20 research outputs found
Liquid-Liquid Phase Transitions for Soft-Core Attractive Potentials
Using event driven molecular dynamics simulations, we study a three
dimensional one-component system of spherical particles interacting via a
discontinuous potential combining a repulsive square soft core and an
attractive square well. In the case of a narrow attractive well, it has been
shown that this potential has two metastable gas-liquid critical points. Here
we systematically investigate how the changes of the parameters of this
potential affect the phase diagram of the system. We find a broad range of
potential parameters for which the system has both a gas-liquid critical point
and a liquid-liquid critical point. For the liquid-gas critical point we find
that the derivatives of the critical temperature and pressure, with respect to
the parameters of the potential, have the same signs: they are positive for
increasing width of the attractive well and negative for increasing width and
repulsive energy of the soft core. This result resembles the behavior of the
liquid-gas critical point for standard liquids. In contrast, for the
liquid-liquid critical point the critical pressure decreases as the critical
temperature increases. As a consequence, the liquid-liquid critical point
exists at positive pressures only in a finite range of parameters. We present a
modified van der Waals equation which qualitatively reproduces the behavior of
both critical points within some range of parameters, and give us insight on
the mechanisms ruling the dependence of the two critical points on the
potential's parameters. The soft core potential studied here resembles model
potentials used for colloids, proteins, and potentials that have been related
to liquid metals, raising an interesting possibility that a liquid-liquid phase
transition may be present in some systems where it has not yet been observed.Comment: 29 pages, 15 figure
Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly
We investigate the phase behavior of a single-component system in 3
dimensions with spherically-symmetric, pairwise-additive, soft-core
interactions with an attractive well at a long distance, a repulsive soft-core
shoulder at an intermediate distance, and a hard-core repulsion at a short
distance, similar to potentials used to describe liquid systems such as
colloids, protein solutions, or liquid metals. We showed [Nature {\bf 409}, 692
(2001)] that, even with no evidences of the density anomaly, the phase diagram
has two first-order fluid-fluid phase transitions, one ending in a
gas--low-density liquid (LDL) critical point, and the other in a
gas--high-density liquid (HDL) critical point, with a LDL-HDL phase transition
at low temperatures. Here we use integral equation calculations to explore the
3-parameter space of the soft-core potential and we perform molecular dynamics
simulations in the interesting region of parameters. For the equilibrium phase
diagram we analyze the structure of the crystal phase and find that, within the
considered range of densities, the structure is independent of the density.
Then, we analyze in detail the fluid metastable phases and, by explicit
thermodynamic calculation in the supercooled phase, we show the absence of the
density anomaly. We suggest that this absence is related to the presence of
only one stable crystal structure.Comment: 15 pages, 21 figure
Constrained optimal discrimination designs for Fourier regression models
In this article, the problem of constructing efficient discrimination designs in a Fourier regression model is considered. We propose designs which maximize the power of the F-test,which discriminates between the two highest order models, subject to the constraints that the tests that discriminate between lower order models have at least some givenrelative power. A complete solution is presented in terms of the canonical moments of the optimal designs, and for the special case of equal constraints even more specific formulaeare availabl