Transition to coarsening for confined one-dimensional interfaces with bending rigidity

TL;DR

This paper investigates the dynamics of confined one-dimensional membranes with bending rigidity, showing how tension, potential asymmetry, and thermal noise influence the transition from frozen states to perpetual coarsening.

Contribution

It demonstrates the conditions under which frozen membrane states transition to coarsening, highlighting the roles of tension, potential asymmetry, and thermal noise in this process.

Findings

Finite tension leads to disappearance of frozen states and induces perpetual coarsening.

Potential asymmetry causes drift force, leading to fast coarsening via kink-antikink annihilation.

Thermal noise restores coarsening with Arrhenius-dependent timescales.

Abstract

We discuss the nonlinear dynamics and fluctuations of interfaces with bending rigidity under the competing attractions of two walls with arbitrary permeabilities. This system mimics the dynamics of confined membranes. We use a two-dimension hydrodynamic model, where membranes are effectively one-dimensional objects. In a previous work [T. Le Goff et al, Phys. Rev. E 90, 032114 (2014)], we have shown that this model predicts frozen states caused by bending rigidity-induced oscillatory interactions between kinks (or domain walls). We here demonstrate that in the presence of tension, potential asymmetry, or thermal noise, there is a finite threshold above which frozen states disappear, and perpetual coarsening is restored. Depending on the driving force, the transition to coarsening exhibits different scenarios. First, for membranes under tension, small tensions can only lead to transient coarsening or partial disordering, while above a finite threshold, membrane oscillations disappear and perpetual coarsening is found. Second, potential asymmetry is relevant in the non-conserved case only, i.e. for permeable walls, where it induces a drift force on the kinks, leading to a fast coarsening process via kink-antikink annihilation. However, below some threshold, the drift force can be balanced by the oscillatory interactions between kinks, and frozen adhesion patches can still be observed. Finally, at long times, noise restores coarsening with standard exponents depending on the permeability of the walls. However, the typical time for the appearance of coarsening exhibits an Arrhenius form. As a consequence, a finite noise amplitude is needed in order to observe coarsening in observable time.