Potential as calculated

Fig. 9.51 Electrostatic potential as calculated by AM CIS for the charge-separated states of exTTF-oFL -C60 triads (n = 1-3). Positive to negative red to blue...

When there is a net current in an eleetrochemical cell, the measured potential across the two electrodes is no longer simply the difference between the two electrode potentials as calculated from the Nernst equation. Two additional phenomena, IR drop and polarization, must be considered when current is present. Because of these phenomena, potentials larger than the thermodynamic potential are needed to operate an electrolytic cell. When present in a galvanic cell, IR drop and polarization result in the development of potentials smaller than predicted. 

A common way of deriving partial atomic charges in force fields is to choose a set of parameters that in a least squares sense generates the best fit to the actual electrostatic potential as calculated from an electronic wave function. The electrostatic... 

The reversible potential of many electrode reactions, notably those involving oxides, depends on the pH. The potential - pH diagrams, also called Pourbaix diagrams, display the reversible potential, as calculated by the Nernst equation, as a... 

The instrument displays the zeta potential as calculated from the Smoluchowski equation. At the point where the particles image is stationary, the displayed potential is the zeta-potential of the sample. The zeta potential can then be converted to electrophoretic mobility by deviding [sic] by an appropriate constant. The concentration of the sample was 0.15% for the cotton fibers. This method allows the measurement of the entire particle cloud simultaneously yielding average mobility values. [2]... 

Thus an electric potential as calculated in Listing 13.13 can be used to evaluate the electric field within each of the triangular spatial elements and this can then snb-sequently be used in a second PDE calculation to evaluate a temperature change in a resistive element such as the square comer resistor. 

On the other hand, in the theoretical calculations of statistical mechanics, it is frequently more convenient to use volume as an independent variable, so it is important to preserve the general importance of the chemical potential as something more than a quantity GTwhose usefulness is restricted to conditions of constant temperature and pressure. 

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

The approach developed by Jungen and Merer (JM) [24] is of a similar level of sophistication. The main difference is that IM prefer to remove the coupling between the electronic states by a transformation of the Hamiltonian matrix (i.e., vibronic energy matrix), rather that of the Hamiltonian itself. They first calculate the large amplitude bending functions for one of the adiabatic potentials, as if it belonged to a E electronic state. These functions are used as... 

Here 0p and 0 correspond to the terms in r" and respectively in Equation (1.8) as already pointed out, these contributions are always present, whereas the electrostatic energies 0, and may or may not be present according to the nature of the adsorbent and the adsorptive. In principle. Equation (1.16) could be used to calculate the numerical value of the interaction potential as a function of the distance z of any given molecule from the surface of a chosen solid. In practice, however, the scope has to be limited to systems composed of a simple type of gas molecule and... 

At the middle of the capillary where the eflect of the walls on chemical potential is negligible, the radius of curvature will be equal to r as calculated by the Kelvin equation (3.20) but it will become progressively larger as the wall is approached. 

An important concept is the shadow cone, which is a region where no ions can penetrate due to the ion—nucleus repulsion (see Figure 2). This effect makes ion scattering surface sensitive. The size of the shadow cone / jCan be calculated for the classical Coulomb potential as ... 

Eqs. (1,4,5) show that to determine the equilibrium properties of an adsorbate and also the adsorption-desorption and dissociation kinetics under quasi-equilibrium conditions we need to calculate the chemical potential as a function of coverage and temperature. We illustrate this by considering a single-component adsorbate. The case of dissociative equilibrium with both atoms and molecules present on the surface has recently been given elsewhere [11]. 

It can be seen from Fig. 7 that V is a linear function of the qf This qV relation was pointed out and discussed at some length in the papers in ref. 6. It is not simple electrostatics in that it would not exist for an arbitrary set of charges on the sites, even if the potentials are calculated exactly. The charges must be the result of a self-consistent LDA calculation. The linearity of the relation and fie closeness of the points to the line is demonstrated by doing a least squares fit to the points. The sums that define the potentials V do not converge at all rapidly, as can be seen by calculating the Coulomb potential from the standard formula for one nn-shell after another. The qV relation leads to a special form for the interatomic Coulomb energy of the alloy... 

Figure 2.Virtual crystal approximation calculations (solid line) compared with coherent potential approximation calculations for Fe-Co (longdashed line), Fe-Ni (dot-dashed line) and Fe-Cu (dashed line). The fcc-bcc energy difference is shown as a function of the atomic number.

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