A perturbation densityfunctional theory for polyatomic fluids. I. Rigid molecules J. Chem. Phys. 97, 9222 (1992); 10.1063/1.463298 Density functional theory of freezing for quantum systems. I. Path integral formulation of general theory J. Chem. Phys. 92, 3034 (1990); 10.1063/1.457900 Density functional theory of nonuniform polyatomic systems. II. Rational closures for integral equations

Articles you may be interested inInterfacial colloidal sedimentation equilibrium. II. Closure-based density functional theory A perturbation density functional theory for polyatomic fluids. II. Flexible molecules With the density functional theory outlined in paper I, we address and formally solve the nonlinear inversion problem associated with identifying the entropy density functional for systems with bonding constraints. With this development, we derive a nonlinear integral equation for the average site density fields of a polyatomic system. When external potential fields are set to zero, the integral equation represents a mean field theory for symmetry breaking and thus phase transformations of polyatomic systems. In the united atom limit where the intramolecular interaction sites become coincident, the mean field theory becomes identical to that developed for simple atomic systems by Ramakrishnan, Yussouff, and others. When the external potential fields are particle producing fields (in the sense introduced long ago by Percus), the integral equation represents a theory for the solvation of a simple spherical solute by a polyatomic solvent. In the united atom limit for the solvent, the theory reduces to the hypernetted chain (HNC) integral equation. This reduction is not found with the so-called "extended" RISM equation; indeed, the extended RISM equation-the theory in which the HNC closure of simple systems is inserted directly into the Chandler-Andersen (i.e., RISM or SSOZ) equation-behaves poorly in the united atom limit. The integral equation derived herein with the density functional approach however suggests a rational closure of the RISM equation which does pass over to the HNC theory in the united atom limit. The new integral equation for pair correlation functions arising from this suggested closure is presented and discussed.

We modeled the effects of temperature, degree of polymerization, and surface coverage on the equilibrium structure of tethered poly(N-isopropylacrylamide) chains immersed in water. We employed a numerical self-consistent field theory where the experimental phase diagram was used as input to the theory. At low temperatures, the composition profiles are approximately parabolic and extend into the solvent. In contrast, at temperatures above the LCST of the bulk solution, the polymer profiles are collapsed near the surface. The layer thickness and the effective monomer fraction within the layer undergo what appears to be a first-order change at a temperature that depends on surface coverage and chain length. Our results suggest that as a result of the tethering constraint, the phase diagram becomes distorted relative to the bulk polymer solution and exhibits closed loop behavior. As a consequence, we find that the relative magnitude of the layer thickness change at 20 and 40 °C is a nonmonotonic function of surface coverage, with a maximum that shifts to lower surface coverage as the chain length increases in qualitative agreement with experiment.

Thermodynamics and local structure of vinyl polymer melts

Polyatomic density functional theory was used to model tridecane chains near a hard wall under melt conditions. Polymer reference interaction site model (PRISM) liquid state theory provided the bulk structure input for the density functional. The density profile, the fractional distribution of sites, and the variation of the end-to-end separation of the chains as a function of distance from wall contact were calculated, and excellent agreement with the results of full multichain simulation was found.

We hypothesize that the shift of the glass transition temperature of polymers in confined geometries can be largely attributed to the inhomogeneous density profile of the liquid. Accordingly, we assume that the glass temperature in the inhomogeneous state can be approximated by the T g of a corresponding homogeneous, bulk polymer, but at a density equal to the average density of the inhomogeneous system. Simple models based on this hypothesis give results which are in agreement with experimental measurements of the glass transition of confined liquids.

Reversible work, also known as the potential of mean force, is used to map explicit atom (EA) onto united atom (UA) potentials for CH, CH2, CH3, and CH4 sites. These UA potentials are found to be temperature dependent and to be described by stretched exponential-6 functions. Although this is fairly dissimilar to the Lennard-Jones 6−12 potential, the one may be mapped onto the other by requiring that the second virial coefficients and locations of the potential minimum be equal for the two forms. When this is done, good agreement with standard UA potentials is found.

,.. " Previous applications of DF theory required asinglechain Monte ', Carlo simulation to be performed within a self-consistent loop. In the current work, a methodology is developed which permits the simulation to be taken out of the iterative loop. Consequently, the calculation of the self-consistent, medium-induced-potential, or field, is decoupled from the simulation. This approach permits different densities, different forms of U~(r), and different wall-polymer interactions to be investigated from a single Monte Carlo simulation. The increase in immense. computational efficiency is DISCLAIMER ~ This repoti was prepared as an account of work