Jamming and crystallization in athermal polymer packings

Abstract

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.

Keywords:

• polymer
• Monte Carlo
• simulation
• hard sphere
• entanglement
• contact network
• crystallization
• maximally random jammed state
• random packing
• knot
• entropy
• phase transition
• athermal packing
• jamming

Acknowledgments

We are grateful to Professors Martin Kröger (ETH, Switzerland), Cameron Abrams (Drexel University, USA) and Marc Mansfield (Steven Institute of Technology, USA) for stimulating discussions. NCK acknowledges support by the Spanish Ministry of Economy and Competitiveness (MINECO) through projects ‘Ramon y Cajal’ (RYC-2009-05413), ‘I3’ and MAT2010-15482. KF acknowledges support by MINECO through projects ‘Ramon y Cajal’ (RYC-2010-06804) and MAT2011-24834. Authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the Centro de Supercomputacion y Visualizacion de Madrid (CeSViMa).