Jeffrey D. Weinhold

Density functional theory for inhomogeneous polymer systems. I. Numerical methods

We present a new real space Newton-based computational approach to computing the properties of inhomogeneous polymer systems with density functional theory (DFT). The DFT is made computationally efficient by modeling the polymers as freely jointed chains and obtaining direct correlation functions from polymer reference interaction site model calculations. The code we present can solve the DFT equations in up to three dimensions using a parallel implementation. In addition we describe our implementation of an arc-length continuation algorithm, which allows us to explore the phase space of possible solutions to the DFT equations. These numerical tools are applied in this paper to hard chains near hard walls and briefly to block copolymer systems. The method is shown to be accurate and efficient. Arc-length continuation calculations of the diblock copolymer systems illustrate the care required to obtain a complete understanding of the structures that may be found with this polymer-DFT approach.

Density functional theory of simple polymers in a slit pore. II. The role of compressibility and field type

Simple tangent, hard site chains near a hard wall are modeled with a density functional (DF) theory that uses the direct correlation function, c(r), as its “input.” Two aspects of this DF theory are focused upon: (1) the consequences of variations in c(r)’s detailed form; and (2) the correct way to introduce c(r) into the DF formalism. The most important aspect of c(r) is found to be its integrated value, ĉ(0). Indeed, it appears that, for fixed ĉ(0), all reasonable guesses of the detailed shape of c(r) result in surprisingly similar density distributions, ρ(r). Of course, the more accurate the c(r), the better the ρ(r). As long as the length scale introduced by c(r) is roughly the hard site diameter and as long as the solution remains liquid-like, the ρ(r) is found to be in good agreement with simulation results. The c(r) is used in DF theory to calculate the medium-induced potential, UM(r), from the density distribution, ρ(r). The form of UM(r) can be chosen to be one of a number of different forms. It ...

Comparisons between integral equation theory and molecular dynamics simulations for realistic models of polyethylene liquids

Previous applications of DF theory required a single chain 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{sub M}(r), and different wall-polymer interactions to be investigated from a single Monte Carlo simulation. The increase in computational efficiency is immense.

The structure of amorphous polymers near surfaces: athermal systems

Abstract The Wall PRISM theory of Yethiraj and Hall for calculating the distribution of a polymer liquid near a hard wall is generalised to the case of polymers with complex monomeric architectures, consisting of multiple sites. Results are shown for freely jointed chains, alkanes, isotactic polypropylene, polyisobutylene, and polydimethyl siloxane. It is found that the side chain groups in the substituted polymers are preferentially present near the wall, and tend to shield the atoms on the chain backbone from the surface. Wall PRISM is found to give accurate results for the polymer density distribution beyond about 2 A from the wall. In the immediate vicinity of the wall, the theory satisfactorily predicts the distribution for a melt of hard chains, but is not rich enough to account for the subtle effect of intermolecular interactions on the local distribution in the immediate vicinity of the surface.