2,397 research outputs found
Saddles in the energy landscape: extensivity and thermodynamic formalism
We formally extend the energy landscape approach for the thermodynamics of
liquids to account for saddle points. By considering the extensive nature of
macroscopic potential energies, we derive the scaling behavior of saddles with
system size, as well as several approximations for the properties of low-order
saddles (i.e., those with only a few unstable directions). We then cast the
canonical partition function in a saddle-explicit form and develop, for the
first time, a rigorous energy landscape approach capable of reproducing trends
observed in simulations, in particular the temperature dependence of the energy
and fractional order of sampled saddles.Comment: 4 pages, 1 figur
Scaled Particle Theory for Hard Sphere Pairs. I. Mathematical Structure
We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle
theory that can serve as a predictive method for the hard sphere pair
correlation function g(r). The reversible cavity creation work is analyzed both
for a single spherical cavity of arbitrary size, as well as for a pair of
identical such spherical cavities with variable center-to-center separation.
These quantities lead directly to prediction of g(r). Smooth connection
conditions have been identified between the small-cavity situation where the
work can be exactly and completely expressed in terms of g(r), and the
large-cavity regime where macroscopic properties become relevant. Closure
conditions emerge which produce a nonlinear integral equation that must be
satisfied by the pair correlation function. This integral equation has a
structure which straightforwardly generates a solution that is a power series
in density. The results of this series replicate the exact second and third
virial coefficients for the hard sphere system via the contact value of the
pair correlation function. The predicted fourth virial coefficient is
approximately 0.6 percent lower than the known exact value. Detailed numerical
analysis of the nonlinear integral equation has been deferred to the sequel
(following paper
Phase diagram of a polydisperse soft-spheres model for liquids and colloids
The phase diagram of soft spheres with size dispersion has been studied by
means of an optimized Monte Carlo algorithm which allows to equilibrate below
the kinetic glass transition for all sizes distribution. The system
ubiquitously undergoes a first order freezing transition. While for small size
dispersion the frozen phase has a crystalline structure, large density
inhomogeneities appear in the highly disperse systems. Studying the interplay
between the equilibrium phase diagram and the kinetic glass transition, we
argue that the experimentally found terminal polydispersity of colloids is a
purely kinetic phenomenon.Comment: Version to be published in Physical Review Letter
Mpemba effect and phase transitions in the adiabatic cooling of water before freezing
An accurate experimental investigation on the Mpemba effect (that is, the
freezing of initially hot water before cold one) is carried out, showing that
in the adiabatic cooling of water a relevant role is played by supercooling as
well as by phase transitions taking place at 6 +/- 1 oC, 3.5 +/- 0.5 oC and 1.3
+/- 0.6 oC, respectively. The last transition, occurring with a non negligible
probability of 0.21, has not been detected earlier. Supported by the
experimental results achieved, a thorough theoretical analysis of supercooling
and such phase transitions, which are interpreted in terms of different
ordering of clusters of molecules in water, is given.Comment: revtex, 4 pages, 2 figure
Test of classical nucleation theory on deeply supercooled high-pressure simulated silica
We test classical nucleation theory (CNT) in the case of simulations of
deeply supercooled, high density liquid silica, as modelled by the BKS
potential. We find that at density ~g/cm, spontaneous nucleation
of crystalline stishovite occurs in conventional molecular dynamics simulations
at temperature T=3000 K, and we evaluate the nucleation rate J directly at this
T via "brute force" sampling of nucleation events. We then use parallel,
constrained Monte Carlo simulations to evaluate , the free energy
to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200
and 3300 K. We find that the prediction of CNT for the n-dependence of fits reasonably well to the data at all T studied, and at 3300 K yields a
chemical potential difference between liquid and stishovite that matches
independent calculation. We find that , the size of the critical nucleus,
is approximately 10 silicon atoms at T=3300 K. At 3000 K, decreases to
approximately 3, and at such small sizes methodological challenges arise in the
evaluation of when using standard techniques; indeed even the
thermodynamic stability of the supercooled liquid comes into question under
these conditions. We therefore present a modified approach that permits an
estimation of at 3000 K. Finally, we directly evaluate at T=3000
K the kinetic prefactors in the CNT expression for J, and find physically
reasonable values; e.g. the diffusion length that Si atoms must travel in order
to move from the liquid to the crystal embryo is approximately 0.2 nm. We are
thereby able to compare the results for J at 3000 K obtained both directly and
based on CNT, and find that they agree within an order of magnitude.Comment: corrected calculation, new figure, accepted in JC
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
Heterogeneous nucleation near a metastable vapour-liquid transition: the effect of wetting transitions
Phase transformations such as freezing typically start with heterogeneous
nucleation. Heterogeneous nucleation near a wetting transition, of a
crystalline phase is studied. The wetting transition occurs at or near a
vapour-liquid transition which occurs in a metastable fluid. The fluid is
metastable with respect to crystallisation, and it is the crystallisation of
this fluid phase that we are interested in. At a wetting transition a thick
layer of a liquid phase forms at a surface in contact with the vapour phase.
The crystalline nucleus is then immersed in this liquid layer, which reduces
the free energy barrier to nucleation and so dramatically increases the
nucleation rate. The variation in the rate of heterogeneous nucleation close to
wetting transitions is calculated for systems in which the longest-range forces
are dispersion forces.Comment: 11 pages including 3 figure
Mode Coupling relaxation scenario in a confined glass former
Molecular dynamics simulations of a Lennard-Jones binary mixture confined in
a disordered array of soft spheres are presented. The single particle dynamical
behavior of the glass former is examined upon supercooling. Predictions of mode
coupling theory are satisfied by the confined liquid. Estimates of the
crossover temperature are obtained by power law fit to the diffusion
coefficients and relaxation times of the late region. The exponent
of the von Schweidler law is also evaluated. Similarly to the bulk, different
values of the exponent are extracted from the power law fit to the
diffusion coefficients and relaxation times.Comment: 5 pages, 4 figures, changes in the text, accepted for publication on
Europhysics Letter
Gaussian excitations model for glass-former dynamics and thermodynamics
We describe a model for the thermodynamics and dynamics of glass-forming
liquids in terms of excitations from an ideal glass state to a Gaussian
manifold of configurationally excited states. The quantitative fit of this
three parameter model to the experimental data on excess entropy and heat
capacity shows that ``fragile'' behavior, indicated by a sharply rising excess
heat capacity as the glass transition is approached from above, occurs in
anticipation of a first-order transition -- usually hidden below the glass
transition -- to a ``strong'' liquid state of low excess entropy. The dynamic
model relates relaxation to a hierarchical sequence of excitation events each
involving the probability of accumulating sufficient kinetic energy on a
separate excitable unit. Super-Arrhenius behavior of the relaxation rates, and
the known correlation of kinetic with thermodynamic fragility, both follow from
the way the rugged landscape induces fluctuations in the partitioning of energy
between vibrational and configurational manifolds. A relation is derived in
which the configurational heat capacity, rather than the configurational
entropy of the Adam Gibbs equation, controls the temperature dependence of the
relaxation times, and this gives a comparable account of the experimental
observations.Comment: 21 pp., 17 fig
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