Poisson-Boltzman model

Figure 18.1 Competitive association between Mg2+ (A) and 20 (mM) Na+ (O) with a 24 bp DNA duplex. Depleted anions are shown by (V) and the net charge is given by ( ). Solid lines are fitted to the Hill equation (Eq. (18.3)), while dotted lines are predictions from the nonlinear Poisson—Boltzman model. Reprinted from Bai ft al. (2007).

The Poisson-Boltzman (P-B) equation commonly serves as the basis from which electrostatic interactions between suspended clay particles in solution are described ([23], see Sec.II. A. 2). In aqueous environments, both inner and outer-sphere complexes may form, and these complexes along with the intrinsic surface charge density are included in the net particle surface charge density (crp, 4). When clay mineral particles are suspended in water, a diffuse double layer (DDL) of ion charge is structured with an associated volumetric charge density (p ) if av 0. Given that the entire system must remain electrically neutral, ap then must equal — f p dx. In its simplest form, the DDL may be described, with the help of the P-B equation, by the traditional Gouy-Chapman [23-27] model, which describes the inner potential variation as a function of distance from the particle surface [23]. 

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

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]. 

Using the MVN model of interface they proposed in 1978, they reinvestigated the transfer of tetraalkylammonium ions from water to nitrobenzene, taking into consideration that the surface concentrations, C, of the transferring ion differed from the bulk concentration, C, according to a Poisson-Boltzman distribution ... 

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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