Effect of chain stiffness and temperature on the dynamics and microstructure of crystallizable bead-spring polymer melts

Ultra-slow self-similar coarsening of physical fibrillar gels formed by semiflexible polymers

Biopolymers tend to form fibrils that self-assemble into open network structures. While permanently crosslinked flexible polymers are relatively well understood, structure-property relationships of open networks and pseudo-gels formed by bundles of biopolymers are still controversial. Here we employ a generic coarse-grained bead-spring chain model incorporating semiflexibility and cohesive nonbonded interactions, that forms physical instead of chemical crosslinks. For flexible chains, the cohesive forces lead to the formation of a droplet phase while, at the same concentration, stiffer chains form bundles that self-assemble into percolated networks. From comprehensive molecular dynamics simulations we find that the reversible crosslinks allow for permanent relaxation processes. However, the associated reorganization of the filamentous network is severely hindered, leading to aging of its topology. Based on morphometric analyses, the ultra-slow coarsening in these systems is proven to be self-similar, which implies a number of scaling relations between structural quantities as the networks age. The percolated structures are characterized by different dynamic regimes of slow, anomalous diffusion with highly non-Gaussian displacements. Relaxation dynamics is found to become extremely slow already on moderate length scales and further slowing down as coarsening proceeds. Using a minimal model supported by observations on filament rupture and rearrangement, our study helps to shed light on various interrelated structural and dynamical aspects of coarsening nonergodic systems relevant for fibrous networks, pseudo-gels, and physical fibrillar gels.

Local and Global Order in Dense Packings of Semi-Flexible Polymers of Hard Spheres

The local and global order in dense packings of linear, semi-flexible polymers of tangent hard spheres are studied by employing extensive Monte Carlo simulations at increasing volume fractions. The chain stiffness is controlled by a tunable harmonic potential for the bending angle, whose intensity dictates the rigidity of the polymer backbone as a function of the bending constant and equilibrium angle. The studied angles range between acute and obtuse ones, reaching the limit of rod-like polymers. We analyze how the packing density and chain stiffness affect the chains' ability to self-organize at the local and global levels. The former corresponds to crystallinity, as quantified by the Characteristic Crystallographic Element (CCE) norm descriptor, while the latter is computed through the scalar orientational order parameter. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies, developing a complete phase diagram as a function of packing density and equilibrium bending angle. A plethora of structures are obtained, ranging between random hexagonal closed packed morphologies of mixed character and almost perfect face centered cubic (FCC) and hexagonal close-packed (HCP) crystals at the level of monomers, and nematic mesophases, with prolate and oblate mesogens at the level of chains. For rod-like chains, a delay is observed between the establishment of the long-range nematic order and crystallization as a function of the packing density, while for right-angle chains, both transitions are synchronized. A comparison is also provided against the analogous packings of monomeric and fully flexible chains of hard spheres.

Isostaticity and the solidification of semiflexible polymer melts

Using molecular dynamics simulations of a tangent-soft-sphere bead-spring polymer model, we examine the degree to which semiflexible polymer melts solidify at isostaticity. Flexible and stiff chains crystallize when they are isostatic as defined by appropriate degree-of-freedom-counting arguments. Semiflexible chains also solidify when isostatic if a generalized isostaticity criterion that accounts for the slow freezing out of configurational freedom as chain stiffness increases is employed. The configurational freedom associated with bond angles (θ) can be associated with the characteristic ratio C_∞ = (1 + 〈cos(θ)〉)/(1 - 〈cos(θ)〉). We find that the dependence of the average coordination number at solidification [Z(T_s)] on chains' characteristic ratio C_∞ has the same functional form [Z ≃ a - b ln(C_∞)] as the dependence of the average coordination number at jamming [Z(ϕ_J)] on C_∞ in athermal systems, suggesting that jamming-related phenomena play a significant role in thermal polymer solidification.