James P. Donley

A DENSITY FUNCTIONAL THEORY FOR PAIR CORRELATION FUNCTIONS IN MOLECULAR LIQUIDS

We employ density functional methods to derive an integral equation for the two‐point intermolecular correlation function in molecular liquids. This radial distribution function is expressed as a two molecule average over a Boltzmann factor involving a ‘‘bare’’ site–site interaction, plus a pairwise additive, intermolecular, medium induced potential which mimics the remaining molecules in the system. This theory is formally exact in the low density limit. While the theory is valid in general for large molecule and polymer liquids, we demonstrate its use here for the case of the simple diatomic liquid. In this application, good agreement is found at all densities for the radial distribution function and equation‐of‐state when compared with computer simulations. Furthermore, the theory appears to give pressures that are more thermodynamically consistent than those obtained with reference interaction site model (RISM) theory.

Microscopic approach to inhomogeneous polymeric liquids

We discuss a liquid‐state theory for the equilibrium structure of inhomogeneous polymeric liquids. The theory consists of an equation for the density profile of a liquid in an external potential, which has been derived previously by density functional methods. In general, this equation must be solved by simulation techniques. However, if the chains are modeled as random walks—which is a reasonable approximation for flexible polymers at melt densities—we show that the theory reduces to a set of coupled integral equations which can be solved numerically. We present results for a single component liquid near a hard wall. Last, we show that, in the Gaussian thread limit, the theory reduces to a form that is very similar to Edwards–Helfand–Tagami ‘‘self‐consistent field’’ theory. However, there are important differences between the two theories for multicomponent liquids (a blend for example) if the types of polymers are structurally dissimilar.

A modified self-consistent-field theory: Application to a homopolymer melt near a hard wall

A modified self‐consistent‐field (SCF) theory is introduced and applied to hard‐site Gaussian chains at meltlike density in contact with a hard wall. The traditional Edwards, quantum theoretical approach to inhomogeneous polymeric systems is used, but the solvent induced potential is calculated by density functional (DF) methods where the polymer reference interaction site model (PRISM) theory is used to calculate the ‘‘input’’ for the potential calculation. Specific calculations were performed with DF theory, Helfand–Tagami SCF theory, and modified‐SCF theory. It is seen that the modified‐SCF theory is capable of capturing the major structural features predicted by DF theory, and it promises to be a useful bridge between the SCF and DF theories.

On the structure of polyelectrolyte solutions near the idealized counterion condensation threshold

In a previous work we derived an equation for the radial distribution function g(r) for molecular liquids. It accounted for density correlations at both the monomer and molecular level. Here, it is shown that the theory can be simplified to a form than allows it to be solved easily by standard numerical methods. The theory is applied to charged, rodlike polymers with explicit counterions in solution near the idealized counterion condensation threshold (λB/b∼1, where λB and b are the Bjerrum and chain bond length, respectively). For densities above chain overlap, ρ*, it is found that the counterion cloud is diffuse about the polymer with a range on the order of the Debye–Huckel screening length. It is shown that the scaling with density of the first nonzero wave vector peak kmax of the polymer–polymer partial structure factor agrees with experiment and previous theory, with kmax∼ρν and ν≈1/2 and 1/3, for densities above and below ρ*, respectively. It is also found that the ratio of the full width at half m...

Density pair correlation functions for molecular liquids: Approximations for polymers

We present a simple, physically motivated equation for the radial distribution function g(r) for molecular liquids, valid for polymers interacting via soft potentials. It is constructed to perform properly at low density for polyelectrolyte solutions. However, it also accounts for intermolecular correlations at both the molecular and monomer level, above those contained in the random phase approximation. We show that this theory reduces in various limits to some well-known polymer theories for g(r). In a preliminary analysis, we apply the equation for soft potentials to two very different systems: a solution of rod polyelectrolytes and a solution of flexible van der Waals chains.

Invariance of density correlations with charge density in polyelectrolyte solutions

We present a theory for the equilibrium structure of polyelectrolyte solutions. A simple and general optimization method is introduced that enables theories such as the random phase approximation to handle the strong repulsive forces present in such systems. Quantitative comparison is made with data from recent neutron-scattering experiments of randomly charged, hydrophilic polymers in salt-free, semidilute solution at various charge densities. We show that the invariance observed at high charge fraction may be the result of polymer-polymer correlations, rather than the conventional explanations involving counterion condensation.

A Model for the Two-Phase Behavior of Fluids in Dilute Porous Media

Experiments show that the coexistence region of a vapor-liquid system or binary liquid mixture is dramatically narrowed when the fluid is confined in a dilute porous medium such as a silica aerogel. We propose a simple model of the gel as a periodic array of cylindrical strands, and study the phase behavior of an Ising system confined in this geometry. Our results suggest that the coexistence region should widen out at lower temperatures, and that the narrowness observed near the critical point may be a fluctuation-induced effect. Disciplines Fluid Dynamics | Physical Sciences and Mathematics | Physics Comments At the time of publication, authors Douglas J. Durian and Andrea J Liu were affiliated with University of California, Los Angeles. Currently, they are faculty members at the Physics Department at the University of Pennsylvania. Author(s) James P. Donley, Rebecca M. Nyquist, Andrea J. Liu, Herman Z. Cummins, Douglas J. Durian, David L. Johnson, and Eugene H. Stanley This book chapter is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/586 A MODEL FOR THE TWO-PHASE BEHAVIOR OF FLUIDS IN DILUTE POROUS MEDIA JAMES P. DONLEY, REBECCA M. NYQUIST and ANDREA J. LIU Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095