(187ac) A Unified Picture of the Thermodynamics of Coil-Helix Block Copolymers Based on Geometric Characteristics of the Helix.

Chirality, which refers to the asymmetry, or handedness of a material is a physical property that can have profound impacts the properties and behavior of soft matter. Specifically for large macromolecules such as polymers, this asymmetry can propagate across hierarchical length scales - chiral monomers can be polymerized into a helical chain of specific handedness that can further self-assemble into chiral mesophases. In block copolymers (BCPs), even if this chirality transfer is not achieved, changes to the underlying thermodynamics can alter the phase diagram. For instance, in poly(n-butyl acrylate)-b-polypeptoid BCPs, making the polypeptoid block completely chiral decreases the temperature of the lamellar ordered-disordered transition (ODT), whereas in polystyrene-b-PLA poly(lactic acid) (PLA), a fully chiral PLA block increased the ODT. These contrasting observations highlight that chirality alone is not sufficient in rationalizing the observed thermodynamics and an underlying geometric framework is required.

Here, we present a geometric description of particle-based, coarse-grained helical polymers and demonstrate how single chain molecular dynamics simulation impact several important thermodynamic driving forces during self-assembly of BCP melts. (1) In the disordered phase, we show helices with shorter molecular pitch reduce the effective Flory-Huggins interaction parameter, whereas large pitch helices increase it. (2) In the lamellar domains, large molecular aspect ratio predicts the emergence of orientational ordering for short pitch helical blocks. This would reduce conformational entropy and stabilize the ordered morphology, which in turn lowers the effective Flory-Huggins interaction parameter required for the ODT. (3) By carefully measuring the ODT, we find a lower ODT for stiff helices with large aspect ratio. But in the absence of orientational order, the ODT shift is predicted by the thermodynamics of the disordered phase. All in all, we expand on the fundamental thermodynamic insights of helix-coil BCP self-assembly and show that geometric properties measured from a single chain simulation are capable of generating actionable information on bulk self-assembly - providing experimentalists with a general framework to develop novel materials from these helical precursors.