Aging of orientation fluctuations in stripe phases

Abstract

Stripe patterns, observed in a large variety of physical systems, often exhibit a slow nonequilibrium dynamics because ordering is impeded by the presence of topological defects. Using computer simulations based on a well-established model for stripe formation, we show that a slow dynamics and aging occur also in stripe patterns free of topological defects. For a wide range of noise strengths, the two-time orientation correlation function follows a scaling form that is typical for systems exhibiting a growing length scale. In our case, the underlying mechanism is the coarsening of orientation fluctuations, ultimately leading to power-law spatial correlations perpendicular to the stripes. Our results show that even for the smallest amount of noise, stripe phases without topological defects do not reach equilibrium. This constitutes an important aspect of the dynamics of modulated phases.

Communication: Microphase equilibrium and assembly dynamics

“…In diblock copolymers, microphase assembly sometimes gets stuck in locally stable structures that lack long-range order 6,16,17 . Upon (effective) cooling, a system would thus first form clusters or percolated clusters, and then rearrange into periodic microphases [17][18][19][20] , with the latter severely hindered by the slow relaxation of topological defects 21,22 . Because lamellae are at their most mobile just below the ODT, the ordering process should then be accelerated in that regime 13 , and a slow annealing near the order-disorder transition be most likely to succeed 18 .…”

Scaling properties of ageing orientation fluctuations in stripe phases

“…This coarsening is reflected in the growth of the characteristic correlation length j ? u in the direction perpendicular to the stripes [48] and in the increase of the dominant modulation length l* k along the stripe direction (this work). The spatial coarsening of the orientation fluctuations is more easily recognized in the snapshots of the orientation fields where fluctuations smaller than l 0 were removed using a Gaussian filter (figure 2d-f ).…”

“…Compared to more sophisticated approaches for simulating block copolymers [46,47], the model given by equation (2.3) has the advantage of being computationally less demanding, which enables us to more easily investigate its long-term behaviour. As detailed in our previous work [48], we prepare the system in a perfectly ordered state consisting of parallel stripes with wavelength l 0 ¼ 2pG 21/4 . The amplitude and wavelength were chosen to minimize the free energy F [c] in a single-mode approximation [37].…”

“…We fix the interaction parameter G as 0.2, for which equation (2.3) exhibits stripe formation [63] with l 0 % 9.3956. The noise strength h was varied, but remains below the critical noise strength h c ¼ 0.020(3), at which long-range order in the stripe pattern is destroyed [48]. Using an efficient pseudo-spectral algorithm [96], we performed simulations of equation (2.3) with periodic boundary conditions in d ¼ 2 dimensions on lattices with size L ¼ 55l 0 .…”

“…The results presented below were averaged over 40 independent realizations. A subset of the data is from [48].…”