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

Entropy-Driven Crystallization of Hard Colloidal Mixtures of Polymers and Monomers

The most trivial example of self-assembly is the entropy-driven crystallization of hard spheres. Past works have established the similarities and differences in the phase behavior of monomers and chains made of hard spheres. Inspired by the difference in the melting points of the pure components, we study, through Monte Carlo simulations, the phase behavior of athermal mixtures composed of fully flexible polymers and individual monomers of uniform size. We analyze how the relative number fraction and the packing density affect crystallization and the established ordered morphologies. As a first result, a more precise determination of the melting point for freely jointed chains of tangent hard spheres is extracted. A synergetic effect is observed in the crystallization leading to synchronous crystallization of the two species. Structural analysis of the resulting ordered morphologies shows perfect mixing and thus no phase separation. Due to the constraints imposed by chain connectivity, the local environment of the individual spheres, as quantified by the Voronoi polyhedron, is systematically more spherical and more symmetric compared to that of spheres belonging to chains. In turn, the local environment of the ordered phase is more symmetric and more spherical compared to that of the initial random packing, demonstrating the entropic origins of the phase transition. In general, increasing the polymer content reduces the degree of crystallinity and increases the melting point to higher volume fractions. According to the present findings, relative concentration is another determining factor in controlling the phase behavior of hard colloidal mixtures based on polymers.

Random close packing of semi-flexible polymers in two dimensions: Emergence of local and global order

Through extensive Monte Carlo simulations, we systematically study the effect of chain stiffness on the packing ability of linear polymers composed of hard spheres in extremely confined monolayers, corresponding effectively to 2D films. First, we explore the limit of random close packing as a function of the equilibrium bending angle and then quantify the local and global order by the degree of crystallinity and the nematic or tetratic orientational order parameter, respectively. A multi-scale wealth of structural behavior is observed, which is inherently absent in the case of athermal individual monomers and is surprisingly richer than its 3D counterpart under bulk conditions. As a general trend, an isotropic to nematic transition is observed at sufficiently high surface coverages, which is followed by the establishment of the tetratic state, which in turn marks the onset of the random close packing. For chains with right-angle bonds, the incompatibility of the imposed bending angle with the neighbor geometry of the triangular crystal leads to a singular intra- and inter-polymer tiling pattern made of squares and triangles with optimal local filling at high surface concentrations. The present study could serve as a first step toward the design of hard colloidal polymers with a tunable structural behavior for 2D applications.

Aggregation and structural phase transitions of semiflexible polymer bundles: A braided circuit topology approach

We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single isolated folded linear chains, the number and arrangement of contacts within the circuitry of a folded chain give rise to increasingly complex fold topologies. Another avenue for achieving complexity is through the interaction and entanglement of two or more folded linear chains. The braided circuit topology approach describes the topology of such multiple-chain systems and offers topological measures such as writhe, complexity, braid length, and isotopy class. This extension of circuit topology to multichains reveals the interplay between collapse, aggregation, and entanglement. In this work, we show that circuit topological motif fractions are ideally suited order parameters to characterize structural phase transitions in entangled systems that can detect structural re-ordering other measures cannot.

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.

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.