How does a flexible chain of active particles swell?

TL;DR

This paper analytically and computationally investigates how active particles in a flexible chain influence its swelling, revealing that activity affects the scaling prefactor but not the Flory exponent, with non-monotonic behavior observed in chain extension.

Contribution

It extends the Rouse model to active monomers, providing analytical solutions and simulations for different confinement scenarios, and clarifies how activity influences chain swelling and scaling laws.

Findings

Swelling scales with monomer number with specific Flory exponents in different scenarios.

Activity modifies the prefactor of the scaling law but not the Flory exponent.

Chain extension exhibits non-monotonic dependence on self-propulsion strength.

Abstract

We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent $\nu$ which is $\nu =1/2, 0, 1$ in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now $\nu = 3/4, 1/4, 1$ and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.