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 field Flory–Huggins expression for the free energy of mixing and our RISM‐MSA theory is determined, along with general analytical connections between the chi parameter and intermolecular pair correlations in the liquid. Detailed numerical applications to athermal and isotopic chain polymer blend models are presented for both the chi parameter and the structure. For athermal blends a negative, concentration‐dependent chi parameter is found which decreases with density, structural asymmetry, and increases with molecular weight. For isotopic blends, the effective (positive) chi parameter is found to be strongly renormalized downward from its mean field enthalpic value by long range fluctuations in monomer concentration induced by polymeric connectivity and excluded volume. Both the renormalization and composition dependence of the chi parameter increase with chain length and proximity to the spinodal instability. The critical temperature is found to be proportional to the square root of the degree of polymerization in stark contrast to the classical mean field prediction of a linear dependence. Comparison of the theoretical predictions with SANS measurements and computer simulations is presented, alongwith brief discussions of nonideal effects and lower critical solution temperature phenomena.

Integral equation theory of the structure and thermodynamics of polymer blends

We report results on the linear viscoelasticity (oscillatory shear in the temperature range Tg (glass-transition temperature) ≤ T ≤ Tg + 90 K) of miscible blends of polystyrene (PS) and poly(vinyl methyl ether) (PVME) and segmental relaxations, measured by dielectric spectroscopy. The Flory−Huggins interaction parameter of this blend is weakly negative, and the glass transitions of the pure components are quite disparate (ΔTg = 125 K). PS/PVME blends have been found to be consistently thermorheologically complex at both the segmental and terminal levels:  the empirical time−temperature superposition (tTS) principle applies to neither their oscillatory shear response nor their dielectric response. Using the tube model, we quantitatively compare dielectric and mechanical results. At low temperatures, the effective time scale for motion of a Kuhn segment (the shortest Rouse mode) is near the long-time end of the distribution of segmental relaxation times of PVME, in both the pure and blended states. The slow...

Dynamics in Miscible Blends of Polystyrene and Poly(vinyl methyl ether)

The interactions between globular proteins in the presence of poly (ethylene glycol) (PEG) are probed through the measurement of the protein solution second virial coefficient (B2). The solution properties of PEG are characterized for four molecular weights (400, 1000, 6000, and 12 000), providing an opportunity for quantitative comparison of measurements and theoretical predictions of B2. PEG displays a buffer and molecular weight-dependent lower critical solution temperature. As the polymer solution approaches phase separation, the consequences of depletion attractions increase significantly. For lysozyme and bovine serum albumin in sulfate buffers with PEG, B2 is not well described by standard depletion models. This failure is accentuated in acetate buffers where B2 is a nonmonotonic function of polymer concentration. The attractive minima in B2 are closely associated with the proximity of the heating-induced phase separation of aqueous PEG solutions. The experimental data for both proteins in the pres...

Effects of polyethylene glycol on protein interactions

Before the application of small-angle neutron scattering (SANS) to the study of polymer structure, chain conformation studies were limited to light and small-angle x-ray scattering techniques, usually conducted in dilute solution owing to the difficulties of separating the inter- and intrachain contributions to the structure. The unique role of neutron scattering in soft condensed matter arises from the difference in the coherent scattering length between deuterium (bD = 0.67 × 10−12 cm) and hydrogen (bH = −0.37 × 10−12 cm), which results in a marked difference in scattering power (contrast) between molecules synthesized from normal (hydrogeneous) and deuterated monomer units. Thus, deuterium labelling techniques may be used to 'stain' molecules and make them 'visible' in the condensed state and other crowded environments, such as concentrated solutions of overlapping chains.For over two decades, SANS has proved to be a powerful tool for studies of structure–property relationships in polymeric systems and has made it possible to extract unique information about their size, shape, conformational changes and molecular associations. These applications are now so numerous that an exhaustive review of the field is no longer practical, so the authors propose to focus on the use of SANS for studies of strongly interacting soft matter systems. This paper will therefore discuss basic theory and practical aspects of the technique and will attempt to explain the physics of scattering with the minimum of unnecessary detail and mathematical rigour. Examples will be given to demonstrate the power of SANS and to show how it has helped to unveil universal aspects of the behaviour of macromolecules in such apparently diverse systems as polymer solutions, blends, polyelectrolytes and supercritical mixtures. The aim of the authors is to aid potential users who have a general scientific background, but no specialist knowledge of scattering, to understand the potential of the technique and, if they so choose, to apply it to provide new information in areas of their own particular research interests.

http://iopscience.iop.org/article/10.1088/0034-4885/68/8/R02/pdf

Recent applications of small-angle neutron scattering in strongly interacting soft condensed matter

The influence of nanometer thick, highly anisotropic organically modified layered silicate (montmorillonite) on the phase behavior of deuterated polystyrene (dPS) and poly(vinyl methyl ether) (PVME) is investigated by a combination of small-angle neutron scattering (SANS) and a two-dimensional combinatorial method based on light scattering and corroborated by single-point static cloud-point light scattering. The presence of layered silicates up to a volume fraction of 0.04 is found to leave the phase diagram essentially unchanged, with the values of the Flory−Huggins χ parameter at high temperatures being nearly independent of added silicate for blends with layered silicates up to a volume fraction of 0.008. These surprising results, in light of the significantly higher polarity of PVME in comparison to PS, allows us to investigate the influence of such layered silicates on the kinetics and morphology of phase separation in polymer blends as detailed in a previous paper.

Phase Behavior of PS-PVME Nanocomposites

The system PVME/d‐PS has been investigated by neutron small angle scattering. By extrapolating the critical scattering, the spinodal was determined and used to calculate the Flory–Huggins parameter χ(φ,T) in the frame of mean field theory. Separating the Gibbs potential of mixing ΔG in a Flory–Huggins term χ(φ,T) and a configurational term for the entropy ΔS, it turns out that χ is independent of the molecular weight, and of the weight distribution, i.e., it is a local or ‘‘segmental’’ quantity. The critical scattering was carefully investigated at the critical concentration. At temperatures Tc−T>2.4 K(Tc=141.9 °C), a mean field behavior of the susceptibility S(Q=0) was clearly observed, with a critical exponent γ=1. However, in a region of Tc−2.4 K≤T<Tc, a crossover occurs to a critical exponent γ≂1.26; it resembles the Ising behavior which is well established for normal liquid mixtures. The function S(Q) also describes the characteristic segmental length σ. Both σ and the range parameter of χ, r0, are i...

R. Thomas

Papers

Investigation of the phase diagram and critical fluctuations of the system polyvenylmethylether and d‐polystyrene with neutron small angle scattering