Shape and Size Tunability of Sheets of Interlocked Ring Copolymers

TL;DR

This study uses simulations to explore how the composition and linking patterns of interlocked ring copolymer sheets influence their shape and size, revealing new possibilities for topological meta-materials with tunable properties.

Contribution

It demonstrates how varying ring composition and interlocking patterns independently control the size and shape of mechanically bonded membranes, including the first example of saddle-shaped sheets with negative Gaussian curvature.

Findings

Ring composition sets overall size.

Linking patterns define membrane shape.

Saddle-shaped membranes with negative Gaussian curvature observed.

Abstract

Mechanically bonded membranes of interlocked ring polymers are a significant generalization of conventional elastic sheets, where connectivity is provided by covalent bonding, and represent a promising class of topological meta-materials. In this context, two open questions regard the large-scale reverberations of the heterogeneous composition of the rings and the inequivalent modes of interlocking neighboring rings. We address these questions with Langevin dynamics simulations of chainmails with honeycomb-lattice connectivity, where the rings are block copolymers with two segments of different rigidity. We considered various combinations of the relative lengths of the two segments and the patterns of the over- and under-passes linking neighboring rings. We find that varying ring composition and linking patterns have independent and complementary effects. While the former sets the overall size of the chainmail, the latter defines the shape, enabling the selection of starkly different conformation types. Notably, one of the considered linking patterns favors saddle-shaped membranes, providing a first example of spontaneous negative Gaussian curvature in mechanically bonded sheets. The results help establish the extent to which mechanically bonded membranes can differ from conventional elastic membranes, particularly for the achievable shape and size tunability.