Intradomain phase transitions in flexible block copolymers with self-aligning segments

We study a model of flexible block copolymers (BCPs) in which there is an enlthalpic preference for local alignment, among like-block segments. We describe a generalization of the self-consistent field theory (SCFT) of flexible BCPs to include inter-segment orientational interactions via a Landau-DeGennes free energy associated with a polar or nematic order parameter for segments of one component of a diblock copolymer. We study the equilibrium states of this model numerically, using a pseudo-spectral approach to solve for chain conformation statistics in the presence of a self-consistent torque generated by inter-segment alignment forces. Applying this theory to the structure of lamellar domains composed of symmetric diblocks possessing a single block of "self-aligning", polar segments, we show the emergence of spatially complex segment order parameters (segment director fields) within a given lamellar domain. Because BCP phase separation gives rise to spatially inhomogeneous orientation order of segments even in the absence of explicit intra-segment aligning forces, the director fields of BCPs, as well as thermodynamics of lamellar domain formation, exhibit a highly non-linear dependence on both the inter-block segregation ($\chi N$) and the enthalpy of alignment ($\varepsilon$). Specifically, we predict the stability of new phases of lamellar order in which distinct regions of alignment coexist within a single mesodomain, and which spontaneously break the symmetry of the lamella pattern of composition in the melt via in-plane tilt of the director in the centers of the like-composition domains. We show further that, in analogy to a Freedericksz transition in confined nematics, that the elastic costs to reorient segments within the domain, as described by Frank elasticity, increase the threshold value $\varepsilon$ needed to induce this intra-domain phase transition.