Grain boundary pinning and glassy dynamics in stripe phases

Abstract

We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value Rg ∼ λ0 ǫ −1/2 exp(|a|/ √ ǫ), where ǫ ≪ 1 is the dimensionless distance away from threshold, λ0 the stripe wavelength, and a a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.

Dislocation dynamics in an anisotropic stripe pattern

“…Factors affecting the measured exponent include external noise and the quantity used to characterize the domains. There is evidence that for small enough quench depths the growth exponent is 1/3 [8,10,13]. An open question is the connection between the simulations and the experiments with the diblock copolymer systems.…”

Glassy behavior of two-dimensional stripe-forming systems

“…There are many reports in the literature showing metastable patterns and slow dynamics at low temperatures, which may be related with glassy physics [3,7,12,13,19,20]. Then it is important to assess the relevance of metastable states for the behavior of thermodynamic and dynamic functions.…”

“…A few experimental results quantifying the low temperature dynamics of quasi-twodimensional stripe forming systems have been reported [3,7]. Experimental and also computer simulation results [12,13] point to the presence of slow dynamics associated with the pinning of topological defects, which are the relevant excitations at low temperatures.…”

Superlattice Patterns in the Complex Ginzburg–Landau Equation with Multiresonant Forcing

“…If the system allows a Lyapunov functional this competition can be characterized in terms of the difference between the energies associated with the respective patterns. Unless the domain walls become pinned by the underlying pattern [49,50], it is expected that the final state arising from random initial conditions consists of the pattern with minimal energy [28,51].…”