Density Functional Theory for the Nonspecific Binding of Salt to Polyelectrolytes: Thermodynamic Properties

Abstract

The thermodynamics of the nonspecific binding of salt to a polyelectrolyte molecule is studied using a density functional approach. The polyelectrolyte molecule is modeled as an infinite, inflexible, and impenetrable charged cylinder and the counterions and co-ions are modeled as charged hard spheres of equal diameter. The density functional theory is based on a hybrid approach where the hard-sphere contribution to the one-particle correlation function is evaluated nonperturbatively and the ionic contribution to the one-particle correlation function is evaluated perturbatively. The advantage of the approach is that analytical expressions are available for all the correlation functions. The calculated single ion preferential interaction coefficients, excess free energy, and activity coefficients show a nonmonotonic variation as a function of polyion charge in the presence of divalent ions. These properties display considerable departure from the predictions of the nonlinear Poisson-Boltzmann (NLPB) equation, with qualitative differences in some cases, which may be attributed to correlation effects neglected in the NLPB theory.

Density functional study on the structures and thermodynamic properties of small ions around polyanionic DNA

“…The preferential interaction coefficient characterizes the interaction between a polyion and its surrounding small ions [43,55]. For each ion species it is obtained by integrating the difference between its local density and its bulk density over the volume outside the polyions.…”

“…Unlike the PB and HNC, DFT starts with the simple thermodynamic principle that the system reaches equilibrium as its grand canonical potential reaches minimum [38]. Many studies of DFT have been carried out for the electrolyte solution next to the charged or uncharged surface with simple geometries, such as planar [39,40], spherical [41], and cylindrical surfaces [42,43]. It has been reported that the results from DFT agree well with MC simulation, better than those from other theories [41,42,44].…”

Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

“…For example, Boda et al [7,8] have applied the theory to a planar double layer (PDL) containing a restricted primitive model (RPM) electrolyte (equisized rigid ions moving in a continuum dielectric) and have obtained structural and thermodynamic results for different ion sizes. The application to the cylindrical (electric) double layer (CDL) has been considered by Patra and Yethiraj [9,10]. Yu et al [11] have employed the technique to spherical double layers (SDL).…”

Density functional study on the osmotic coefficient for the DNA–electrolyte solutions

“…To consider the exclude volume effect and ion correlation, several theoretical approaches are proposed. These approaches including the hypernetted-chain/mean-spherical (HNC/MSA) [7], modified Poisson-Boltzmann theory [8,9] and density functional theories [6,10] lead to a good description of the electrical double layer in various geometries, but most of them are limited to the restricted primitive model of electrolyte around DNA. Recently, we have extended the DFT to DNA-electrolyte solutions with the mixed-sized counterions and found that the DFT is fine for these systems [11].…”