Correlations in Disordered Melts of Asymmetric Diblock Copolymers

Simulations of several different coarse-grained models are used to characterize how the structure factor S(q) in melts of compositionally asymmetric diblock copolymers varies with changes in the volume fraction f of the minority block, the parameter χ_eN (where χ_e is an effective interaction parameter and N is degree of polymerization), and the invariant degree of polymerization N. We focus here on systems with 0.25 ≤ f < 0.5. Results obtained with several different models are consistent in the expected sense, demonstrating the validity of the corresponding states principle when applied to asymmetric copolymers. Analysis is simplified by a demonstration that the effective χ parameter for these simple models is almost independent of composition. Results are compared to renormalized one-loop theory predictions, which become rapidly less accurate with increasing asymmetry. In the absence of an adequate predictive theory, a quantitative empirical relationship is developed to describe the dependence of peak intensity on χ_eN, f, and N over the range 0.25 < f < 0.5. The dependences of the peak intensity on χN in asymmetric and symmetric copolymers are qualitatively similar and exhibit a crossover from a weakly fluctuating regime in which the random-phase approximation (RPA) is nearly valid to a regime of strong composition fluctuations, with a crossover centered on the RPA spinodal value of χN. This crossover becomes noticeably sharper for more asymmetric systems, however, reflecting a more abrupt appearance of well-segregated disordered domains with increasing χ in asymmetric copolymer melts.