The equilibrium properties of block copolymer liquids are studied using liquid state theory. We first present the formal extension of the polymer reference interaction site model theory to treat block copolymers of general architectures, and then apply this to the symmetric block copolymer using the Gaussian thread model. Contact with Leibler mean field theory is made by employing the ‘‘reference molecular mean spherical approximation’’ closure within the thread idealization. A host of density and concentration fluctuation effects are studied using the ‘‘reference molecular Percus–Yevick’’ closure. In particular, the dependence of the effective chi-parameter and peak scattering intensity on density, chain length, temperature, composition, and spatial range of interactions is examined. Within the thread-polymer/effective incompressibility assumption the chain length dependence of the fluctuation stabilization in the vicinity of the mean field spinodal is found to be the same as in the Brazovskii–Fredrickson–Helfand theory. However, a rich dependence on the nonuniversal prefactors, and the enthalpic origin of the feedback mechanism, distinguishes these results from previous field theoretic work.

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The spatially local and long wavelength properties of diblock copolymer melts are studied using the polymer reference interaction site model theory. Two new molecular based closure approximations, the ‘‘reference-molecular mean spherical approximation’’ (R-MMSA) and the ‘‘reference-molecular Percus–Yevick’’ (R-MPY) approximation are investigated numerically for structurally symmetric, flexible, and semiflexible copolymers with finite hard-core diameters. For these models both closures lead to a destruction of all spinodal instabilities for finite degrees of polymerization. Results using the R-MMSA closure for the larger chain lengths studied approach the analytic predictions of the Gaussian thread model. On the other hand, numerical results for the R-MPY closure show a temperature regime in which there is an apparent chain length independent fluctuation stabilization for moderate degrees of polymerization in qualitative agreement with recent Monte Carlo simulations. However, we believe this apparent scaling arises from a very slow approach towards the asymptotic, finite size fluctuation behavior analytically derived in the previous paper for the Gaussian thread model. In accord with recent simulations, the peak scattering wave vector exhibits temperature dependence due to collective, many chain fluctuation effects. Predictions of the local structure and composition in the disordered phase are made which show that considerable length scale dependent deviations from homopolymer melt packing emerge at low temperatures.

Thermally induced packing correlations and apparent microphase spinodal boundaries are studied for conformationally asymmetric diblock copolymer melts using the "polymer reference interaction site model" (PRISM) theory. Microphase instabilities are deduced from predictions of the collective scattering intensities and are correlated with the degree of conformational mismatch. For diblocks interacting through attractive van der Waals forces, but where the Flory mean field -parameter is identically zero, the predictions reveal rich dependencies of the apparent microphase spinodal boundaries on the degree of structural asymmetry between blocks which are consistent with recent polyolefin diblock melt experiments. This demonstrates the importance of the coupling between local packing correlations and attractive interactions, and the fundamental inseparability of enthalpic and entropic contributions to the effective -parameter governing miscibility. Length-scale-dependent "effective compositions" above and near an apparent microphase spinodal temperature are also calculated. Large enrichments of the local composition are predicted in the highly fluctuating, low temperature, regime which depend on copolymer composition, density, and nonuniversal chain structural features. Marked enhancements of this clustering relative to melt behavior are predicted for concentrated diblock solutions. The present numerical calculations are also compared to previous analytical Gaussian thread model PRISM predictions, and general qualitative consistency is found. Numerical calculations for blends of the same polymers are also performed and demonstrate a very large reduction of concentration fluctuation effects and physical clustering for this macrophase separation case.

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