revealed for the first time to be solely due to ion adsorption on the surface, rather than proton dissociation at the interface. Different salts were found to produce opposite signs of the zeta potentials. This behavior can be attributed to ion solvation effects and the strong ordering of acetonitrile molecules at the interface. Furthermore, a trend of the electroviscous effect was observed, in agreement with the standard electrokinetic theory. These findings demonstrate that electrokinetics in acetonitrile, a polar aprotic solvent, can be treated in the same manner as in water.

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Introduction

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The zeta potential of the solid/liquid interface is an important quantity because it characterizes the amount of charges at the interface. (1,2) The charged liquid interfaces are ubiquitous and have various applications such as the stabilization of colloidal dispersions (1) and electrokinetic devices. (3) However, in contrast to the solid/water interface, electrokinetics at the solid/organic liquids interface has received less attention until recently, (4−8) although it has been recognized as important for capillary electrophoresis, (9−14) nonaqueous colloidal dispersions, (15−28) and nonaqueous electrochemistry. (29−32) Organic solvents have unique and various physicochemical properties which the water does not have. The polarity of liquids is one of the most important properties of the solvent. (33) The polarity strength can be characterized by the dielectric constant of the liquids, and the water has ε = 78 at 25 °C and 1 atm. The water dielectric constant is relatively high compared to those of other organic liquids, except for some amides, and thus, the water is a good solvent for ions. Another important classification is protonation ability. (33) An amphiprotic solvent is one that can both donate and accept a proton. These solvents typically exhibit self-ionization through protonation and deprotonation as the water does. Because water is a polar amphiprotic solvent, the dissociable groups with a labile proton on surfaces in contact with water are deprotonated depending on the pH of water. The electrification mechanism of the water interface is well understood except for hydrophobic surfaces. (2) However, the electrification of solid surfaces in contact with polar aprotic solvents is less understood compared to water, because pKa of the dissociable groups in such solvent is either unknown or significantly different from that in water. (34,35) Furthermore, the pH of aprotic solvents cannot be controlled easily.
Let us summarize the previous work on the zeta potentials in organic liquids. The electrification of fused silica surfaces in contact with various organic liquids has been studied in the field of capillary electrophoresis. (10,12,13) These studies revealed that the electro-osmotic mobility of fused-silica capillaries has a linear correlation with the ratio of dielectric constant and viscosity ε/η for various polar aprotic solvents as well as amphiprotic solvents. (12) Thus, the silanol groups on the silica surface donate protons to aprotic solvents such as acetonitrile as well as amphiprotic solvents. Focusing on acetonitrile, the zeta potential of fused silica surfaces in contact with salt-free acetonitrile is about −200 mV, (10,12) which is much larger than that of the silica/salt-free water interface, about −100 mV. Here the zeta potential was calculated by the Helmholtz–Smoluchowski equation, ζ = −(η/εε0)μ where ζ is the zeta potential, η is the viscosity of the liquids, ε is the dielectric constant of the liquid, ε0 is the vacuum permittivity, and μ is the electro-osmotic mobility. When salts are added to the acetonitrile, the magnitude of zeta potential decreases as a function of the salt concentration, (36) which qualitatively agrees with the Gouy–Chapman theory of fixing the surface charge density. (37,38) Thus, the electric double-layer structure of the polar aprotic solvent seems to be well described by the Gouy–Chapman theory as aqueous electric double layers. Inagi and co-workers, however, measured the streaming potential of cotton membranes with various salts in different polar aprotic solvents. (32) They found that the combination of salts and solvents can change the sign of the streaming potential. This implies that the electrification of the cotton membrane in polar aprotic solvents is different from that of the silica surface.
In this study, the zeta potential of cotton membranes in contact with acetonitrile is further investigated by the streaming potential measurements, bulk conductivity measurements, and the comparison with the standard electrokinetic theory. The theory includes the Gouy–Chapman theory, (37,38) the Langmuir adsorption isotherm of ions, (2,39) and the electrokinetics in a thin capillary. (40) The comparison between the experimental data and the theory reveals that the zeta potential of the cotton/acetonitrile interface is governed not by the dissociable groups on the membrane surface but by the surface adsorption of the ions dissociated from the added salts. Thus, the sign of the zeta potentials depend on the type of salts. Furthermore, a tendency of the electroviscous effect was found, in agreement with the theoretical prediction. These findings will be a key step to understanding the electrokinetics in organic liquids.

Experimental Section

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Materials

Acetonitrile (Fujifilm Wako, super dehydrated, 99.8%) was used for the solvent. The dielectric constant of acetonitrile is ε = 35.9 at 298 K, (41) which is about half of that of water (ε = 78). The viscosity of acetonitrile is η = 0.344 mPa·s at 298 K, (41) which is again about half of that of water (η = 0.89 mPa·s). For the electrolytes, two different salts were selected to show different solvation properties: tetrabutylammonium hexafluorophosphate (Bu4NPF6, Fujifilm Wako, 97%) and lithium tetrafluoroborate (LiBF4, Tokyo Chemical Industry, >98%). The both anions, hexafluorophosphate ions (PF6–) and tetrafluoroborate ions (BF4–), were hydrophobic, whereas the cations have a different hydrophobicities: tetrabutylammonium ions (Bu4N+) is hydrophobic, while lithium ions (Li+) is hydrophilic. All salts and solvents were used without further purification. Medical cotton wool (Hakujuji, 11006) was used for the membrane by packing it tightly into a tube. Platinum (Pt) wires (Nilaco, ϕ0.6 mm) were used as the electrodes for the streaming potential measurements.

Methods

The methods to measure the streaming potential and pressure difference were the same as those described in the previous work. (32) The experimental system of the streaming potential measurements was illustrated in Figure 1. Two custom-made plastic chambers (polyether ether ketone, PEEK) were connected by a PEEK tube (inner diameter, d = 0.5 mm), in which approximately 6 mg of cotton wool was tightly packed with the length of L = 50 mm. An electrolyte solution was fed by a pump with a constant volume flux Q (>0), and the pressure difference Δp (>0) was measured. The voltage difference, i.e., streaming potential Δψ, across the cotton membrane was measured on a voltmeter (Sanwa, PC773) and recorded using software (Sanwa, PC Link 7) with Pt wire electrodes. The voltage difference is defined as the electrostatic potential at the upper side of the membrane relative to the lower side, which is the opposite of the definition used in the previous work. (32) Because the voltmeter ideally has infinite resistance, the condition of zero current I = 0 was satisfied. The voltage difference became nearly stationary 30 s after applying the flow, and the measured value was determined by averaging the stationary data over 90 s. The linearity of the streaming potential with respect to pressure was verified in the Supporting Information of the previous paper, (32) and thus we fixed the volume flux at Q = 0.5 mL/min. The bulk conductivities of the sample solutions were measured using a conductivity electrode (Horiba, 3552-10D), and scanning electron microscopy (SEM) observations were conducted using a JEOL JSM 6610.

Figure 1

Figure 1. Illustration of the experimental setup. The volume flux of the sample solution, Q, is controlled by the pump, whereas the pressure difference Δp and the voltage difference Δψ are measured. The zero current condition I = 0 is satisfied because the electric circuit is open.

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Results with Discussion

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Zeta Potential

First, the zeta potentials of the cotton/acetonitrile interface in the Bu4NPF6 solution are investigated. Figure 2a shows the streaming potential Δψ of the three different cotton membranes filled with acetonitrile as a function of the Bu4NPF6 concentration, denoted by c. The color represents the different cotton membranes #1 (red circle), #2 (blue triangle), and #3 (green square). Measurements in ascending order of the salt concentrations are shown with open symbols and solid lines, whereas measurements in descending order are shown with filled symbols and broken lines. The streaming potential shows minor difference between each membrane, and a slight hysteresis was observed in the ascending and descending order of salt concentrations. In contrast to the streaming potential, the induced pressure Δp, as shown in Figure 2b, significantly depends on both the individual membrane and the order of the concentrations. This aspect is discussed in the section on the electroviscous effect.

Figure 2

Figure 2. (a) Streaming potential of cotton membranes filled with acetonitrile as a function of the Bu4NPF6 concentration when a solution flux of Q = 0.5 mL/min was applied. (b) Induced pressure difference as a function of the Bu4NPF6 concentration. The color represents the different cotton membranes #1 (red circle), #2 (blue triangle), and #3 (green square). Measurements in ascending order of the salt concentrations (→ in the label) are shown with open symbols and solid lines, whereas measurements in descending order (← in the label) are shown with filled symbols and broken lines.

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In Figure 3, the bulk conductivity, σ, of the solution of Bu4NPF6 is plotted as a function of the concentration. The points are the experimental data, whereas the solid line corresponds to the linear equation predicted by the molar limiting conductivity of the cation λ+ = 61.3 S·cm2/mol (41) and of the anion λ– = 103.5 S·cm2/mol. (41) Since the experimental data approximately follow the linear equation, the salts in acetonitrile behave as strong electrolytes.

Figure 3

Figure 3. Bulk conductivity of a Bu4NPF6 solution in acetonitrile as a function of concentration. The solid line represents the linear fit calculated by the molar limiting conductivity of the salts, 164.8 S·cm2/mol. (41) The broken line is a guide for the eye.

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To convert these data into the zeta potential, (1,2)
Δψ=εε0ζησΔp
(1)
was used, where ε is the dielectric constant of the solution, ε0 is the electric permittivity of vacuum, ζ is the zeta potential of the cotton membrane, and η is the solution viscosity. Figure 4a shows the zeta potential derived from eq 1. The obtained zeta potential is negative, and its magnitude increases with salt concentration up to 3 mM. For comparison, Figure 4b shows the zeta potentials of the silica/acetonitrile interface as a function of salt concentration from previous work. (36) In contrast, the zeta potential of the silica/acetonitrile interface decreases in magnitude with increasing salt concentration. (36) In that study, the electrolyte used was 1-butyl-3-methylimidazolium trifluoroacetate. Because the silica surface is relatively acidic even in acetonitrile, the silanol groups donate the protons to the acetonitrile. (10,12,36) To validate this electrification mechanism, the salinity dependence of the zeta potential is calculated using the Grahame equation (1,2) with a constant surface charge density, as given by
σ0=2kBTeεε0κsinheζ2kBT
(2)
where σ0 is the surface charge density, kB is the Boltzmann constant, T is the temperature, and κ–1 = (2e2c/εε0kBT)−1/2 is the Debye length. The black solid line in Figure 4b is calculated using eq 2 with ε = 35.9, T = 298 K, and σ0 = −0.08 e/nm2, which agrees with the experimental data. (36) Thus, the silica surface appears to be fully dissociated in that experiment, even though the pKa of the silanol group in water is about 7.5. (42,43)

Figure 4

Figure 4. (a) Zeta potentials of the cotton/acetonitrile interface as a function of Bu4NPF6 concentration. The points are derived from experimental data using eq 1 whereas the lines represent theoretical fits based on eqs 2 and 3 with α– = −1.2 and Γ0 as denoted in the figure. Other parameters are z* = 0.5 nm, ε = 35.9, and T = 298 K. Due to the lack of experimental bulk conductivity data at low salinity, the linear slope from Figure 3 was used to calculate the zeta potential for the membrane #3. (b) Zeta potentials of the silica/acetonitrile interface as a function of salt concentration. (36) The original data are provided in Figure 2a of the ref (36). as the electro-osmotic mobility. Zeta potentials were calculated using ζ = −(η/εε0)μ, where η/εε0 = 1.08 × 106 s·V2/m2. The solid line is calculated using eq 2 with ε = 35.9, T = 298 K, and σ0 = −0.08 e/nm2.

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On the contrary, the salinity dependence of the zeta potential of the cotton/acetonitrile interface differs from that of the silica/acetonitrile interface. The primary component of cotton is cellulose, a polysaccharide consisting of d-glucose units. Since the pKa of the hydroxy group in cellulose in water is approximately 12, (44,45) these groups are considered weak acids. Consequently, in acetonitrile solutions, the hydroxy groups of cellulose does not dissociate protons, although they can act as donors for hydrogen bonds with the nitrogen atoms of acetonitrile molecules. A hypothesis is that the surface charge density of the cotton membrane originates from ion adsorption. To test this hypothesis, anion adsorption is modeled using the Langmuir adsorption isotherm, (2,39) given by
σ0=−eΓ0(z*/Γ0)ceeζ/kBT−α−1+(z*/Γ0)ceeζ/kBT−α−
(3)
where z* is the thickness of the adsorption layer, α– is the adsorption energy of the anion in the unit of kBT, and Γ0 is the adsorption site density per area. The black solid and broken lines in Figure 4a represent the fitting results calculated using eqs 2 and 3. The thickness of the adsorption layer was set to z* = 0.5 nm, consistent with previous works. (2,46) The fit parameters are α– and Γ0. The value of α = −1.2 was used for all the membranes, whereas Γ0 = 0.007/nm2 (solid line) was used for membrane #1 and 0.003/nm2 (broken line) for membranes #2 and #3. The theoretical calculation well captures the experimental zeta potential of the cotton/acetonitrile interface, suggesting that the surface charge density of the cotton membrane is due to ion adsorption. However, in Figure 4a, there is a small discrepancy between the experimental results and the theoretical predictions at low salt concentrations. The experimental data exhibit a linear relationship with c whereas the theory predicts a dependence of c.
Next, we discuss the zeta potentials associated with LiBF4 salts. Lithium salts are known to change the sign of the surface charge from negative to positive at both silica/acetonitrile interfaces (47−50) and cotton/acetonitrile interfaces. (32) Figure 5a shows the zeta potential of a cotton membrane filled with a LiBF4 solution in acetonitrile. In contrast to the Bu4NPF6 solution, the zeta potential of the LiBF4 solution is positive, suggesting that lithium ions adsorb to the cotton interface. Figure 5b–d are the streaming potential, (32) the induced pressure difference, and the bulk conductivity of the LiBF4 solution in acetonitrile, respectively, which were used to calculate the zeta potentials. The bulk conductivity demonstrate a linear dependence on concentration, with the limiting molar conductivity of LiBF4 determined to be 165.5 S·cm2/mol. The positive charging observed with LiBF4 is consistent with recent studies on the rectification of ionic current through conical nanopores, which found that alkali metal salts in polar aprotic solvents induce positive surface charges on various nanopore surfaces. (6,7,47,48,51) The adsorption of alkali metal cations in polar aprotic solvents was attributed to the formation of strongly solvated cations (48,52,53) and the strong ordering of acetonitrile molecules at the interface. (49,50,54) Based on these studies, (49,50) acetonitrile molecules form a lipid-bilayer-like structure at the cotton interface similar to that at the silica interface, as cellulose has hydroxy groups that act as donors of hydrogen bonds. In the first layer of this strongly ordered structure, the cyano groups accept hydrogen bonds from the surface hydroxy groups, while in the second layer, the cyano groups point in the opposite direction. Our results suggest that interfacial Bu4N+ are well solvated between the two layers of methyl groups of acetonitrile, while PF6– ions segregate between the cotton interface and the first layer of interfacial acetonitrile molecules. In contrast, BF4– ions are well solvated between the hydrophobic methyl groups in the first and second layers of interfacial acetonitrile molecules, whereas Li+ ions adsorb to the cotton interface.

Figure 5

Figure 5. (a) Zeta potential of a cotton membrane filled with a LiBF4 solution in acetonitrile, calculated using the data shown in b–d, and eq 1. (b) Streaming potential of the cotton membrane with a flux of Q = 0.5 mL/min, data previously published. (32) (c) Induced pressure difference across the cotton membrane. (d) Bulk conductivity of the LiBF4 solution in acetonitrile. The solid line represents the linear fit of the experimental data, with a molar limiting conductivity of 165.5 S·cm2/mol. The broken lines in a–c are guides for the eye.

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To finalize this section, we discuss the relationship between the zeta potential of cotton/water interfaces and that of cotton/acetonitrile interfaces. The zeta potential of cotton/water interfaces is typically negative in pH-neutral solutions. (55−57) However, the origin of this charge at the cotton/water interface remains unclear. The isoelectric point of cotton is around pH = 3, suggesting that the electrification of the cotton/water interface is governed by similar mechanisms as those for hydrophobic surfaces, (58) despite cotton being a hydrophilic fiber. There is ongoing debate regarding whether hydroxide ions adsorb to the interface or if a small amount of impurity at the interface dissociates protons. (58) The zeta potentials of these surfaces in salt-free water remain negative and finite, similar to those of silica surface. This contrasts with the result shown in Figure 4a, where the zeta potential of the cotton/acetonitrile interface approaches zero in the salt-free limit. This observation does not contradict the findings, as the surface adsorption of hydroxide ions is negligible in polar aprotic solvents, and impurities at the interface do not dissociate protons.

Electroviscous Effect

So far, the discussion has been based on the assumption that the Debye length is much smaller than the pore size of the membrane. We will now examine this assumption. The analytic equations for the electrokinetic coefficients of a bundle of thin capillaries with radius R, length L, and zeta potential ζ are given by, (40)
L11=NπR48ηL
(4)
L12=L21=−Nεε0ζηπR2L(1−2F(κR)κR)
(5)
L22=NσπR2L[1+β(2F(κR)κR+F(κR)2−1)]
(6)
where N is the numbers of the capillaries, the flux and the electric current are defined by Q = L11Δp + L12Δψ and I = L21Δp + L22Δψ. Additionally, β = (ηκ2/σ)·(εε0ζ/η)2 = β*(eζ/kBT)2, and F(x) is defined by F(x) = I1(x)/I0(x) where I0(x) and I1(x) are the modified Bessel functions of the first kind. Note that these equations are derived under the linear approximation of eζ/kBT in the Poisson–Boltzmann equation.
The cotton membrane used in the experiments can be modeled as a bundle of thin capillaries. To estimate the pore size R, we use eqs 4–6. The relation between Q and Δp under the condition of I = 0 is given by
Q=L11(1−L12L21L11L22)Δp
(7)
In the limit of large salt concentration, Q/Δp approaches L11. In the experiments, Δp = 13 MPa with Q = 0.5 mL/min in this limit as shown in Figure 2b, and thus L11 = 1.3 × 10–6 mm3/(Pa·s) is obtained. The volume fraction of the cotton fiber in the membrane was 0.39, calculated using the mass density of cotton 1.55 g/cm3 (59) and the membrane volume πd2L/4 = 9.8 mm3. Assuming the area fraction of the membrane cross-section is the same as the volume fraction, we obtained NπR2 = 0.61πd2/4 = 0.12 mm2. Thus, the pore size is calculated as R=8ηLL11/NπR2=1.2μm. Figure 6 shows the SEM images of the cotton membrane. The thickness of the cotton fibers is about 10 μm, and they are packed tightly. The estimated pore size of 1.2 μm is realistic and consistent with the SEM images.

Figure 6

Figure 6. Scanning electron microscopy images of the cotton membrane. (a) The scale bar is 100 μm. (b) The scale bar is 50 μm.

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When eqs 4–6 are considered, the streaming potential as a function of κR and ζ is given by
ΔψΔp=εε0ζησ1−2F(κR)κR1+β*(eζkBT)2(2F(κR)κR+F(κR)2−1)
(8)
instead of eq 1, where β* = 0.28 for Bu4NPF6 in acetonitrile, using the limiting molar conductivity. Eq 8 can be analytically solved for ζ using the quadratic formula. However, when eq 8 is used to convert the experimental streaming potential into the zeta potential, no significant difference is observed compared to using eq 1 because κR > 1 is satisfied with R = 1.2 μm where κ–1 = 205 nm for c = 10–3 mM.
Next, the electroviscous effect is examined. This effect describes the increase in apparent viscosity when the capillary size is on the same order as the Debye length. (40,60) Using eq 7 and the pressure difference at large salt concentrations, Δp0 = Q/L11, the electroviscous effect can be represented by
ΔpΔp0=[1−8β(κR)2(1−2F(κR)κR)21+β(2F(κR)κR+F(κR)2−1)]−1
(9)
where the maximum of eq 9 with fixed ζ occurs at approximately κR = 2.2. (40,60) To theoretically calculate the zeta potential without the assumption of κR ≫ 1, eq 2 should be replaced with the one for cylindrical geometry. Although no analytical equation is known for arbitrary ζ, (61,62) the linear approximation with ζ yields
σ0=εε0κζF(κR)
(10)
Figure 7 shows the normalized pressure difference as a function of Bu4NPF6 concentrations. The solid lines represent theoretical calculations based on eqs 3, 9, and 10 with the parameters α– = −1.2, z* = 0.5 nm, Γ0 = 0.003/nm2, ε = 35.9, T = 298 K, η = 0.344 mPa·s, λ+ = 61.3 S·cm2/mol, and λ– = 103.5 S·cm2/mol. The colors of the solid lines correspond to different pore radii as R = 1 μm (green), 2 μm (blue), and 8 μm (red). The lines exhibit a maximum at a concentration of approximately 10–3 mM where the Debye length is κ–1 = 205 nm. The maximum value decreases with increasing R. The maximum at a concentration where κR > 2.2 results from the combined effects of double-layer overlap and concentration-dependent zeta potentials. The points represent experimental data for Bu4NPF6 solutions, where Δp0 is used for the pressure difference at c = 5 mM for membranes #1 and #2 and at 1 mM for membrane #3. The experimental data in the ascending order (open symbol) increase with concentration, which does not agree with the theoretical predictions. However, the descending order data (filled symbol) decrease with concentration, matching the theoretical predictions for R = 1 μm (#3, green) and R = 2 μm (#2, blue). This is consistent with the estimated R = 1.2 μm and the SEM images.

Figure 7

Figure 7. Normalized pressure difference as a function of Bu4NPF6 concentration. Theoretical curves are calculated using eqs 3, 8, and 9 with the parameters α– = −1.2, z* = 0.5 nm, Γ0 = 0.003/nm2, ε = 35.9, T = 298 K, η = 0.344 mPa·s, λ+ = 61.3 S·cm2/mol, and λ– = 103.5 S·cm2/mol. Experimental data points are for Bu4NPF6 solutions where Δp0 is used for the pressure difference at c = 5 mM for membranes #1 and #2 and at 1 mM for membrane #3.

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The reason for the no electroviscous effect in the data of the ascending order is not clear. We consider that the cotton fibers were not rigid, and during the flow-forcing experiment, they deformed and blocked some pores. In the experiments, the measurements in the ascending order were conducted first, and a few days later, those in the descending order were done. Thus, flow-forcing and aging made the membrane mechanically stable. The zeta potential was not affected by this aging because it is independent of the pore size as long as κR ≫ 1 is satisfied. This is probably why the induced pressure differences plotted in Figure 2b are scattered, whereas the streaming potentials in Figure 2a are not.

Conclusions

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The zeta potential of the cotton membrane in the acetonitrile solution was experimentally determined using streaming potential and bulk conductivity measurements. Fitting the Langmuir adsorption isotherm of ions to the experimental zeta potentials reveals that the zeta potential of the cotton membrane is induced not by the dissociation of the proton on the surface but by ion adsorption. This fact contrasts with silica/acetonitrile interfaces because acetonitrile can accept protons dissociated from the silanol groups on the silica surface, as reported previously. (36) The fitted adsorption energy of anions was −1.2 in the unit of thermal energy for Bu4NPF6 solutions in acetonitrile. Furthermore, it was demonstrated that LiBF4 electrifies the cotton/acetonitrile interface positively, which agrees with the recent works on nanopore rectification (6,7,47,48,51) and the strong ordering of acetonitrile molecules at the interface. (49,50)
In addition to the analysis of the zeta potential, the salt-concentration dependence of the induced pressure difference during the flow-forcing measurements was analyzed in terms of the electroviscous effect. Some experimental data exhibit an enhancement of the pressure difference, i.e., the apparent viscosity, at low salt concentrations, which agrees with the theoretical prediction for the micrometer-sized pore size.
These experimental results and the analysis with the standard electrokinetic theory suggest that electrokinetics in acetonitrile, a polar aprotic solvent, can be treated similarly to electrokinetics in water. However, the electrification mechanisms and the ion-specific effect in nonaqueous solvents could differ from those in water. We hope that this work will inspire further studies in the field of electrokinetics in organic liquids.

Author Information

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  • Corresponding Author
    • Yuki Uematsu - Department of Physics and Information Technology, Kyushu Institute of Technolohy, Iizuka 820-8502, Japan;  PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan;  Orcidhttps://orcid.org/0000-0002-4970-4696;  Email: [email protected]
  • Authors
    • Suguru Iwai - Department of Chemical Science and Engineering, School of Materials and Chemical Technology, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
    • Mariko Konishi - Department of Chemical Science and Engineering, School of Materials and Chemical Technology, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan
    • Shinsuke Inagi - Department of Chemical Science and Engineering, School of Materials and Chemical Technology, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan;  Orcidhttps://orcid.org/0000-0002-9867-1210
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by JST PRESTO Grant No. JPMJPR21O2 and JST FOREST Grant No. JPMJFR211G.

References

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    Siria, A.; Poncharal, P.; Biance, A.-L.; Fulcrand, R.; Blase, X.; Purcell, S. T.; Bocquet, L. Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. Nature 2013, 494, 455– 458,  DOI: 10.1038/nature11876
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    3
    Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube
    Siria, Alessandro; Poncharal, Philippe; Biance, Anne-Laure; Fulcrand, Remy; Blase, Xavier; Purcell, Stephen T.; Bocquet, Lyderic
    Nature (London, United Kingdom) (2013), 494 (7438), 455-458CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    New models of fluid transport are expected to emerge from the confinement of liqs. at the nanoscale, with potential applications in ultrafiltration, desalination and energy conversion. Nevertheless, advancing our fundamental understanding of fluid transport on the smallest scales requires mass and ion dynamics to be ultimately characterized across an individual channel to avoid averaging over many pores. A major challenge for nanofluidics thus lies in building distinct and well-controlled nanochannels, amenable to the systematic exploration of their properties. Here we describe the fabrication and use of a hierarchical nanofluidic device made of a boron nitride nanotube that pierces an ultrathin membrane and connects two fluid reservoirs. Such a transmembrane geometry allows the detailed study of fluidic transport through a single nanotube under diverse forces, including elec. fields, pressure drops and chem. gradients. Using this device, we discover very large, osmotically induced elec. currents generated by salinity gradients, exceeding by two orders of magnitude their pressure-driven counterpart. We show that this result originates in the anomalously high surface charge carried by the nanotube's internal surface in water at large pH, which we independently quantify in conductance measurements. The nano-assembly route using nanostructures as building blocks opens the way to studying fluid, ionic and mol. transport on the nanoscale, and may lead to biomimetic functionalities. Our results furthermore suggest that boron nitride nanotubes could be used as membranes for osmotic power harvesting under salinity gradients.
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  4. 4
    Gortner, R. A. Electrokinetics XXIII. Electrokinetics as a tool for the study of the molecular structure of organic compounds. Trans. Faraday Soc. 1940, 35, 63,  DOI: 10.1039/TF9403500063
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  5. 5
    Westermann-Clark, G.; Christoforou, C. Note on nonaqueous electrokinetic transport in charged porous media. J. Membr. Sci. 1984, 20, 325– 338,  DOI: 10.1016/S0376-7388(00)82009-8
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    Note on nonaqueous electrokinetic transport in charged porous media
    Westermann-Clark, G. B.; Christoforou, C. C.
    Journal of Membrane Science (1984), 20 (3), 325-39CODEN: JMESDO; ISSN:0376-7388.
    A model for electrokinetic transport in charged capillaries is compared with expts. by using nonaq. LiCl solns. The electrokinetic parameters considered are the pore fluid cond. and the concn. potential. Methanol/water mixts. were the solvents and track-etched mica membranes with a well-characterized pore structure were the porous medium. The electrolyte concns. used were such that the Debye lengths of solns. in pores ranged from much smaller to much larger than the radii of the pores. The space-charge model is capable of describing qual. the trend of the electrokinetic data, but as expected, at higher concns. the model fails, probably because the assumption that ion-ion interactions are negligible no longer holds. The pore fluid cond. depends strongly on the dielec. const. of the solvent; the abs. value of the pore wall charge tends to decrease with the lowering of the solvent dielec. const., and the wall charge tends to increase with the concn. of the chloride ion.
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  6. 6
    Lucas, R. A.; Lin, C.-Y.; Siwy, Z. S. Electrokinetic Phenomena in Organic Solvents. J. Phys. Chem. B 2019, 123, 6123– 6131,  DOI: 10.1021/acs.jpcb.9b04969
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    Electrokinetic Phenomena in Organic Solvents
    Lucas, Rachel A.; Lin, Chih-Yuan; Siwy, Zuzanna S.
    Journal of Physical Chemistry B (2019), 123 (28), 6123-6131CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Solid/liq. interfaces play a key role in sepn. processes, energy storage devices, and transport in nanoscale systems. Nanopores and mesopores with well-defined geometry and chem. characteristics have been a valuable tool to unravel electrochem. properties of interfaces, but the majority of studies have been focused on aq. solns. Here, we present expts. and numerical modeling aimed at characterizing effective surface charge of polymer pores in mixts. of water and alcs. as well as in propylene carbonate and acetone. The charge properties of pore walls are probed through anal. of current-voltage curves recorded in the presence of salt concn. gradients. The presence and direction of electro-osmotic flow lead to asym. current-voltage curves, with rectification characteristics detd. by the polarity of surface charge. The results suggest that the effective surface charge of the pore walls depends not only on the type of solvent but also on the concn. of the electrolyte and voltage. We identified conditions at which polymer pores that are neg. charged in aq. solns. become pos. charged in propylene carbonate and acetone. The findings are of importance for nonaq. sepns., fundamental knowledge on solid/liq. interfaces in org. media, and prepn. of porous devices with tunable surface charge characteristics.
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  7. 7
    Russell, W. S.; Siwy, Z. Enhanced electro-osmosis in propylene carbonate salt solutions. J. Chem. Phys. 2021, 154, 134707,  DOI: 10.1063/5.0044402
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    7
    Enhanced electro-osmosis in propylene carbonate salt solutions
    Russell, Wilfred Shelby; Siwy, Zuzanna
    Journal of Chemical Physics (2021), 154 (13), 134707CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Properties of solid-liq. interfaces and surface charge characteristics mediate ionic and mol. transport through porous systems, affecting many processes such as sepns. Herein, the authors report expts. designed to probe the electrochem. properties of solid-liq. interfaces using a model system of a single polyethylene terephthalate (PET) pore in contact with aq. and propylene carbonate solns. of LiClO4. First, the existence and polarity of surface charges were inferred from current-voltage curves recorded when a pore was placed in contact with a LiClO4 concn. gradient. Second, the electroosmotic transport of uncharged polystyrene particles through the PET pore provided information on the polarity and the magnitude of the pore walls' zeta potential. The authors' expts. show that the PET pores become effectively pos. charged when in contact with LiClO4 solns. in propylene carbonate, even though in aq. LiClO4, the same pores are neg. charged. Addnl., the electroosmotic velocity of the particles revealed a significantly higher magnitude of the pos. zeta potential of the pores in propylene carbonate compared to the magnitude of the neg. zeta potential in H2O. The presented methods of probing the properties of solid-liq. interfaces are expected to be applicable to a wide variety of solid and liq. systems. (c) 2021 American Institute of Physics.
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  8. 8
    Suzuki, Y.; Mizuhata, M. Predictive Zeta Potential Measurement Method Applicable to Nonaqueous Solvents in High-concentration Dispersion Systems for the System of LiClO4–Propylene Carbonate Solution and LiCoO2 Powder Sheet. Electrochemistry 2022, 90, 103001– 103001,  DOI: 10.5796/electrochemistry.22-66050
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  9. 9
    Schwer, C.; Kenndler, E. Electrophoresis in fused-silica capillaries: the influence of organic solvents on the electroosmotic velocity and the zeta potential. Anal. Chem. 1991, 63, 1801– 1807,  DOI: 10.1021/ac00017a026
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    Electrophoresis in fused-silica capillaries: the influence of organic solvents on the electroosmotic velocity and the ζ potential
    Schwer, Christine; Kenndler, Ernst
    Analytical Chemistry (1991), 63 (17), 1801-7CODEN: ANCHAM; ISSN:0003-2700.
    The influence of pH and solvent compn. on the electroosmotic flow in fused-silica capillaries was studied. Binary mixts. of H2O and a protic (MeOH, EtOH, iso-PrOH) or an aprotic dipolar solvent (MeCN, Me2CO, DMSO) were used for the buffer electrolyte. The dependence of the electroosmotic flow on the pH was detd. in the pH range from 3 to 11 for pure aq. soln. and for solns. contg. 50 vol.% org. solvent. Adding org. solvents to the electrolyte, the inflection points of the resulting curves, corresponding to the pK values of the surface silanol groups, are shifted to higher values. At high pH, increasing the fraction of org. cosolvent generally decreases the electroosmotic velocity. Zeta potentials were calcd. from the Smoluchowski equation by using electroosmotic velocity data and values for the ratio of the viscosity coeff. and dielec. const. for binary mixts., taken from the authors own measurements and from the literature. With the exception of Me2CO-H2O mixts., the ζ potentials obtained show a similar trend to that of the electroosmotic velocity; they decrease with increasing content of org. solvent. This trend is explained by changes of the dielec. properties of the elec. double layer and of the charge generation on the fused-silica surface.
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  10. 10
    Wright, P. B.; Lister, A. S.; Dorsey, J. G. Behavior and Use of Nonaqueous Media without Supporting Electrolyte in Capillary Electrophoresis and Capillary Electrochromatography. Anal. Chem. 1997, 69, 3251– 3259,  DOI: 10.1021/ac9613186
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    Behavior and Use of Nonaqueous Media without Supporting Electrolyte in Capillary Electrophoresis and Capillary Electrochromatography
    Wright, Paul B.; Lister, Ashley S.; Dorsey, John G.
    Analytical Chemistry (1997), 69 (16), 3251-3259CODEN: ANCHAM; ISSN:0003-2700. (American Chemical Society)
    Five nonaq. solvents (acetonitrile, methanol, DMF, DMSO, formamide) and deionized water were studied for their ability to support electroosmotic flow (EOF) without electrolytic additives. In general, flow is equal to or greater than flow with typical CE buffer systems. The magnitude of EOF was detd. for each solvent by open tubular capillary electrophoresis (CE) and related to viscosity (η), dielec. const. (ε), and the ratio of dielec. const. to viscosity (ε/η). Zeta potentials (ζ) were derived indirectly from flow data and tabulated. Comparisons of flow behavior and ζ were made between pure solvents and conventional CE buffers, and questions of equilibration and reproducibility were addressed. Similar expts. were performed using hydroorg. mobile phases (ACN/water, MeOH/water) across the complete compositional range (100% water-100% org.), with flow characteristics and ζ reported for each mobile phase system. Packed capillary columns (5-μm ODS) were evaluated for flow and retention stability under capillary electrochromatog. (CEC) conditions. A sepn. of 11 polycyclic arom. hydrocarbons was performed in under 13 min by CEC with an ACN/water mobile phase. Reduced plate heights (h) were calcd. between 2.5 and 3.0 for solutes with capacity factors (k') up to 4.5 for the most retained solute.
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  11. 11
    Tjo̷rnelund, J.; Hansen, S. H. The effect of water on separations in non-aqueous capillary electrophoresis systems. Chromatographia 1997, 44, 5– 9,  DOI: 10.1007/BF02466508
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    Valkó, I. E.; Sirén, H.; Riekkola, M.-L. Characteristics of electroosmotic flow in capillary electrophoresis in water and in organic solvents without added ionic species. J. Microcolumn Sep. 1999, 11, 199– 208,  DOI: 10.1002/(SICI)1520-667X(1999)11:3<199::AID-MCS5>3.0.CO;2-D
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    12
    Characteristics of electroosmotic flow in capillary electrophoresis in water and in organic solvents without added ionic species
    Valko, Istvan E.; Siren, Heli; Riekkola, Marja-Liisa
    Journal of Microcolumn Separations (1999), 11 (3), 199-208CODEN: JMSEEJ; ISSN:1040-7685. (John Wiley & Sons, Inc.)
    Although proper buffering is essential for repeatable sepns. in capillary electrophoresis, electroosmotic flow can be developed in many solvents without the addn. of buffer components. In this study we detected electroosmotic flow in fused silica capillary in the following solvents without the addn. of ionic species: water, deuterium oxide, acetonitrile, acetone, 2-butanone, formamide, N-methylformamide, N,N-dimethylformamide, methanol, ethanol, 1-propanol, DMSO, Et acetate, THF, and morpholine. The electroosmotic flow was in the range of 3.4 X 10-9-1.8 X 10-7 m2/V s. About 100 times weaker electroosmosis was detected in glacial acetic acid. We also detected electroosmotic flow in N-methylacetamide, which is solid at room temp. (melting range 28-30°C). No electroosmotic flow was found in inert solvents such as n-hexane and chloroform. The zeta potential of the fused silica capillary was calcd. for the solvents where electroosmotic flow was found. The zeta potential of the capillary wall was also studied in water-methanol mixts., where it has a max. at about 40% methanol concn.
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    Riekkola, M.-L.; Jussila, M.; Porras, S. P.; Valkó, I. E. Non-aqueous capillary electrophoresis. J. Chromatogr. A 2000, 892, 155– 170,  DOI: 10.1016/S0021-9673(00)00108-4
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    Geiser, L.; Mirgaldi, M.; Veuthey, J.-L. Determination of electroosmotic flow in nonaqueous capillary electrophoresis. J. Chromatogr. A 2005, 1068, 75– 81,  DOI: 10.1016/j.chroma.2005.02.001
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    Kitahara, A. Zeta potential in nonaqueous media and its effect on dispersion stability. Prog. Org. Coat. 1973, 2, 81– 98,  DOI: 10.1016/0300-9440(73)80001-3
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    Zeta potential in nonaqueous media and its effect on dispersion stability
    Kitahara, Ayao
    Progress in Organic Coatings (1973), 2 (2), 81-98CODEN: POGCAT; ISSN:0300-9440.
    A review is given with 38 refs. The properties and stability of org. coatings in relation to zeta potential are also discussed.
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    Fowkes, F. Dispersions of ceramic powders in organic media. Adv. Ceram.: Ceram. Powder Sci. 1987, 21, 411– 421
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    Van Der Hoeven, P.; Lyklema, J. Electrostatic stabilization in non-aqueous media. Adv. Colloid Interface Sci. 1992, 42, 205– 277,  DOI: 10.1016/0001-8686(92)80024-R
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    Electrostatic stabilization in non-aqueous media
    Van der Hoeven, Ph. C.; Lyklema, J.
    Advances in Colloid and Interface Science (1992), 42 (), 205-77CODEN: ACISB9; ISSN:0001-8686.
    A review on electrostatic stabilization of non-aq. dispersions with particular emphasis on the roles of dielec. const. and ionic strength. The liq. dielec. const. controls the degree of ionization of the stabilizing electrolyte and 3 regimes (semipolar, low-polar, apolar) can be distinguished. When attraction between suspended salt particles in nonionic liqs. is weak, electrostatic stabilization is achieved easily. 107 Refs.
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    Siffert, B.; Jada, A.; Eleli-Letsango, J. Stability Calculations of TiO2 Nonaqueous Suspensions: Thickness of the Electrical Double Layer. J. Colloid Interface Sci. 1994, 167, 281– 286,  DOI: 10.1006/jcis.1994.1362
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    Hughes, D. F. K.; Robb, I. D.; Dowding, P. J. Stability of Copper Phthalocyanine Dispersions in Organic Media. Langmuir 1999, 15, 5227– 5231,  DOI: 10.1021/la981389v
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    Stability of Copper Phthalocyanine Dispersions in Organic Media
    Hughes, D. F. K.; Robb, Ian D.; Dowding, Peter J.
    Langmuir (1999), 15 (16), 5227-5231CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    It was found that quite small surface potentials (a few millivolts) were sufficient to stabilize the dil. dispersions of the particles in solvents of low dielec. const. (possibly because this would be a const. charge system) though insufficient to stabilize particles in solvents with dielec. consts. above about 20. Addn. of org. acids enhanced the particles' stability, probably by a proton-exchange mechanism, and addn. of an org.-sol. electrolyte, tetrabutylammonium bromide, caused all systems to flocculate. The presence of a polymer at concns. above about 1% caused flocculation to occur, probably by a depletion mechanism. The attractive depletion energy increased with polymer concn., resulting in the sedimentation vol. increasing with polymer concn.
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  20. 20
    Kosmulski, M. Zeta potentials in nonaqueous media: how to measure and control them. Colloids Surf., A 1999, 159, 277– 281,  DOI: 10.1016/S0927-7757(99)00273-3
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    Zeta potentials in nonaqueous media. How to measure and control them
    Kosmulski, M.
    Colloids and Surfaces, A: Physicochemical and Engineering Aspects (1999), 159 (2-3), 277-281CODEN: CPEAEH; ISSN:0927-7757. (Elsevier Science B.V.)
    A review, with 20 refs. The effect of traces of water in nonaq. solvents on the ζ-potential is overrated, and the role of impurities in presumably pure org. solvents is often overlooked. Oxides can serve as potentiometric sensors to det. the concn. and nature of impurities. Even in very inert solvents the counter-charge in soln. must exist. Small ions are stabilized by homoconjugation and by amphiphilic nonionic compds. The electrokinetic phenomena of the second kind are more common in nonaq. solvents and they lead to very high abs. values of mobility at high field strengths.
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    Kosmulski, M.; Eriksson, P.; Brancewicz, C.; Rosenholm, J. B. Zeta potentials of monodispersed, spherical silica particles in mixed solvents as a function of cesium chloride concentration. Colloids Surf., A 2000, 162, 37– 48,  DOI: 10.1016/S0927-7757(99)00027-8
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    21
    Zeta potentials of monodispersed, spherical silica particles in mixed solvents as a function of cesium chloride concentration
    Kosmulski, Marek; Eriksson, Patrik; Brancewicz, Chris; Rosenholm, Jarl B.
    Colloids and Surfaces, A: Physicochemical and Engineering Aspects (2000), 162 (1-3), 37-48CODEN: CPEAEH; ISSN:0927-7757. (Elsevier Science B.V.)
    Zeta potentials of silica are neg. in most mixed solvents (99% org. co-solvent, 1% water), but in t-butanol and pyridine they are pos. When CsCl is added to the suspension as a probe substance, two types of behavior are obsd. In solvents of ε >25, the zeta potential asymptotically approaches zero, while in solvents of lower dielec. const., the sign of zeta potential is reversed to pos. at a sufficiently high CsCl concn., crev. To evaluate the nature of interaction leading to different solvent responses, a range of frequently used solvent scales relating to specific interactions between the components of the system were compared. A moderate correlation was found between crev for silica and one solvent property alone, and those previously found for anatase, resp. Using linear combinations of 2 solvent scales improved the correlation, but it was still not satisfactory. However, considering sep. the contributions from both solvent components, a nearly statistically significant correlation was found. The results are evaluated considering the particular behavior of each solvent group, and the specific influence of the material properties of silica and of possible impurities present in the system.
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  22. 22
    Zhukov, A. Integrated investigations of the electrosurface properties of nonaqueous disperse and capillary systems. Adv. Colloid Interface Sci. 2007, 134–135, 330– 345,  DOI: 10.1016/j.cis.2007.04.014
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    Hamieh, T.; Toufaily, J.; Alloul, H. Physicochemical Properties of the Dispersion of Titanium Dioxide in Organic Media by Using Zetametry Technique. J. Dispers. Sci. Technol. 2008, 29, 1181– 1188,  DOI: 10.1080/01932690701856626
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    Kosmulski, M.; Prochniak, P.; Rosenholm, J. B. Control of the Zeta Potential in Semiconcentrated Dispersions of Titania in Polar Organic Solvents. J. Phys. Chem. C 2009, 113, 12806– 12810,  DOI: 10.1021/jp903845e
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    24
    Control of the Zeta Potential in Semiconcentrated Dispersions of Titania in Polar Organic Solvents
    Kosmulski, Marek; Prochniak, Piotr; Rosenholm, Jarl B.
    Journal of Physical Chemistry C (2009), 113 (29), 12806-12810CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    The electrokinetic potential of com. titania powder (chiefly anatase) in its 1-10% dispersions in water, lower aliph. alcs., and DMSO is pos., and rather insensitive to the nature of the solvent. The sign of the electrokinetic potential can be reversed to neg. by addn. of phosphoric acid, or of combination of phosphoric acid with triethylamine or with alkali hydroxide. The crit. concn. of surface-active compds., which induces a sign reversal, depends on the nature of the solvent, and it is higher in org. solvents than in water. The crit. surface concn. of surface-active compds. for given org. solvent is rather insensitive to the solid-to-liq. ratio, and typically it is in the range of a few micromoles per square meter.
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    Cihlar, J.; Drdlik, D.; Cihlarova, Z.; Hadraba, H. Effect of acids and bases on electrophoretic deposition of alumina and zirconia particles in 2-propanol. J. Eur. Ceram. Soc. 2013, 33, 1885– 1892,  DOI: 10.1016/j.jeurceramsoc.2013.02.017
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    Lyklema, J. Principles of interactions in non-aqueous electrolyte solutions. Curr. Opin. Colloid Interface Sci. 2013, 18, 116– 128,  DOI: 10.1016/j.cocis.2013.02.002
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    Principles of interactions in non-aqueous electrolyte solutions
    Lyklema, Johannes
    Current Opinion in Colloid & Interface Science (2013), 18 (2), 116-128CODEN: COCSFL; ISSN:1359-0294. (Elsevier Ltd.)
    In this paper a review is presented on the mol. interactions in non-aq. media of low dielec. permittivity. Qual. and quant. distinctions with aq. solns. are emphasized. The reviewed themes include dispersion forces, dissocn. and assocn. equil., discrimination between electrostatic and non-electrostatic interactions, ionic specificity, cond., electrokinetics and colloid interaction. Distinctions between so-called primitive and non-primitive interpretations and between individual and collective behavior are discussed; in these respects the colloid stability phenomena behave differently from the corresponding ones in aq. solvents.
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    Mazzini, V.; Craig, V. S. Specific-ion effects in non-aqueous systems. Curr. Opin. Colloid Interface Sci. 2016, 23, 82– 93,  DOI: 10.1016/j.cocis.2016.06.009
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    Specific-ion effects in non-aqueous systems
    Mazzini, Virginia; Craig, Vincent S. J.
    Current Opinion in Colloid & Interface Science (2016), 23 (), 82-93CODEN: COCSFL; ISSN:1359-0294. (Elsevier Ltd.)
    A review. It is widely acknowledged that specific-ion effects are ubiquitous in aq. systems and undoubtedly are essential to the fundamental processes of life, although a deep fundamental understanding of specific-ion effects remains an important challenge. Specific-ion effects in non-aq. solvents are known but have attracted far less attention, yet knowledge of specific-ion effects in non-aq. systems is likely to provide important information for guiding, evaluating and testing our theories of specific-ion effects. Here, the literature on specific-ion effects in non-aq. solvents is surveyed with a view to detg. if the Hofmeister series or lyotropic series so universally obsd. in aq. systems is widely evident in non-aq. systems. Particular attention has been applied to expts. on non-aq. systems that are known to exhibit Hofmeister series in aq. systems with the aim of detg. if a consistent ion ordering in the strength of specific-ion effects is obsd. in other solvents. We find that specific-ion effects are ubiquitous in non-aq. solvents, that both Hofmeister and lyotropic series are widely obsd., although not necessarily for the same class of expt. Moreover, we find that Hofmeister and lyotropic series are obsd. in non-aq. solvents even for expts. in which these series are not obsd. for water. Addnl., series reversal is seen for a given expt. when the solvent is changed. All this poses significant challenges for our understanding of specific-ion effects in aq. and non-aq. systems and also provides guideposts for future investigations.
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    Rosenholm, J. B. Evaluation of particle charging in non-aqueous suspensions. Adv. Colloid Interface Sci. 2018, 259, 21– 43,  DOI: 10.1016/j.cis.2018.06.004
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    Evaluation of particle charging in non-aqueous suspensions
    Rosenholm, Jarl B.
    Advances in Colloid and Interface Science (2018), 259 (), 21-43CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)
    Factors influencing the sign and size of effective surface (zeta) potential in suspensions of very low dielec. consts. are evaluated. For non-aq. suspensions it was found that Gutmann's donor no. (DN = neg. Lewis type molar acid-base adduct formation enthalpy) was successfully related to zeta potential changes, similarly as pH is optimal for aq. suspensions. Neg. molar proton dissocn. enthalpy (Br.vphi.nsted type HD no.), neg. hydrogen bond enthalpy (HB no.), logarithmic hydrogen bond equil. const. (molar Gibbs free energy), std. redn. potential of solvated protons (Eo(H+L/H2)), electrolytic dissocn. potential of water (Eo(H2O/H2, O2)) and electron exchange Fermi potentials could equally well be related to zeta potential changes. All these properties were linearly dependent on each other. When evaluating factors contributing to attractive and repulsive interaction energies, it is found that in order for the models to be relevant the extension of diffuse charging has to be much larger than the distance to repulsive barrier ensuring suspension stability. At this limit and at high surface potentials, the repulsive energy grows exceptionally large being in the range of lattice energy of each solid. The models fail when surface potential is low and the extension of diffuse charging is much smaller than the distance to repulsive barrier.
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    Iwai, S.; Suzuki, T.; Sakagami, H.; Miyamoto, K.; Chen, Z.; Konishi, M.; Villani, E.; Shida, N.; Tomita, I.; Inagi, S. Electropolymerization without an electric power supply. Commun. Chem. 2022, 5, 66,  DOI: 10.1038/s42004-022-00682-8
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    Electropolymerization without an electric power supply
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    Communications Chemistry (2022), 5 (1), 66CODEN: CCOHCT; ISSN:2399-3669. (Nature Portfolio)
    Abstr.: Electrifying synthesis is now a common slogan among synthetic chemists. In addn. to the conventional two- or three-electrode systems that use batch-type cells, recent progress in org. electrochem. processes has been significant, including microflow electrochem. reactors, Li-ion battery-like technol., and bipolar electrochem. Herein we demonstrate an advanced electrosynthesis method without the application of elec. power based on the concept of streaming potential-driven bipolar electrochem. As a proof-of-concept study, the electrochem. oxidative polymn. of arom. monomers successfully yielded the corresponding polymer films on an electrode surface, which acted as an anode under the flow of electrolyte in a microchannel without an elec. power supply.
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    Kolthoff, I. M. Acid-base equilibriums in dipolar aprotic solvents. Anal. Chem. 1974, 46, 1992– 2003,  DOI: 10.1021/ac60349a005
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    Acid-base equilibriums in dipolar aprotic solvents
    Kolthoff, I. M.
    Analytical Chemistry (1974), 46 (13), 1992-2003CODEN: ANCHAM; ISSN:0003-2700.
    A classification of org. solvents is proposed. The main emphasis is on the effect of homo- and heteroconjugate formation by H bonding on acid-base equilibria and on conductometric and potentiometric titrn. curves in dipolar aprotic solvents. The relation is discussed between resolution of acid strength and transfer activity coeffs. of ions and mols. A brief review is presented of analytical uses of protophobic solvents for the titrn. of very weak bases and of protophilic solvents for the titrn. of very weak acids. 77 Refs.
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    Rossini, E.; Knapp, E. Proton solvation in protic and aprotic solvents. J. Comput. Chem. 2016, 37, 1082– 1091,  DOI: 10.1002/jcc.24297
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    Proton solvation in protic and aprotic solvents
    Rossini, Emanuele; Knapp, Ernst-Walter
    Journal of Computational Chemistry (2016), 37 (12), 1082-1091CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    Protonation pattern strongly affects the properties of mol. systems. To det. protonation equil., proton solvation free energy, which is a central quantity in soln. chem., needs to be known. In this study, proton affinities (PAs), electrostatic energies of solvation, and pKA values were computed in protic and aprotic solvents. The proton solvation energy in acetonitrile (MeCN), methanol, water, and DMSO was detd. from computed and measured pKA values for a specially selected set of org. compds. pKA values were computed with high accuracy using a combination of quantum chem. and electrostatic approaches. Quantum chem. d. functional theory computations were performed evaluating PA in the gas-phase. The electrostatic contributions of solvation were computed solving the Poisson equation. The computations yield proton solvation free energies with high accuracy, which are in MeCN, MeOH, water, and DMSO -255.1, -265.9, -266.3, and -266.4 kcal/mol, resp., where the value for water is close to the consensus value of -265.9 kcal/mol. The pKA values of MeCN, MeOH, and DMSO in water correlates well with the corresponding proton solvation energies in these liqs., indicating that the solvated proton was attached to a single solvent mol. © 2016 Wiley Periodicals, Inc.
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    Rossini, E.; Bochevarov, A. D.; Knapp, E. W. Empirical Conversion of pKa Values between Different Solvents and Interpretation of the Parameters: Application to Water, Acetonitrile, Dimethyl Sulfoxide, and Methanol. ACS Omega 2018, 3, 1653– 1662,  DOI: 10.1021/acsomega.7b01895
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    Empirical Conversion of pKa Values between Different Solvents and Interpretation of the Parameters: Application to Water, Acetonitrile, Dimethyl Sulfoxide, and Methanol
    Rossini, Emanuele; Bochevarov, Art D.; Knapp, Ernst Walter
    ACS Omega (2018), 3 (2), 1653-1662CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)
    An empirical conversion method (ECM) that transforms pKa values of arbitrary org. compds. from one solvent to the other is introduced. We demonstrate the method's usefulness and performance on pKa conversions involving water and org. solvents acetonitrile (MeCN), DMSO (Me2SO), and methanol (MeOH). We focus on the pKa conversion from the known ref. value in water to the other three org. solvents, although such a conversion can also be performed between any pair of the considered solvents. The ECM works with an additive parameter that is specific to a solvent and a mol. family (essentially characterized by a functional group that is titrated). We formally show that the method can be formulated with a single additive parameter, and that the extra multiplicative parameter used in other works is not required. The values of the additive parameter are detd. from known pKa data, and their interpretation is provided on the basis of physicochem. concepts. The data set of known pKa values is augmented with pKa values computed with the recently introduced electrostatic transform method, whose validity is demonstrated. For a validation of our method, we consider pKa conversions for two data sets of titratable compds. The first data set involves 81 relatively small mols. belonging to 19 different mol. families, with the pKa data available in all four considered solvents. The second data set involves 76 titratable mols. from 5 addnl. mol. families. These mols. are typically larger, and their exptl. pKa values are available only in Me2SO and water. The validation tests show that the agreement between the exptl. pKa data and the ECM predictions is generally good, with abs. errors often on the order of 0.5 pH units. The presence of a few outliers is rationalized, and obsd. trends with respect to mol. families are discussed.
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    Constitution of the Electric Charge at the Surface of an Electrolyte
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    Chapman, D. L. A contribution to the theory of electrocapillarity. London Edinb. Philos. Mag. 1913, 25, 475– 481,  DOI: 10.1080/14786440408634187
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    Langmuir, I. THE ADSORPTION OF GASES ON PLANE SURFACES OF GLASS, MICA AND PLATINUM. J. Am. Chem. Soc. 1918, 40, 1361– 1403,  DOI: 10.1021/ja02242a004
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    The adsorption of gases on plane surfaces of glass, mica and platinum
    Langmuir, I.
    Journal of the American Chemical Society (1918), 40 (), 1361-1402CODEN: JACSAT; ISSN:0002-7863.
    According to L.'s hypothesis, gaseous mols. impinging on a liquid or solid surface do not in general rebound from it elastically, but are held or adsorbed on the surface by forces similar to those holding the atoms or group mols. of solid bodies. The adsorbed film should not exceed one mol. in thickness. Adsorption of permanent gases involves only secondary valence forces. In metals particularly, adsorption may be governed by primary valence forces. It is suggested that stoichiometric relations should govern the adsorption on a surface unless interfering effects caused by steric hindrance are involved. At room temp. the absorption by glass and mica was negligible, not over 1 % of the surface being covered by a single layer of mols. At lower temps. much larger quantities of gas were taken up. With Pt no absorption was observed at - 183° unless the Pt were first activated by proper heating. The adsorption of O2 was irreversible and corresponded to a monomolecular layer. CO likewise showed the same behavior. In the presence of one or the other gas adsorbed on the Pt the adsorbed and unadsorbed gases reacted immediately to form CO2.
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    Electrokinetic flow in a narrow cylindrical capillary
    Rice, C. L.; Whitehead, R.
    Journal of Physical Chemistry (1965), 69 (11), 4017-24CODEN: JPCHAX; ISSN:0022-3654.
    An anal. study was made of electrokinetic flow in cylindrical capillaries with radii on the order of 10-5 cm. The work extends that of Burgreen and Nakache (CA 61, 15683b). Expressions are given for electroosmosis, streaming potential, and c.d. distribution. The results lead to a prediction of a max. in the electroviscous effect.
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    Goldfarb, D. L.; Longinotti, M. P.; Corti, H. R. Electrical Conductances of Tetrabutylammonium and Decamethylferrocenium Hexafluorophosphate in Organic Solvents. J. Solution Chem. 2001, 30, 307– 322,  DOI: 10.1023/A:1010334021934
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    Hiemstra, T.; De Wit, J.; Van Riemsdijk, W. Multisite proton adsorption modeling at the solid/solution interface of (hydr)oxides: A new approach. J. Colloid Interface Sci. 1989, 133, 105– 117,  DOI: 10.1016/0021-9797(89)90285-3
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    Multisite proton adsorption modeling at the solid/solution interface of (hydr)oxides: a new approach. II. Application to various important (hydr)oxides
    Hiemstra, T.; De Wit, J. C. M.; Van Riemsdijk, W. H.
    Journal of Colloid and Interface Science (1989), 133 (1), 105-17CODEN: JCISA5; ISSN:0021-9797.
    At the solid/soln. interface of metal (hydro)oxides various types of O(H) and OH(H) groups are present, which differ in th no. of coordinating metal ions. The σ0-pH curves of metal (hydr)oxides are strongly detd. by the compn. and the relative extent of the various crystal planes of (hydr)oxides. The charging behavior is discuss for gibbsite (Al(OH)3), goethite (FeOOH), hematite (Fe2O3), rutile (TiO2), and silica (SiO2. New exptl. σ0-pH data for goethite and gibbsite are presented. Several important (hydr)oxides exhibit crystal faces which do not develop surface charge over a relatively wide pH range. An uncharged crystal face may be due to the presence of surface groups which are not reactive (inert) in the pH range under consideration, like the 001 face of gibbsite ad the 0001 face of hematite, or caused by the presence of two types of interacting charged surface groups of which the charge of one type is fully compensated by the other like at the 100 face of goethite. The charging behavior of silica and the 001 face of gibbsite is detd. by one type of reactive surface group with a large ΔpK for the consecutive protonation steps. The crystal structure imposes the presence of uncharged surface groups and this results in a quite different shape of σ0-pH curves for gibbsite and silica in comparison with the commonly obsd. σ0-pH curves for gibbsite and silica in comparison with the commonly obsd. σ0-pH curves of metal (hydr)oxides. The MUltiSIte complexation (MUSIC) model as developed by T. Hiemstra, et al. (1989) leads to a rather good prediction of σ0-pH curves for various metal (hydr)oxides using predicted affinity consts. for the various types of surface groups and Stern layer capacitance values and pair formation consts. estd. from the literature.
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    The charge of glass and silica surfaces
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    Journal of Chemical Physics (2001), 115 (14), 6716-6721CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present a method of calcg. the elec. charge d. of glass and silica surfaces in contact with aq. electrolytes for two cases of practical relevance that are not amenable to std. techniques: surfaces of low specific area at low ionic strength and surfaces interacting strongly with a second anionic surface.
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    Bialik, E.; Stenqvist, B.; Fang, Y.; Östlund, Å.; Furó, I.; Lindman, B.; Lund, M.; Bernin, D. Ionization of Cellobiose in Aqueous Alkali and the Mechanism of Cellulose Dissolution. J. Phys. Chem. Lett. 2016, 7, 5044– 5048,  DOI: 10.1021/acs.jpclett.6b02346
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    Ionization of Cellobiose in Aqueous Alkali and the Mechanism of Cellulose Dissolution
    Bialik, Erik; Stenqvist, Bjoern; Fang, Yuan; Oestlund, Aasa; Furo, Istvan; Lindman, Bjoern; Lund, Mikael; Bernin, Diana
    Journal of Physical Chemistry Letters (2016), 7 (24), 5044-5048CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Cellulose, one of the most abundant renewable resources, is insol. in most common solvents but dissolves in aq. alkali under a narrow range of conditions. To elucidate the solubilization mechanism, we performed electrophoretic NMR on cellobiose, a subunit of cellulose, showing that cellobiose acts as an acid with two dissocn. steps at pH 12 and 13.5. Chem. shift differences between cellobiose in NaOH and NaCl were estd. using 2D NMR and compared to DFT shift differences upon deprotonation. The dissocn. steps are the deprotonation of the hemiacetal OH group and the deprotonation of one of four OH groups on the nonreducing anhydroglucose unit. MD simulations reveal that aggregation is suppressed upon charging cellulose chains in soln. Our findings strongly suggest that cellulose is to a large extent charged in concd. aq. alkali, a seemingly crucial factor for solubilization. This insight, overlooked in the current literature, is important for understanding cellulose dissoln. and for synthesis of new sustainable materials.
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    Malerz, S.; Mudryk, K.; Tomaník, L.; Stemer, D.; Hergenhahn, U.; Buttersack, T.; Trinter, F.; Seidel, R.; Quevedo, W.; Goy, C.; Wilkinson, I.; Thürmer, S.; Slavíček, P.; Winter, B. Following in Emil Fischer’s Footsteps: A Site-Selective Probe of Glucose Acid–Base Chemistry. J. Phys. Chem. A 2021, 125, 6881– 6892,  DOI: 10.1021/acs.jpca.1c04695
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    Following in Emil Fischer's Footsteps: A Site-Selective Probe of Glucose Acid-Base Chemistry
    Malerz, Sebastian; Mudryk, Karen; Tomanik, Lukas; Stemer, Dominik; Hergenhahn, Uwe; Buttersack, Tillmann; Trinter, Florian; Seidel, Robert; Quevedo, Wilson; Goy, Claudia; Wilkinson, Iain; Thuermer, Stephan; Slavicek, Petr; Winter, Bernd
    Journal of Physical Chemistry A (2021), 125 (32), 6881-6892CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    Liq.-jet photoelectron spectroscopy was applied to det. the first acid dissocn. const. (pKa) of aq.-phase glucose while simultaneously identifying the spectroscopic signature of the resp. deprotonation site. Valence spectra from solns. at pH values below and above the first pKa reveal a change in glucose's lowest ionization energy upon the deprotonation of neutral glucose and the subsequent emergence of its anionic counterpart. Site-specific insights into the soln.-pH-dependent mol. structure changes are also shown to be accessible via C 1s photoelectron spectroscopy. The spectra reveal a considerably lower C 1s binding energy of the carbon site assocd. with the deprotonated hydroxyl group. The occurrence of photoelectron spectral fingerprints of cyclic and linear glucose prior to and upon deprotonation are also discussed. The exptl. data are interpreted with the aid of electronic structure calcns. Our findings highlight the potential of liq.-jet photoelectron spectroscopy to act as a site-selective probe of the mol. structures that underpin the acid-base chem. of polyprotic systems with relevance to environmental chem. and biochem.
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    Uematsu, Y.; Bonthuis, D. J.; Netz, R. R. Charged Surface-Active Impurities at Nanomolar Concentration Induce Jones–Ray Effect. J. Phys. Chem. Lett. 2018, 9, 189– 193,  DOI: 10.1021/acs.jpclett.7b02960
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    Charged Surface-Active Impurities at Nanomolar Concentration Induce Jones-Ray Effect
    Uematsu, Yuki; Bonthuis, Douwe Jan; Netz, Roland R.
    Journal of Physical Chemistry Letters (2018), 9 (1), 189-193CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    The electrolyte surface tension exhibits a characteristic min. around a salt concn. of 1 mM for all ion types, known as the Jones-Ray effect. A consistent description of the exptl. surface tension of salts, bases, and acids is possible by assuming charged impurities in the water with a surface affinity typical for surfactants. Comparison with exptl. data yields an impurity concn. in the nanomolar range, well below the typical exptl. detection limit. Modeling reveals salt-screening enhanced impurity adsorption as the mechanism behind the Jones-Ray effect: for very low salt concn. added salt screens the electrostatic repulsion between impurities at the surface, which dramatically increases impurity adsorption and thereby reduces the surface tension.
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    Plett, T.; Shi, W.; Zeng, Y.; Mann, W.; Vlassiouk, I.; Baker, L. A.; Siwy, Z. S. Rectification of nanopores in aprotic solvents–transport properties of nanopores with surface dipoles. Nanoscale 2015, 7, 19080– 19091,  DOI: 10.1039/C5NR06340J
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    Nasir, S.; Ali, M.; Ramirez, P.; Froehlich, K.; Cervera, J.; Mafe, S.; Ensinger, W. Ionic conduction through single-pore and multipore polymer membranes in aprotic organic electrolytes. J. Membr. Sci. 2021, 635, 119505  DOI: 10.1016/j.memsci.2021.119505
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    Ionic conduction through single-pore and multipore polymer membranes in aprotic organic electrolytes
    Nasir, Saima; Ali, Mubarak; Ramirez, Patricio; Froehlich, Kristina; Cervera, Javier; Mafe, Salvador; Ensinger, Wolfgang
    Journal of Membrane Science (2021), 635 (), 119505CODEN: JMESDO; ISSN:0376-7388. (Elsevier B.V.)
    We exptl. characterize the ionic conduction of single and multipore nanoporous membranes in aprotic org. electrolytes. To this end, soft-etched (SE) membranes with pore diams. in the nanometer range and track-etched (TE) membranes with pore diams. in the tens of nanometers range are investigated. In aq. conditions, the membrane ionic conduction rates follow the same trend of the bulk soln. conductivities. However, the ionic transport through the narrow SE-nanopores dramatically decreases in aprotic electrolytes due to the formation of solvated metal cations and their adsorption on the pore surface. The current-voltage recordings of single conical nanopores in aprotic electrolyte solns. with different water mole fractions reveal that the solvated metal ion (M) species [M-(solvent)4]+ formed in acetonitrile solvent are more tightly bounded to the pore walls compared with the cationic chelates obtained in propylene carbonate solvent. The basic findings reported here should be of interest for ionic/mol. nanofiltration processes in non-aq. conditions as well as for moisture sensitive and energy storage nanofluidic devices.
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    Polster, J. W.; Souna, A. J.; Motevaselian, M. H.; Lucas, R. A.; Tran, J. D.; Siwy, Z. S.; Aluru, N. R.; Fourkas, J. T. The electrical-double layer revisited. Nat. Sci. 2022, 2, e20210099  DOI: 10.1002/ntls.20210099
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    Souna, A. J.; Motevaselian, M. H.; Polster, J. W.; Tran, J. D.; Siwy, Z. S.; Aluru, N. R.; Fourkas, J. T. Beyond the electrical double layer model: ion-dependent effects in nanoscale solvent organization. Phys. Chem. Chem. Phys. 2024, 26, 6726– 6735,  DOI: 10.1039/D3CP05712G
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    Ionic Current Rectification in Organic Solutions with Quartz Nanopipettes
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  • Abstract

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    Figure 1

    Figure 1. Illustration of the experimental setup. The volume flux of the sample solution, Q, is controlled by the pump, whereas the pressure difference Δp and the voltage difference Δψ are measured. The zero current condition I = 0 is satisfied because the electric circuit is open.

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    Figure 2

    Figure 2. (a) Streaming potential of cotton membranes filled with acetonitrile as a function of the Bu4NPF6 concentration when a solution flux of Q = 0.5 mL/min was applied. (b) Induced pressure difference as a function of the Bu4NPF6 concentration. The color represents the different cotton membranes #1 (red circle), #2 (blue triangle), and #3 (green square). Measurements in ascending order of the salt concentrations (→ in the label) are shown with open symbols and solid lines, whereas measurements in descending order (← in the label) are shown with filled symbols and broken lines.

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    Figure 3

    Figure 3. Bulk conductivity of a Bu4NPF6 solution in acetonitrile as a function of concentration. The solid line represents the linear fit calculated by the molar limiting conductivity of the salts, 164.8 S·cm2/mol. (41) The broken line is a guide for the eye.

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    Figure 4

    Figure 4. (a) Zeta potentials of the cotton/acetonitrile interface as a function of Bu4NPF6 concentration. The points are derived from experimental data using eq 1 whereas the lines represent theoretical fits based on eqs 2 and 3 with α– = −1.2 and Γ0 as denoted in the figure. Other parameters are z* = 0.5 nm, ε = 35.9, and T = 298 K. Due to the lack of experimental bulk conductivity data at low salinity, the linear slope from Figure 3 was used to calculate the zeta potential for the membrane #3. (b) Zeta potentials of the silica/acetonitrile interface as a function of salt concentration. (36) The original data are provided in Figure 2a of the ref (36). as the electro-osmotic mobility. Zeta potentials were calculated using ζ = −(η/εε0)μ, where η/εε0 = 1.08 × 106 s·V2/m2. The solid line is calculated using eq 2 with ε = 35.9, T = 298 K, and σ0 = −0.08 e/nm2.

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    Figure 5

    Figure 5. (a) Zeta potential of a cotton membrane filled with a LiBF4 solution in acetonitrile, calculated using the data shown in b–d, and eq 1. (b) Streaming potential of the cotton membrane with a flux of Q = 0.5 mL/min, data previously published. (32) (c) Induced pressure difference across the cotton membrane. (d) Bulk conductivity of the LiBF4 solution in acetonitrile. The solid line represents the linear fit of the experimental data, with a molar limiting conductivity of 165.5 S·cm2/mol. The broken lines in a–c are guides for the eye.

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    Figure 6

    Figure 6. Scanning electron microscopy images of the cotton membrane. (a) The scale bar is 100 μm. (b) The scale bar is 50 μm.

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    Figure 7

    Figure 7. Normalized pressure difference as a function of Bu4NPF6 concentration. Theoretical curves are calculated using eqs 3, 8, and 9 with the parameters α– = −1.2, z* = 0.5 nm, Γ0 = 0.003/nm2, ε = 35.9, T = 298 K, η = 0.344 mPa·s, λ+ = 61.3 S·cm2/mol, and λ– = 103.5 S·cm2/mol. Experimental data points are for Bu4NPF6 solutions where Δp0 is used for the pressure difference at c = 5 mM for membranes #1 and #2 and at 1 mM for membrane #3.

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      Schwer, Christine; Kenndler, Ernst
      Analytical Chemistry (1991), 63 (17), 1801-7CODEN: ANCHAM; ISSN:0003-2700.
      The influence of pH and solvent compn. on the electroosmotic flow in fused-silica capillaries was studied. Binary mixts. of H2O and a protic (MeOH, EtOH, iso-PrOH) or an aprotic dipolar solvent (MeCN, Me2CO, DMSO) were used for the buffer electrolyte. The dependence of the electroosmotic flow on the pH was detd. in the pH range from 3 to 11 for pure aq. soln. and for solns. contg. 50 vol.% org. solvent. Adding org. solvents to the electrolyte, the inflection points of the resulting curves, corresponding to the pK values of the surface silanol groups, are shifted to higher values. At high pH, increasing the fraction of org. cosolvent generally decreases the electroosmotic velocity. Zeta potentials were calcd. from the Smoluchowski equation by using electroosmotic velocity data and values for the ratio of the viscosity coeff. and dielec. const. for binary mixts., taken from the authors own measurements and from the literature. With the exception of Me2CO-H2O mixts., the ζ potentials obtained show a similar trend to that of the electroosmotic velocity; they decrease with increasing content of org. solvent. This trend is explained by changes of the dielec. properties of the elec. double layer and of the charge generation on the fused-silica surface.
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    10. 10
      Wright, P. B.; Lister, A. S.; Dorsey, J. G. Behavior and Use of Nonaqueous Media without Supporting Electrolyte in Capillary Electrophoresis and Capillary Electrochromatography. Anal. Chem. 1997, 69, 3251– 3259,  DOI: 10.1021/ac9613186
      10
      Behavior and Use of Nonaqueous Media without Supporting Electrolyte in Capillary Electrophoresis and Capillary Electrochromatography
      Wright, Paul B.; Lister, Ashley S.; Dorsey, John G.
      Analytical Chemistry (1997), 69 (16), 3251-3259CODEN: ANCHAM; ISSN:0003-2700. (American Chemical Society)
      Five nonaq. solvents (acetonitrile, methanol, DMF, DMSO, formamide) and deionized water were studied for their ability to support electroosmotic flow (EOF) without electrolytic additives. In general, flow is equal to or greater than flow with typical CE buffer systems. The magnitude of EOF was detd. for each solvent by open tubular capillary electrophoresis (CE) and related to viscosity (η), dielec. const. (ε), and the ratio of dielec. const. to viscosity (ε/η). Zeta potentials (ζ) were derived indirectly from flow data and tabulated. Comparisons of flow behavior and ζ were made between pure solvents and conventional CE buffers, and questions of equilibration and reproducibility were addressed. Similar expts. were performed using hydroorg. mobile phases (ACN/water, MeOH/water) across the complete compositional range (100% water-100% org.), with flow characteristics and ζ reported for each mobile phase system. Packed capillary columns (5-μm ODS) were evaluated for flow and retention stability under capillary electrochromatog. (CEC) conditions. A sepn. of 11 polycyclic arom. hydrocarbons was performed in under 13 min by CEC with an ACN/water mobile phase. Reduced plate heights (h) were calcd. between 2.5 and 3.0 for solutes with capacity factors (k') up to 4.5 for the most retained solute.
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    11. 11
      Tjo̷rnelund, J.; Hansen, S. H. The effect of water on separations in non-aqueous capillary electrophoresis systems. Chromatographia 1997, 44, 5– 9,  DOI: 10.1007/BF02466508
      There is no corresponding record for this reference.
    12. 12
      Valkó, I. E.; Sirén, H.; Riekkola, M.-L. Characteristics of electroosmotic flow in capillary electrophoresis in water and in organic solvents without added ionic species. J. Microcolumn Sep. 1999, 11, 199– 208,  DOI: 10.1002/(SICI)1520-667X(1999)11:3<199::AID-MCS5>3.0.CO;2-D
      12
      Characteristics of electroosmotic flow in capillary electrophoresis in water and in organic solvents without added ionic species
      Valko, Istvan E.; Siren, Heli; Riekkola, Marja-Liisa
      Journal of Microcolumn Separations (1999), 11 (3), 199-208CODEN: JMSEEJ; ISSN:1040-7685. (John Wiley & Sons, Inc.)
      Although proper buffering is essential for repeatable sepns. in capillary electrophoresis, electroosmotic flow can be developed in many solvents without the addn. of buffer components. In this study we detected electroosmotic flow in fused silica capillary in the following solvents without the addn. of ionic species: water, deuterium oxide, acetonitrile, acetone, 2-butanone, formamide, N-methylformamide, N,N-dimethylformamide, methanol, ethanol, 1-propanol, DMSO, Et acetate, THF, and morpholine. The electroosmotic flow was in the range of 3.4 X 10-9-1.8 X 10-7 m2/V s. About 100 times weaker electroosmosis was detected in glacial acetic acid. We also detected electroosmotic flow in N-methylacetamide, which is solid at room temp. (melting range 28-30°C). No electroosmotic flow was found in inert solvents such as n-hexane and chloroform. The zeta potential of the fused silica capillary was calcd. for the solvents where electroosmotic flow was found. The zeta potential of the capillary wall was also studied in water-methanol mixts., where it has a max. at about 40% methanol concn.
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    13. 13
      Riekkola, M.-L.; Jussila, M.; Porras, S. P.; Valkó, I. E. Non-aqueous capillary electrophoresis. J. Chromatogr. A 2000, 892, 155– 170,  DOI: 10.1016/S0021-9673(00)00108-4
      There is no corresponding record for this reference.
    14. 14
      Geiser, L.; Mirgaldi, M.; Veuthey, J.-L. Determination of electroosmotic flow in nonaqueous capillary electrophoresis. J. Chromatogr. A 2005, 1068, 75– 81,  DOI: 10.1016/j.chroma.2005.02.001
      There is no corresponding record for this reference.
    15. 15
      Kitahara, A. Zeta potential in nonaqueous media and its effect on dispersion stability. Prog. Org. Coat. 1973, 2, 81– 98,  DOI: 10.1016/0300-9440(73)80001-3
      15
      Zeta potential in nonaqueous media and its effect on dispersion stability
      Kitahara, Ayao
      Progress in Organic Coatings (1973), 2 (2), 81-98CODEN: POGCAT; ISSN:0300-9440.
      A review is given with 38 refs. The properties and stability of org. coatings in relation to zeta potential are also discussed.
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    16. 16
      Fowkes, F. Dispersions of ceramic powders in organic media. Adv. Ceram.: Ceram. Powder Sci. 1987, 21, 411– 421
      There is no corresponding record for this reference.
    17. 17
      Van Der Hoeven, P.; Lyklema, J. Electrostatic stabilization in non-aqueous media. Adv. Colloid Interface Sci. 1992, 42, 205– 277,  DOI: 10.1016/0001-8686(92)80024-R
      17
      Electrostatic stabilization in non-aqueous media
      Van der Hoeven, Ph. C.; Lyklema, J.
      Advances in Colloid and Interface Science (1992), 42 (), 205-77CODEN: ACISB9; ISSN:0001-8686.
      A review on electrostatic stabilization of non-aq. dispersions with particular emphasis on the roles of dielec. const. and ionic strength. The liq. dielec. const. controls the degree of ionization of the stabilizing electrolyte and 3 regimes (semipolar, low-polar, apolar) can be distinguished. When attraction between suspended salt particles in nonionic liqs. is weak, electrostatic stabilization is achieved easily. 107 Refs.
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    18. 18
      Siffert, B.; Jada, A.; Eleli-Letsango, J. Stability Calculations of TiO2 Nonaqueous Suspensions: Thickness of the Electrical Double Layer. J. Colloid Interface Sci. 1994, 167, 281– 286,  DOI: 10.1006/jcis.1994.1362
      There is no corresponding record for this reference.
    19. 19
      Hughes, D. F. K.; Robb, I. D.; Dowding, P. J. Stability of Copper Phthalocyanine Dispersions in Organic Media. Langmuir 1999, 15, 5227– 5231,  DOI: 10.1021/la981389v
      19
      Stability of Copper Phthalocyanine Dispersions in Organic Media
      Hughes, D. F. K.; Robb, Ian D.; Dowding, Peter J.
      Langmuir (1999), 15 (16), 5227-5231CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      It was found that quite small surface potentials (a few millivolts) were sufficient to stabilize the dil. dispersions of the particles in solvents of low dielec. const. (possibly because this would be a const. charge system) though insufficient to stabilize particles in solvents with dielec. consts. above about 20. Addn. of org. acids enhanced the particles' stability, probably by a proton-exchange mechanism, and addn. of an org.-sol. electrolyte, tetrabutylammonium bromide, caused all systems to flocculate. The presence of a polymer at concns. above about 1% caused flocculation to occur, probably by a depletion mechanism. The attractive depletion energy increased with polymer concn., resulting in the sedimentation vol. increasing with polymer concn.
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    20. 20
      Kosmulski, M. Zeta potentials in nonaqueous media: how to measure and control them. Colloids Surf., A 1999, 159, 277– 281,  DOI: 10.1016/S0927-7757(99)00273-3
      20
      Zeta potentials in nonaqueous media. How to measure and control them
      Kosmulski, M.
      Colloids and Surfaces, A: Physicochemical and Engineering Aspects (1999), 159 (2-3), 277-281CODEN: CPEAEH; ISSN:0927-7757. (Elsevier Science B.V.)
      A review, with 20 refs. The effect of traces of water in nonaq. solvents on the ζ-potential is overrated, and the role of impurities in presumably pure org. solvents is often overlooked. Oxides can serve as potentiometric sensors to det. the concn. and nature of impurities. Even in very inert solvents the counter-charge in soln. must exist. Small ions are stabilized by homoconjugation and by amphiphilic nonionic compds. The electrokinetic phenomena of the second kind are more common in nonaq. solvents and they lead to very high abs. values of mobility at high field strengths.
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    21. 21
      Kosmulski, M.; Eriksson, P.; Brancewicz, C.; Rosenholm, J. B. Zeta potentials of monodispersed, spherical silica particles in mixed solvents as a function of cesium chloride concentration. Colloids Surf., A 2000, 162, 37– 48,  DOI: 10.1016/S0927-7757(99)00027-8
      21
      Zeta potentials of monodispersed, spherical silica particles in mixed solvents as a function of cesium chloride concentration
      Kosmulski, Marek; Eriksson, Patrik; Brancewicz, Chris; Rosenholm, Jarl B.
      Colloids and Surfaces, A: Physicochemical and Engineering Aspects (2000), 162 (1-3), 37-48CODEN: CPEAEH; ISSN:0927-7757. (Elsevier Science B.V.)
      Zeta potentials of silica are neg. in most mixed solvents (99% org. co-solvent, 1% water), but in t-butanol and pyridine they are pos. When CsCl is added to the suspension as a probe substance, two types of behavior are obsd. In solvents of ε >25, the zeta potential asymptotically approaches zero, while in solvents of lower dielec. const., the sign of zeta potential is reversed to pos. at a sufficiently high CsCl concn., crev. To evaluate the nature of interaction leading to different solvent responses, a range of frequently used solvent scales relating to specific interactions between the components of the system were compared. A moderate correlation was found between crev for silica and one solvent property alone, and those previously found for anatase, resp. Using linear combinations of 2 solvent scales improved the correlation, but it was still not satisfactory. However, considering sep. the contributions from both solvent components, a nearly statistically significant correlation was found. The results are evaluated considering the particular behavior of each solvent group, and the specific influence of the material properties of silica and of possible impurities present in the system.
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    22. 22
      Zhukov, A. Integrated investigations of the electrosurface properties of nonaqueous disperse and capillary systems. Adv. Colloid Interface Sci. 2007, 134–135, 330– 345,  DOI: 10.1016/j.cis.2007.04.014
      There is no corresponding record for this reference.
    23. 23
      Hamieh, T.; Toufaily, J.; Alloul, H. Physicochemical Properties of the Dispersion of Titanium Dioxide in Organic Media by Using Zetametry Technique. J. Dispers. Sci. Technol. 2008, 29, 1181– 1188,  DOI: 10.1080/01932690701856626
      There is no corresponding record for this reference.
    24. 24
      Kosmulski, M.; Prochniak, P.; Rosenholm, J. B. Control of the Zeta Potential in Semiconcentrated Dispersions of Titania in Polar Organic Solvents. J. Phys. Chem. C 2009, 113, 12806– 12810,  DOI: 10.1021/jp903845e
      24
      Control of the Zeta Potential in Semiconcentrated Dispersions of Titania in Polar Organic Solvents
      Kosmulski, Marek; Prochniak, Piotr; Rosenholm, Jarl B.
      Journal of Physical Chemistry C (2009), 113 (29), 12806-12810CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      The electrokinetic potential of com. titania powder (chiefly anatase) in its 1-10% dispersions in water, lower aliph. alcs., and DMSO is pos., and rather insensitive to the nature of the solvent. The sign of the electrokinetic potential can be reversed to neg. by addn. of phosphoric acid, or of combination of phosphoric acid with triethylamine or with alkali hydroxide. The crit. concn. of surface-active compds., which induces a sign reversal, depends on the nature of the solvent, and it is higher in org. solvents than in water. The crit. surface concn. of surface-active compds. for given org. solvent is rather insensitive to the solid-to-liq. ratio, and typically it is in the range of a few micromoles per square meter.
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    25. 25
      Cihlar, J.; Drdlik, D.; Cihlarova, Z.; Hadraba, H. Effect of acids and bases on electrophoretic deposition of alumina and zirconia particles in 2-propanol. J. Eur. Ceram. Soc. 2013, 33, 1885– 1892,  DOI: 10.1016/j.jeurceramsoc.2013.02.017
      There is no corresponding record for this reference.
    26. 26
      Lyklema, J. Principles of interactions in non-aqueous electrolyte solutions. Curr. Opin. Colloid Interface Sci. 2013, 18, 116– 128,  DOI: 10.1016/j.cocis.2013.02.002
      26
      Principles of interactions in non-aqueous electrolyte solutions
      Lyklema, Johannes
      Current Opinion in Colloid & Interface Science (2013), 18 (2), 116-128CODEN: COCSFL; ISSN:1359-0294. (Elsevier Ltd.)
      In this paper a review is presented on the mol. interactions in non-aq. media of low dielec. permittivity. Qual. and quant. distinctions with aq. solns. are emphasized. The reviewed themes include dispersion forces, dissocn. and assocn. equil., discrimination between electrostatic and non-electrostatic interactions, ionic specificity, cond., electrokinetics and colloid interaction. Distinctions between so-called primitive and non-primitive interpretations and between individual and collective behavior are discussed; in these respects the colloid stability phenomena behave differently from the corresponding ones in aq. solvents.
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    27. 27
      Mazzini, V.; Craig, V. S. Specific-ion effects in non-aqueous systems. Curr. Opin. Colloid Interface Sci. 2016, 23, 82– 93,  DOI: 10.1016/j.cocis.2016.06.009
      27
      Specific-ion effects in non-aqueous systems
      Mazzini, Virginia; Craig, Vincent S. J.
      Current Opinion in Colloid & Interface Science (2016), 23 (), 82-93CODEN: COCSFL; ISSN:1359-0294. (Elsevier Ltd.)
      A review. It is widely acknowledged that specific-ion effects are ubiquitous in aq. systems and undoubtedly are essential to the fundamental processes of life, although a deep fundamental understanding of specific-ion effects remains an important challenge. Specific-ion effects in non-aq. solvents are known but have attracted far less attention, yet knowledge of specific-ion effects in non-aq. systems is likely to provide important information for guiding, evaluating and testing our theories of specific-ion effects. Here, the literature on specific-ion effects in non-aq. solvents is surveyed with a view to detg. if the Hofmeister series or lyotropic series so universally obsd. in aq. systems is widely evident in non-aq. systems. Particular attention has been applied to expts. on non-aq. systems that are known to exhibit Hofmeister series in aq. systems with the aim of detg. if a consistent ion ordering in the strength of specific-ion effects is obsd. in other solvents. We find that specific-ion effects are ubiquitous in non-aq. solvents, that both Hofmeister and lyotropic series are widely obsd., although not necessarily for the same class of expt. Moreover, we find that Hofmeister and lyotropic series are obsd. in non-aq. solvents even for expts. in which these series are not obsd. for water. Addnl., series reversal is seen for a given expt. when the solvent is changed. All this poses significant challenges for our understanding of specific-ion effects in aq. and non-aq. systems and also provides guideposts for future investigations.
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    28. 28
      Rosenholm, J. B. Evaluation of particle charging in non-aqueous suspensions. Adv. Colloid Interface Sci. 2018, 259, 21– 43,  DOI: 10.1016/j.cis.2018.06.004
      28
      Evaluation of particle charging in non-aqueous suspensions
      Rosenholm, Jarl B.
      Advances in Colloid and Interface Science (2018), 259 (), 21-43CODEN: ACISB9; ISSN:0001-8686. (Elsevier B.V.)
      Factors influencing the sign and size of effective surface (zeta) potential in suspensions of very low dielec. consts. are evaluated. For non-aq. suspensions it was found that Gutmann's donor no. (DN = neg. Lewis type molar acid-base adduct formation enthalpy) was successfully related to zeta potential changes, similarly as pH is optimal for aq. suspensions. Neg. molar proton dissocn. enthalpy (Br.vphi.nsted type HD no.), neg. hydrogen bond enthalpy (HB no.), logarithmic hydrogen bond equil. const. (molar Gibbs free energy), std. redn. potential of solvated protons (Eo(H+L/H2)), electrolytic dissocn. potential of water (Eo(H2O/H2, O2)) and electron exchange Fermi potentials could equally well be related to zeta potential changes. All these properties were linearly dependent on each other. When evaluating factors contributing to attractive and repulsive interaction energies, it is found that in order for the models to be relevant the extension of diffuse charging has to be much larger than the distance to repulsive barrier ensuring suspension stability. At this limit and at high surface potentials, the repulsive energy grows exceptionally large being in the range of lattice energy of each solid. The models fail when surface potential is low and the extension of diffuse charging is much smaller than the distance to repulsive barrier.
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    29. 29
      Barthel, J.; Gores, H.-J.; Schmeer, G.; Wachter, R. Topics in Current Chemistry; Springer: Berlin Heidelberg, 1983; pp 33– 144.
      There is no corresponding record for this reference.
    30. 30
      Izutsu, K. Electrochemistry in Nonaqueous Solutions; Wiley-VCH Verlag GmbH & Co. KGaA, 2002.
      There is no corresponding record for this reference.
    31. 31
      Iwasaki, H.; Kimura, Y.; Uematsu, Y. Ubiquitous Preferential Water Adsorption to Electrodes in Water/1-Propanol Mixtures Detected by Electrochemical Impedance Spectroscopy. J. Phys. Chem. C 2023, 127, 23382– 23389,  DOI: 10.1021/acs.jpcc.3c05320
      There is no corresponding record for this reference.
    32. 32
      Iwai, S.; Suzuki, T.; Sakagami, H.; Miyamoto, K.; Chen, Z.; Konishi, M.; Villani, E.; Shida, N.; Tomita, I.; Inagi, S. Electropolymerization without an electric power supply. Commun. Chem. 2022, 5, 66,  DOI: 10.1038/s42004-022-00682-8
      32
      Electropolymerization without an electric power supply
      Iwai, Suguru; Suzuki, Taichi; Sakagami, Hiroki; Miyamoto, Kazuhiro; Chen, Zhenghao; Konishi, Mariko; Villani, Elena; Shida, Naoki; Tomita, Ikuyoshi; Inagi, Shinsuke
      Communications Chemistry (2022), 5 (1), 66CODEN: CCOHCT; ISSN:2399-3669. (Nature Portfolio)
      Abstr.: Electrifying synthesis is now a common slogan among synthetic chemists. In addn. to the conventional two- or three-electrode systems that use batch-type cells, recent progress in org. electrochem. processes has been significant, including microflow electrochem. reactors, Li-ion battery-like technol., and bipolar electrochem. Herein we demonstrate an advanced electrosynthesis method without the application of elec. power based on the concept of streaming potential-driven bipolar electrochem. As a proof-of-concept study, the electrochem. oxidative polymn. of arom. monomers successfully yielded the corresponding polymer films on an electrode surface, which acted as an anode under the flow of electrolyte in a microchannel without an elec. power supply.
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    33. 33
      Kolthoff, I. M. Acid-base equilibriums in dipolar aprotic solvents. Anal. Chem. 1974, 46, 1992– 2003,  DOI: 10.1021/ac60349a005
      33
      Acid-base equilibriums in dipolar aprotic solvents
      Kolthoff, I. M.
      Analytical Chemistry (1974), 46 (13), 1992-2003CODEN: ANCHAM; ISSN:0003-2700.
      A classification of org. solvents is proposed. The main emphasis is on the effect of homo- and heteroconjugate formation by H bonding on acid-base equilibria and on conductometric and potentiometric titrn. curves in dipolar aprotic solvents. The relation is discussed between resolution of acid strength and transfer activity coeffs. of ions and mols. A brief review is presented of analytical uses of protophobic solvents for the titrn. of very weak bases and of protophilic solvents for the titrn. of very weak acids. 77 Refs.
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    34. 34
      Rossini, E.; Knapp, E. Proton solvation in protic and aprotic solvents. J. Comput. Chem. 2016, 37, 1082– 1091,  DOI: 10.1002/jcc.24297
      34
      Proton solvation in protic and aprotic solvents
      Rossini, Emanuele; Knapp, Ernst-Walter
      Journal of Computational Chemistry (2016), 37 (12), 1082-1091CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      Protonation pattern strongly affects the properties of mol. systems. To det. protonation equil., proton solvation free energy, which is a central quantity in soln. chem., needs to be known. In this study, proton affinities (PAs), electrostatic energies of solvation, and pKA values were computed in protic and aprotic solvents. The proton solvation energy in acetonitrile (MeCN), methanol, water, and DMSO was detd. from computed and measured pKA values for a specially selected set of org. compds. pKA values were computed with high accuracy using a combination of quantum chem. and electrostatic approaches. Quantum chem. d. functional theory computations were performed evaluating PA in the gas-phase. The electrostatic contributions of solvation were computed solving the Poisson equation. The computations yield proton solvation free energies with high accuracy, which are in MeCN, MeOH, water, and DMSO -255.1, -265.9, -266.3, and -266.4 kcal/mol, resp., where the value for water is close to the consensus value of -265.9 kcal/mol. The pKA values of MeCN, MeOH, and DMSO in water correlates well with the corresponding proton solvation energies in these liqs., indicating that the solvated proton was attached to a single solvent mol. © 2016 Wiley Periodicals, Inc.
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    35. 35
      Rossini, E.; Bochevarov, A. D.; Knapp, E. W. Empirical Conversion of pKa Values between Different Solvents and Interpretation of the Parameters: Application to Water, Acetonitrile, Dimethyl Sulfoxide, and Methanol. ACS Omega 2018, 3, 1653– 1662,  DOI: 10.1021/acsomega.7b01895
      35
      Empirical Conversion of pKa Values between Different Solvents and Interpretation of the Parameters: Application to Water, Acetonitrile, Dimethyl Sulfoxide, and Methanol
      Rossini, Emanuele; Bochevarov, Art D.; Knapp, Ernst Walter
      ACS Omega (2018), 3 (2), 1653-1662CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)
      An empirical conversion method (ECM) that transforms pKa values of arbitrary org. compds. from one solvent to the other is introduced. We demonstrate the method's usefulness and performance on pKa conversions involving water and org. solvents acetonitrile (MeCN), DMSO (Me2SO), and methanol (MeOH). We focus on the pKa conversion from the known ref. value in water to the other three org. solvents, although such a conversion can also be performed between any pair of the considered solvents. The ECM works with an additive parameter that is specific to a solvent and a mol. family (essentially characterized by a functional group that is titrated). We formally show that the method can be formulated with a single additive parameter, and that the extra multiplicative parameter used in other works is not required. The values of the additive parameter are detd. from known pKa data, and their interpretation is provided on the basis of physicochem. concepts. The data set of known pKa values is augmented with pKa values computed with the recently introduced electrostatic transform method, whose validity is demonstrated. For a validation of our method, we consider pKa conversions for two data sets of titratable compds. The first data set involves 81 relatively small mols. belonging to 19 different mol. families, with the pKa data available in all four considered solvents. The second data set involves 76 titratable mols. from 5 addnl. mol. families. These mols. are typically larger, and their exptl. pKa values are available only in Me2SO and water. The validation tests show that the agreement between the exptl. pKa data and the ECM predictions is generally good, with abs. errors often on the order of 0.5 pH units. The presence of a few outliers is rationalized, and obsd. trends with respect to mol. families are discussed.
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    36. 36
      Borissova, M.; Gorbatšova, J.; Ebber, A.; Kaljurand, M.; Koel, M.; Vaher, M. Nonaqueous CE using contactless conductivity detection and ionic liquids as BGEs in ACN. Electrophoresis 2007, 28, 3600– 3605,  DOI: 10.1002/elps.200700067
      There is no corresponding record for this reference.
    37. 37
      Gouy, M. Sur la constitution de la charge électrique à la surface d’un électrolyte. J. Phys. Theor. Appl. 1910, 9, 457– 468,  DOI: 10.1051/jphystap:019100090045700
      37
      Constitution of the Electric Charge at the Surface of an Electrolyte
      Gouy
      (1910), 9 (), 457-67 ISSN:.
      An amplification of an article previously abstracted (C. A., 4, 698).
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    38. 38
      Chapman, D. L. A contribution to the theory of electrocapillarity. London Edinb. Philos. Mag. 1913, 25, 475– 481,  DOI: 10.1080/14786440408634187
      There is no corresponding record for this reference.
    39. 39
      Langmuir, I. THE ADSORPTION OF GASES ON PLANE SURFACES OF GLASS, MICA AND PLATINUM. J. Am. Chem. Soc. 1918, 40, 1361– 1403,  DOI: 10.1021/ja02242a004
      39
      The adsorption of gases on plane surfaces of glass, mica and platinum
      Langmuir, I.
      Journal of the American Chemical Society (1918), 40 (), 1361-1402CODEN: JACSAT; ISSN:0002-7863.
      According to L.'s hypothesis, gaseous mols. impinging on a liquid or solid surface do not in general rebound from it elastically, but are held or adsorbed on the surface by forces similar to those holding the atoms or group mols. of solid bodies. The adsorbed film should not exceed one mol. in thickness. Adsorption of permanent gases involves only secondary valence forces. In metals particularly, adsorption may be governed by primary valence forces. It is suggested that stoichiometric relations should govern the adsorption on a surface unless interfering effects caused by steric hindrance are involved. At room temp. the absorption by glass and mica was negligible, not over 1 % of the surface being covered by a single layer of mols. At lower temps. much larger quantities of gas were taken up. With Pt no absorption was observed at - 183° unless the Pt were first activated by proper heating. The adsorption of O2 was irreversible and corresponded to a monomolecular layer. CO likewise showed the same behavior. In the presence of one or the other gas adsorbed on the Pt the adsorbed and unadsorbed gases reacted immediately to form CO2.
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    40. 40
      Rice, C. L.; Whitehead, R. Electrokinetic Flow in a Narrow Cylindrical Capillary. J. Phys. Chem. 1965, 69, 4017– 4024,  DOI: 10.1021/j100895a062
      40
      Electrokinetic flow in a narrow cylindrical capillary
      Rice, C. L.; Whitehead, R.
      Journal of Physical Chemistry (1965), 69 (11), 4017-24CODEN: JPCHAX; ISSN:0022-3654.
      An anal. study was made of electrokinetic flow in cylindrical capillaries with radii on the order of 10-5 cm. The work extends that of Burgreen and Nakache (CA 61, 15683b). Expressions are given for electroosmosis, streaming potential, and c.d. distribution. The results lead to a prediction of a max. in the electroviscous effect.
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    41. 41
      Goldfarb, D. L.; Longinotti, M. P.; Corti, H. R. Electrical Conductances of Tetrabutylammonium and Decamethylferrocenium Hexafluorophosphate in Organic Solvents. J. Solution Chem. 2001, 30, 307– 322,  DOI: 10.1023/A:1010334021934
      There is no corresponding record for this reference.
    42. 42
      Hiemstra, T.; De Wit, J.; Van Riemsdijk, W. Multisite proton adsorption modeling at the solid/solution interface of (hydr)oxides: A new approach. J. Colloid Interface Sci. 1989, 133, 105– 117,  DOI: 10.1016/0021-9797(89)90285-3
      42
      Multisite proton adsorption modeling at the solid/solution interface of (hydr)oxides: a new approach. II. Application to various important (hydr)oxides
      Hiemstra, T.; De Wit, J. C. M.; Van Riemsdijk, W. H.
      Journal of Colloid and Interface Science (1989), 133 (1), 105-17CODEN: JCISA5; ISSN:0021-9797.
      At the solid/soln. interface of metal (hydro)oxides various types of O(H) and OH(H) groups are present, which differ in th no. of coordinating metal ions. The σ0-pH curves of metal (hydr)oxides are strongly detd. by the compn. and the relative extent of the various crystal planes of (hydr)oxides. The charging behavior is discuss for gibbsite (Al(OH)3), goethite (FeOOH), hematite (Fe2O3), rutile (TiO2), and silica (SiO2. New exptl. σ0-pH data for goethite and gibbsite are presented. Several important (hydr)oxides exhibit crystal faces which do not develop surface charge over a relatively wide pH range. An uncharged crystal face may be due to the presence of surface groups which are not reactive (inert) in the pH range under consideration, like the 001 face of gibbsite ad the 0001 face of hematite, or caused by the presence of two types of interacting charged surface groups of which the charge of one type is fully compensated by the other like at the 100 face of goethite. The charging behavior of silica and the 001 face of gibbsite is detd. by one type of reactive surface group with a large ΔpK for the consecutive protonation steps. The crystal structure imposes the presence of uncharged surface groups and this results in a quite different shape of σ0-pH curves for gibbsite and silica in comparison with the commonly obsd. σ0-pH curves for gibbsite and silica in comparison with the commonly obsd. σ0-pH curves of metal (hydr)oxides. The MUltiSIte complexation (MUSIC) model as developed by T. Hiemstra, et al. (1989) leads to a rather good prediction of σ0-pH curves for various metal (hydr)oxides using predicted affinity consts. for the various types of surface groups and Stern layer capacitance values and pair formation consts. estd. from the literature.
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    43. 43
      Behrens, S. H.; Grier, D. G. The charge of glass and silica surfaces. J. Chem. Phys. 2001, 115, 6716– 6721,  DOI: 10.1063/1.1404988
      43
      The charge of glass and silica surfaces
      Behrens, Sven H.; Grier, David G.
      Journal of Chemical Physics (2001), 115 (14), 6716-6721CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We present a method of calcg. the elec. charge d. of glass and silica surfaces in contact with aq. electrolytes for two cases of practical relevance that are not amenable to std. techniques: surfaces of low specific area at low ionic strength and surfaces interacting strongly with a second anionic surface.
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    44. 44
      Bialik, E.; Stenqvist, B.; Fang, Y.; Östlund, Å.; Furó, I.; Lindman, B.; Lund, M.; Bernin, D. Ionization of Cellobiose in Aqueous Alkali and the Mechanism of Cellulose Dissolution. J. Phys. Chem. Lett. 2016, 7, 5044– 5048,  DOI: 10.1021/acs.jpclett.6b02346
      44
      Ionization of Cellobiose in Aqueous Alkali and the Mechanism of Cellulose Dissolution
      Bialik, Erik; Stenqvist, Bjoern; Fang, Yuan; Oestlund, Aasa; Furo, Istvan; Lindman, Bjoern; Lund, Mikael; Bernin, Diana
      Journal of Physical Chemistry Letters (2016), 7 (24), 5044-5048CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Cellulose, one of the most abundant renewable resources, is insol. in most common solvents but dissolves in aq. alkali under a narrow range of conditions. To elucidate the solubilization mechanism, we performed electrophoretic NMR on cellobiose, a subunit of cellulose, showing that cellobiose acts as an acid with two dissocn. steps at pH 12 and 13.5. Chem. shift differences between cellobiose in NaOH and NaCl were estd. using 2D NMR and compared to DFT shift differences upon deprotonation. The dissocn. steps are the deprotonation of the hemiacetal OH group and the deprotonation of one of four OH groups on the nonreducing anhydroglucose unit. MD simulations reveal that aggregation is suppressed upon charging cellulose chains in soln. Our findings strongly suggest that cellulose is to a large extent charged in concd. aq. alkali, a seemingly crucial factor for solubilization. This insight, overlooked in the current literature, is important for understanding cellulose dissoln. and for synthesis of new sustainable materials.
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    45. 45
      Malerz, S.; Mudryk, K.; Tomaník, L.; Stemer, D.; Hergenhahn, U.; Buttersack, T.; Trinter, F.; Seidel, R.; Quevedo, W.; Goy, C.; Wilkinson, I.; Thürmer, S.; Slavíček, P.; Winter, B. Following in Emil Fischer’s Footsteps: A Site-Selective Probe of Glucose Acid–Base Chemistry. J. Phys. Chem. A 2021, 125, 6881– 6892,  DOI: 10.1021/acs.jpca.1c04695
      45
      Following in Emil Fischer's Footsteps: A Site-Selective Probe of Glucose Acid-Base Chemistry
      Malerz, Sebastian; Mudryk, Karen; Tomanik, Lukas; Stemer, Dominik; Hergenhahn, Uwe; Buttersack, Tillmann; Trinter, Florian; Seidel, Robert; Quevedo, Wilson; Goy, Claudia; Wilkinson, Iain; Thuermer, Stephan; Slavicek, Petr; Winter, Bernd
      Journal of Physical Chemistry A (2021), 125 (32), 6881-6892CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      Liq.-jet photoelectron spectroscopy was applied to det. the first acid dissocn. const. (pKa) of aq.-phase glucose while simultaneously identifying the spectroscopic signature of the resp. deprotonation site. Valence spectra from solns. at pH values below and above the first pKa reveal a change in glucose's lowest ionization energy upon the deprotonation of neutral glucose and the subsequent emergence of its anionic counterpart. Site-specific insights into the soln.-pH-dependent mol. structure changes are also shown to be accessible via C 1s photoelectron spectroscopy. The spectra reveal a considerably lower C 1s binding energy of the carbon site assocd. with the deprotonated hydroxyl group. The occurrence of photoelectron spectral fingerprints of cyclic and linear glucose prior to and upon deprotonation are also discussed. The exptl. data are interpreted with the aid of electronic structure calcns. Our findings highlight the potential of liq.-jet photoelectron spectroscopy to act as a site-selective probe of the mol. structures that underpin the acid-base chem. of polyprotic systems with relevance to environmental chem. and biochem.
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    46. 46
      Uematsu, Y.; Bonthuis, D. J.; Netz, R. R. Charged Surface-Active Impurities at Nanomolar Concentration Induce Jones–Ray Effect. J. Phys. Chem. Lett. 2018, 9, 189– 193,  DOI: 10.1021/acs.jpclett.7b02960
      46
      Charged Surface-Active Impurities at Nanomolar Concentration Induce Jones-Ray Effect
      Uematsu, Yuki; Bonthuis, Douwe Jan; Netz, Roland R.
      Journal of Physical Chemistry Letters (2018), 9 (1), 189-193CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      The electrolyte surface tension exhibits a characteristic min. around a salt concn. of 1 mM for all ion types, known as the Jones-Ray effect. A consistent description of the exptl. surface tension of salts, bases, and acids is possible by assuming charged impurities in the water with a surface affinity typical for surfactants. Comparison with exptl. data yields an impurity concn. in the nanomolar range, well below the typical exptl. detection limit. Modeling reveals salt-screening enhanced impurity adsorption as the mechanism behind the Jones-Ray effect: for very low salt concn. added salt screens the electrostatic repulsion between impurities at the surface, which dramatically increases impurity adsorption and thereby reduces the surface tension.
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    47. 47
      Plett, T.; Shi, W.; Zeng, Y.; Mann, W.; Vlassiouk, I.; Baker, L. A.; Siwy, Z. S. Rectification of nanopores in aprotic solvents–transport properties of nanopores with surface dipoles. Nanoscale 2015, 7, 19080– 19091,  DOI: 10.1039/C5NR06340J
      There is no corresponding record for this reference.
    48. 48
      Nasir, S.; Ali, M.; Ramirez, P.; Froehlich, K.; Cervera, J.; Mafe, S.; Ensinger, W. Ionic conduction through single-pore and multipore polymer membranes in aprotic organic electrolytes. J. Membr. Sci. 2021, 635, 119505  DOI: 10.1016/j.memsci.2021.119505
      48
      Ionic conduction through single-pore and multipore polymer membranes in aprotic organic electrolytes
      Nasir, Saima; Ali, Mubarak; Ramirez, Patricio; Froehlich, Kristina; Cervera, Javier; Mafe, Salvador; Ensinger, Wolfgang
      Journal of Membrane Science (2021), 635 (), 119505CODEN: JMESDO; ISSN:0376-7388. (Elsevier B.V.)
      We exptl. characterize the ionic conduction of single and multipore nanoporous membranes in aprotic org. electrolytes. To this end, soft-etched (SE) membranes with pore diams. in the nanometer range and track-etched (TE) membranes with pore diams. in the tens of nanometers range are investigated. In aq. conditions, the membrane ionic conduction rates follow the same trend of the bulk soln. conductivities. However, the ionic transport through the narrow SE-nanopores dramatically decreases in aprotic electrolytes due to the formation of solvated metal cations and their adsorption on the pore surface. The current-voltage recordings of single conical nanopores in aprotic electrolyte solns. with different water mole fractions reveal that the solvated metal ion (M) species [M-(solvent)4]+ formed in acetonitrile solvent are more tightly bounded to the pore walls compared with the cationic chelates obtained in propylene carbonate solvent. The basic findings reported here should be of interest for ionic/mol. nanofiltration processes in non-aq. conditions as well as for moisture sensitive and energy storage nanofluidic devices.
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    49. 49
      Polster, J. W.; Souna, A. J.; Motevaselian, M. H.; Lucas, R. A.; Tran, J. D.; Siwy, Z. S.; Aluru, N. R.; Fourkas, J. T. The electrical-double layer revisited. Nat. Sci. 2022, 2, e20210099  DOI: 10.1002/ntls.20210099
      There is no corresponding record for this reference.
    50. 50
      Souna, A. J.; Motevaselian, M. H.; Polster, J. W.; Tran, J. D.; Siwy, Z. S.; Aluru, N. R.; Fourkas, J. T. Beyond the electrical double layer model: ion-dependent effects in nanoscale solvent organization. Phys. Chem. Chem. Phys. 2024, 26, 6726– 6735,  DOI: 10.1039/D3CP05712G
      There is no corresponding record for this reference.
    51. 51
      Yin, X.; Zhang, S.; Dong, Y.; Liu, S.; Gu, J.; Chen, Y.; Zhang, X.; Zhang, X.; Shao, Y. Ionic Current Rectification in Organic Solutions with Quartz Nanopipettes. Anal. Chem. 2015, 87, 9070– 9077,  DOI: 10.1021/acs.analchem.5b02337
      51
      Ionic Current Rectification in Organic Solutions with Quartz Nanopipettes
      Yin, Xiaohong; Zhang, Shudong; Dong, Yitong; Liu, Shujuan; Gu, Jing; Chen, Ye; Zhang, Xin; Zhang, Xianhao; Shao, Yuanhua
      Analytical Chemistry (Washington, DC, United States) (2015), 87 (17), 9070-9077CODEN: ANCHAM; ISSN:0003-2700. (American Chemical Society)
      The study of behaviors of ionic current rectification (ICR) in org. solns. with quartz nanopipettes is reported. ICR can be obsd. even in org. solns. using quartz pipets with diams. varied from several to dozens of nanometers, and the direction of ICR is quite different from the ICR obsd. in aq. phase. The influences of pore size, electrolyte concn., and surface charge on the ICR were studied carefully. Water in org. solns. affects the direction and extent of ICR significantly. Mechanisms about the formation of an elec. double layer (EDL) on silica in org. solns. with different amt. of water are proposed. An improved method, which can be employed to detect trace water in org. solns., was implemented based on Au ultramicroelectrodes with cathodic differential pulse stripping voltammetry.
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    52. 52
      Spångberg, D.; Hermansson, K. The solvation of Li+ and Na+ in acetonitrile from ab initio-derived many-body ion–solvent potentials. Chem. Phys. 2004, 300, 165– 176,  DOI: 10.1016/j.chemphys.2004.01.011
      52
      The solvation of Li+ and Na+ in acetonitrile from ab initio-derived many-body ion-solvent potentials
      Spangberg, Daniel; Hermansson, Kersti
      Chemical Physics (2004), 300 (1-3), 165-176CODEN: CMPHC2; ISSN:0301-0104. (Elsevier Science B.V.)
      Several Li+- and Na+-acetonitrile models were derived from ab initio calcns. at the counterpoise-cor. MP2/TZV++(d,p) level for distorted ion-(MeCN)n clusters with n=1, 4 and 6. Two different many-body ion-acetonitrile models were constructed: an effective three-body potential for use with the six-site effective pair model of Bohm et al., and an effective polarizable many-body model. The polarizable acetonitrile model used in the latter model is a new empirical model which was also derived in the present paper. Mainly for comparative purposes, two ion-acetonitrile pair potentials were also constructed from the ab initio cluster calcns.: one pure pair potential and one effective pair potential. Using all these potential models, MD simulations in the NPT ensemble were performed for the pure acetonitrile liq. and for Li+(MeCN) and Na+(MeCN) solns. with 1 ion in 512 solvent mols. and with a simulation time of at least 120 ps per system. Thermodn. properties, solvation-shell structure and the self-diffusion coeff. of the ions and of the solvent mols. were calcd. and compared between the different models and with exptl. data, where available. The Li+ ion is found to be four-coordinated when the new many-body potentials are used, in contrast to the six-coordinated structure obtained for the pure pair and effective pair potentials. The coordination no. of Na+ is close to six for all the models derived here, although the coordination no. becomes slightly smaller with the many-body potentials. For both ions, the solvent mols. in the first shell point their nitrogen ends towards the cation, while in the second shell the opposite orientation is the most common.
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    53. 53
      Amara, S.; Toulc’Hoat, J.; Timperman, L.; Biller, A.; Galiano, H.; Marcel, C.; Ledigabel, M.; Anouti, M. Comparative Study of Alkali-Cation-Based (Li+, Na+, K+) Electrolytes in Acetonitrile and Alkylcarbonates. ChemPhysChem 2019, 20, 581– 594,  DOI: 10.1002/cphc.201801064
      53
      Comparative Study of Alkali-Cation-Based (Li+, Na+, K+) Electrolytes in Acetonitrile and Alkylcarbonates
      Amara, Samia; Toulc'Hoat, Joel; Timperman, Laure; Biller, Agnes; Galiano, Herve; Marcel, Corinne; Ledigabel, Matthieu; Anouti, Meriem
      ChemPhysChem (2019), 20 (4), 581-594CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The development of a suitable functional electrolyte is urgently required for fast-charging and high-voltage alkali-ion (Li, Na, K) batteries as well as next-generation hybrids supercapacitors. Many recent works focused on an optimal selection of electrolytes for alkali-ion based systems and their electrochem. performance but the understanding of the fundamental aspect that explains their different behavior is rare. Herein, we report a comparative study of transport properties for LiPF6, NaPF6, KPF6 in acetonitrile (AN) and a binary mixt. of ethylene carbonate (EC), di-Me carbonate (DMC): (EC/DMC : 1/1, weigh) through conductivities, densities and viscosities measurements in wide temp. domain. By application of the Stokes-Einstein, Nernst-Einstein, and Jones Dole equations, the effective ionic solvated radius of cation (reff), the ionic dissocn. coeff. (αD) and structuring Jones Dole's parameters (A, B) for salt are calcd. and discussed according to solvent or cation nature as a function of temp. From the results, we demonstrate that better mobility of potassium can be explained by the nature of the ion-ion and ion-solvent interactions due to its polarizability. In the same time, the predominance of triple ions in the case of K+, is a disadvantage at high concn.
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    54. 54
      Ding, F.; Hu, Z.; Zhong, Q.; Manfred, K.; Gattass, R. R.; Brindza, M. R.; Fourkas, J. T.; Walker, R. A.; Weeks, J. D. Interfacial Organization of Acetonitrile: Simulation and Experiment. J. Phys. Chem. C 2010, 114, 17651– 17659,  DOI: 10.1021/jp104597z
      54
      Interfacial Organization of Acetonitrile: Simulation and Experiment
      Ding, Feng; Hu, Zhonghan; Zhong, Qin; Manfred, Katherine; Gattass, Rafael R.; Brindza, Michael R.; Fourkas, John T.; Walker, Robert A.; Weeks, John D.
      Journal of Physical Chemistry C (2010), 114 (41), 17651-17659CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Mol. dynamics simulations and vibrational sum frequency generation (VSFG) expts. in the methyl-stretching spectral region have been used to study acetonitrile at the silica/liq., silica/vapor, and liq./vapor interfaces. Our simulations show that, at the silica/liq. interface, acetonitrile takes on a considerably different structure than in the bulk liq. The interfacial structure is reminiscent of a lipid bilayer, and this type of ordering persists for tens of Ångstroms into the bulk liq. This result has important implications for processes involving solid/acetonitrile interfaces, such as heterogeneous catalysis and chromatog. sepns. Fitting of VSFG data that have an extremely low nonresonant background contribution provides strong evidence for interfacial populations pointing in opposite directions at these interfaces, in agreement with our simulations. The picture developed from our simulations and expts. reconciles conflicting interpretations of data from previous exptl. studies of interfacial acetonitrile.
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    55. 55
      Pusić, T.; Grancarić, A. M.; Soljaçić, I.; Ribitsch, V. The effect of mercerisation on the electrokinetic potential of cotton. Color. Technol. 1999, 115, 121– 124,  DOI: 10.1111/j.1478-4408.1999.tb00308.x
      There is no corresponding record for this reference.
    56. 56
      Sadeghi-Kiakhani, M.; Safapour, S. Salt-free reactive dyeing of the cotton fabric modified with chitosan-poly(propylene imine) dendrimer hybrid. Fibers and Polym. 2015, 16, 1075– 1081,  DOI: 10.1007/s12221-015-1075-9
      There is no corresponding record for this reference.
    57. 57
      Grancarić, A. M.; Tarbuk, A.; Hadžić, S.; Simončič, B. From Raw to Finished Cotton─Characterization by Interface Phenomena. Autex Res. J. 2023, 23, 184– 192,  DOI: 10.2478/aut-2021-0055
      There is no corresponding record for this reference.
    58. 58
      Uematsu, Y.; Bonthuis, D. J.; Netz, R. R. Nanomolar Surface-Active Charged Impurities Account for the Zeta Potential of Hydrophobic Surfaces. Langmuir 2020, 36, 3645– 3658,  DOI: 10.1021/acs.langmuir.9b03795
      58
      Nanomolar Surface-Active Charged Impurities Account for the Zeta Potential of Hydrophobic Surfaces
      Uematsu, Yuki; Bonthuis, Douwe Jan; Netz, Roland R.
      Langmuir (2020), 36 (13), 3645-3658CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      The electrification of hydrophobic surfaces is an intensely debated subject in phys. chem. We theor. study the ζ potential of hydrophobic surfaces for varying pH and salt concn. by solving the Poisson-Boltzmann and Stokes equations with individual ionic adsorption affinities. Using the ionic surface affinities extd. from the exptl. measured surface tension of the air-electrolyte interface, we first show that the interfacial adsorption and repulsion of small inorg. ions such as H3O+, OH-, HCO3-, and CO32- cannot account for the ζ potential obsd. in expts. because the surface affinities of these ions are too small. Even if we take hydrodynamic slip into account, the characteristic dependence of the ζ potential on pH and salt concn. cannot be reproduced. Instead, to explain the sizable exptl. measured ζ potential of hydrophobic surfaces, we assume minute amts. of impurities in the water and include the impurities' acidic and basic reactions with water. We find good agreement between our predictions and the reported exptl. ζ potential data of various hydrophobic surfaces if we account for impurities that consist of a mixt. of weak acids (pKa = 5-7) and weak bases (pKb = 12) at a concn. of the order of 10-7 M.
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    59. 59
      Sghaier, S.; Zbidi, F.; Zidi, M. Characterization of Doum Palm Fibers After Chemical Treatment. Text. Res. J. 2009, 79, 1108– 1114,  DOI: 10.1177/0040517508101623
      There is no corresponding record for this reference.
    60. 60
      Brož, Z.; Epstein, N. Electrokinetic flow through porous media composed of fine cylindrical capillaries. J. Colloid Interface Sci. 1976, 56, 605– 612,  DOI: 10.1016/0021-9797(76)90127-2
      There is no corresponding record for this reference.
    61. 61
      Levine, S.; Marriott, J.; Neale, G.; Epstein, N. Theory of electrokinetic flow in fine cylindrical capillaries at high zeta-potentials. J. Colloid Interface Sci. 1975, 52, 136– 149,  DOI: 10.1016/0021-9797(75)90310-0
      There is no corresponding record for this reference.
    62. 62
      Uematsu, Y.; Netz, R. R.; Bocquet, L.; Bonthuis, D. J. Crossover of the Power-Law Exponent for Carbon Nanotube Conductivity as a Function of Salinity. J. Phys. Chem. B 2018, 122, 2992– 2997,  DOI: 10.1021/acs.jpcb.8b01975
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      Crossover of the Power-Law Exponent for Carbon Nanotube Conductivity as a Function of Salinity
      Uematsu, Yuki; Netz, Roland R.; Bocquet, Lyderic; Bonthuis, Douwe Jan
      Journal of Physical Chemistry B (2018), 122 (11), 2992-2997CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      On the basis of the Poisson-Boltzmann equation in cylindrical coordinates, we calc. the cond. of a single charged nanotube filled with electrolyte. The cond. as a function of the salt concn. follows a power-law, the exponent of which has been controversially discussed in the literature. We use the co-ion-exclusion approxn. and obtain the crossover between different asymptotic power-law behaviors anal. Numerically solving the full Poisson-Boltzmann equation, we also calc. the complete diagram of exponents as a function of the salt concn. and the pH for tubes with different radii and pKa values. We apply our theory to recent exptl. results on carbon nanotubes using the pKa as a fit parameter. In good agreement with the exptl. data, the theory shows power-law behavior with the exponents 1/3 at high pH and 1/2 at low pH, with a crossover depending on salt concn., tube radius and pKa.
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