70 research outputs found
Thermodynamic anomalies in a lattice model of water
We investigate a lattice-fluid model of water, defined on a three-dimensional
body centered cubic lattice. Model molecules possess a tetrahedral symmetry,
with four equivalent bonding arms, aiming to mimic the formation of hydrogen
bonds. The model is similar to the one proposed by Roberts and Debenedetti [J.
Chem. Phys. 105, 658 (1996)], simplified in that no distinction between bond
"donors" and "acceptors" is imposed. Bond formation depends both on orientation
and local density. In the ground state, we show that two different ordered
(ice) phases are allowed. At finite temperature, we analyze homogeneous phases
only, working out phase diagram, response functions, the temperature of maximum
density locus, and the Kauzmann line. We make use of a generalized first order
approximation on a tetrahedral cluster. In the liquid phase, the model exhibits
several anomalous properties observed in real water. In the low temperature
region (supercooled liquid), there are evidences of a second critical point
and, for some range of parameter values, this scenario is compatible with the
existence of a reentrant spinodal.Comment: 12 pages, 9 figures, 1 tabl
Low-Temperature Expansion for a First Order Surface Transition
The question concerning the possibility of a first order surface transition
in a semi--infinite Blume--Capel model is addressed by means of low temperature
expansions. It is found that such a transition can exist, according to mean
field and cluster variation approximations, and contrarily to renormalization
group results.Comment: 9 pages (plain TeX) + 1 figure (PostScript, appended),
POLFIS-TH.03/9
Thermodynamic anomalies in a lattice model of water: Solvation properties
We investigate a lattice-fluid model of water, defined on a 3-dimensional
body-centered cubic lattice. Model molecules possess a tetrahedral symmetry,
with four equivalent bonding arms. The model is similar to the one proposed by
Roberts and Debenedetti [J. Chem. Phys. 105, 658 (1996)], simplified by
removing distinction between "donors" and "acceptors". We focus on solvation
properties, mainly as far as an ideally inert (hydrophobic) solute is
concerned. As in our previous analysis, devoted to neat water [J. Chem. Phys.
121, 11856 (2004)], we make use of a generalized first order approximation on a
tetrahedral cluster. We show that the model exhibits quite a coherent picture
of water thermodynamics, reproducing qualitatively several anomalous properties
observed both in pure water and in solutions of hydrophobic solutes. As far as
supercooled liquid water is concerned, the model is consistent with the second
critical point scenario.Comment: 12 pages, 9 figures, 1 tabl
Revisiting waterlike network-forming lattice models
In a previous paper [J. Chem. Phys. 129, 024506 (2008)] we studied a 3
dimensional lattice model of a network-forming fluid, recently proposed in
order to investigate water anomalies. Our semi-analytical calculation, based on
a cluster-variation technique, turned out to reproduce almost quantitatively
several Monte Carlo results and allowed us to clarify the structure of the
phase diagram, including different kinds of orientationally ordered phases.
Here, we extend the calculation to different parameter values and to other
similar models, known in the literature. We observe that analogous ordered
phases occur in all these models. Moreover, we show that certain "waterlike"
thermodynamic anomalies, claimed by previous studies, are indeed artifacts of a
homogeneity assumption made in the analytical treatment. We argue that such a
difficulty is common to a whole class of lattice models for water, and suggest
a possible way to overcome the problem.Comment: 13 pages, 12 figure
Cluster-variation approximation for a network-forming lattice-fluid model
We consider a 3-dimensional lattice model of a network-forming fluid, which
has been recently investigated by Girardi and coworkers by means of Monte Carlo
simulations [J. Chem. Phys. \textbf{126}, 064503 (2007)], with the aim of
describing water anomalies. We develop an approximate semi-analytical
calculation, based on a cluster-variation technique, which turns out to
reproduce almost quantitatively different thermodynamic properties and phase
transitions determined by the Monte Carlo method. Nevertheless, our calculation
points out the existence of two different phases characterized by long-range
orientational order, and of critical transitions between them and to a
high-temperature orientationally-disordered phase. Also, the existence of such
critical lines allows us to explain certain ``kinks'' in the isotherms and
isobars determined by the Monte Carlo analysis. The picture of the phase
diagram becomes much more complex and richer, though unfortunately less
suitable to describe real water.Comment: 10 pages, 9 figures, submitted to J. Chem. Phy
Hydration of an apolar solute in a two-dimensional waterlike lattice fluid
In a previous work, we investigated a two-dimensional lattice-fluid model,
displaying some waterlike thermodynamic anomalies. The model, defined on a
triangular lattice, is now extended to aqueous solutions with apolar species.
Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3
(equilateral triangle) symmetry, with three equivalent bonding arms. Bond
formation depends both on orientation and local density. The insertion of inert
molecules displays typical signatures of hydrophobic hydration: large positive
transfer free energy, large negative transfer entropy (at low temperature),
strong temperature dependence of the transfer enthalpy and entropy, i.e., large
(positive) transfer heat capacity. Model properties are derived by a
generalized first order approximation on a triangle cluster.Comment: 9 pages, 5 figures, 1 table; submitted to Phys. Rev.
Cluster Variation Approach to the Random-Anisotropy Blume-Emery-Griffiths Model
The random--anisotropy Blume--Emery--Griffiths model, which has been proposed
to describe the critical behavior of He--He mixtures in a porous
medium, is studied in the pair approximation of the cluster variation method
extended to disordered systems. Several new features, with respect to mean
field theory, are found, including a rich ground state, a nonzero percolation
threshold, a reentrant coexistence curve and a miscibility gap on the high
He concentration side down to zero temperature. Furthermore, nearest
neighbor correlations are introduced in the random distribution of the
anisotropy, which are shown to be responsible for the raising of the critical
temperature with respect to the pure and uncorrelated random cases and
contribute to the detachment of the coexistence curve from the line.Comment: 14 pages (plain TeX) + 12 figures (PostScript, appended), Preprint
POLFIS-TH.02/9
Phase transitions in a spin-1 model with plaquette interaction on the square lattice
An extension of the Blume-Emery-Griffiths model with a plaquette four-spin interaction term, on the square lattice, is investigated by means of the cluster variation method in the square approximation. The ground state of the model, for negative plaquette interaction, exhibits several new phases, including frustrated ones. At finite temperature we obtain a quite rich phase diagram with two new phases, a ferrimagnetic and a weakly ferromagnetic one, and several multicritical points
Spectral action beyond the weak-field approximation
The spectral action for a non-compact commutative spectral triple is computed
covariantly in a gauge perturbation up to order 2 in full generality. In the
ultraviolet regime, , the action decays as in any even
dimension.Comment: 17 pages Few misprints correcte
Partial integration and local mean-field approach for a vector lattice model of microemulsions
A vector model on the simple cubic lattice, describing a mixture of water, oil, and amphiphile, is considered. An integration over the amphiphile orientational degrees of freedom is performed exactly in order to obtain an effective Hamiltonian for the system. The resulting model is a three-state (spin-1) system and contains many-site interaction terms. The analysis of the ground state reveals the presence of the water-oil-rich phase as well as the amphiphile-rich and the cubic phases. The temperature phase diagram of the system is analyzed in a local mean-field approach, and a triple line of water-rich, oil-rich, and microemulsion coexistence is obtained. For some values of the model parameters, lamellar phases also appear in the system, but only at finite temperature. The Lifshitz line is determined in a semianalytical way in order to locate the microemulsion region of the disordered phase
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