# Structure of Stacked Aggregates of Semiflexible Rings Under Spherical Confinement: A Computational Study

## TL;DR

This study uses simulations to show how semiflexible ring polymers arrange under spherical confinement, revealing how their structure changes with cavity size.

## Contribution

The paper introduces a computational investigation of semiflexible ring polymer conformations under varying spherical confinement sizes.

## Key findings

- Semiflexible ring polymers transition from flexible coils to disk-like conformations as bending energy increases.
- Stacked aggregates of semiflexible ring polymers form under strong confinement (R < 2Rg) and reach maximum order at R ≈ 2Rg.
- Increased cavity size (R > 3Rg) reduces the order of stacked aggregates, with the orientational-order parameter dropping to S ≈ 0.05.

## Abstract

How ordered and mutually independent are semiflexible ring polymers (RPs) confined to a spherical cavity of variable radius? By varying the cavity radius, we systematically investigate the effect of the confinement size on the conformations of RPs using the coarse-grained molecular dynamics simulations. The results reveal that as the bending energy increases, the RPs exhibit a transition from a purely flexible coil to an elongated oblate-shaped object and, eventually, to a disk-like conformation. Simultaneously, the stacked aggregates composed of adjacent, mutually nearly parallel, semiflexible RPs emerge for stiffer chains. We find that the structural modulation of the stacked aggregates is regulated by the confinement size. For the conditions of strong confinement (R<2Rg, where Rg is the radius of gyration of an RP), the semiflexible RPs undergo peculiar deformations and twisting that lead to disruption of the stacked aggregates. At R≈2Rg, the average number of the RPs per stack reaches a maximum. Concurrently, the order of spatial alignment of all semiflexible RPs is maximized with the global orientational-order parameter reaching the value S≈0.79. As the cavity radius further increases, at R>3Rg, the semiflexible RPs gain greater mobility resulting in diverse orientations of the aggregates being formed, with the order parameter dropping to S≈0.05. These findings provide important quantitative insights for future applications of the RPs, i.e., in micro- and nanodevice assembly.