Local and microdomain concentration fluctuation effects in block copolymer solutions

On the basis of the simplest Gaussian thread model for structurally symmetric copolymers, the polymer reference interaction site model (PRISM) theory is applied to study the equilibrium properties of diblock copolymer solutions under neutral solvent conditions. Analytic predictions are obtained for the influence of local and microdomain scale concentration fluctuations on the relationship between temperature, degree of polymerization, and polymer concentration at the order-disorder transition (ODT). In the semidilute regime, PRISM predictions agree with blob scaling and fluctuation-corrected field theoretic analyses. However, in the concentrated solution and melt regime strong disagreements occur, and the naive mean field dilution approximation is found to fail. Nevertheless, apparent scaling laws emerge under concentrated conditions with effective exponents which depend on solvent quality, melt screening length, and other nonuniversal structural features. The primary origin of the dilution approximation failure is interchain nonrandom mixing, which is concentration dependent and driven by local packing effects. Microdomain scale fluctuations yield corrections of secondary importance which vanish in the long chain limit. For concentrated solutions and good solvents, the predicted apparent exponent is fortuitously in close agreement with semidilute blob scaling results, and also agrees with recent measurements on polystyrene-polyisoprene diblocks by Lodge and co-workers. Smaller effective exponents are found under Θ solvent conditions Systematic PRISM model calculations for properties strongly affected by microdomain scale fluctuations, such as small angle scattering intensity and local physical clustering, are also presented. Significant physical clustering is found in solutions of compositionally asymmetric diblocks even very far from the ODT.