SCFT variational theory

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... 

Although F inthe variational theory is the same as in SCFT (cf Eq. (6.128)), other contributions involving the free ions, the chain entropy, and so on (that means Ff) differ significantly in terms of computational details. In SCFT, Ff is computed after solving for fields experienced by different components in the system, which arise as a result of interactions of a particular component with the others. On the other hand, in variational calculations [1], a single polyelectrolyte chain, whose monomers interact with the excluded volume and the electrostatic interactions in the presence of the small ions is approximated by an effective Gaussian chain, whose conformational statistics depend on the different kinds of interactions in the system. To compute the equilibrium free energy, its variational ansatz is minimized with respect to the... 

Figure 6.31 A discrepancy between SCFT and variational theory for the polymer-solvent interaction energy and solvent entropy contributions arise at high monomer densities.

Comparison of Theories SCFT and Variational Formalism 325 Table 6.2 Comparison of contributions to Ff in SCFT and variational formalism. 

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