Two-stage athermal solidification of semiflexible polymers and fibers

The influence of molecular shape on glass-forming behavior in a minimalist trimer model

In this study, we employed molecular dynamics simulations to probe the influence of molecular morphological changes on the dynamic behavior of a model consisting of trimer molecules. This model, comprising a chain of three particles, facilitates the exploration of variations in the internal angle between these particles. Our findings highlight the significant impact of molecular conformation: systems with more linear conformations, characterized by larger internal angles, exhibit relaxation times several orders of magnitude greater than their counterparts with smaller internal angles. Furthermore, we delve into the role of angular interaction rigidity, uncovering a pronounced deceleration in dynamics and an increase in dynamic heterogeneity as rigidity escalates. This model not only provides insights into azobenzene-type systems but also sets the stage for subsequent research into the microscopic nuances of related systems, with potential extensions to composite systems.

Force transmission during repose of flexible granular chains

We study the mechanics of standing columns formed during the repose of flexible granular chains. It is one of the many intriguing behaviours exhibited by granular materials when links capable of transmitting tension exist between particles. We develop and calibrate a discrete element method contact model to simulate the mechanics of the macroscopic flexible granular chains and conduct simulations of the angle of repose experiments of these chains by extracting a chain-filled cylinder and allowing the material to flow out under gravity and repose. We evaluate various micro-mechanical, topological and macroscopic parameters to elucidate the mechanics of the repose behaviour of chain ensembles. It is the ability of the links connecting the individual particles to transmit tensile forces along the chain backbone that provides lateral stability to the column, enabling them to stand. In particular, the contact force rearrangement inside the columns generates a self-confining radial stress near the base of the columns, which provides an important stabilizing stress.

Fine-tuning of colloidal polymer crystals by molecular simulation

Through extensive molecular simulations we determine a phase diagram of attractive, fully flexible polymer chains in two and three dimensions. A rich collection of distinct crystal morphologies appear, which can be finely tuned through the range of attraction. In three dimensions these include the face-centered cubic, hexagonal close packed, simple hexagonal, and body-centered cubic crystals and the Frank-Kasper phase. In two dimensions the dominant structures are the triangular and square crystals. A simple geometric model is proposed, based on the concept of cumulative neighbors of ideal crystals, which can accurately predict most of the observed structures and the corresponding transitions. The attraction range can thus be considered as an adjustable parameter for the design of colloidal polymer crystals with tailored morphologies.

Polymorph Stability and Free Energy of Crystallization of Freely-Jointed Polymers of Hard Spheres

The free energy of crystallization of monomeric hard spheres as well as their thermodynamically stable polymorph have been known for several decades. In this work, we present semianalytical calculations of the free energy of crystallization of freely-jointed polymers of hard spheres as well as of the free energy difference between the hexagonal closed packed (HCP) and face-centered cubic (FCC) polymorphs. The phase transition (crystallization) is driven by an increase in translational entropy that is larger than the loss of conformational entropy of chains in the crystal with respect to chains in the initial amorphous phase. The conformational entropic advantage of the HCP polymer crystal over the FCC one is found to be ΔschHCP-FCC≈0.331×10-5k per monomer (expressed in terms of Boltzmann's constant k). This slight conformational entropic advantage of the HCP crystal of chains is by far insufficient to compensate for the larger translational entropic advantage of the FCC crystal, which is predicted to be the stable one. The calculated overall thermodynamic advantage of the FCC over the HCP polymorph is supported by a recent Monte Carlo (MC) simulation on a very large system of 54 chains of 1000 hard sphere monomers. Semianalytical calculations using results from this MC simulation yield in addition a value of the total crystallization entropy for linear, fully flexible, athermal polymers of Δs≈0.93k per monomer.

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.

Polymorphism and Perfection in Crystallization of Hard Sphere Polymers

We present results on polymorphism and perfection, as observed in the spontaneous crystallization of freely jointed polymers of hard spheres, obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous configuration, after an initial dominance of the hexagonal closed packed (HCP) polymorph and a transitory random hexagonal close packed (rHCP) morphology, the system crystallizes in a final, stable, face centered cubic (FCC) crystal of very high perfection. An analysis of chain conformational characteristics, of the spatial distribution of monomers and of the volume accessible to them shows that the phase transition is caused by an increase in translational entropy that is larger than the loss of conformational entropy of the chains in the crystal, compared to the amorphous state. In spite of the significant local re-arrangements, as reflected in the bending and torsion angle distributions, the average chain size remains unaltered during crystallization. Polymers in the crystal adopt ideal random walk statistics as their great length renders local conformational details, imposed by the geometry of the FCC crystal, irrelevant.

Start-up shear of spherocylinder packings: Effect of friction

We study the response to shear deformations of packings of long spherocylindrical particles that interact via frictional forces with friction coefficient μ. The packings are produced and deformed with the help of molecular dynamics simulations combined with minimization techniques performed on a GPU. We calculate the linear shear modulus g_{∞}, which is orders of magnitude larger than the modulus g_{0} in the corresponding frictionless system. The motion of the particles responsible for these large frictional forces is governed by and increases with the length ℓ of the spherocylinders. One consequence of this motion is that the shear modulus g_{∞} approaches a finite value in the limit ℓ→∞, even though the density of the packings vanishes, ρ∝ℓ^{-2}. By way of contrast, the frictionless modulus decreases to zero, g_{0}∼ℓ^{-2}, in accordance with the behavior of density. Increasing the strain beyond a value γ_{c}∼μ, the packing strain weakens from the large frictional to the smaller frictionless modulus when contacts saturate at the Coulomb inequality and start to slide. In this regime, sliding friction contributes a "yield stress" σ_{y}=g_{∞}γ_{c} and the stress behaves as σ=σ_{y}+g_{0}γ. The interplay between static and sliding friction gives rise to hysteresis in oscillatory shear simulations.

Entropy-Driven Heterogeneous Crystallization of Hard-Sphere Chains under Unidimensional Confinement

We investigate, through Monte Carlo simulations, the heterogeneous crystallization of linear chains of tangent hard spheres under confinement in one dimension. Confinement is realized through flat, impenetrable, and parallel walls. A wide range of systems is studied with respect to their average chain lengths (N = 12 to 100) and packing densities (ϕ = 0.50 to 0.61). The local structure is quantified through the Characteristic Crystallographic Element (CCE) norm descriptor. Here, we split the phenomenon into the bulk crystallization, far from the walls, and the projected surface crystallization in layers adjacent to the confining surfaces. Once a critical volume fraction is met, the chains show a phase transition, starting from regions near the hard walls. The established crystal morphologies consist of alternating hexagonal close-packed or face-centered cubic layers with a stacking direction perpendicular to the confining walls. Crystal layer perfection is observed with an increasing concentration. As in the case of the unconstrained phase transition of athermal polymers at high densities, crystal nucleation and growth compete with the formation of sites of a fivefold local symmetry. While surface crystallites show perfection with a predominantly triangular character, the morphologies of square crystals or of a mixed type are also formed. The simulation results show that the rate of perfection of the surface crystallization is not significantly faster than that of the bulk crystallization.