Excess-entropy scaling relationships for diffusivity and viscosity of Lennard-Jones chain fluids are tested using molecular dynamics simulations for chain sizes that are sufficiently small that chain entanglement effects are insignificant. The thermodynamic excess entropy S(e) is estimated using self-associating fluid theory (SAFT). A structural measure of the entropy S(2) is also computed from the monomer-monomer pair correlation function, g(m)(r). The thermodynamic and structural estimators for the excess entropy are shown to be very strongly correlated. The dimensionless center-of-mass diffusivities, D(cm) (*), obtained by dividing the diffusivities by suitable macroscopic reduction parameters, are shown to conform to the excess entropy scaling relationship, D(cm) (*)=A(n) exp(alpha(n)S(e)), where the scaling parameters depend on the chain length n. The exponential parameter alpha(n) varies as -(1n) while A(n) varies approximately as n(-0.5). The scaled viscosities obey a similar relationship with scaling parameters B(n) and beta(n) where beta(n) varies as 1n and B(n) shows an approximate n(0.6) dependence. In accordance with the Stokes-Einstein law, for a given chain length, alpha(n)=-beta(n) within statistical error. The excess entropy scaling parameters associated with the transport properties therefore display a simple dependence on chain length.

A density functional theory is presented for the distribution of charged hard spheres (model for salt) around an infinite, rigid, and impenetrable charged cylinder (model for DNA or tobacco mosaic virus). The theory is based on a weighted density approach where the hard-sphere contribution to the one-particle correlation function is evaluated nonperturbatively using a position dependent effective density, and the ionic part is obtained through a second-order functional Taylor expansion around a uniform fluid. The theory is in good agreement with Monte Carlo simulations for the density distribution of monovalent, divalent, and mixed salts. For axial charge densities corresponding to DNA, the hypernetted chain integral equation theory is not as accurate as the density functional theory, but both liquid state approaches are superior to the Poisson-Boltzmann theory. For higher axial charge densities the density functional theory predicts interesting charge inversion effects that are absent in the nonlinear Poisson-Boltzmann theory.

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The structure of polyelectrolyte solutions at a charged surface is studied using density functional theory and Monte Carlo simulations. The polymer molecules are modeled as freely jointed chains of charged hard spheres, the counterions and co-ions as charged hard spheres, and the surface is a planar, impenetrable hard wall with a uniform surface charge density. The density functional theory treats the ideal gas contribution exactly, uses a weighted density approximation for the hard sphere contribution, and a generalized van der Waals approximation for the electrostatic contribution. At a fixed surface charge density, with increasing concentration of the polyion, the simulations show layering as well as charge inversion phenomena resulting from an interplay between excluded volume and electrostatic interactions. The integrated surface excess is a monotonically decreasing function of polymer concentration at high surface charge densities, but a nonmonotonic function of polymer concentration at lower surface charge densities. The density functional theory is in qualitative agreement with simulations for the density profiles but fails to capture the layering and charge inversion effects. This suggests that liquid-state correlations and coupling between electrostatic and excluded volume effects are important factors in the adsorption of charged polymers at surfaces.

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.