# Minimal energy packings and collapse of sticky tangent hard-sphere polymers

Minimal energy packings and collapse of sticky tangent hard-sphere polymers. Hoy R.S. and O'Hern C.S. (2010). Phys. Rev. Lett. 105, 068001.

Leon Furchtgott, APP 225. Fall 2010.

## Summary/Introduction

This paper is related to work investigating The Free Energy Landscape of Hard Sphere Clusters (experimental) and Minimal Energy Clusters of Hard Spheres with Short Ranged Attractions (theoretical). In these papers, Arkus et al. were interested in enumerating minimal energy packings (MEPs) for 10 sticky hard spheres and predicting and measuring the probabilities of different configurations.

This paper looks at packings of sticky tangent hard-sphere polymers, which can model polymer collapse, protein folding and protein interactions. This is particularly interesting and different from the case of sticky hard spheres because of the addition of covalent-bond and chain uncrossability constraints.

This paper looks at 2 overarching questions. (1) How do the probabilities for obtaining polymer MEPs differ from those for sticky hard-sphere MEPs? (2) How do the properties of single compact polymers depend on collapse dynamics?

(1) Polymer constraints reduce the number of MEP configurations. This is because of *dividing surfaces* which split the packings into disjoint regions.

(2) For slow temperature quenches, single chains undergo a sharp transition to crystallites with a close-packed core. As the quench rate increases, the core size decreases and the exterior becomes more disordered.