Kenneth S. Schweizer

Equilibrium theory of polymer liquids: Linear chains

An equilibrium theory of polymer melts, developed previously by us for polymer rings, is generalized to include linear polymer chains. This theory is based on the reference interaction site model (RISM) integral equation approach developed by Chandler and co‐workers for molecular liquids. We are able to construct a tractable formalism for the high polymer problem by employing the fact that a polymer molecule in a melt is ideal. This leads to a set of coupled, nonlinear integral equations for the intermolecular radial distribution functions. A simple optimized perturbative scheme is developed for long linear chains based on the relative unimportance of end effects. To lowest order, the theory reduces to a single nonlinear integral equation. Chain end corrections to the site‐averaged intermolecular correlation functions vanish according to N−2, where N is the degree of polymerization. Numerical techniques were used to compute the radial distribution function and structure factor for hard core linear Gaussia...

Integral equation theory of the structure and thermodynamics of polymer blends

Our recently developed RISM integral equation theory of the structure and thermodynamics of homopolymer melts is generalized to polymer mixtures. The mean spherical approximation (MSA) closure to the generalized Ornstein–Zernike equations is employed, in conjunction with the neglect of explicit chain end effects and the assumption of ideality of intramolecular structure. The theory is developed in detail for binary blends, and the random phase approximation (RPA) form for concentration fluctuation scattering is rigorously obtained by enforcing incompressibility. A microscopic, wave vector‐dependent expression for the effective chi parameter measured in small angle neutron scattering (SANS) experiments is derived in terms of the species‐dependent direct correlation functions of the blend. The effective chi parameter is found to depend, ingeneral, on thermodynamic state, intermolecular forces, intramolecular structure, degree of polymerization, and global architecture. The relationship between the mean fiel...

A comparison between integral equation theory and molecular dynamics simulations of dense, flexible polymer liquids

Recently we (J.G.C. and K.S.S.) formulated a tractable ‘‘reference interaction site model’’ (RISM) integral equation theory of flexible polymer liquids. The purpose of this paper is to compare the results of the theory with recent molecular dynamics simulations (G.S.G. and K.K.) on dense chain liquids of degree of polymerization N=50 and 200. Specific comparisons were made between theory and simulation for the intramolecular structure factor ω(k) and the intermolecular radial distribution function g(r) in the liquid. In particular it was possible to independently test the assumptions inherent in the RISM theory and the additional ideality approximation that was made in the initial application of the theory. This comparison was accomplished by calculating the intermolecular g(r) using the simulated intramolecular structure factor, as well as, ω(k) derived from a freely jointed chain model.The RISM theory results, using the simulated ω(k), were found to be in excellent agreement, over all length scales, ...

RISM theory of polymer liquids: Analytical results for continuum models of melts and alloys

Abstract Exact and approximate analytical solutions to the polymer RISM integral equation theory for melts and alloys are derived for long, flexible Gaussian chains. Comparisons of predictions for the isothermal compressibility and site-site intermolecular pair correlation function with exact numerical results reveals that the simplifications invoked to achieve analytic solutions are surprisingly accurate. A detailed study of the effective chi-parameter and critical temperature of binary isotopic blends of linear chains and copolymers of various microstructures is presented. In three dimensions, novel non-mean field predictions for the scaling of the critical temperature with degree of polymerization and copolymer architecture are found, and a rich dependence of the corresponding prefactor on system-specific features is determined. The breakdown of Flory-Huggins theory is due to a relatively long range, but weak, concentration fluctuation process which is a consequence of the combined influences of chain connectivity, intermolecular excluded volume and dispersion-like interactions. Physical analogies with critical phenomena ideas are developed, and comparisons are made of the theoretical predictions with recent small-angle neutron scattering observations.

Equation of state of polymer melts: General formulation of a microscopic integral equation theory

A microscopic statistical mechanical theory for the virial equation of state of polymer liquids is developed by combining reference interaction site model (RISM) integral equation methods for flexible chain molecules with a superposition approximation for three‐body orientational correlation functions. A compact expression for the pressure is obtained for athermal (hard core) fluids by neglecting explicit chain end effects. An analytical analysis of three‐body contributions to the equation of state is carried out for flexible polymers and the scaling dependence on chain length and monomer density is derived. The merits and disadvantages of the compressibility route to the equation of state are briefly discussed, along with the inclusion of attractive intermolecular forces via thermodynamic perturbation theory.

Equation of state of polymer melts: Numerical results for athermal freely jointed chain fluids

Our microscopic RISM integral equation theory for the virial equation of state of polymer liquids developed in the preceding paper is numerically implemented for athermal melts composed of freely‐jointed chains interacting via hard core site–site potentials. A modified ideal description of the single chain intramolecular correlations is employed which rigorously enforces the nonoverlapping core condition and leads to significant local coil expansion. Comparison of the theoretically computed virial pressure for tangent diatomics and short chains with available Monte Carlo simulation results over a wide range of packing fractions suggests the theory is quite accurate. Significant inconsistencies between the pressure computed via the virial and compressibility routes are found and discussed in light of the known limitations of the RISM method and the importance of self‐consistency corrections for flexible chain molecule liquids. A detailed numerical study of the density and degree of polymerization dependenc...

Order–disorder transitions of π‐conjugated polymers in condensed phases. II. Model calculations

Numerical calculations of the phase behavior and spectroscopic properties of π‐conjugated polymers are presented based on the theory developed in the preceding paper. The specific model studied includes the single chain statistics and the configuration‐dependent polymer–solvent interactions. The detailed dependence of the transition temperature and coexistence region on solvent, defect formation energy, chain length, and polydispersity is established. Relevance of the equilibrium calculations to electronic absorption and light scattering measurements is discussed. Experimental implications of the results for the polydiacetylenes, and the effects of system‐specific generalizations of the theory, are briefly considered.

Absorption spectrum of flexible conjugated polymers: the weak-disorder limit

Abstract Purely conformational contributions to dipole transition moments lead to a general new expression for the absorption spectrum of flexible conjugated polymers with persistence length ξ c and alternation δ. Blue-shifts are found at rod-to-coil transitions without invoking rotational defects that break the conjugation. Conformational coupling in the weak-disorder limit increases the effective alternation.

Order−disorder transitions of conjugated polymers in solution

Abstract A novel, statistical mechanical theory of the order-disorder transitions of conjugated polymers in dilute solution is proposed. Energetic stabilization of the rod-like conformation occurs via the interaction of the delocalized polymer electronic structure with the polarizable solvent. Model calculations reveal that system specific, discontinuous transition behavior can result.

Polymer crystallization: density functional theory and application to polyethylene

Abstract A general microscopic approach for the crystallization of flexible polymer melts is formulated and applied to polyethylene.