Abstract
We characterize the fluctuation properties of a polymer chain under external tension and the fluctuation-induced forces between two ring molecules threaded around the chain. The problem is relevant in the context of fluctuation-induced forces in soft-matter systems, features of liquid interfaces, and to describe the properties of polyrotaxanes and slide-ring materials. We perform molecular-dynamics simulations of the Kremer-Grest bead-spring model for the polymer and a simple ring-molecule model in the canonical ensemble. We study transverse fluctuations of the stretched chain as a function of chain stretching and in the presence of ring-shaped threaded molecules. The fluctuation spectra of the chains are analyzed in equilibrium at constant temperature, and the differences in the presence of two-ring molecules are compared. For the rings located at fixed distances, we find an attractive fluctuation-induced force between the rings, proportional to the temperature and decaying with the ring distance. We characterize this force as a function of ring distance, chain stretching, and ring radius, and we measure the differences between the free chain spectrum and the fluctuations of the chain constrained by the rings. We also compare the dependence and range of the force found in the simulations with theoretical models coming from different fields.
Highlights
Fluctuation-induced forces have attracted enormous attention starting from the renowned Casimir effect, which was discovered in the context of quantum electrodynamics[1]
Within the context of soft matter, we study the fluctuation-induced forces between ring molecules threaded around a polymer chain under tension at thermal equilibrium
In this work we study the properties of a fluctuating chain under tension with and without threaded rings fixed at given positions, which act as physical constraints of the fluctuation of the chains
Summary
Fluctuation-induced forces have attracted enormous attention starting from the renowned Casimir effect, which was discovered in the context of quantum electrodynamics[1]. A variety of physical systems were found to present effective forces of the same origin due to thermal fluctuations of material fields and molecules. Within the context of soft matter, we study the fluctuation-induced forces between ring molecules threaded around a polymer chain under tension at thermal equilibrium. In this work we study the properties of a fluctuating chain under tension with and without threaded rings fixed at given positions , which act as physical constraints of the fluctuation of the chains. For the polymer chain without rings, we find a transversal fluctuation spectrum compatible with ∼ 1/q2 dependence at high stretchings, and a deviation from it at shorter chain stretchings We show how this spectrum is modified by the presence of two rings fixed in space, and the appearence of an attractive fluctuation-induced force between the rings.
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