Modified Poisson-Boltzmann theory

Das T, Bratko D, Bhuiyan LB, Outhwaite CW. Modified Poisson-Boltzmann theory applied to linear polyelectrolyte solutions. J. Phys. Chem. 1995 99 410. 

R. Jinnouchl and A. B. Anderson. Electronic structure calculations of liquid-solid Interfaces Combination of density functional theory and modified Poisson-Boltzmann theory. Phys. Rev. B, 77(245417), 2008. 

AppKcation of MPB model to ITIES was made first by Torrie and Val-leau [28]. Cui and coworkers [29] applied the modified Poisson-Boltzmann theory (MPB4) to the ITIES and found... 

In addition to the solvent contributions, the electrochemical potential can be modeled. Application of an external electric field within a metal/vacuum interface model has been used to investigate the impact of potential alteration on the adsorption process [111, 112]. Although this approach can model the effects of the electrical double layer, it does not consider the adsorbate-solvent, solvent-solvent, and solvent-metal interactions at the electrode-electrolyte interface. In another approach, N0rskov and co-workers model the electrochemical environment by changing the number of electrons and protons in a water bilayer on a Pt(lll) surface [113-115]. Jinnouchi and Anderson used the modified Poisson-Boltzmann theory and DFT to simulate the solute-solvent interaction to integrate a continuum approach to solvation and double layer affects within a DFT system [116-120]. These methods differ in the approximations made to represent the electrochemical interface, as the time and length scales needed for a fiilly quantum mechanical approach are unreachable. 

FIGURE 3.17 Surface-ion distribution function for a 2 1 electrolyte with a = 0.30 nm and c = 1.0 M for (a) a fixed dimensionless potential at the Helmholtz plane P(a/2) = -0.15 (b) a fixed dimensionless surface charge = a a lq = 0.1685. Symbols MC simulations solid line, MPB5 dash-dotted fine, MPB6 dotted line, DPT dashed line, GCS (Bhuiyan and Outhwaite, 2004, Comparison of the modified Poisson-Boltzmann theory with recent density functional theory and simulation results in the planar electric double layer. Physical Chemistry Chemical Physics, 6, no. 13, 3467. Reproduced by permission of The Royal Society of Chemistry.)... 

Bhuiyan, L. B., and C. W. Outhwaite. 2004. Comparison of the modified Poisson-Boltzmann theory with recent density functional theory and simulation results in the planar electric double layer. Physical Chemistry Chemical Physics 6, no. 13 3467. doi 10.1039/ b316098j. 

Bhuiyan, L. B., C. W. Outhwaite, and D. Henderson. 2007. Some simulation and modified Poisson-Boltzmann theory results for the contact values of an electrolyte near a charged electrode. Journal of Electroanalytical Chemistry 607, no. 1-2 54-60. doi 10.1016/ j.jelechem.2006.10.010. 

Jinnouchi, R. and Anderson, A.B. 2008. Structure calculations of liquid—solid interfaces A combination of density fimctional theory and modified Poisson-boltzmann theory. 

C. W. Outhwaite, M. Molero, and L. B. Bhuiyan,/. Chem. Soc. Faraday Trans. 2, 87, 3227 (1991). Symmetrical Poisson-Boltzmaim and Modified Poisson-Boltzmann Theories. 

Primitive Model Electrolytes in the Modified Poisson-Boltzmann Theory. 

Simulation results were compared with the predictions of the Ornstein-Zernike (OZ) equation with the hypernetted chain (HNC) closure approximation and the non-linear Poisson-Boltzmann equation, both augmented by pertinent Lifshitz NES potentials. We show in Fig. 1 that there is very good agreement between modified Poisson-Boltzmann theory, MC simulations, and HNC calculations when the counterions and co-ions are monovalent. There is also good agreement between the different approaches with divalent co-ions (not shown here). However, the results from MPBE cannot account for ion correlation effects that occur in Fig. 2 when the counterions are divalent. The reason is simply that the... 

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