220 research outputs found
Comment on ``Theory of Spinodal Decomposition''
I comment on a paper by S. B. Goryachev [PRL vol 72, p.1850 (1994)] that
presents a theory of non-equilibrium dynamics for scalar systems quenched into
an ordered phase. Goryachev incorrectly applies only a global conservation
constraint to systems with local conservation laws.Comment: 2 pages LATeX (REVTeX macros), no figures. REVISIONS --- more to the
point. microscopic example added, presentation streamlined, long-range
interactions mentioned, to be published in Phys. Rev. Let
Instabilities and disorder of the domain patterns in the systems with competing interactions
The dynamics of the domains is studied in a two-dimensional model of the
microphase separation of diblock copolymers in the vicinity of the transition.
A criterion for the validity of the mean field theory is derived. It is shown
that at certain temperatures the ordered hexagonal pattern becomes unstable
with respect to the two types of instabilities: the radially-nonsymmetric
distortions of the domains and the repumping of the order parameter between the
neighbors. Both these instabilities may lead to the transformation of the
regular hexagonal pattern into a disordered pattern.Comment: ReVTeX, 4 pages, 3 figures (postscript); submitted to Phys. Rev. Let
Grain boundary pinning and glassy dynamics in stripe phases
We study numerically and analytically the coarsening of stripe phases in two
spatial dimensions, and show that transient configurations do not achieve long
ranged orientational order but rather evolve into glassy configurations with
very slow dynamics. In the absence of thermal fluctuations, defects such as
grain boundaries become pinned in an effective periodic potential that is
induced by the underlying periodicity of the stripe pattern itself. Pinning
arises without quenched disorder from the non-adiabatic coupling between the
slowly varying envelope of the order parameter around a defect, and its fast
variation over the stripe wavelength. The characteristic size of ordered
domains asymptotes to a finite value $R_g \sim \lambda_0\
\epsilon^{-1/2}\exp(|a|/\sqrt{\epsilon})\epsilon\ll 1\lambda_0a$ a constant of order unity. Random fluctuations allow defect motion to
resume until a new characteristic scale is reached, function of the intensity
of the fluctuations. We finally discuss the relationship between defect pinning
and the coarsening laws obtained in the intermediate time regime.Comment: 17 pages, 8 figures. Corrected version with one new figur
Surface Transitions for Confined Associating Mixtures
Thin films of binary mixtures that interact through isotropic forces and
directionally specific "hydrogen bonding" are considered through Monte Carlo
simulations. We show, in good agreement with experiment, that the single phase
of these mixtures can be stabilized or destabilized on confinement. These
results resolve a long standing controversy, since previous theories suggest
that confinement only stabilizes the single phase of fluid mixtures.Comment: LaTeX document, documentstyle[aps,preprint]{revtex}, psfig.sty,
bibtex, 13 pages, 4 figure
Anisotropic dynamical scaling in a spin model with competing interactions
Results are presented for the kinetics of domain growth of a two-dimensional
Ising spin model with competing interactions quenched from a disordered to a
striped phase. The domain growth exponent are and for
single-spin-flip and spin-exchange dynamics, as found in previous simulations.
However the correlation functions measured in the direction parallel and
transversal to the stripes are different as suggested by the existence of
different interface energies between the ground states of the model. In the
case of single-spin-flip dynamics an anisotropic version of the
Ohta-Jasnow-Kawasaki theory for the pair scaling function can be used to fit
our data.Comment: 4 pages, REVTeX fil
Effect of Ordering on Spinodal Decomposition of Liquid-Crystal/Polymer Mixtures
Partially phase-separated liquid-crystal/polymer dispersions display highly
fibrillar domain morphologies that are dramatically different from the typical
structures found in isotropic mixtures. To explain this, we numerically explore
the coupling between phase ordering and phase separation kinetics in model
two-dimensional fluid mixtures phase separating into a nematic phase, rich in
liquid crystal, coexisting with an isotropic phase, rich in polymer. We find
that phase ordering can lead to fibrillar networks of the minority polymer-rich
phase
Weak selection and stability of localized distributions in Ostwald ripening
We support and generalize a weak selection rule predicted recently for the
self-similar asymptotics of the distribution function (DF) in the
zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation
theory is developed that, when combined with an exact invariance property of
the system, yields the selection rule, predicts a power-law convergence towards
the selected self-similar DF and agrees well with our numerical simulations for
the interface- and diffusion-controlled OR.Comment: 4 pages, 2 figures, submitted to PR
Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach
We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian
with a competing long-range repulsive term in the presence of an external
magnetic field. The model is analytically solved within the self consistent
Hartree approximation for two different initial conditions: disordered or zero
field cooled (ZFC), and fully magnetized or field cooled (FC). To test the
predictions of the approximation we develop a suitable numerical scheme to
ensure the isotropic nature of the interactions. Both the analytical approach
and the numerical simulations of two-dimensional finite systems confirm a
simple aging scenario at zero temperature and zero field. At zero temperature a
critical field is found below which the initial conditions are relevant
for the long time dynamics of the system. For a logarithmic growth of
modulated domains is found in the numerical simulations but this behavior is
not captured by the analytical approach which predicts a growth law at
Stability of periodic domain structures in a two-dimensional dipolar model
We investigate the energetic ground states of a model two-phase system with
1/r^3 dipolar interactions in two dimensions. The model exhibits spontaneous
formation of two kinds of periodic domain structure. A striped domain structure
is stable near half filling, but as the area fraction is changed, a transition
to a hexagonal lattice of almost-circular droplets occurs. The stability of the
equilibrium striped domain structure against distortions of the boundary is
demonstrated, and the importance of hexagonal distortions of the droplets is
quantified. The relevance of the theory for physical surface systems with
elastic, electrostatic, or magnetostatic 1/r^3 interactions is discussed.Comment: Revtex (preprint style, 19 pages) + 4 postscript figures. A version
in two-column article style with embedded figures is available at
http://electron.rutgers.edu/~dhv/preprints/index.html#ng_do
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