141 research outputs found
Simulation and theory of fluid demixing and interfacial tension of mixtures of colloids and non-ideal polymers
An extension of the Asakura-Oosawa-Vrij model of hard sphere colloids and
non-adsorbing polymers, that takes polymer non-ideality into account through a
repulsive stepfunction pair potential between polymers, is studied with grand
canonical Monte Carlo simulations and density functional theory. Simulation
results validate previous theoretical findings for the shift of the bulk fluid
demixing binodal upon increasing strength of polymer-polymer repulsion,
promoting the tendency to mix. For increasing strength of the polymer-polymer
repulsion, simulation and theory consistently predict the interfacial tension
of the free colloidal liquid-gas interface to decrease significantly for fixed
colloid density difference in the coexisting phases, and to increase for fixed
polymer reservoir packing fraction.Comment: 10 pages, 4 figure
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
Reduced-order hybrid multiscale method combining the molecular dynamics and the discontinuous-galerkin method
We present a new reduced-order hybrid multiscale method to simulate com-
plex fluids. continuum and molecular descriptions.
We follow the framework of the heterogeneous multi-scale method (HMM) that makes use of
the scale separation into macro- and micro-levels. On the macro-level, the governing equations of
the incompressible flow are the continuity and momentum equations. The equations are
solved using a high-order accurate discontinuous Galerkin Finite Element Method (dG) and
implemented in the BoSSS code. The missing information on the macro-level is represented
by the unknown stress tensor evaluated by means of the molecular dynam- ics (MD) simulations on
the micro-level. We shear the microscopic system by applying Lees-Edwards boundary
conditions and either an isokinetic or Lowe-Andersen thermostat. The data obtained from the MD
simulations underlie large stochastic errors that can be controlled by means of the least-square
approximation. In order to reduce a large number of computationally expensive MD runs, we apply
the reduced order approach. Nume al
experiments confirm the robustness of our newly developed hybrid MD-dG method
Monte Carlo study of the evaporation/condensation transition on different Ising lattices
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous
proof for the behavior of the 2D Ising lattice gas, at a finite volume and a
fixed excess \delta M of particles (spins) above the ambient gas density
(spontaneous magnetisation). By identifying a dimensionless parameter \Delta
(\delta M) and a universal constant \Delta_c, they showed in the limit of large
system sizes that for \Delta < \Delta_c the excess is absorbed in the
background (``evaporated'' system), while for \Delta > \Delta_c a droplet of
the dense phase occurs (``condensed'' system).
To check the applicability of the analytical results to much smaller,
practically accessible system sizes, we performed several Monte Carlo
simulations for the 2D Ising model with nearest-neighbour couplings on a square
lattice at fixed magnetisation M. Thereby, we measured the largest minority
droplet, corresponding to the condensed phase, at various system sizes (L=40,
>..., 640). With analytic values for for the spontaneous magnetisation m_0, the
susceptibility \chi and the Wulff interfacial free energy density \tau_W for
the infinite system, we were able to determine \lambda numerically in very good
agreement with the theoretical prediction.
Furthermore, we did simulations for the spin-1/2 Ising model on a triangular
lattice and with next-nearest-neighbour couplings on a square lattice. Again,
finding a very good agreement with the analytic formula, we demonstrate the
universal aspects of the theory with respect to the underlying lattice. For the
case of the next-nearest-neighbour model, where \tau_W is unknown analytically,
we present different methods to obtain it numerically by fitting to the
distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl
On the size of knots in ring polymers
We give two different, statistically consistent definitions of the length l
of a prime knot tied into a polymer ring. In the good solvent regime the
polymer is modelled by a self avoiding polygon of N steps on cubic lattice and
l is the number of steps over which the knot ``spreads'' in a given
configuration. An analysis of extensive Monte Carlo data in equilibrium shows
that the probability distribution of l as a function of N obeys a scaling of
the form p(l,N) ~ l^(-c) f(l/N^D), with c ~ 1.25 and D ~ 1. Both D and c could
be independent of knot type. As a consequence, the knot is weakly localized,
i.e. ~ N^t, with t=2-c ~ 0.75. For a ring with fixed knot type, weak
localization implies the existence of a peculiar characteristic length l^(nu) ~
N^(t nu). In the scaling ~ N^(nu) (nu ~0.58) of the radius of gyration of the
whole ring, this length determines a leading power law correction which is much
stronger than that found in the case of unrestricted topology. The existence of
such correction is confirmed by an analysis of extensive Monte Carlo data for
the radius of gyration. The collapsed regime is studied by introducing in the
model sufficiently strong attractive interactions for nearest neighbor sites
visited by the self-avoiding polygon. In this regime knot length determinations
can be based on the entropic competition between two knotted loops separated by
a slip link. These measurements enable us to conclude that each knot is
delocalized (t ~ 1).Comment: 29 pages, 14 figure
Curvature Dependence of Surface Free Energy of Liquid Drops and Bubbles: A Simulation Study
We study the excess free energy due to phase coexistence of fluids by Monte
Carlo simulations using successive umbrella sampling in finite LxLxL boxes with
periodic boundary conditions. Both the vapor-liquid phase coexistence of a
simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases
of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the
density rho in the simple fluid or the relative concentration x_A of A in the
binary mixture, respectively. The character of phase coexistence changes from a
spherical droplet (or bubble) of the minority phase (near the coexistence
curve) to a cylindrical droplet (or bubble) and finally (in the center of the
miscibility gap) to a slab-like configuration of two parallel flat interfaces.
Extending the analysis of M. Schrader, P. Virnau, and K. Binder [Phys. Rev. E
79, 061104 (2009)], we extract the surface free energy gamma (R) of both
spherical and cylindrical droplets and bubbles in the vapor-liquid case, and
present evidence that for R -> Infinity the leading order (Tolman) correction
for droplets has sign opposite to the case of bubbles, consistent with the
Tolman length being independent on the sign of curvature. For the symmetric
binary mixture the expected non-existence of the Tolman length is confirmed. In
all cases {and for a range of radii} R relevant for nucleation theory, gamma(R)
deviates strongly from gamma (Infinity) which can be accounted for by a term of
order gamma(Infinity)/gamma(R)-1 ~ 1/R^2. Our results for the simple
Lennard-Jones fluid are also compared to results from density functional theory
and we find qualitative agreement in the behavior of gamma(R) as well as in the
sign and magnitude of the Tolman length.Comment: 25 pages, submitted to J. Chem. Phy
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