Chandra N. Patra

Excess entropy scaling of transport properties of Lennard-Jones chains

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.

Density functional theory for nonuniform polymers: Accurate treatment of the effect of attractive interactions

A density functional theory is presented for the effect of fluid–fluid and fluid–surface attractive interactions on the structure of polymers at surfaces. The theory treats the ideal gas free-energy functional exactly and uses a weighted density approximation for the hard chain contribution to the excess free-energy functional. The attractive interactions are calculated using the bulk fluid direct correlation function obtained from the polymer reference interaction site model theory. The predictions of the theory are in good agreement with computer simulation results for the density profiles of freely rotating fused-sphere chains at surfaces for a wide range of densities and temperatures. The results emphasize the importance of using different approximations for the hard sphere and attractive interactions in density functional theories for polymers.

Structure of electric double layers: A self-consistent weighted-density-functional approach

A self-consistent weighted-density-functional approach is developed for the structure of electric double layer using the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The one-particle correlation function of this inhomogeneous system is evaluated using suitably averaged weighted densities for the short range hard sphere as well as the long range electrical components. The hard-sphere contribution is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the ionic density profile and the mean electrostatic potential near the electrode surface at several surface charge densities are found to show very good agreement with the available simulation results.

Density functional theory for the nonspecific binding of salt to polyelectrolytes: thermodynamic properties.

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.

A nonlocal density‐functional theory of electric double layer: Charge‐asymmetric electrolytes

A nonlocal density‐functional theory of inhomogeneous ionic fluids proposed by us recently [J. Chem. Phys. 100, 5219 (1994)] for symmetric electrolytes is extended to study the structure of electric double layer for a charge‐asymmetric (2:1) situation involving hard sphere ions of equal diameter with a continuum or neutral hard sphere model for the solvent. The hard sphere contributions to the excess free energy density and its derivatives for the inhomogeneous system are evaluated nonperturbatively through a position‐dependent effective weighted density, which is also used to obtain the corresponding ionic contributions through a second‐order functional Taylor expansion. The calculated results for the continuum solvent model show reasonably good agreement with the available simulation results, while the layering effect due to hard sphere exclusion and the charge inversion phenomena are some of the interesting consequences arising from the molecular nature of the solvent.

Generalized van der Waals density functional theory for nonuniform polymers

A density functional theory is presented for the effect of attractions on the structure of polymers at surfaces. The theory treats the ideal gas functional exactly, and uses a weighted density approximation for the hard chain contribution to the excess free energy functional. The attractive interactions are treated using a van der Waals approximation. The theory is in good agreement with computer simulations for the density profiles at surfaces for a wide range of densities and temperatures, except for low polymer densities at low temperatures where it overestimates the depletion of chains from the surface. This deficiency is attributed to the neglect of liquid state correlations in the van der Waals term of the free energy functional.

Structure of inhomogeneous dipolar fluids: A density functional approach

A density functional approach is developed for inhomogeneous dipolar fluids consisting of dipolar hard spheres in presence of external electric fields. The theory is applied to two systems, viz. a confined fluid between two planar charged walls where the field is uniform, and also a fluid where the dipoles are subjected to a radial field due to a uniformly charged hard sphere ion at the centre. A nonperturbative weighted density approximation is employed to incorporate the effect of short range hard sphere-like correlations while the long-range effects are obtained perturbatively. The nonuniform density is expanded in terms of spherical harmonics and the correlation function used as input corresponds to the mean spherical approximation. In the case of planar geometry, the calculated density and polarization profiles are quite comparable with the available simulation and other results. In the presence of the radial field, the polarization exhibits oscillations showing a clear variation of the effective die...

Structure of electric double layers: A simple weighted density functional approach

A simple weighted density functional approach is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter. The formalism is nonperturbative with both hard-sphere and electrical contributions to the one-particle correlation function evaluated through a suitably averaged weighted density, the only input being the second-order direct correlation functions of the corresponding uniform system. The approach is designed in such a way, that the calculation of the weight function is decoupled from the weighted density. Numerical results on the ionic density profile and the mean electrostatic potential near a hard wall at several surface charge densities are shown to compare well with available simulation results. The corresponding results for the nonprimitive molecular solvent model provide insight into the layering effect and the charge inversion phenomena.

Structure of Spherical Electric Double Layers Containing Mixed Electrolytes: A Systematic Study by Monte Carlo Simulations and Density Functional Theory

The structure of spherical electric double layers in the presence of mixed electrolytes is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modeled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres, and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard-sphere contribution to the one-particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in canonical ensemble. The system is studied at varying ionic concentrations, at different concentration ratios of mono- and multivalent counterions of mixed electrolytes, at different diameters of hard spheres, at different macroion radius, and at varying polyion surface charge densities. The theoretical predictions in terms of the density profiles and the mean electrostatic potential profiles are found to be in good agreement with the simulation results. This model study shows clear manipulations of ionic size and charge correlations in dictating a number of interesting phenomena relating to width of the diffuse layer and charge inversion under different parametric conditions.

Structure of spherical electric double layers: A density functional approach

A density functional theory is presented for the structure of spherical electric double layers within the restricted primitive model, where the macroion is considered as a hard sphere having uniform surface charge density, the small ions as charged hard spheres, and the solvent is taken as a dielectric continuum. The theory is partially perturbative as the hard-sphere contribution to the one-particle correlation function is evaluated using suitably averaged weighted density and the ionic part is obtained through a second-order functional Taylor expansion around the uniform fluid. The theory is in quantitative agreement with Monte Carlo simulation for the density profiles and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations. The theory is able to provide interesting insights about the layering and the charge inversion phenomena occurring at the interface.