The Effect of the Capping Agents of Nanoparticles on Their Redox Potential

Engineered metallic nanoparticles, which are found in numerous applications, are usually stabilized by organic ligands influencing their interfacial properties. We found that the ligands affect tremendously the electrochemical peak oxidation potentials of the nanoparticles. In this work, identical gold nanoparticles were ligand-exchanged and carefully analyzed to enable a precise and highly reproducible comparison. The peak potential difference between gold nanoparticles stabilized by various ligands, such as 2- and 4-mercaptobenzoic acid, can be as high as 71 mV, which is substantial in energetic terms. A detailed study supported by density functional theory (DFT) calculations aimed to determine the source of this interesting effect. The DFT simulations of the ligand adsorption modes on Au surfaces were used to calculate the redox potentials through the thermodynamic cycle method. The DFT results of the peak potential shift were in good agreement with the experimental results for a few ligands, but showed some discrepancy, which was attributed to kinetic effects. The kinetic rate constant of the oxidation of Au nanoparticles stabilized by 4-mercaptobenzoic acid was found to be twice as large as that of the Au nanoparticles stabilized by citrate, as calculated from Laviron’s theory and the Tafel equation. Finally, these findings could be applied to some novel applications such as determining the distribution of nanoparticle population in a dispersion as well as monitoring the ligand exchange between nanoparticles.


Particles per surface from charge calculation
In order to calculate the amount of AuNPs dissolved from the surface, we look at the total charge,   , by taking the integral of the linear sweep voltammetry (LSV) peak.  -the charge under the LSV curve is proportional to the number of particles that dissolute from the surface through the relation: Where   is the total number of AuNPs that are immobilized on the surface and   is the charge achieved by oxidizing a single particle.By considering the full oxidation of all atoms in the NP to  3+ , the charge   , can be expressed as: Where  -= 1.6 ⋅ 10 -19  is the charge of an electron and   is the number of atoms in a single particle.
To calculate   , we start by looking at the unit cell of FCC Au with a lattice constant of 4.078Å. 1 The volume of each unit cell in the lattice is 67.82Å 3 , and there are 4 total atoms per unit cell.
Therefore, we get: Where   is the volume of each particle expressed as the volume of a sphere ( = 4 3  3 ) and   is the volume of the unit cell.
Assuming the mean radius of a particle across the surface is 50Å, the charge of a single particle derived from equation 2 and equation 3 is: The results for the number of particles oxidized per cm2 is given in Table 4.The curve for the clean Au (blue) is smooth as the surface slowly adapts to the elevation of the atom, and at around 5Å above the surface, the system energy converges.For the different ligands, the energy converges only when putting the loose atom higher, as there are geometric constraints of the molecules.For example, the 4-MBA molecule (yellow), which "stands" up as it is ordered in a self-assembled monolayer, converges only at larger distances from the slab itself where there is no interaction with the molecular layer.The sublimation energy for the third layer converges into a single value for all the different surfaces, as the effects inside the Au are not influenced by the surface chemistry but rather by the bulk metal.
For the 2-/4-MBA ligands the sublimation energy increases with the depth, which implies that the surface atoms are more likely to detach during the oxidation process, reinforcing the idea that atoms are initially extracted from the surface.
The clean Au on the other hand, shows a different behavior.The lowest sublimation energy is found for the second layer, whereas that of the third layer converges with the bulk.This phenomenon can be explained by the surface reconstruction of Au (111).The surface undergoes a surface reconstruction for the 22 × 3 supercell, where an additional atom from the bulk diffuses to the surface. 2 3 This shows that the 3 × 4 unit cell is unstable and the Au atom is therefore removed from the second layer in this case.

Plieth equation
Plieth's equation is: Where   and   are the oxidation potential of the AuNP and bulk gold, respectively.γ is the surface tension,   is the molar volume, z, and F, are the number of electrons and Faraday's constant, respectively.Finally, r is the radius of the NP.AuNPs-citrate AuNPs-4-MBA

Table S2 :
Comparison of number of particles per surface derived from equation 1 and equation 4. Mean NP radius is taken from size statistics of the SEM images of the different surfaces and total oxidation charge is integrated from Figure 1 curves.

Figure S4 :
Figure S4: Sublimation energy convergence vs. the height of the detached atom above the gold surface.

Figure S5 :
Figure S5: Sublimation energy vs. the layer from which the atom was removed.The weakest bound atom was chosen for each of the layers.

Figure S6 :
Figure S6: The oxidation potential shift of AuNPs as a function of their radius according to equation 5.For AuNPs with a diameter of 10 nm, the potential shift is −19.33 mV.

Figure S7 :
Figure S7: The displacement of the top Au layers of the electrode, by the adsorbed molecules.(A) Is the clean Au surface with the top layer at Z=9.37 Å. (B) Represents the lifting of the gold due to the adsorption of 2-MBA.The average of the lifted Au layer height is Z=9.54 Å, with the highest Au atom 0.51 Å above the average.(C) Shows the lifting of the Au by adsorbed 4-MBA.The average lifted Au layer height is Z=9.55 Å, with two Au atoms lifted 0.60 and 0.25 Å above the average for the FCC and HCP sites, respectively.

Figure S11 :
Figure S11: E p vs. the natural logarithm of the potential scan rate for the data shown in Figure 7 and their linear fits.