Crystal, Fivefold and Glass Formation in Clusters of Polymers Interacting with the Square Well Potential

Abstract

We present results, from Monte Carlo (MC) simulations, on polymer systems of freely jointed chains with spherical monomers interacting through the square well potential. Starting from athermal packings of chains of tangent hard spheres, we activate the square well potential under constant volume and temperature corresponding effectively to instantaneous quenching. We investigate how the intensity and range of pair-wise interactions affected the final morphologies by fixing polymer characteristics such as average chain length and tolerance in bond gaps. Due to attraction chains are brought closer together and they form clusters with distinct morphologies. A wide variety of structures is obtained as the model parameters are systematically varied: weak interactions lead to purely amorphous clusters followed by well-ordered ones. The latter include the whole spectrum of crystal morphologies: from virtually perfect hexagonal close packed (HCP) and face centered cubic (FCC) crystals, to random hexagonal close packed layers of single stacking direction of alternating HCP and FCC layers, to structures of mixed HCP/FCC character with multiple stacking directions and defects in the form of twins. Once critical values of interaction are met, fivefold-rich glassy clusters are formed. We discuss the similarities and differences between energy-driven crystal nucleation in thermal polymer systems as opposed to entropy-driven phase transition in athermal polymer packings. We further calculate the local density of each site, its dependence on the distance from the center of the cluster and its correlation with the crystallographic characteristics of the local environment. The short- and long-range conformations of chains are analyzed as a function of the established cluster morphologies.

Identification of Local Structure in 2-D and 3-D Atomic Systems through Crystallographic Analysis

“…The protocol behind these simulations is a generalization of those presented in Refs. [40,47,48] containing chain-connectivity-altering moves, cluster identification/displacement algorithms, and compression/volume fluctuation processes in the bulk or under various conditions of confinement. In the present work two different models have been used to describe interactions between atoms.…”

“…Then, two patterns are followed: i) a SW potential is activated on the polymer configurations at dilute (3-D) or dense (2-D) conditions under constant volume and temperature (T = 1/kB, kB being the Boltzmann constant); ii) all bonds are eliminated so that the system consists now of monomers and the SW potential is further activated. For the polymer-based systems the equilibration algorithm and the corresponding MC moves are similar to the ones used for HS [29,32,33,[47][48][49][50][51][52] and SW [40] chains. For the monomer-based systems two moves are employed: simple sphere displacements whose amplitude is auto-configured based on the acceptance rate and cluster-based displacements following the cluster detection/translation algorithm presented in Ref.…”

“…For the monomer-based systems two moves are employed: simple sphere displacements whose amplitude is auto-configured based on the acceptance rate and cluster-based displacements following the cluster detection/translation algorithm presented in Ref. [40]. Simulations on 3-D SW polymers and monomers are conducted under conditions of constant volume (NVT ensemble) and pressure (NPT ensemble), respectively.…”

“…Once the SW potential is activated, chains or monomers form clusters, whose stability depends strongly on the values of the intensity and range of attraction [40]. Under specific conditions the clusters grow in size and aggregate, eventually leading to a single cluster which contains all sites.…”

“…A CCE variant, denoted as short-range order symmetry parameter (SSP), has also been adopted to explore short-range order and distortion in bulk metallic glasses [39]. More recently it has been applied to study cluster, crystal formation and vitrification, under dilute conditions, of polymers whose sites interact through the square well (SW) potential [40].…”