Polarization idea, basic

Almost all interfacial phenomena are influenced to various extents by forces that have their origin in atomic- and molecular-level interactions due to the induced or permanent polarities created in molecules by the electric fields of neighboring molecules or due to the instantaneous dipoles caused by the positions of the electrons around the nuclei. These forces consist of three major categories known as Keesom interactions (permanent dipole/permanent dipole interactions), Debye interactions (permanent dipole/induced dipole interactions), and London interactions (induced dipole/induced dipole interactions). The three are known collectively as the van der Waals interactions and play a major role in determining material properties and behavior important in colloid and surface chemistry. The purpose of the present chapter is to outline the basic ideas and equations behind these forces and to illustrate how they affect some of the material properties of interest to us. 

The basic idea is that we assume that we can separate the free energy contributions of the vdW and polar interactions and that these contributions are additive ... 

We will first try to understand the basic outlines of the phenomena on the basis of the framework of polarization moments, as treated in the preceding chapters. In order to avoid overloading the text with excessive formalism and in order to achieve easier understanding, we will consider a simplified model in the present chapter which gives an idea of the essence of the phenomena. The possibility of a more comprehensive quantum mechanical description will be offered by the equations presented in the following chapter. 

An important lesson from this is that the idea of nucleophilicity in the real world of organic reactions is not easy to pigeonhole. Polarizability is important, but basicity is also very important and can be influenced by solvation. Values of the pKa of a given compound vary as a function of solvent, and so does basicity. You can make a species, anions in particular, more reactive by putting them in solvents that don t solvate them very well. Dipolar aprotic solvents interact nicely with cations, but not so well with anions. Polar protic solvents (e. g., water, alcohols) can hydrogen bond to anions, diminishing their basicity and literally blocking them sterically. 

Over the last years, the basic concepts embedded within the SCRF formalism have undergone some significant improvements, and there are several commonly used variants on this idea. To exemplify the different methods and how their results differ, one recent work from this group [52] considered the sensitivity of results to the particular variant chosen. Due to its dependence upon only the dipole moment of the solute, the older approach is referred to herein as the dipole variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM) [53,54,55] embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF) [56,57], A variant of this method is the conductor-polarized continuum model (CPCM) [58] wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The self-consistent isodensity PCM procedure [59] determines the cavity self-consistently from an isodensity surface. The UAHF (United Atom model for Hartree-Fock/6-31 G ) definition [60] was used for the construction of the solute cavity. 

Finally, the basic equivalence of the two measuring techniques should be appreciated. Although there are many ways to approach such a comparison, the following simplified explanation will, we hope, give a more intuitive feeling for the relationship between EIS and PR measurements. As stated above, both techniques rely on the frequency dependence of the impedance of the double-layer capacitance in order to determine the polarization resistance. EIS uses low frequencies to force the capacitor to act like an open circuit. PR measurements use a slow scan rate to do the same thing. To make comparisons, the idea of equivalent scan rate is useful. Suppose that a particular electrochemical system requires EIS measurements to be made down to 1 mHz in order to force 99% of the current through Rp. What would the equivalent scan rate be for PR measurements A frequency of 1 mHz corresponds to a period of 1000 s. If the sine wave is... 

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