Electrostatic layer correction

This formula is called electrostatic layer correction (ELC) term [22] forces can be obtained by simple differentiation. Since this yields - up to a desired precision - the contribution of all periodic image layers, they can be subtracted from the result of a standard 3d-method with slabwise summation order to obtain the result for two periodic coordinates. In addition, the error estimates for MMM2D can be adapted for ELC, giving a maximal pairwise error of... 

A theoretical approach based on the electrical double layer correction has been proposed to explain the observed enhancement of the rate of ion transfer across zwitter-ionic phospholipid monolayers at ITIES [17]. If the orientation of the headgroups is such that the phosphonic group remains closer to the ITIES than the ammonium groups, the local concentration of cations is increased at the ITIES and hence the current observed due to cation transfer is larger than in the absence of phospholipids at the interface. This enhancement is evaluated from the solution of the PB equation, and calculations have been carried out for the conditions of the experiments presented in the literature. The theoretical results turn out to be in good agreement with those experimental studies, thus showing the importance of the electrostatic correction on the rate of ion transfer across an ITIES with adsorbed phospholipids. 

Variation in the metal surface composition is, then, generally expected to yield large variations in the observed rate constant for inner-sphere pathways since the reaction energetics will be sensitive to the chemical nature of the metal surface. For outer-sphere reactions, on the other hand, the rate constants are anticipated to be independent of the electrode material after correction for electrostatic work terms provided that adiabatic (or equally non-adiabatic) pathways are followed. Although a number of studies of the dependence of the rate constants for supposed outer-sphere reactions on the nature of the electrode material have been reported, relatively few refer to sufficiently well-defined conditions where double-layer corrections are small or can be applied with confidence [111-115]. Several of these studies indeed... 

Since anions and cations adsorb at oxide electrodes positive and negative to the pzc, respectively, electrostatic work terms (double layer corrections) should contribute to the activation free energy barrier for adsorbed electroactive ions depending on the position of the reaction site. Not much attention has been paid to this phenomenon yet. Trasatti and co-workers... 

In the case of charged surfaces, Henderson and Lozada-Cassou pointed out that the physical origin of the hydration repulsion can be attributed to the presence of a layer of lower dielectric constant, e, in the vicinity of the interface. It was demonstrated that the DLVO theory complemented with such a layer correctly predicts the dependence of hydration repulsion on the electrolyte concentration. A further extension of this approach was given by Basu and Sharma, who incorporated the effect of the variation of e in the theory of electrostatic disjoining pressure. Their model provides quantitative agreement with the experimental data at low electrolyte concentration and pH, and qualitative agreement at higher electrolyte concentration and pH. 

Contrary to outer sphere electron transfer reactions, the validity of the Butler-Volmer law for ion transfer reactions is doubtful. Conway and coworkers [225] have collected data for a number of proton and ion transfer reactions and find a pronounced dependence of the transfer coefficient on temperature in all cases. These findings were supported by experiments conducted in liquid and frozen aqueous electrolytes over a large temperature range [226, 227]. On the other hand, Tsionskii et al. [228] have claimed that any apparent dependence of the transfer coefficient on temperature is caused by double layer effects, a statement which is difficult to validate because double layer corrections, in particular their temperature dependence, depend on an exact knowledge of the distribution of the electrostatic potential at the interface, which is not available experimentally. Here, computer simulations may be helpful in the future. Theoretical treatments of ion transfer reactions are few they are generally based on variants of electron transfer theory, which is surprising in view of the different nature of the elementary act [229]. 

The vacuum layer calculation is then used to establish a reference in the uncharged cell such that the workfunction of the closed neutral cell can be determined. We refer to the closed neutral cell calculation as qO. To do this, the potential at the middle of the metal layer is determined in the open, vacuum cell, relative to vacuum [0m,vac in Figure 3.9(a)]. The potential profile in the closed qO cell is then plotted and shifted by a constant [A0shift in Figure 3.9(b)] such that the potential at the middle of the metal layer of qO [0m,qo, Figure 3.9(b)] is the same as that in the vacuum referenced cell (0m,vac)-The workfunction of the solvated cell can then be calculated by applying the same electrostatic potential correction to the DFT determined metal Fermi level (0DFT. with reference unspecified) ... 

In the crudest approximation, the effect of the efectrical double layer on electron transfer is taken into account by introduction of the electrostatic energy -e /i of the electron in the acceptor into the free energy of the transition AF [Frumkin correction see Eq. (34.25)], so that corrected Tafel plots are obtained in the coordinates In i vs. e(E - /i). Here /i is the average electric potential at the site of location of the acceptor ion. It depends on the concentration of supporting electrolyte and is small at large concentrations. Such approach implies in fact that the reacting ion represents a probe ion (i.e., it does not disturb the electric held distribution). 

Metal binding by a hydrous oxide from a 10 7 M solution (SOH + Me2+ OMe+ + H+) for a set of equilibrium constants (see Eqs. (i) - (iii) from Example 2.3) and concentration conditions (see text). Corrected for electrostatic interactions by the diffuse double layer model (Gouy Chapman) for 1 = 01 The hydrolysis of Me2+ is neglected. 

Nevertheless, an important application of electrostatic models is to the interface between two immiscible electrolyte solutions. This can be viewed as two electrolyte double layers arranged back to back. In reality, however, total immiscibility never occurs and the degree of miscibility increases with the presence of electrolyte, so that corrections to the models need to be introduced. 

The rate constants for such outer-sphere reactions can therefore differ markedly from those corresponding to true weak-overlap pathways, even after correction for electrostatic double-layer effects. This can cause some difficulties with the operational definition of inner-sphere electrocatalysis considered above, whereby outer-sphere reactions are regarded as "non-catalytic processes. In addition, there is evidence that inner- rather than outer-sphere pathways can provide the normally preferred pathways at metal-aqueous interfaces for reactants containing hydrophobic functional groups [116]. 

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