How far is far from critical point in polymer blends? Lattice cluster theory computations for structured monomer, compressible systems

Abstract

Although the lattice cluster theory (LCT) incorporates many features which are essential in describing real polymer blends, such as compressibility, monomer structures, local correlations, chain connectivity, and polymer–polymer interactions, it still remains a mean field theory and is therefore not applicable in the vicinity of the critical point where critical fluctuations become large. The LCT, however, permits formulating the Ginzburg criterion, which roughly specifies the temperature range in which mean field applies. The present treatment abandons the conventional assumptions of incompressibility and of composition and the molecular weight independent effective interaction parameter χeff upon which all prior analyses of the Ginzburg criterion are based. Blend compressibility, monomer structure, and local correlations are found to exert profound influences on the blend phase diagram and other critical properties and, thus, exhibit a significant impact on the estimate of the size of the nonclassical region. The LCT is also used to test various methods which employ available experimental data in computations of the Ginzburg number Gi. The reduced temperature τ=‖T−Tc‖/T defining the range of the validity of mean field theory (τ≳τMF) and the onset of the Ising-type scaling regime (τ≳τcrit) are quite different, and renormalization group estimates of τMF and τcrit are presented as a function of Gi to more precisely specify these scaling regimes.