3,001 research outputs found
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 () alignment is generically unstable and perpendicular ()
alignment is stable against long-wavelength undulations. We also find,
surprisingly, that both and 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.
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