Dynamical Scaling of Polymerized Membranes

TL;DR

This study uses Monte Carlo simulations to analyze the sub-diffusive behavior of monomers in polymerized membranes, revealing distinct diffusion exponents and deriving Langevin equations to describe the dynamics, including effects of hydrodynamics.

Contribution

The paper introduces a detailed analysis of monomer sub-diffusion in membranes, deriving generalized Langevin equations and exploring the impact of hydrodynamic interactions.

Findings

Distinct diffusion exponents for in-plane and out-of-plane components

Derived Langevin equations with negative power-law memory kernels

Hydrodynamic interactions modify the diffusion exponents

Abstract

Monte Carlo simulations have been performed to analyze the sub-diffusion dynamics of a tagged monomer in self-avoiding polymerized membranes in the flat phase. By decomposing the mean square displacement into the out-of-plane ($\parallel$) and the in-plane ($\perp$) components, we obtain good data collapse with two distinctive diffusion exponents $2 \alpha_{\parallel} = 0.36 \pm 0.01$ and $2 \alpha_{\perp} = 0.21 \pm 0.01$, and the roughness exponents $\zeta_{\parallel} = 0.6 \pm 0.05$ and $\zeta_{\perp} = 0.25 \pm 0.05 $, respectively for each component. Their values are consistent with the relation from the rotational symmetry. We derive the generalized Langevin equations to describe the sub-diffusional behaviors of a tagged monomer in the intermediate time regime where the collective effect of internal modes in the membrane dominate the dynamics to produce negative memory kernels with a power-law. We also briefly discuss how the long-range hydrodynamic interactions alter the exponents.