The connection between polymer collapse and the onset of jamming

TL;DR

This study compares the structural and mechanical properties of collapsed attractive polymers to various reference systems, revealing that their packing and jamming characteristics are similar to those of static repulsive packings, despite differences in contact numbers.

Contribution

It demonstrates that attractive collapse leads to packings with properties akin to repulsive systems, highlighting the role of effective isostaticity in polymer jamming behavior.

Findings

Attractive systems at low temperature have similar packing fractions to static repulsive packings.

Repulsive polymers are hypostatic at jamming but effectively isostatic with quartic modes.

Weakly attractive packings exhibit mechanical properties similar to isostatic repulsive packings.

Abstract

Previous studies have shown that the interiors of proteins are densely packed, reaching packing fractions that are as large as those found for static packings of individual amino-acid-shaped particles. How can the interiors of proteins take on such high packing fractions given that amino acids are connected by peptide bonds and many amino acids are hydrophobic with attractive interactions? We investigate this question by comparing the structural and mechanical properties of collapsed attractive disk-shaped bead-spring polymers to those of three reference systems: static packings of repulsive disks, of attractive disks, and of repulsive disk-shaped bead-spring polymers. We show that attractive systems quenched to temperatures below the glass transition $T \ll T_g$ and static packings of both repulsive disks and bead-spring polymers possess similar interior packing fractions. Previous studies have shown that static packings of repulsive disks are isostatic at jamming onset, i.e. the number of contacts $N_c$ matches the number of degrees of freedom, which strongly influences their mechanical properties. We find that repulsive polymers are hypostatic at jamming onset, but effectively isostatic when including quartic modes. While attractive disk and polymer packings are hyperstatic, we identify a definition for interparticle contacts for which they can also be considered as effectively isostatic. As a result, we show that the mechanical properties (e.g. scaling of the potential energy with excess contact number and low-frequency contribution to the density of vibrational modes) of weakly attractive disk and polymer packings are similar to those of ${\it isostatic}$ repulsive disk and polymer packings. Our results demonstrate that static packings generated via attractive collapse or compression of repulsive particles possess similar structural and mechanical properties.