Random Close Packing of Semi-Flexible Polymers in Two Dimensions: Emergence of Local and Global Order

TL;DR

This study uses Monte Carlo simulations to investigate how chain stiffness influences the packing and structural order of semi-flexible polymers in two dimensions, revealing complex phase transitions and unique tiling patterns.

Contribution

It provides a detailed analysis of the structural behavior of semi-flexible polymers in 2D, highlighting the emergence of local and global order and novel packing patterns not seen in 3D.

Findings

Identification of isotropic to nematic transition at high surface coverage

Discovery of tetratic state preceding random close packing

Unique tiling patterns of squares and triangles for right-angle bonds

Abstract

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 surfaces 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 towards the design of hard colloidal polymers with tunable structural behavior for 2D applications.