Rouse model in crowded environment modeled by “diffusing diffusivity”

Abstract

We derive exact results for the dynamics of Rouse model in crowded environment modeled by stochastically varying diffusivity, the concept of “diffusing diffusivity”. We specifically generalize the initial analytical formulation of this concept of diffusivity in single particle diffusion to many particle systems with localized interactions, particularly to chains of connected beads, the Rouse model. Independent Rouse modes are allowed to diffuse with stochastically varying time dependent diffusivities to model diffusion in the crowded rearranging environment, where zeroth mode represents the chain center of mass coordinate. We develop an analytical formalism to calculate the probability distribution of these individual mode displacements and subsequently average bead displacement distribution of the Rouse chain and its moments in terms of these modes. The resulting diffusion behavior of thus modified Rouse model is a function of mode resolved parameters which model local interactions and crowded environment collectively. Our analytically tractable implementation of the “diffusing diffusivity” concept to Rouse model is one of its kind that yields non-Gaussian diffusion with the scope of being anomalous and plausibly applied to dynamics in polymeric liquids.