John G. Curro

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, ...

A non‐Gaussian theory of rubberlike elasticity based on rotational isomeric state simulations of network chain configurations. II. Bimodal poly(dimethylsiloxane) networks

Bimodal, poly(dimethylsiloxane) (PDMS) networks containing a large mole fraction of very short chains have been shown to be unusually tough elastomers. The purpose of this investigation is to understand the rubber elasticity behavior of these bimodal networks. As a first approach, we have assumed that the average chain deformation is affine. This deformation, however, is partitioned nonaffinely between the long and short chains so that the free energy is minimized. Gaussian statistics are used for the long chains. The distribution function for the short chains is found from Monte Carlo calculations. This model predicts an upturn in the stress‐strain curve, the steepness depending on the network composition, as is observed experimentally.

A non‐Gaussian theory of rubberlike elasticity based on rotational isomeric state simulations of network chain configurations. I. Polyethylene and polydimethylsiloxane short‐chain unimodal networks

The present theoretical approach to rubberlike elasticity is novel in that it utilizes the wealth of information which rotational isomeric state theory provides on the spatial configurations of chain molecules. Specifically, Monte Carlo calculations based on the rotational isomeric state approximation are used to simulate spatial configurations, and thus distribution functions for the end‐to‐end separation r of the chains. Results are presented for polyethylene (PE) [CH−2] and polydimethylsiloxane (PDMS) [Si(CH3)2–O–] chains most of which are quite short, in order to elucidate non‐Gaussian effects due to limited chain extensibility. Large values of r were found to be more prevalent in PDMS than in PE, primarily because of the unusually large Si–O–Si bond angle in the PDMS chain, which increases its spatial extension. The use of these distribution functions in place of the Gaussian function for network chains gives upturns in modulus at high elongations, because of the rapidly diminishing number of configu...

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.

Local structure of polyethylene melts

Polymer‐RISM (Reference‐interaction‐site‐model) theory is used to examine the local structure of a dense polyethylene melt near the freezing point. Predictions for the static structure factor are found to be in near quantitative agreement with new x‐ray diffraction data obtained at 430 K and 1 atm.

Reference interaction site model theory of polymeric liquids: Self‐consistent formulation and nonideality effects in dense solutions and melts

The reference interaction site model (RISM) integral‐equation approach to polymeric liquids is generalized to allow a self‐consistent determination of single‐chain and intermolecular pair correlations. Nonlinear medium‐induced effects on intrachain statistics are described at the level of self‐consistent pair interactions. Tractable schemes to implement the self‐consistency aspect are formulated for semiflexible and rotational isomeric state chain models, and applied numerically to concentrated solutions and melts of semiflexible polymers. Theoretical results are in good agreement with off‐lattice molecular dynamics simulations, and a rich dependence of the renormalized persistence length on temperature, aspect ratio, density, and degree of polymerization is found. The general formalism for polymer alloys is sketched and the potentially important role of local density and concentration fluctuations as nonuniversal mechanisms for inducing conformational perturbations is emphasized. A detailed analysis is m...

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.

Conjectures on the glass transition of polymers in confined geometries

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 Tg 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.