Surface potential and screening

The actual Debye screening constant must be retained to give the correct decay at large distances from the surface. We determine the effective valence by requiring that the approximate solution give the correct surface potential and, after a little algebra, find that satisfies... 

The first simulation studies of full double layers with molecular models of ions and solvent were performed by Philpott and coworkers [51,54,158] for the NaCl solution, using the fast multipole method for the calculation of Coulomb interactions. The authors studied the screening of a negative surface charge by free ions in several highly concentrated NaCl solutions. A combination of (9-3) LJ potential and image charges was used to describe the metal surface. 

Select benzene from the molecules on screen, and select Surfaces. Potential Map refers to an electrostatic potential map. Select Transparent to present it as a transparent (actually translucent) solid. This will allow you to see the molecular skeleton underneath. The surface is colored red in the n system (indicating negative potential and the fact that this region is attracted to a positive charge), and blue in the a system (indicating positive potential and the fact that this region is repelled by a positive charge). 

The Polarizable Continuum Model (PCM) employs a van der Waals surface type cavity, a detailed description of the electrostatic potential, and parameterizes the cavity/ dispersion contributions based on the surface area. The COnductor-like Screening... 

Accordingly, Neurock and co-workers have developed models for the electrochemical interface that retain this concept of hexagonal stmcture over close-packed metal surfaces [FiUiol and Neurock, 2006 Taylor et al., 2006c]. With the use of a screening charge as described in Section 4.3, the sensitivity of the stmctural parameters of water with respect to the electrochemical environment were explored [Taylor et al., 2006a]. The predominant effect stems from the polar nature of the water molecule, in which the water molecules are observed to rotate as a function of the applied potential. 

Unlike charges attract and like charges repel each other, so there is a high concentration of counterions attracted to the particle surface whilst co-ions (those with the same sign charge as that of the surface) are repelled. Thermal motion, i.e. diffusion, opposes this local concentration gradient so that the counterions are in a diffuse cloud around the particle. Of course particles which have a like charge will also repel each other but the interaction of the particle surfaces will be screened by the counterion clouds between the particles. The interaction potential is a function of the surface potential, i]/o, and the permittivity of the fluid phase, e = r80, where r is the relative permittivity.12,27... 

Because the inverse Debye length is calculated from the ionic surfactant concentration of the continuous phase, the only unknown parameter is the surface potential i/io this can be obtained from a fit of these expressions to the experimental data. The theoretical values of FeQx) are shown by the continuous curves in Eig. 2.5, for the three surfactant concentrations. The agreement between theory and experiment is spectacular, and as expected, the surface potential increases with the bulk surfactant concentration as a result of the adsorption equilibrium. Consequently, a higher surfactant concentration induces a larger repulsion, but is also characterized by a shorter range due to the decrease of the Debye screening length. 

Among the quantities which have proven of value as graphical models are the molecular orbitals, the electron density, the spin density (for radicals and other molecules with unpaired electrons), the electrostatic potential and the local ionization potential. These may all be expressed as three-dimensional functions of the coordinates. One way to display them on a two-dimensional video screen (or on a printed page) is to define a surface of constant value, a so-called isovalue surface or, more simply, isosurface. ... 

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