Self-Consistent Field Poisson-Boltzmann Theory

A quantitative analysis of counterion localization in a salt-free solution of star-like PEs is carried out on the basis of an exact numerical solution of the corresponding Poisson-Boltzmann (PB) problem (Sect. 5). Here, the conformational degrees of freedom of the flexible branches are accounted for within the Scheutjens-Fleer self-consistent field (SF-SCF) framework. The latter is used to prove and to quantify the applicability of the concept of colloidal charge renormalization to PE stars, that exemplify soft charged colloidal objects. The predictions of analytical and numerical SCF-PB theories are complemented by results of Monte Carlo (MC) and molecular dynamics (MD) simulations. The available experimental data on solution properties of PE star polymers are discussed in the light of theoretical predictions (Sect. 6). 

In the light of the above arguments, we present a brief review on the theoretical methods and simulation results. We restrict ourselves to isolated flexible polyelectrolyte chains in solutions. In terms of simulations, we only consider the Langevin dynamics method. For the theory part, we present a variational theory and self-consistent field theory (SCFT), both of which start from an effective Hamiltonian appropriate for flexible charged chains. The background plasma is treated at different levels of sophistication, ranging from the Debye-Hiickel (DH) to the Poisson-Boltzmann descriptions. In this chapter, we have stayed away from less... 

Brownian Dynamics Continuum Solvation Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Monte Carlo Simulations for Complex Fluids Monte Carlo Simulations for Liquids Poisson-Boltzmann Type Equations Numerical Methods Rates of Chemical Reactions Supercritical Water and Aqueous Solutions Molecular Simulation Transition State Theory. 

These workers also calculated the relative stability of the tautomers lOa-c in the gas phase by ab initio and density functional theory (DFT) methods and in solution using several continuum solvation models such as self-consistent reaction fields (SCRF) and the Poisson-Boltzmann method. These results showed good agreement between the experimental and theoretical approaches. 

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