Optimized cluster theory of polymer blends: General formulation and application to isotopic polyethylene mixtures

Closure to the PRISM equation derived from nonlinear response theory

Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular generalization of the mean spherical approximation (MSA) closure of Lebowitz and Percus to the atomic Ornstein-Zernike (OZ) equation and is similar in some aspects to the reference "molecular" MSA (R-MMSA) closure of Schweizer and Yethiraj to PRISM. For a model binary blend of freely-jointed chains, the new closure predicts an unmixing critical temperature, Tc, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. Predictions for Tc of the new closure differ greatest from those of the R-MMSA at intermediate N, the latter being about 40% higher than the former there, but at large N, both theories give about the same values. For an isotopic blend of polyethylene, the new and R-MMSA closures predict a Tc about 25% higher than the experimental value, which is only moderately less accurate than the prediction of atomic OZ-MSA theory for Tc of methane. In this way, the derivation and its consequences help to identify the ingredients in a theory needed to properly model the equilibrium properties of a polymeric liquid at both short and long lengthscales.

Liquids in equilibrium: beyond the hypernetted chain

Density functional techniques are used to derive a charging expression for the non-uniform density of a molecular liquid. In the atomic limit the equation reduces to an exact form due to Fixman. The theory is simplified greatly via a physical approximation that accounts for three-body correlations beyond those included in the hypernetted chain (HNC) closure of the Ornstein-Zernike (OZ) equation. The radial distribution function is obtained as a special case. The theory is tested by examining the phase behavior of two fundamental complex fluids: the homopolymer blend and diblock copolymer melts. For the former it is found, contrary to HNC theory and its molecular generalizations, that a critical temperature Tc is predicted from the structure route. This To scales linearly with degree of polymerization N in agreement with Flory theory. The simplest form of the theory can be considered as a way to incorporate attractive interactions within a formalism that is very similar to that of the OZ or reference interaction site model (RISM). The relevance of the theory to charged liquids is also discussed.

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.