54 research outputs found
Conceptual aspects of line tensions
We analyze two representative systems containing a three-phase-contact line:
a liquid lens at a fluid--fluid interface and a liquid drop in contact with a
gas phase residing on a solid substrate. We discuss to which extent the
decomposition of the grand canonical free energy of such systems into volume,
surface, and line contributions is unique in spite of the freedom one has in
positioning the Gibbs dividing interfaces. In the case of a lens it is found
that the line tension is independent of arbitrary choices of the Gibbs dividing
interfaces. In the case of a drop, however, one arrives at two different
possible definitions of the line tension. One of them corresponds seamlessly to
that applicable to the lens. The line tension defined this way turns out to be
independent of choices of the Gibbs dividing interfaces. In the case of the
second definition,however, the line tension does depend on the choice of the
Gibbs dividing interfaces. We provide equations for the equilibrium contact
angles which are form-invariant with respect to notional shifts of dividing
interfaces which only change the description of the system. Conceptual
consistency requires to introduce additional stiffness constants attributed to
the line. We show how these constants transform as a function of the relative
displacements of the dividing interfaces. The dependences of the contact angles
on lens or drop volumes do not render the line tension alone but a combination
of the line tension, the Tolman length, and the stiffness constants of the
line.Comment: 34 pages, 9 figure
Microcanonical Determination of the Interface Tension of Flat and Curved Interfaces from Monte Carlo Simulations
The investigation of phase coexistence in systems with multi-component order
parameters in finite systems is discussed, and as a generic example, Monte
Carlo simulations of the two-dimensional q-state Potts model (q=30) on LxL
square lattices (40<=L<=100) are presented. It is shown that the microcanonical
ensemble is well-suited both to find the precise location of the first order
phase transition and to obtain an accurate estimate for the interfacial free
energy between coexisting ordered and disordered phases. For this purpose, a
microcanonical version of the heatbath algorithm is implemented. The finite
size behaviour of the loop in the curve describing the inverse temperature
versus energy density is discussed, emphasizing that the extrema do not have
the meaning of van der Waals-like "spinodal points" separating metastable from
unstable states, but rather describe the onset of heterophase states:
droplet/bubble evaporation/condensation transitions. Thus all parts of these
loops, including the parts that correspond to a negative specific heat,
describe phase coexistence in full thermal equilibrium. However, the estimates
for the curvature-dependent interface tension of the droplets and bubbles
suffer from unexpected and unexplained large finite size effects which need
further study.Comment: submitted to special issue "Liquid Matter" of Journal of Physics C:
Condensed Matter on occasion of the 8th Liquid Matter Conference held Sept.
6-10, 2011 in Vienna, Austri
Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
Here, we review the basic concepts and applications of the
phase-field-crystal (PFC) method, which is one of the latest simulation
methodologies in materials science for problems, where atomic- and microscales
are tightly coupled. The PFC method operates on atomic length and diffusive
time scales, and thus constitutes a computationally efficient alternative to
molecular simulation methods. Its intense development in materials science
started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88
(2002), p. 245701]. Since these initial studies, dynamical density functional
theory and thermodynamic concepts have been linked to the PFC approach to serve
as further theoretical fundaments for the latter. In this review, we summarize
these methodological development steps as well as the most important
applications of the PFC method with a special focus on the interaction of
development steps taken in hard and soft matter physics, respectively. Doing
so, we hope to present today's state of the art in PFC modelling as well as the
potential, which might still arise from this method in physics and materials
science in the nearby future.Comment: 95 pages, 48 figure
Magnetization of ferrofluids with dipolar interactions - a Born--Mayer expansion
For ferrofluids that are described by a system of hard spheres interacting
via dipolar forces we evaluate the magnetization as a function of the internal
magnetic field with a Born--Mayer technique and an expansion in the dipolar
coupling strength. Two different approximations are presented for the
magnetization considering different contributions to a series expansion in
terms of the volume fraction of the particles and the dipolar coupling
strength.Comment: 19 pages, 11 figures submitted to PR
Local Anisotropy of Fluids using Minkowski Tensors
Statistics of the free volume available to individual particles have
previously been studied for simple and complex fluids, granular matter,
amorphous solids, and structural glasses. Minkowski tensors provide a set of
shape measures that are based on strong mathematical theorems and easily
computed for polygonal and polyhedral bodies such as free volume cells (Voronoi
cells). They characterize the local structure beyond the two-point correlation
function and are suitable to define indices of
local anisotropy. Here, we analyze the statistics of Minkowski tensors for
configurations of simple liquid models, including the ideal gas (Poisson point
process), the hard disks and hard spheres ensemble, and the Lennard-Jones
fluid. We show that Minkowski tensors provide a robust characterization of
local anisotropy, which ranges from for vapor
phases to for ordered solids. We find that for fluids,
local anisotropy decreases monotonously with increasing free volume and
randomness of particle positions. Furthermore, the local anisotropy indices
are sensitive to structural transitions in these simple
fluids, as has been previously shown in granular systems for the transition
from loose to jammed bead packs
NaCl nucleation from brine in seeded simulations: Sources of uncertainty in rate estimates
This work reexamines seeded simulation results for NaCl nucleation from a supersaturated aqueous solution at 298.15 K and 1 bar pressure. We present a linear regression approach for analyzing seeded simulation data that provides both nucleation rates and uncertainty estimates. Our results show that rates obtained from seeded simulations rely critically on a precise driving force for the model system. The driving force vs. solute concentration curve need not exactly reproduce that of the real system, but it should accurately describe the thermodynamic properties of the model system. We also show that rate estimates depend strongly on the nucleus size metric. We show that the rate estimates systematically increase as more stringent local order parameters are used to count members of a cluster and provide tentative suggestions for appropriate clustering criteria
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