Orientational phase transitions in the hexagonal phase of a diblock copolymer melt under shear flow

We generalize the earlier theory by Fredrickson [J. Rheol. v.38, 1045 (1994)] to study the orientational behaviour of the hexagonal phase of diblock copolymer melt subjected to steady shear flow. We use symmetry arguments to show that the orientational ordering in the hexagonal phase is a much weaker effect than in the lamellae. We predict the parallel orientation to be stable at low and the perpendicular orientation at high shear rates. Our analysis reproduces the experimental results by Tepe et al. [Macromolecules v.28, 3008 (1995)] and explains the difficulties in experimental observation of the different orientations in the hexagonal phase.Comment: 21 pages, 6 eps figures, submitted to Physical Review

Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow

We develop a theory to describe the reorientation phenomena in the lamellar phase of block copolymer melt under reciprocating shear flow. We show that similar to the steady-shear, the oscillating flow anisotropically suppresses fluctuations and gives rise to the parallel-perpendicular orientation transition. The experimentally observed high-frequency reverse transition is explained in terms of interaction between the melt and the shear-cell walls.Comment: RevTex, 3 pages, 1 figure, submitted to PR

The effect of shear on persistence in coarsening systems

We analytically study the effect of a uniform shear flow on the persistence properties of coarsening systems. The study is carried out within the anisotropic Ohta-Jasnow-Kawasaki (OJK) approximation for a system with nonconserved scalar order parameter. We find that the persistence exponent theta has a non-trivial value: theta = 0.5034... in space dimension d=3, and theta = 0.2406... for d=2, the latter being exactly twice the value found for the unsheared system in d=1. We also find that the autocorrelation exponent lambda is affected by shear in d=3 but not in d=2.Comment: 6 page

Evidence of a Critical time in Constrained Kinetic Ising models

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses.Comment: 20 Pages + 7 Figures, Revte

Facilitated spin models: recent and new results

Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the surrounding configuration fulfills a simple local constraint which \emph{does not involve} the chosen variable itself. Such simple models are quite popular in the glass community since they display some of the peculiar features of glassy dynamics, in particular they can undergo a dynamical arrest reminiscent of the liquid/glass transitiom. Due to the fact that the jumps rates of the Markov process can be zero, the whole analysis of the long time behavior becomes quite delicate and, until recently, KCSM have escaped a rigorous analysis with the notable exception of the East model. In these notes we will mainly review several recent mathematical results which, besides being applicable to a wide class of KCSM, have contributed to settle some debated questions arising in numerical simulations made by physicists. We will also provide some interesting new extensions. In particular we will show how to deal with interacting models reversible w.r.t. to a high temperature Gibbs measure and we will provide a detailed analysis of the so called one spin facilitated model on a general connected graph.Comment: 30 pages, 3 figure

Derivation of an Abelian effective model for instanton chains in 3D Yang-Mills theory

In this work, we derive a recently proposed Abelian model to describe the interaction of correlated monopoles, center vortices, and dual fields in three dimensional SU(2) Yang-Mills theory. Following recent polymer techniques, special care is taken to obtain the end-to-end probability for a single interacting center vortex, which constitutes a key ingredient to represent the ensemble integration.Comment: 18 pages, LaTe

Steady State of microemulsions in shear flow

Steady-state properties of microemulsions in shear flow are studied in the context of a Ginzburg-Landau free-energy approach. Explicit expressions are given for the structure factor and the time correlation function at the one loop level of approximation. Our results predict a four-peak pattern for the structure factor, implying the simultaneous presence of interfaces aligned with two different orientations. Due to the peculiar interface structure a non-monotonous relaxation of the time correlator is also found.Comment: 5 pages, 3 figure

Stability of Quasicrystals Composed of Soft Isotropic Particles

Quasicrystals whose building blocks are of mesoscopic rather than atomic scale have recently been discovered in several soft-matter systems. Contrary to metallurgic quasicrystals whose source of stability remains a question of great debate to this day, we argue that the stability of certain soft-matter quasicrystals can be directly explained by examining a coarse-grained free energy for a system of soft isotropic particles. We show, both theoretically and numerically, that the stability can be attributed to the existence of two natural length scales in the pair potential, combined with effective three-body interactions arising from entropy. Our newly gained understanding of the stability of soft quasicrystals allows us to point at their region of stability in the phase diagram, and thereby may help control the self-assembly of quasicrystals and a variety of other desired structures in future experimental realizations.Comment: Revised abstract, more detailed explanations, and better images of the numerical minimization of the free energ

Shear Alignment and Instability of Smectic Phases

We consider the shear flow of well-aligned one-component smectic phases, such as thermotropic smectics and lamellar diblock copolymers, below the critical region. We show that, as a result of thermal fluctuations of the layers, parallel ($c$) alignment is generically unstable and perpendicular ($a$) alignment is stable against long-wavelength undulations. We also find, surprisingly, that both $a$ and $c$ are stable for a narrow window of values for the anisotropic viscosity.Comment: To appear in PRL. Revtex, 1 figure

Influence of confinement on the orientational phase transitions in the lamellar phase of a block copolymer melt under shear flow

In this work we incorporate some real-system effects into the theory of orientational phase transitions under shear flow (M. E. Cates and S. T. Milner, Phys. Rev. Lett. v.62, p.1856 (1989) and G. H. Fredrickson, J. Rheol. v.38, p.1045 (1994)). In particular, we study the influence of the shear-cell boundaries on the orientation of the lamellar phase. We predict that at low shear rates the parallel orientation appears to be stable. We show that there is a critical value of the shear rate at which the parallel orientation loses its stability and the perpendicular one appears immediately below the spinodal. We associate this transition with a crossover from the fluctuation to the mean-field behaviour. At lower temperatures the stability of the parallel orientation is restored. We find that the region of stability of the perpendicular orientation rapidly decreases as shear rate increases. This behaviour might be misinterpreted as an additional perpendicular to parallel transition recently discussed in literature.Comment: 25 pages, 4 figures, submitted to Phys. Rev.