1,625 research outputs found
Molecular correlations and solvation in simple fluids
We study the molecular correlations in a lattice model of a solution of a
low-solubility solute, with emphasis on how the thermodynamics is reflected in
the correlation functions. The model is treated in Bethe-Guggenheim
approximation, which is exact on a Bethe lattice (Cayley tree). The solution
properties are obtained in the limit of infinite dilution of the solute. With
, , and the three pair correlation functions
as functions of the separation (subscripts 1 and 2 referring to solvent and
solute, respectively), we find for lattice steps that
. This illustrates a general
theorem that holds in the asymptotic limit of infinite . The three
correlation functions share a common exponential decay length (correlation
length), but when the solubility of the solute is low the amplitude of the
decay of is much greater than that of , which in turn is
much greater than that of . As a consequence the amplitude of the
decay of is enormously greater than that of . The
effective solute-solute attraction then remains discernible at distances at
which the solvent molecules are essentially no longer correlated, as found in
similar circumstances in an earlier model. The second osmotic virial
coefficient is large and negative, as expected. We find that the
solvent-mediated part of the potential of mean force between solutes,
evaluated at contact, , is related in this model to the Gibbs free energy
of solvation at fixed pressure, , by , where is the coordination number of the lattice, the
pressure, and the volume of the cell associated with each lattice site. A
large, positive associated with the low solubility is thus
reflected in a strong attraction (large negative at contact), which is the
major contributor to the second osmotic virial coefficient. In this model, the
low solubility (large positive ) is due partly to an unfavorable
enthalpy of solvation and partly to an unfavorable solvation entropy, unlike in
the hydrophobic effect, where the enthalpy of solvation itself favors high
solubility, but is overweighed by the unfavorable solvation entropy.Comment: 9 pages, 2 figure
Quantum density anomaly in optically trapped ultracold gases
We show that the Bose-Hubbard Model exhibits an increase in density with
temperature at fixed pressure in the regular fluid regime and in the superfluid
phase. The anomaly at the Bose-Einstein condensate is the first density anomaly
observed in a quantum state. We propose that the mechanism underlying both the
normal phase and the superfluid phase anomalies is related to zero point
entropies and ground state phase transitions. A connection with the typical
experimental scales and setups is also addressed. This key finding opens a new
pathway for theoretical and experimental studies of water-like anomalies in the
area of ultracold quantum gases
Multiple liquid-liquid critical points and anomalies in core-softened potentials
The relation between liquid-liquid phase transitions and waterlike density
anomalies in core-softened potentials of fluids was investigated in an exactly
solvable one dimensional lattice model and a in a three dimensional fluid with
fermi-like potential, the latter by molecular dynamics. Both systems were shown
to present three liquid phases, two liquid-liquid phase transitions closely
connected to two distinct regions of anomalous density increase. We propose
that an oscillatory behavior observed on the thermal expansion coefficient as a
function of pressure can be used as a signature of the connection between
liquid-liquid phase and density
Solution of an associating lattice gas model with density anomaly on a Husimi lattice
We study a model of a lattice gas with orientational degrees of freedom which
resemble the formation of hydrogen bonds between the molecules. In this model,
which is the simplified version of the Henriques-Barbosa model, no distinction
is made between donors and acceptors in the bonding arms. We solve the model in
the grand-canonical ensemble on a Husimi lattice built with hexagonal
plaquettes with a central site. The ground-state of the model, which was
originally defined on the triangular lattice, is exactly reproduced by the
solution on this Husimi lattice. In the phase diagram, one gas and two liquid
(high density-HDL and low density-LDL) phases are present. All phase
transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three
phases coexist at a triple point. A line of temperatures of maximum density
(TMD) in the isobars is found in the metastable GAS phase, as well as another
line of temperatures of minimum density (TmD) appears in the LDL phase, part of
it in the stable region and another in the metastable region of this phase.
These findings are at variance with simulational results for the same model on
the triangular lattice, which suggested a phase diagram with two critical
points. However, our results show very good quantitative agreement with the
simulations, both for the coexistence loci and the densities of particles and
of hydrogen bonds. We discuss the comparison of the simulations with our
results.Comment: 12 pages, 5 figure
Groupoid symmetry and constraints in general relativity
When the vacuum Einstein equations are cast in the form of hamiltonian
evolution equations, the initial data lie in the cotangent bundle of the
manifold M\Sigma\ of riemannian metrics on a Cauchy hypersurface \Sigma. As in
every lagrangian field theory with symmetries, the initial data must satisfy
constraints. But, unlike those of gauge theories, the constraints of general
relativity do not arise as momenta of any hamiltonian group action. In this
paper, we show that the bracket relations among the constraints of general
relativity are identical to the bracket relations in the Lie algebroid of a
groupoid consisting of diffeomorphisms between space-like hypersurfaces in
spacetimes. A direct connection is still missing between the constraints
themselves, whose definition is closely related to the Einstein equations, and
our groupoid, in which the Einstein equations play no role at all. We discuss
some of the difficulties involved in making such a connection.Comment: 22 pages, major revisio
Waterlike density anomaly in fermions
In this work we explore the one-dimensional extended Hubbard model as a fluid
system modelling liquid phases of different densities. This model naturally
displays two length scales of interaction, which are connected with waterlike
anomalies. We analyze the density anomaly as a function of the model
parameters, namely the hopping, on-site and first neighbor interactions. We
show that this anomaly is present for a wide range of model parameters and is
connected to a ground-state liquid-liquid critical point.Comment: 15 pages, 9 figure
i-Rheo: determining the linear viscoelastic moduli of colloidal dispersions from step-stress measurements
We report on the application of a Fourier transform based method, `i-Rheo', to evaluate the linear viscoelastic moduli of hard-sphere colloidal dispersions, both in the fluid and glass states, from a direct analysis of raw step-stress (creep) experimental data. We corroborate the efficacy of i-Rheo by comparing the outputs of creep tests performed on homogenous complex fluids to conventional dynamic frequency sweeps. A similar approach is adopted for a number of colloidal suspensions over a broad range of volume fractions. For these systems, we test the limits of the method by varying the applied stress across the materials' linear and non-linear viscoelastic regimes, and we show that the best results are achieved for stress values close to the upper limit of the materials' linear viscoelastic regime; where the signal-to-noise ratio is at its highest and the non-linear phenomena have not appeared yet. We record that, the range of accessible frequencies is controlled at the higher end by the relative weight between the inertia of the instrument and the elasticity of the complex material under investigation; whereas, the lowest accessible frequency is dictated by the extent of the materials' linear viscoelastic regime. Nonetheless, despite these constrains, we confirm the effectiveness of i-Rheo for gaining valuable information on the materials' linear viscoelastic properties even from creep ringing data, confirming its potency and general validity as an accurate method for determining the material's rheological behaviour for a variety of complex systems
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