10 research outputs found
Modeling liquid-liquid phase transitions and quasicrystal formation
Thesis (Ph. D.)--Boston University, 2003.In this thesis, studies which concern two different subjects related to phase transitions
in fluids and crystalline solids are presented. Condensed matter formation,
structure, and phase transitions are modeled using molecular dynamics simulations
of simple discontinuous potentials with attractive and repulsive interactions. Novel
phase diagrams are proposed for quasicrystals, crystals, and liquids.
In the first part of the thesis, the formation of a quasicrystal in a two dimensional
monodisperse system is investigated using molecular dynamics simulations of
hard sphere particles interacting via a two-dimensional square-well potential. It is
found that for certain values of the square-well parameters more than one stable
crystalline phase can form. By quenching the liquid phase at a very low temperature,
an amorphous phase is obtained. When this the amorphous phase is heated,
a quasicrystalline structure with five-fold symmetry forms. From estimations of the
Helmholtz potentials of the stable crystalline phases and of the quasicrystal, it is
concluded that within a specific temperature range, the observed quasicrystal phase
can be the stable phase.
The second part of the thesis concerns a study of the liquid-liquid phase transition
for a single-component system in three dimensions, interacting via an isotropic
potential with a repulsive soft-core shoulder at short distance and an attractive well
at an intermediate distance. The potential is similar to potentials used to describe [TRUNCATED
Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range
We investigate how the phase diagram of a repulsive soft-core attractive potential, with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We extend our previous work on short soft-core ranges to the case of large soft-core ranges, by using an integral equation approach in the hypernetted-chain approximation. We show, using a modified van der Waals equation we recently introduced, that if there is a balance between the attractive and repulsive part of the potential this potential has two fluid-fluid critical points well separated in temperature and in density. This implies that for the repulsive (attractive) energy
U
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(
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and the repulsive (attractive) range
w
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(
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)
the relation
U
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holds for short soft-core ranges, while
U
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3
w
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holds for large soft-core ranges
Liquid-Liquid Phase Transition for an Attractive Isotropic Potential with Wide Repulsive Range
Recent experimental and theoretical results have shown the existence of a
liquid-liquid phase transition in isotropic systems, such as biological
solutions and colloids, whose interaction can be represented via an effective
potential with a repulsive soft-core and an attractive part. We investigate how
the phase diagram of a schematic general isotropic system, interacting via a
soft-core squared attractive potential, changes by varying the parameters of
the potential. It has been shown that this potential has a phase diagram with a
liquid-liquid phase transition in addition to the standard gas-liquid phase
transition and that, for a short-range soft-core, the phase diagram resulting
from molecular dynamics simulations can be interpreted through a modified van
der Waals equation. Here we consider the case of soft-core ranges comparable
with or larger than the hard-core diameter. Because an analysis using molecular
dynamics simulations of such systems or potentials is too time-demanding, we
adopt an integral equation approach in the hypernetted-chain approximation.
Thus we can estimate how the temperature and density of both critical points
depend on the potential's parameters for large soft-core ranges. The present
results confirm and extend our previous analysis, showing that this potential
has two fluid-fluid critical points that are well separated in temperature and
in density only if there is a balance between the attractive and repulsive part
of the potential. We find that for large soft-core ranges our results satisfy a
simple relation between the potential's parameters
Generic mechanism for generating a liquid-liquid phase transition
Recent experimental results indicate that phosphorus, a single-component
system, can have two liquid phases: a high-density liquid (HDL) and a
low-density liquid (LDL) phase. A first-order transition between two liquids of
different densities is consistent with experimental data for a variety of
materials, including single-component systems such as water, silica and carbon.
Molecular dynamics simulations of very specific models for supercooled water,
liquid carbon and supercooled silica, predict a LDL-HDL critical point, but a
coherent and general interpretation of the LDL-HDL transition is lacking. Here
we show that the presence of a LDL and a HDL can be directly related to an
interaction potential with an attractive part and two characteristic
short-range repulsive distances. This kind of interaction is common to other
single-component materials in the liquid state (in particular liquid metals),
and such potentials are often used to decribe systems that exhibit a density
anomaly. However, our results show that the LDL and HDL phases can occur in
systems with no density anomaly. Our results therefore present an experimental
challenge to uncover a liquid-liquid transition in systems like liquid metals,
regardless of the presence of the density anomaly.Comment: 5 pages, 3 ps Fig
Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range
We investigate how the phase diagram of a repulsive soft-core attractive potential, with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We extend our previous work on short soft-core ranges to the case of large soft-core ranges, by using an integral equation approach in the hypernetted-chain approximation. We show, using a modified van der Waals equation we recently introduced, that if there is a balance between the attractive and repulsive part of the potential this potential has two fluid-fluid critical points well separated in temperature and in density. This implies that for the repulsive (attractive) energy
U
R
(
U
A
)
and the repulsive (attractive) range
w
R
(
w
A
)
the relation
U
R
â
U
A
â
w
R
â
w
A
holds for short soft-core ranges, while
U
R
â
U
A
â
3
w
R
â
w
A
holds for large soft-core ranges
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 three 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 (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gasÂżlow-density-liquid (LDL) critical point, and the other in a gasÂżhigh-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and 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
Liquid-liquid phase transition for soft-core attractive potential
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 C1 and a liquid-liquid critical point C2. 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 gives us insight on the mechanisms ruling the dependence of the two critical points on the potentialÂżs 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
A Molecular Dynamics Study of the Response of Lipid Bilayers and Monolayers to Trehalose
Surface tensions evaluated from molecular dynamics simulations of fully hydrated dipalmitoylphosphatidylcholine bilayers and monolayers at surface areas/lipid of 54, 64, and 80 Ă
(2) are uniformly lowered 4â8 dyn/cm upon addition of trehalose in a 1:2 trehalose/lipid ratio. Constant surface tension simulations of bilayers yield the complementary result: an increase in surface area consistent with the surface pressure-surface area (Ï-A) isotherms. Hydrogen bonding by trehalose, replacement of waters in the headgroup region, and modulation of the dipole potential are all similar in bilayers and monolayers at the same surface area. These results strongly support the assumption that experimental measurements on the interactions of surface active components such as trehalose with monolayers can yield quantitative insight to their effects on bilayers. The simulations also indicate that the 20â30 dyn/cm difference in surface tension of the bilayer leaflet and monolayer arises from differences in the chain regions, not the headgroup/water interfaces