Equipotential surface model

Points-on-an-Equipotential-Surface Model Metal clusters display features that are difficult to model with MM force fields. A particularly vexing problem is the dynamic behavior of carbonyl (CO) ligands. Carbonyl ligands... 

Thus the contribution of the structured ionic cloud to the total potential at the surface of the central ion will not be as it is in the DH theory, and because the electrostatic model requires an equipotential surface to be maintained there, a new model is needed. We therefore approximate an ion to a dielectric sphere of radius a, characterized by the dielectric constant of the solvent D, and having a charge Q, residing on an infinitesimally thin conducting surface. This type of model has been exploited by previous workers (17,18) and may be reconciled with a quantum-mechanical description (18). 

The most serious limitation remaining after modifying the reaction field method as mentioned above is the neglect of solute polarizability. The reaction field that acts back on the solute will affect its charge distribution as well as the cavity shape as the equipotential surface changes. To solve this problem while still using the polarizable continuum model (PCM) for the solvent, one has to calculate the surface charges on the solute by quantum chemical methods and represent their interaction with the solvent continuum as in classical electrostatics. The Hamiltonian of the system thus is written as the sum of the Hamilton operator for the isolated solute molecule and its interaction with the macroscopic... 

The frequency dispersion of porous electrodes can be described based on the finding that a transmission line equivalent circuit can simulate the frequency response in a pore. The assumptions of de Levi s model (transmission line model) include cylindrical pore shape, equal radius and length for all pores, electrolyte conductivity, and interfacial impedance, which are not the function of the location in a pore, and no curvature of the equipotential surface in a pore is considered to exist. The latter assumption is not applicable to a rough surface with shallow pores. It has been shown that the impedance of a porous electrode in the absence of faradaic reactions follows the linear line with the phase angle of 45° at high frequency and then... 

Computer programs for empirical force-field calculations that use other concepts have been tested, and some of these will be discussed elsewhere in this book. Among these approaches are one based on a pure central force-field model, used for simple organic compounds [208], an equipotential surface force-field model, used for carbonyl cluster complexes [99,103], and a program that includes ligand field terms, developed for transition metal complexes in the LFMM model (ligand field molecular mechanics) [21, 105, 108]. 

This geometry is close to that introduced by Macfarlane and Torgerson in their pioneering studies in PDMS in 1976, which marked a major step forward in the development of TOP techniques. As in the simple model, ions were ejected from an equipotential surface (by fission fragment bombardment in this case), so the spatial spreads that had limited the performance of earlier instru-ments were removed. 

In most electrochemical modeling applications, a commonly invoked and valid assumption is that the electrode constitutes an equipotential surface. This is due to the characteristically low electrolyte conductivity (/c 0.1 S/cm) as compared with metallic conductivities, which are larger by about a factor of one million. However, in some applications, when very long and thin electrodes are present, e.g., in reel-to-reel ( strip ) plating, or when only a thin... 

Figure 53. Idealized half-cell response of a thin solid electrolyte cell, (a) Cell geometry including working electrodes A and B and reference electrode (s). (b) Equivalent circuit model for the cell in a, where the electrolyte and two electrodes have area-specific resistances and capacitances as indicated, (c) Total cell and half-cell impedance responses, calculated assuming the reference electrode remains equipotential with a planar surface located somewhere in the middle of the active region, halfway between the two working electrodes, as shown in a.

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