Surface potential model

One of the main assumptions of the Donnan partition model is that two well-defined phases (polymer and solution) exist and the electrostatic potential presents a sharp transition between them. This approximation is fulfilled when the typical decay length of the electrostatic potential (Debye length) is much shorter than the film thickness. The other limiting situation is that where all the redox sites are located in a plane and thus the Debye length is larger than the film thickness. This situation can be described by the surface potential model ... 

Variable charge and surface potential model (VSC-VSP) by Bowden and coworkers ... 

The solvent molecules form an oriented parallel, producing an electric potential that is added to the surface potential. This layer of solvent molecules can be protruded by the specifically adsorbed ions, or inner-sphere complexed ions. In this model, the solvent molecules together with the specifically adsorbed, inner-sphere complexed ions form the inner Helmholtz layer. Some authors divide the inner Helmholtz layer into two additional layers. For example, Grahame (1950) and Conway et al. (1951) assume that the relative permittivity of water varies along the double layer. In addition, the Stern variable surface charge-variable surface potential model (Bowden et al. 1977, 1980 Barrow et al. 1980, 1981) states that hydrogen and hydroxide ions, specifically adsorbed and inner-sphere... 

FIGURE 9.4 Reduced potential energy V (h) — Kl64nkT)V h) as a function of scaled plate separation Kh for the constant surface charge density model calculated with Eq. (9.125) for a = 0, 0.1, and 1 in comparison with V h) = (K/64nkT)V h) for the constant surface potential model calculated with Eq. (9.141). 

In this chapter, we discuss two models for the electrostatic interaction between two parallel dissimilar hard plates, that is, the constant surface charge density model and the surface potential model. We start with the low potential case and then we treat with the case of arbitrary potential. 

Comparison is made with the results for the two conventional models for hard plates given by Honig and Mul [11]. We see that the values of the interaction energy calculated on the basis of the Donnan potential regulation model lie between those calculated from the conventional interaction models (i.e., the constant surface potential model and the constant surface charge density model) and are close to the results obtained the linear superposition approximation. 

The model recently proposed by Bowden aT. ( 7) avoids the use of the assumption that the surface potential varies in a Nernstian fashion with pH. In the VSC-VSP (variable surface charge-variable surface potential) model, the surface charge density Og is produced as the result of a chemical interaction between surface sites specific for adsorption only of the potentialdetermining ions H+ and OH . These ions are recognized as having finite sizes, resulting in a maximum adsorption density Ng of such ions which can be physically located on the surface. 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

Our potential is a sum of smooth surface potentials that model amino acid-solvent interactions and of smooth pair potentials that model amino acid-amino acid interactions. As in [24], we take as essential only the Ca atoms. 

Mdissociates as a positive ion. Conversely, the enhanced ion yields of the cesium ion beam can be explained using a work function model, which postulates that because the work function of a cesiated surface is drastically reduced, there are more secondary electrons excited over the surface potential barrier to result in enhanced formation of negative ions. The use of an argon primary beam does not enhance the ion yields of either positive or negative ions, and is therefore, much less frequently used in SIMS analyses. 

III. MODELS AND SURFACE POTENTIALS A. Methods for Computing Potentials... 

Recently, many experiments have been performed on the structure and dynamics of liquids in porous glasses [175-190]. These studies are difficult to interpret because of the inhomogeneity of the sample. Simulations of water in a cylindrical cavity inside a block of hydrophilic Vycor glass have recently been performed [24,191,192] to facilitate the analysis of experimental results. Water molecules interact with Vycor atoms, using an empirical potential model which consists of (12-6) Lennard-Jones and Coulomb interactions. All atoms in the Vycor block are immobile. For details see Ref. 191. We have simulated samples at room temperature, which are filled with water to between 19 and 96 percent of the maximum possible amount. Because of the hydrophilicity of the glass, water molecules cover the surface already in nearly empty pores no molecules are found in the pore center in this case, although the density distribution is rather wide. When the amount of water increases, the center of the pore fills. Only in the case of 96 percent filling, a continuous aqueous phase without a cavity in the center of the pore is observed. 

The calculations were performed in the framework of a one-step model of photoe-mission derived from the one originally formulated by Pendry [1]. Nowadays the model includes relativistic effects [2-5], the possibility of having several atoms per unit cell [6], different types of layers and a realistic model for the surface potential [7]. It is further possible to consider ov erlayers on a surface. We will not review the theory here, which has been done already in several publications [2,4,6,8], but instead concentrate on the results. 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

Fig. 5. Tentative mixed potential model for the sodium-potassium pump in biological membranes the vertical lines symbolyze the surface of the ATP-ase and at the same time the ordinate of the virtual current-voltage curves on either side resulting in different Evans-diagrams. The scale of the absolute potential difference between the ATP-ase and the solution phase is indicated in the upper left comer of the figure. On each side of the enzyme a mixed potential (= circle) between Na+, K+ and also other ions (i.e. Ca2+ ) is established, resulting in a transmembrane potential of around — 60 mV. This number is not essential it is also possible that this value is established by a passive diffusion of mainly K+-ions out of the cell at a different location. This would mean that the electric field across the cell-membranes is not uniformly distributed.

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