Scaling properties of ageing orientation fluctuations in stripe phases

Abstract

We investigate the non-equilibrium dynamics of an ordered stripe-forming system free of topological defects. In particular, we study the ageing and the coarsening of orientation fluctuations parallel and perpendicular to the stripes via computer simulations based on a minimal phase-field model (model B with Coulomb interactions). Under the influence of noise, the stripe orientation field develops fluctuations parallel to the stripes, with the dominant modulation length λ* increasing with time as λ* ∼ and the correlation length perpendicular to the stripes increasing as ∼. We explain these anisotropic coarsening dynamics with an analytic theory based on the linear elastic model for stripe displacements first introduced by Landau and Peierls. We thus obtain the scaling forms and the scaling exponents characterizing the correlation functions and the structure factor of the stripe orientation field. Our results reveal how the coarsening of orientation fluctuations prevents a periodically modulated phase free of topological defects from reaching equilibrium.

Direct Imaging of Interfacial Fluctuations in Confined Block Copolymer with in Situ Slow-Scan-Disabled Atomic Force Microscopy

“…Our SSD measurements, which show long-range coherence extending across multiple domains to encompass the trench, only examine behavior perpendicular to the cylinder alignment. Previous studies have found that small-angle fluctuations in BCP patterns form anisotropic grains oriented orthogonally to BCP pattern. , Although inaccessible to our one-dimensional measurement technique, we expect a shorter length scale for correlations along the axis parallel to the stripes, which have predominant wavelength contributions on the order L 0 .…”

“…Ultimately, this method provides direct experimental insight of BCP fluctuations in real time and real space, illuminating their contribution to interfacial roughness, defect healing, 39 and pattern aging. 43,44 RESULTS AND DISCUSSION SSD Imaging. To optimize our time resolution, images are acquired in the slow-scan-disabled (SSD) AFM mode.…”

“…In this report, we describe the use of slow-scan-disabled AFM imaging to directly capture and quantify the interdomain fluctuations in confined BCP and show that these fluctuations increase in intensity and become spatially coherent with temperature. Ultimately, this method provides direct experimental insight of BCP fluctuations in real time and real space, illuminating their contribution to interfacial roughness, defect healing, and pattern aging. , …”

Emergence and function of complex form in self-assembly and biological cells

“…While shape and form adapt through evolution, this process is mediated by the physical forces and principles that actually shape the material. Again, this collection offers some insights, both relating to the very same forces that Thompson was considering (surface tension, [16]), as well as more complex interfacial forces [17] and interactions [18], as well as entropic principles [19] and non-equilibrium effects in pattern formation [20]. In our view, science must ultimately reconcile the geometry and forces approaches, that remain largely divorced from each other.…”