112 research outputs found
Stability of the iterative solutions of integral equations as one phase freezing criterion
A recently proposed connection between the threshold for the stability of the
iterative solution of integral equations for the pair correlation functions of
a classical fluid and the structural instability of the corresponding real
fluid is carefully analyzed. Direct calculation of the Lyapunov exponent of the
standard iterative solution of HNC and PY integral equations for the 1D hard
rods fluid shows the same behavior observed in 3D systems. Since no phase
transition is allowed in such 1D system, our analysis shows that the proposed
one phase criterion, at least in this case, fails. We argue that the observed
proximity between the numerical and the structural instability in 3D originates
from the enhanced structure present in the fluid but, in view of the arbitrary
dependence on the iteration scheme, it seems uneasy to relate the numerical
stability analysis to a robust one-phase criterion for predicting a
thermodynamic phase transition.Comment: 11 pages, 2 figure
Anomalous phase behavior of a soft-repulsive potential with a strictly monotonic force
We study the phase behavior of a classical system of particles interacting
through a strictly convex soft-repulsive potential which, at variance with the
pairwise softened repulsions considered so far in the literature, lacks a
region of downward or zero curvature. Nonetheless, such interaction is
characterized by two length scales, owing to the presence of a range of
interparticle distances where the repulsive force increases, for decreasing
distance, much more slowly than in the adjacent regions. We investigate, using
extensive Monte Carlo simulations combined with accurate free-energy
calculations, the phase diagram of the system under consideration. We find that
the model exhibits a fluid-solid coexistence line with multiple re-entrant
regions, an extremely rich solid polymorphism with solid-solid transitions, and
water-like anomalies. In spite of the isotropic nature of the interparticle
potential, we find that, among the crystal structures in which the system can
exist, there are also a number of non-Bravais lattices, such as cI16 and
diamond.Comment: 21 pages, 7 figures, in press on Phys. Rev.
The zero-temperature phase diagram of soft-repulsive particle fluids
Effective pair interactions with a soft-repulsive component are a well-known
feature of polymer solutions and colloidal suspensions, but they also provide a
key to interpret the high-pressure behaviour of simple elements. We have
computed the zero-temperature phase diagram of four different model potentials
with various degrees of core softness. Among the reviewed crystal structures,
there are also a number of non-Bravais lattices, chosen among those observed in
real systems. Some of these crystals are indeed found to be stable for the
selected potentials. We recognize an apparently universal trend for unbounded
potentials, going from high- to low-coordinated crystal phases and back upon
increasing the pressure. Conversely, a bounded repulsion may lead to
intermittent appearance of compact structures with compression and no eventual
settling down in a specific phase. In both cases, the fluid phase repeatedly
reenters at intermediate pressures, as suggested by a cell-theory treatment of
the solids. These findings are of relevance for soft matter in general, but
they also offer fresh insight into the mechanisms subtended to solid
polymorphism in elemental substances.Comment: 16 pages, 5 figures, to be published on Soft Matte
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