Anomalous lateral diffusion in a viscous membrane surrounded by viscoelastic media

¹ Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University Tokyo 192-0397, Japan
² Physique des Polymères, Université Libre de Bruxelles - Campus Plaine, CP 223, B-1050 Brussels, Belgium, EU
³ National Institute of Advanced Industrial Science and Technology (AIST) - Ibaraki 305-8565, Japan

^a komura@tmu.ac.jp

Received: 4 December 2011
Accepted: 17 February 2012

Abstract

We investigate the lateral dynamics in a purely viscous lipid membrane surrounded by viscoelastic media such as polymeric solutions. We first obtain the generalized frequency-dependent mobility tensor and focus on the case in which the solvent is sandwiched by hard walls. Due to the viscoelasticity of the solvent, the mean square displacement of a disk embedded in the membrane exhibits an anomalous diffusion. A useful relation which connects the mean square displacement and the solvent modulus is provided. We also calculate the cross-correlation of the particle displacements which can be applied for two-particle tracking experiments.