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Abstract We present a theory of melting kinetics of semicrystalline polymers at temperatures above the equilibrium melting temperature, by accounting for conformational entropy of chains during melting. We have derived free energy landscapes for escape of individual chains from a lamella into the amorphous phase as a function of the characteristics of the initial lamella, such as the lamellar thickness, number of chain folds, fold‐ and lateral‐surface free energies, and mean energy of a monomer inside the lamella. We show that melting of lamellae is always accompanied by a free energy barrier which is entirely entropic in origin. In terms of the parameters characterizing the lamellae and the extent of superheating, closed‐form formulas are presented for the equilibrium melting temperature, driving force for crystallization, free energy barrier height, average expulsion time of a single chain from a lamella, and the melting velocity of lamellae. The present entropic barrier theory predicts that the dependence of melting velocity on superheating is nonlinear and non‐Arrhenius, in qualitative agreement with experimental observations reported in the literature. The derived formulas open an opportunity to further explore the role of various molecular features of semicrystalline polymers on their melting kinetics. 

When a solution of interpenetrating and entangled long flexible polymer chains is cooled to low enough temperatures, the chains crystallize into thin lamellae of nanoscopic thickness and microscopic lateral dimensions. Depending on the nature of the solvent and growth conditions, the lamellae exhibit several sectors that have differing growth kinetics and melting temperatures. Remarkably, these lamellae can spontaneously form tentlike morphology. The experimentally well-documented phenomenology of lamellar sectorization and tent formation has so far eluded a fundamental understanding of their origins. We present a theoretical model to explain this longstanding challenge and derive conditions for the relative stabilities of planar, sectored, and tent morphologies for polymer lamellae in terms of their elastic constants and interfacial tensions. While the present model offers an explanation of the origin of the spontaneous formation of sectored tentlike morphology as well as sectored planar morphology, in contrast to planar unsectored morphology, predictions are made for morphology transformations based on the materials properties of the polymeric lamellae. 

Aqueous solutions of oppositely charged macromolecules exhibit the ubiquitous phenomenon of coacervation. This subject is of considerable current interest due to numerous biotechnological applications of coacervates and the general premise of biomolecular condensates. Towards a theoretical foundation of structural features of coacervates, we present a field-theoretic treatment of coacervates formed by uniformly charged flexible polycations and polyanions in an electrolyte solution. We delineate different regimes of polymer concentration fluctuations and structural features of coacervates based on the concentrations of polycation and polyanion, salt concentration, and experimentally observable length scales. We present closed-form formulas for correlation length of polymer concentration fluctuations, scattering structure factor, and radius of gyration of a labelled polyelectrolyte chain inside a concentrated coacervate. Using random phase approximation suitable for concentrated polymer systems, we show that the inter-monomer electrostatic interaction is screened by interpenetration of all charged polymer chains and that the screening length depends on the individual concentrations of the polycation and the polyanion, as well as the salt concentration. Our calculations show that the scattering intensity decreases monotonically with scattering wave vector at higher salt concentrations, while it exhibits a peak at intermediate scattering wave vector at lower salt concentrations. Furthermore, we predict that the dependence of the radius of gyration of a labelled chain on its degree of polymerization generally obeys the Gaussian chain statistics. However, the chain is modestly swollen, the extent of which depending on polyelectrolyte composition, salt concentration, and the electrostatic features of the polycation and polyanion such as the degree of ionization. 

Using theory and simulations, we have investigated the phonons and their role in thermal energy transport in semicrystalline polyethylenes. Considering alternating stacks of lamellae and amorphous regions, and labeling one polyethylene chain interwoven among two amorphous regions and one lamella, we have explored the underlying mechanism of thermal conductivity of polyethylene in its semicrystalline state. We report that hairpin-like folds at the crystalline–amorphous interface significantly scatter phonons, allowing only less than half of the phonons to transmit through polyethylene backbone. Monitoring the phonon propagation and scattering at the interfaces, we have computed thermal conductivity of semicrystalline polyethylene. We have derived a design principle to control thermal conductivity of semicrystalline polyethylene in terms of lamellar thickness and the number of folds per chain at the crystalline–amorphous interface. 

We present a general theory of the phase behavior of concentrated multicomponent solutions of charged flexible heteropolymers with specific chemical sequences. Using a field theoretic formalism, we have accounted for sequence specificity, electrostatic and van der Waals interactions among all constituent species, and topological correlations among all heteropolymer chains in the system. Our general expression for the Helmholtz free energy of the system is in terms of density profiles of the various components and is an explicit function of the sequence specificity of the heteropolymers, polymer concentration, salt concentration, chemical mismatch among the various monomers and solvent, and temperature. We illustrate our general theory in the context of the self-assembly of intrinsically disordered proteins by considering solutions of sequence-specific charged-neutral heteropolymers. For the heteropolymers under consideration, the system exhibits microphase separation. The boundaries of order–disorder transition and the relative stabilities of the canonical microphase-separated morphologies (lamellar, cylindrical, and spherical) are presented in the weak segregation limit as functions of sequence, polymer concentration, chemical mismatch parameters, and salt concentration. Unique mapping between heteropolymer sequence and morphology diagram is presented. The derived general theory is of broad applicability in addressing sequence effects on the thermodynamic behavior of any multicomponent system containing flexible heteropolymers. 

We have investigated the structural evolution in solutions of the intrinsically disordered protein, α-synuclein, as a function of protein concentration and added salt concentration. Accounting for electrostatic and excluded volume interactions based on the protein sequence, our Langevin dynamics simulations reveal that α-synuclein molecules assemble into aggregates and percolated structures with a spontaneous selection of a dominant structure characteristic of microphase separation. This microphase assembly is mainly driven by electrostatic interactions between the residues in N-terminal and C-terminal of the protein molecules, and presence of salt loosens the compactness of the microstructures. We have quantified the features of the spontaneously formed microstructures using interchain radial distribution functions, and experimentally measurable inter-residue contact maps and static structure factors. Our results are in contrast to the commonly hypothesized mechanism of liquid–liquid phase separation (LLPS) for the formation of droplets in solutions of intrinsically disordered proteins, opening a new paradigm to understand the birth and structure of membraneless organelles. In general, construction of phase diagrams of intrinsically disordered proteins and other biomacromolecular systems needs to incorporate features of microphase separation into other mechanisms of macrophase separation and percolation.