Dynamical Scaling of Polymerized Membranes

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.

arXiv comment6 pages, 5 figures, (Europhysics Letters, in press)

References in corpus (2)

• Anomalous diffusion of a tethered membrane: A Monte Carlo investigation
• Dynamical Eigenmodes of a Polymerized Membrane

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