11,657 research outputs found
Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in 2D : A study using deposition-evaporation kinetics
Deposition and evaporation of infinitely thin hard rods (needles) is studied
in two dimensions using Monte Carlo simulations. The ratio of deposition to
evaporation rates controls the equilibrium density of rods, and increasing it
leads to an entropy-driven transition to a nematic phase in which both static
and dynamical orientational correlation functions decay as power laws, with
exponents varying continuously with deposition-evaporation rate ratio. Our
results for the onset of the power-law phase agree with those for a conserved
number of rods. At a coarse-grained level, the dynamics of the non-conserved
angle field is described by the Edwards-Wilkinson equation. Predicted relations
between the exponents of the quadrupolar and octupolar correlation functions
are borne out by our numerical results. We explore the effects of spatial
inhomogeneity in the deposition-evaporation ratio by simulations, entropy-based
arguments and a study of the new terms introduced in the free energy. The
primary effect is that needles tend to align along the local spatial gradient
of the ratio. A uniform gradient thus induces a uniformly aligned state, as
does a gradient which varies randomly in magnitude and sign, but acts only in
one direction. Random variations of deposition-evaporation rates in both
directions induce frustration, resulting in a state with glassy
characteristics.Comment: modified version, Accepted for publication in Physical Review
Kinetics of Phase Separation in Thin Films: Simulations for the Diffusive Case
We study the diffusion-driven kinetics of phase separation of a symmetric
binary mixture (AB), confined in a thin-film geometry between two parallel
walls. We consider cases where (a) both walls preferentially attract the same
component (A), and (b) one wall attracts A and the other wall attracts B (with
the same strength). We focus on the interplay of phase separation and wetting
at the walls, which is referred to as {\it surface-directed spinodal
decomposition} (SDSD). The formation of SDSD waves at the two surfaces, with
wave-vectors oriented perpendicular to them, often results in a metastable
layered state (also referred to as ``stratified morphology''). This state is
reminiscent of the situation where the thin film is still in the one-phase
region but the surfaces are completely wet, and hence coated with thick wetting
layers. This metastable state decays by spinodal fluctuations and crosses over
to an asymptotic growth regime characterized by the lateral coarsening of
pancake-like domains. These pancakes may or may not be coated by precursors of
wetting layers. We use Langevin simulations to study this crossover and the
growth kinetics in the asymptotic coarsening regime.Comment: 39 pages, 19 figures, submitted to Phys.Rev.
Polymer Brushes in Cylindrical Pores: Simulation versus Scaling Theory
The structure of flexible polymers endgrafted in cylindrical pores of
diameter D is studied as a function of chain length N and grafting density
\sigma, assuming good solvent conditions. A phenomenological scaling theory,
describing the variation of the linear dimensions of the chains with \sigma, is
developed and tested by Molecular Dynamics simulations of a bead-spring model.Comment: 35 pages, 38 figure
Domain Growth in Ising Systems with Quenched Disorder
We present results from extensive Monte Carlo (MC) simulations of domain
growth in ferromagnets and binary mixtures with quenched disorder. These are
modeled by the "random-bond Ising model" and the "dilute Ising model" with
either nonconserved (Glauber) spin-flip kinetics or conserved (Kawasaki)
spin-exchange kinetics. In all cases, our MC results are consistent with
power-law growth with an exponent which depends on the
quench temperature and the disorder amplitude . Such exponents
arise naturally when the coarsening domains are trapped by energy barriers
which grow logarithmically with the domain size. Our MC results show excellent
agreement with the predicted dependence of .Comment: 11 pages, 15 figure
Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model
A polymer chain tethered to a surface may be compact or extended, adsorbed or
desorbed, depending on interactions with the surface and the surrounding
solvent. This leads to a rich phase diagram with a variety of transitions. To
investigate these transitions we have performed Monte Carlo simulations of a
bond-fluctuation model with Wang-Landau and umbrella sampling algorithms in a
two-dimensional state space. The simulations' density of states results have
been evaluated for interaction parameters spanning the range from good to poor
solvent conditions and from repulsive to strongly attractive surfaces. In this
work, we describe the simulation method and present results for the overall
phase behavior and for some of the transitions. For adsorption in good solvent,
we compare with Metropolis Monte Carlo data for the same model and find good
agreement between the results. For the collapse transition, which occurs when
the solvent quality changes from good to poor, we consider two situations
corresponding to three-dimensional (hard surface) and two-dimensional (very
attractive surface) chain conformations, respectively. For the hard surface, we
compare tethered chains with free chains and find very similar behavior for
both types of chains. For the very attractive surface, we find the
two-dimensional chain collapse to be a two-step transition with the same
sequence of transitions that is observed for three-dimensional chains: a
coil-globule transition that changes the overall chain size is followed by a
local rearrangement of chain segments.Comment: 17 pages, 12 figures, to appear in J. Chem. Phy
Chain length dependence of the polymer-solvent critical point parameters
We report grand canonical Monte Carlo simulations of the critical point
properties of homopolymers within the Bond Fluctuation model. By employing
Configurational Bias Monte Carlo methods, chain lengths of up to N=60 monomers
could be studied. For each chain length investigated, the critical point
parameters were determined by matching the ordering operator distribution
function to its universal fixed-point Ising form. Histogram reweighting methods
were employed to increase the efficiency of this procedure. The results
indicate that the scaling of the critical temperature with chain length is
relatively well described by Flory theory, i.e. \Theta-T_c\sim N^{-0.5}. The
critical volume fraction, on the other hand, was found to scale like \phi_c\sim
N^{-0.37}, in clear disagreement with the Flory theory prediction \phi_c\sim
N^{-0.5}, but in good agreement with experiment. Measurements of the chain
length dependence of the end-to-end distance indicate that the chains are not
collapsed at the critical point.Comment: 13 Pages Revtex, 9 epsf embedded figs. gzipped tar file. To appear in
J. Chem. Phy
Langevin Dynamics simulations of a 2-dimensional colloidal crystal under confinement and shear
Langevin Dynamics simulations are used to study the effect of shear on a
two-dimensional colloidal crystal confined by structured parallel walls. When
walls are sheared very slowly, only two or three crystalline layers next to the
walls move along with them, while the inner layers of the crystal are only
slightly tilted. At higher shear velocities, this inner part of the crystal
breaks into several pieces with different orientations. The velocity profile
across the slit is reminiscent of shear-banding in flowing soft materials,
where liquid and solid regions coexist; the difference, however, is that in the
latter case the solid regions are glassy while here they are crystalline. At
even higher shear velocities, the effect of the shearing becomes smaller again.
Also the effective temperature near the walls (deduced from the velocity
distributions of the particles) decreases again when the wall velocity gets
very large. When the walls are placed closer together, thereby introducing a
misfit, a structure containing a soliton staircase arises in simulations
without shear. Introducing shear increases the disorder in these systems until
no solitons are visible any more. Instead, similar structures like in the case
without misfit result. At high shear rates, configurations where the
incommensurability of the crystalline structure is compensated by the creation
of holes become relevant
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