Anomalous diffusion of a tethered membrane: A Monte Carlo investigation

Abstract

Using a continuum bead-spring Monte Carlo model, we study the anomalous diffusion dynamics of a self-avoiding tethered membrane by means of extensive computer simulations. We focus on the subdiffusive stochastic motion of the membrane's central node in the regime of flat membranes at temperatures above the membrane folding transition. While at times, larger than the characteristic membrane relaxation time τ R , the mean-square displacement of the center of mass of the sheet,c , as well as that of its central node, R 2 n , show the normal Rouse diffusive behavior with a diffusion coefficient D N scaling as D N ∝ N −1 with respect to the number of segments N in the membrane, for short times t ≤ τ R we observe a multiscale dynamics of the central node, R 2 n ∝ t α , where the anomalous diffusion exponent α changes from α ≈ 0.86 to α ≈ 0.27, and then to α ≈ 0.5, before diffusion turns eventually to normal. By means of simple scaling arguments we show that our main result, α ≈ 0.27, can be related to particular mechanisms of membrane dynamics which involve different groups of segments in the membrane sheet. A comparative study involving also linear polymers demonstrates that the diffusion coefficient of self-avoiding tethered membranes, containing N segments, is three times smaller than that of linear polymer chains with the same number of segments.

Dynamical eigenmodes of a polymerized membrane

“…In contrast to the equilibrium properties, the dynamical properties of membranes have been studied with less intensity. Apart from scaling analyses [27][28][29], the bulk of the research on the dynamics of polymerized membranes are heavily dominated by computer simulations [30][31][32][33], leaving exact analytical results on the dynamics of membranes a relatively open area.…”

Defect dynamics in crystalline buckled membranes

“…The phase behavior and equilibrium structure of fluid membranes have been investigated intensively in recent years through different methods, including Monte Carlo [28,29], molecular dynamics [30], and phase field models [27].…”

Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature

“…From these characteristics it has been shown that anomalous diffusion in polymeric systems can be modeled by a generalized Langevin equation (GLE) with a memory kernel, and it belongs to the class of fBm [30]. The fBm characteristics of anomalous diffusion have been verified for flexible [31,32] and semiflexible polymers [33] and for polymer membranes [34][35][36]. Importantly, they have been used to successfully explain the dynamics of translocation of polymers across membranes [37][38][39][40].…”