Poisson-Boltzman equation

Gur, Y. Ravina, I. Babchin, A. J., On the electrical double layer theory. II. The Poisson-Boltzman equation including hydration forces, J. Colloid Inter. Sci. 64, 333-341... 

Thermochemistry. Chen et al.168 combined the Kohn-Sham formalism with finite difference calculations of the reaction field potential. The effect of mobile ions into on the reaction field potential SCRF method to study solvation energies, dipole moments of solvated molecules, and absolute pKa values for a variety of small organic molecules. The list of molecules studied with this approach was subsequently extended182. A simplified version, where the reaction field was calculated only at the end of the SCF cycle, was applied to study redox potentials of several iron-sulphur clusters181. 

The catalytic effect for reactions involving an ionic reactant usually shows a strong dependence on the total amphiphile concentration. The maximal effective rate constant is attained at concentrations just over the CMC. Romsted284 showed that this occurs due to the competition between the ion binding of the reactive ions (OH- in the example above) and the counterions of the amphiphile. Recently, Diekman and Frahm285 286 showed that it is possible to rationalize the kinetic data by describing the ion distribution through a solution of the Poisson-Boltzman equation. (See Fig. 5.1). 

Nicholls A, Honig B (1991) Rapid finite difference alogrithm, utililizing successive over-relaxation to solve the Poisson-Boltzman equation, J Comput Chem, 12 435-445... 

A similar approach was employed in Hecht et al. (1995) for determining the electrostatic potential near the surface of calf thymus DNA. Spin-spin interaction between an N-nitroxide derivative of 9-aminoacridine attached to DNA and free 15N-labeled nitroxides of different charges was monitored by electron-electron double resonance (ELDOR). The electrostatic potential near the surface of DNA was calculated using a nonlinear Poisson-Boltzman equation. The calculated results agreed with the experimental potentials. 

The electric potential j/ created by the micelle was calculated using a numerical integration of the Poisson-Boltzman Equation by the Runge-Kutta method on an electronic computer. We shall outline briefly the method used (14,15,16). The Poisson-Boltzman Equation can be written (for programming commodities) in the following form ... 

Calculated using a Poisson-Boltzman equation with nonelectrostatic effects modeled by a linear solvent accessible surface area dependence with B3LYP/6-31-H-G. ... 

Let us consider an infinite flat surface, which has a surface charge density phases separated by the surface are a nonaqueous phase having a dielectric constant e, and an electrolyte phase with dielectric constant e. In this situation, the electrical potential at a distance x in the electrolyte solution from the surface is given by the Poisson-Boltzman equation [Eq. (7)]. 

In the EDL, the electric potential and net charge density are described by the Poisson-Boltzman equation [1-4]. 

For the special case of a symmetric electrol)rte solution (z z = 1 1) the Poisson-Boltzman equation reduces to ... 

Proper inclusion of the solvent into the calculations is unfortunately quite difficult [46]. One can use classical molecular dynamics or Monte Carlo simulations, classical continuum models based on the Poisson-Boltzman equation, and quantum-chemical studies using various variants of the Self Consistent Reaction Field (SCRF) approach at the semiempirical or ab initio level. There are serious approximations associated with these methods. Continuous models neglect the specific solute-solvent interactions which are very important for polar solvent. Classical methods neglect the changes in the electronic structure of the solute due to the solvent effects. These uncertainties can be illustrated using the predicted solvation energy of adenine treated by various modem approaches. The calculated values vary from -8 to -20 kcal/mol [68]. 

All these experimental results have been recently complemented by a very useful theoretical study by Kharkats and Ulstrup," who calculated analytically the electrostatic Gibbs energy profile of an ion between two dielectric phases separated by a planar boundary, incorporating both the ionic finite size and the dielectric image interactions. The profile obtained, illustrated in Fig. 4, shows that there is no discontinuity as the ion traverses the boundary and that cation and anion concentration distribution will differ if they have different ionic radii, as they will penetrate the boundary to a different extent. This has important repercussions on the Poisson-Boltzman equation as the work term is not only the electrical energy, —but also an electrostatic contribution to the Gibbs energy of solvation as the ion... 

For electrodes with dimensions in the tens of nm range, the diffusion layer is decreased to achieve dimensions comparable with the thickness of the electrical double layer. Electrostatic forces within the double layer can accelerate the flux of oppositely charged redox species, so generating the conditions for a further enhancement of the mass transport to the nanoelectrodes surface. Dickinson and Compton presented numerical solution of the Poisson-Boltzman equation, for... 

Palladium oxide 80 Partial charges model 183 Peptization 267. 269 Perovskites oxides 174 structure 175 synthesis 175 Phosphate 30 complexation 149 Phosphatoanlimonales 151 Phosphaiotungstates 152 7i-bond 15. 108, 112, 131, 137, 149, 193 Platinum oxide 80 Poisson-Boltzman equation 237 Point of zero surface tension 278 Polymers... 

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