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

Abstract

We study a model of flexible block copolymers (BCPs) in which there is an enlthalpic preference for orientational order, or local alignment, among like-block segments. We describe a generalization of the self-consistent field theory of flexible BCPs to include inter-segment orientational interactions via a Landau-de Gennes 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 (χN) and the enthalpy of alignment (ε). Specifically, we predict the stability of new phases of lamellar order in which distinct regions of alignment coexist within the single mesodomain and spontaneously break the symmetries of the lamella (or smectic) pattern of composition in the melt via in-plane tilt of the director in the centers of the like-composition domains. We further show that, in analogy to Freedericksz transition confined nematics, the elastic costs to reorient segments within the domain, as described by the Frank elasticity of the director, increase the threshold value ε needed to induce this intra-domain phase transition.

Open-source code for self-consistent field theory calculations of block polymer phase behavior on graphics processing units

“…The original PSCF code [14] was designed to utilize only a single CPU core. This provides adequate speed for many tasks, and has allowed the code to be successfully used to analyze block copolymer phase behavior [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. To determine the relative stability of different candidate morphologies in a region of the block polymer parameter space, a SCFT calculation must be performed for each competing morphology at many points in parameter space.…”

Breaking Mirror Symmetry of Double Gyroids via Self-Assembly of Chiral Block Copolymers

“…A methodology to probe homochiral evolution was thus established for BCP*, which probes the chirality of monomeric entities (i.e., molecular chirality) via electronic circular dichroism (ECD), while the helical disposition of these groups on the backbone of chiral blocks (i.e., conformational chirality) is probed by vibrational circular dichroism (VCD). ,, In addition, the specific handedness (i.e., hierarchical chirality) of helical hierarchical superstructures was identified by electron microscopy tomography . The hypothetical mechanism for forming helical hierarchical superstructures through interdomain twisting and shifting was proposed and tested experimentally , and compared to distinct mechanisms for chirality transfer, including the tilt chiral lipid bilayer (TCLB) model , and orientational self-consistent field theory (oSCFT), − both pointing to the importance of interchain chiral interactions for the formation of H*. Although chirality transfer at different length scales could be achieved in the cylindrical morphology self-assembly of BCPs*, the hierarchical chirality through intersegment chiral interactions for self-assembled nanonetworks such as double gyroid (DG) and double diamond (DD) remains unknown.…”

“…To verify this hypothesis, oSCF calculations were performed for comparison among different self-assembled morphologies, using chiral diblocks composed of 38% chiral block fraction at a fixed segregation strength χN = 15 (see SI for details). In the oSCF model for chiral diblocks, the strength of chiral intermolecular forces is parametrized by q ̅ 0 , − which is inversely proportional to the preferred cholesteric pitch of interchain packing of chiral segments. By symmetry, it is known that chiral segments acquire a thermodynamic preference for handed twist gradients (corresponding to a nonzero value of q ̅ 0 in the generalized Frank energy in EQ S2), analogous to the well-established effects of chirality in small-molecule liquid crystals.…”