Hexagonal phase ordering in strongly segregated copolymer films

Glasner, Karl

doi:10.1103/physreve.92.042602

Cited by 6 publications

(7 citation statements)

References 48 publications

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“…Instead, simple reaction rate laws s(c) have been analyzed [45,50,51,59,156]. For instance, it has been shown that first-order rate laws are equivalent to systems with long-ranged interactions of the Coulomb type [50,157] and that such interactions affect pattern formation [52,53,[158][159][160], e.g., in block copolymers [157,[161][162][163][164].…”

Section: Phase Separation With Broken Detailed Balance Of the Ratesmentioning

confidence: 99%

Physics of active emulsions

et al. 2019

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Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call active emulsions. These systems are driven by external energy input for example provided by an external fuel reservoir. The external energy input gives rise to novel phenomena that are not present in passive systems. For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions. Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled and they can spontaneously divide. In this review we discuss the physics of phase separation and emulsions and show how the concepts that governs such phenomena can be extended to capture the physics of active emulsions. This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development novel applications in chemical engineering and models for the origin of life.

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Section: Phase Separation With Broken Detailed Balance Of the Ratesmentioning

confidence: 99%

Physics of active emulsions

et al. 2019

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“…More precisely, we are interested in systems that exhibit stable or metastable ordered states, such as stripes, or spots arranged in hexagonal lattices. Examples of such systems arise for example in di‐block copolymers , phase‐field models , and other phase separative systems , as well as in phyllotaxis , and reaction–diffusion systems . Throughout, we will focus on a paradigmatic model, the Swift–Hohenberg equation

u_{t} = - {(1 + Δ)}^{2} u + μ u - u^{3},

where

u = u (t, x, y) \in R

false(x, y false) \in {double-struckR}^{2}

t \in R

, subscripts denote partial derivatives, and

Δ u = u_{x x} + u_{y y}

.…”

Section: Introductionmentioning

confidence: 99%

Pattern‐forming fronts in a Swift–Hohenberg equation with directional quenching — parallel and oblique stripes

Goh

Scheel

2018

J. London Math. Soc.

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We study the effect of domain growth on the orientation of striped phases in a Swift–Hohenberg equation. Domain growth is encoded in a step‐like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in the complement, while the boundary of the pattern‐forming region is propagating with fixed normal velocity. We construct front solutions that leave behind stripes in the pattern‐forming region that are parallel to or at a small oblique angle to the boundary. Technically, the construction of stripe formation parallel to the boundary relies on ill‐posed, infinite‐dimensional spatial dynamics. Stripes forming at a small oblique angle are constructed using a functional‐analytic, perturbative approach. Here, the main difficulties are the presence of continuous spectrum and the fact that small oblique angles appear as a singular perturbation in a traveling‐wave problem. We resolve the former difficulty using a farfield‐core decomposition and Fredholm theory in weighted spaces. The singular perturbation problem is resolved using preconditioners and boot‐strapping.

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“…Previous investigations of cylindrical BCP ordering have suggested an initial period of more rapid grain growth, , that slows once hexagonal order has developed and may even cease at late stages as grain boundaries are pinned . Glasner has recently highlighted these ordering regimes through simulations based on a dynamical model of hexagonal pattern coarsening. At early stages, coarsening dominated by defect annihilation gives rise to an ∼ t 0.51 power law; at an intermediate stage an ∼ t 0.23 power law is observed based on grain boundary migration and consumption of smaller grains; and at late stages the correlation length ceases to increase due to grain boundary pinning.…”

Section: Resultsmentioning

confidence: 99%

Thickness-Dependent Ordering Kinetics in Cylindrical Block Copolymer/Homopolymer Ternary Blends

Doerk

Fukuto

et al. 2018

Macromolecules

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The slow kinetics of block copolymer self-assembly may hinder, or even prevent, the realization of expected equilibrium ordered morphologies. Here we investigate the self-assembly kinetics of cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) and its corresponding ternary blends with low molecular weight PS and PMMA in thin films ranging from <1 to several cylinder layers in thickness. In situ grazing-incidence X-ray scattering coupled with ex situ electron microscopy reveals pathway-dependent ordering substantially altered by homopolymer blending. In particular, the neat (unblended) block copolymer (BCP) is kinetically frustrated in films more than ∼1 cylinder layer thick and is unable to reach a state of ordered hexagonally packed cylinders during the annealing interval. On the other hand, while blends exhibit similar pattern coarsening behavior to neat BCPs for hexagonally ordered cylinders, reorientation transitions between vertical or horizontal cylinders are dramatically accelerated in blend thin films. We infer that more rapid early stage ordering observed in blends can be attributed in part to faster reorientation transitions.

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Hexagonal phase ordering in strongly segregated copolymer films

Cited by 6 publications

References 48 publications

Physics of active emulsions

Physics of active emulsions

Pattern‐forming fronts in a Swift–Hohenberg equation with directional quenching — parallel and oblique stripes

Thickness-Dependent Ordering Kinetics in Cylindrical Block Copolymer/Homopolymer Ternary Blends

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