Polymer Semiflexibility Induces Nonuniversal Phase Transitions in Diblock Copolymers

The stress deformation response influenced by the chain rigidity for mesostructures in diblock copolymers

A self-consistent field theory formalism based on the wormlike chain model is developed to investigate the stress-strain relation for mesostructures in diblock copolymers under the influence of chain rigidity, involving the adjustable simulation cell in the non-orthogonal coordinates by means of optimization of free energy. We elucidate the effect of the chain persistency broadly spanning from the Gaussian chain to the rigid rodlike chain on the elastic response of mesophases that deviate from the initial equilibrium structures. We analytically and numerically demonstrate that our current approach in the long chain limit recovers to the Gaussian-chain-based theory. Being ascribed to the distinct conformational behaviors for flexible chains and rigid rodlike chains, the tensile and compressive stresses applied to lamellae exhibit asymmetric deformation behaviors and the shear stress applied to the initial equilibrium hexagonal cylinders results in noticeable deviations in the shape and spatial arrangement of cylindroids for various chain rigidity values. For the zero stress, in addition, our approach can be straightforwardly utilized to explore the optimal size and shape of the simulation cell in order to achieve a stress free configuration of systems.

Biology and Physics of Heterochromatin-Like Domains/Complexes

The hallmarks of constitutive heterochromatin, HP1 and H3K9me2/3, assemble heterochromatin-like domains/complexes outside canonical constitutively heterochromatic territories where they regulate chromatin template-dependent processes. Domains are more than 100 kb in size; complexes less than 100 kb. They are present in the genomes of organisms ranging from fission yeast to human, with an expansion in size and number in mammals. Some of the likely functions of domains/complexes include silencing of the donor mating type region in fission yeast, preservation of DNA methylation at imprinted germline differentially methylated regions (gDMRs) and regulation of the phylotypic progression during vertebrate development. Far cis- and trans-contacts between micro-phase separated domains/complexes in mammalian nuclei contribute to the emergence of epigenetic compartmental domains (ECDs) detected in Hi-C maps. A thermodynamic description of micro-phase separation of heterochromatin-like domains/complexes may require a gestalt shift away from the monomer as the "unit of incompatibility" that determines the sign and magnitude of the Flory-Huggins parameter, χ. Instead, a more dynamic structure, the oligo-nucleosomal "clutch", consisting of between 2 and 10 nucleosomes is both the long sought-after secondary structure of chromatin and its unit of incompatibility. Based on this assumption we present a simple theoretical framework that enables an estimation of χ for domains/complexes flanked by euchromatin and thereby an indication of their tendency to phase separate. The degree of phase separation is specified by χN, where N is the number of "clutches" in a domain/complex. Our approach could provide an additional tool for understanding the biophysics of the 3D genome.

Field theoretic approach for block polymer melts: SCFT and FTS

This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

Polymer science has been driven by ever-increasing molecular complexity, as polymer synthesis expands an already-vast palette of chemical and architectural parameter space. Copolymers represent a key example, where simple homopolymers have given rise to random, alternating, gradient, and block copolymers. Polymer physics has provided the insight needed to explore this monomer sequence parameter space. The future of polymer science, however, must contend with further increases in monomer precision, as this class of macromolecules moves ever closer to the sequence-monodisperse polymers that are the workhorses of biology. The advent of sequence-defined polymers gives rise to opportunities for material design, with increasing levels of chemical information being incorporated into long-chain molecules; however, this also raises questions that polymer physics must address. What properties uniquely emerge from sequence-definition? Is this circumstance-dependent? How do we define and think about sequence dispersity? How do we think about a hierarchy of sequence effects? Are more sophisticated characterization methods, as well as theoretical and computational tools, needed to understand this class of macromolecules? The answers to these questions touch on many difficult scientific challenges, setting the stage for a rich future for sequence-defined polymers in polymer physics.

Fluctuation Effects in Semiflexible Diblock Copolymers

We present a simulation study of the equilibrium thermodynamic behavior of semiflexible diblock copolymer melts. Using discretized wormlike chains and field-theoretic Monte Carlo, we find that concentration fluctuations play a critical role in controlling phase transitions of semiflexible diblock copolymers. Polymer flexibility and aspect ratio control the order-disorder transition Flory-Huggins parameter χ_ODTN. For polymers with low aspect ratios, fluctuations strongly elevate the phase transition χ_ODTN at finite molecular weights. For high aspect-ratio polymers, chain semiflexibility decreases the phase transition χ_ODTN. We find that the simulated phase behavior agrees well with our recently developed fluctuation theory based on wormlike chain configurations and a one-loop treatment of concentration fluctuations.