Ion size effects

It may seem that the prospeets are bleak for the GvdW approach to electrolytes but, in fact, the reverse is the ease. We need only follow Debye and Hiickel [18] into their analysis of the sereening meehanism, almost as successful as the van der Waals analysis of short-range fluids, to see that the mean-field approximation can be applied to the correlation mechanism with great advantage. In fact, we can then add finite ion size effects to the analysis and thereby unify these two most successful traditional theories. 

Thus we have found that the screening should be more efficient than in the Debye-Hiickel theory. The Debye length l//c is shorter by the factor 1 — jl due to the hard sphere holes cut in the Coulomb integrals which reduce the repulsion associated with counterion accumulation. A comparison with Monte Carlo simulation results [20] bears out this view of the ion size effect [19]. 

G. M. Torrie, P. G. Kusalik, and G. N. Patey,/. Chem. Phys., 91,6367 (1989). Theory of the Electrical Double Layer Ion Size Effects in Molecular Solvent. 

In the model, the smaller ion gives the stronger ion binding. However, it seems that in most cases other factors, e.g., ion hydration and ion polarizability, dominate over the ion size effect, particularly for anions, (cf. Sect. 4). 

As already stated in the preceding section, the PB equation neglects ion size effects and interparticle correlations. One route to improve the theory can be done on a density functional level. The PB equation can be derived via a variational principle out of a local density functional [25, 31]. This is also a convenient formulation to overcome its major deficiencies, namely the neglect of ion size effects and interparticle correlations. The Hohenberg-Kohn theorem gives an existence proof of a density functional that will produce the correct density profile upon variation. However, it does not specify its... 

Presence of ion transport control due to a strong disequilibrium between the concentration of cations in the electrolyte and the material, because ion diffusion constants vary over the gradients of ion activity coefficients, solvent content, and electrostatic ion size effects. 

In the limit of very dilute solutions where ion size effects may be neglected, equation (6.9.24) becomes... 

Fig. 6.10 Plot of the equivalent conductance of NaCl in water according to equation (6.9.1) against the square root of the ionic strength at 25°C. The solid curve shows the prediction of the Debye-Onsager equation with a = 0.4 nm, and the straight line, the prediction of this model in the limit that ion size effects may be neglected.

The electrolyte can also have another effect, not commonly recognized by many researchers, the chaotropic effect.40 This effect, more commonly discussed in biochemical circles, is related to variations in the water-structuring ability of different salts. This ability is used, for example, to dehydrate and salt out macromolecular proteins. The same effect can be expected with conducting polymers. As well as ion-size effects, this may be used to explain the large shifts in switching potentials observed in different electrolytes41 when the cation was varied and the difference in overoxidation potentials observed in different electrolytes.42... 

There have been considerable efforts to move beyond the simplified Gouy-Chapman description of double layers at the electrode-electrolyte interface, which are based on the solution of the Poisson-Boltzmann equation for point charges. So-called modified Poisson-Boltzmann (MPB) models have been developed to incorporate finite ion size effects into double layer theory [61]. An early attempt to apply such restricted primitive models of the double layer to the ITIES was made by Cui et al. [62], who treated the problem via the MPB4 approach and compared their results with experimental data for the more problematic water-DCE interface. This work allowed for the presence of the compact layer, although the potential drop across this layer was imposed, rather than emerging as a self-consistent result of the theory. The expression used to describe the potential distribution across this layer was... 

Solvent and Ion Size Effects to Achieve Higher Actuation... 

Franceschetti model involves relatively general boundary conditions at the electrodes and so includes the possibility of charge transfer reactions and specific adsorption. Because of its generality, however, the model prediction for Z,((o) is very complicated and, in general, cannot be well represented by even a complicated equivalent circuit. The Z,(m) expression, may, however, be used directly in CNLS fitting. Here, for simplicity, we shall consider only those specific situations where an approximate equivalent circuit is applicable. Idealizations involved in the model include the usual assumption of diffusion coefficients independent of field and position, the use of the simplified Chang-Jaff6 [1952] boundary conditions, and the omission of all inner layer and finite-ion-size effects. Some rectification of the latter two idealizations will be discussed later. 

Fawcett, W. R. 2009. Monte Carlo studies of ion size effects in the diffuse double layer. Electrochimica Acta 54, no. 22 4997-5005. doi 10.1016/j.electacta.2009.02.025. 

Smagala, T. G., and W. R. Fawcett. 2007. Series approach to modeling ion size effects for symmetric electrolytes in the diffuse double layer. The Journal of Physical Chemistry B 111, no. 6 1443-1448. doi 10.1021/jp067039w. 

The calculations we performed can only be reasonably interpreted on a quahtative basis, since we had to make several approximations. Moreover, the used models are continuum models and they break down at smaller distances, which are, however, important in our experiment. Ion-size effects and the discreteness of the charges have to be taken into consideration when discussing the interaction in more detail. It has been recog-... 

The comparison ofEq. (51)fromDFT andEq. (53) from PB clearly indicates the physical essence of the crude approximation involved in PB theory, i.e., both the ion size effect and correlation contribution are completely ignored, and therefore PB theory is applicable only for dilute electrolyte systems in which the direct Coulombic interaction dominates and the size effect is neghgible. 

Chowdhuri, S., and Chandra, A. 2003. Hydration structure and diffusion of ions in supercooled water Ion size effects. J. Chem. Phys. 118 9719. 

Interpretation of the Hofmeister Series Many different explanations of the Hofmeister series of ions have been proposed over the years. Specific ion interactions with specific sites of the biomolecules must be taken into account and a subtle balance of several competing evenly matched interactions, such as differences in hydration strength, dispersion forces, polarization, ion size effects, and the impact on interfacial water structure, is involved according to Koelsch et al. [116] and Tobias and Hemminger [117]. 

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