45 research outputs found
Universality class of criticality in the restricted primitive model electrolyte
The 1:1 equisized hard-sphere electrolyte or restricted primitive model has
been simulated via grand-canonical fine-discretization Monte Carlo. Newly
devised unbiased finite-size extrapolation methods using temperature-density,
(T, rho), loci of inflections, Q = ^2/ maxima, canonical and C_V
criticality, yield estimates of (T_c, rho_c) to +- (0.04, 3)%. Extrapolated
exponents and Q-ratio are (gamma, nu, Q_c) = [1.24(3), 0.63(3); 0.624(2)] which
support Ising (n = 1) behavior with (1.23_9, 0.630_3; 0.623_6), but exclude
classical, XY (n = 2), SAW (n = 0), and n = 1 criticality with potentials
phi(r)>Phi/r^{4.9} when r \to \infty
Coexistence and Criticality in Size-Asymmetric Hard-Core Electrolytes
Liquid-vapor coexistence curves and critical parameters for hard-core 1:1
electrolyte models with diameter ratios lambda = sigma_{-}/\sigma_{+}=1 to 5.7
have been studied by fine-discretization Monte Carlo methods. Normalizing via
the length scale sigma_{+-}=(sigma_{+} + sigma_{-})/2 relevant for the low
densities in question, both Tc* (=kB Tc sigma_{+-}/q^2 and rhoc* (= rhoc sigma
_{+-}^{3}) decrease rapidly (from ~ 0.05 to 0.03 and 0.08 to 0.04,
respectively) as lambda increases. These trends, which unequivocally contradict
current theories, are closely mirrored by results for tightly tethered dipolar
dimers (with Tc* lower by ~ 0-11% and rhoc* greater by 37-12%).Comment: 4 pages, 5 figure
Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte
Grand canonical simulations at various levels, -20, of fine- lattice
discretization are reported for the near-critical 1:1 hard-core electrolyte or
RPM. With the aid of finite-size scaling analyses it is shown convincingly
that, contrary to recent suggestions, the universal critical behavior is
independent of (\grtsim 4); thus the continuum RPM
exhibits Ising-type (as against classical, SAW, XY, etc.) criticality. A
general consideration of lattice discretization provides effective
extrapolation of the {\em intrinsically} erratic -dependence, yielding
(\Tc^ {\ast},\rhoc^{\ast})\simeq (0.0493_{3},0.075) for the
RPM.Comment: 4 pages including 4 figure
Asymmetric Fluid Criticality II: Finite-Size Scaling for Simulations
The vapor-liquid critical behavior of intrinsically asymmetric fluids is
studied in finite systems of linear dimensions, , focusing on periodic
boundary conditions, as appropriate for simulations. The recently propounded
``complete'' thermodynamic scaling theory incorporating pressure
mixing in the scaling fields as well as corrections to scaling
, is extended to finite , initially in a grand
canonical representation. The theory allows for a Yang-Yang anomaly in which,
when , the second temperature derivative,
, of the chemical potential along the phase
boundary, , diverges when T\to\Tc -. The finite-size
behavior of various special {\em critical loci} in the temperature-density or
plane, in particular, the -inflection susceptibility loci and the
-maximal loci -- derived from where -- is carefully elucidated and
shown to be of value in estimating \Tc and \rhoc. Concrete illustrations
are presented for the hard-core square-well fluid and for the restricted
primitive model electrolyte including an estimate of the correlation exponent
that confirms Ising-type character. The treatment is extended to the
canonical representation where further complications appear.Comment: 23 pages in the two-column format (including 13 figures) This is Part
II of the previous paper [arXiv:cond-mat/0212145
Asymmetric Fluid Criticality I: Scaling with Pressure Mixing
The thermodynamic behavior of a fluid near a vapor-liquid and, hence,
asymmetric critical point is discussed within a general ``complete'' scaling
theory incorporating pressure mixing in the nonlinear scaling fields as well as
corrections to scaling. This theory allows for a Yang-Yang anomaly in which
\mu_{\sigma}^{\prime\prime}(T), the second temperature derivative of the
chemical potential along the phase boundary, diverges like the specific heat
when T\to T_{\scriptsize c}; it also generates a leading singular term,
|t|^{2\beta}, in the coexistence curve diameter, where t\equiv
(T-T_{\scriptsize c}) /T_{\scriptsize c}. The behavior of various special loci,
such as the critical isochore, the critical isotherm, the k-inflection loci, on
which \chi^{(k)}\equiv \chi(\rho,T)/\rho^{k} (with \chi = \rho^{2}
k_{\scriptsize B}TK_{T}) and C_{V}^{(k)}\equiv C_{V}(\rho,T)/\rho^{k} are
maximal at fixed T, is carefully elucidated. These results are useful for
analyzing simulations and experiments, since particular, nonuniversal values of
k specify loci that approach the critical density most rapidly and reflect the
pressure-mixing coefficient. Concrete illustrations are presented for the
hard-core square-well fluid and for the restricted primitive model electrolyte.
For comparison, a discussion of the classical (or Landau) theory is presented
briefly and various interesting loci are determined explicitly and illustrated
quantitatively for a van der Waals fluid.Comment: 21 pages in two-column format including 8 figure
Dipolar origin of the gas-liquid coexistence of the hard-core 1:1 electrolyte model
We present a systematic study of the effect of the ion pairing on the
gas-liquid phase transition of hard-core 1:1 electrolyte models. We study a
class of dipolar dimer models that depend on a parameter R_c, the maximum
separation between the ions that compose the dimer. This parameter can vary
from sigma_{+/-} that corresponds to the tightly tethered dipolar dimer model,
to R_c --> infinity, that corresponds to the Stillinger-Lovett description of
the free ion system. The coexistence curve and critical point parameters are
obtained as a function of R_c by grand canonical Monte Carlo techniques. Our
results show that this dependence is smooth but non-monotonic and converges
asymptotically towards the free ion case for relatively small values of R_c.
This fact allows us to describe the gas-liquid transition in the free ion model
as a transition between two dimerized fluid phases. The role of the unpaired
ions can be considered as a perturbation of this picture.Comment: 16 pages, 13 figures, submitted to Physical Review
Phase Diagram of the Two Dimensional Lattice Coulomb Gas
We use Monte Carlo simulations to map out the phase diagram of the two
dimensional Coulomb gas on a square lattice, as a function of density and
temperature. We find that the Kosterlitz-Thouless transition remains up to
higher charge densities than has been suggested by recent theoretical
estimates.Comment: 4 pages, including 6 in-line eps figure
Sine-Gordon mean field theory of a Coulomb Gas
Sine-Gordon field theory is used to investigate the phase diagram of a
neutral Coulomb gas. A variational mean field free energy is constructed and
the corresponding phase diagrams in two (2d) and three dimensions (3d) are
obtained. When analyzed in terms of chemical potential, the Sine-Gordon theory
predicts the phase diagram topologically identical with the Monte Carlo
simulations and a recently developed Debye-H\"uckel-Bjerrum (DHBj) theory. In
2d we find that the infinite order Kosterlitz-Thouless line terminates in a
tricritical point, after which the metal-insulator transition becomes first
order. However, when the transformation from chemical potential to the density
is made the whole of the insulating phase is mapped onto zero density.Comment: 5 pages, Revtex with twocolumn style, 2 Postscript figures. Submitted
to PR
Ginzburg Criterion for Coulombic Criticality
To understand the range of close-to-classical critical behavior seen in
various electrolytes, generalized Debye-Hueckel theories (that yield density
correlation functions) are applied to the restricted primitive model of
equisized hard spheres. The results yield a Landau-Ginzburg free-energy
functional for which the Ginzburg criterion can be explicitly evaluated. The
predicted scale of crossover from classical to Ising character is found to be
similar in magnitude to that derived for simple fluids in comparable fashion.
The consequences in relation to experiments are discussed briefly.Comment: 4 pages, revtex, 2 tables (latex2.09 required due to revtex's
incompatibility with latex2e tables
Criticality in confined ionic fluids
A theory of a confined two dimensional electrolyte is presented. The positive
and negative ions, interacting by a potential, are constrained to move on
an interface separating two solvents with dielectric constants and
. It is shown that the Debye-H\"uckel type of theory predicts that
the this 2d Coulomb fluid should undergo a phase separation into a coexisting
liquid (high density) and gas (low density) phases. We argue, however, that the
formation of polymer-like chains of alternating positive and negative ions can
prevent this phase transition from taking place.Comment: RevTex, no figures, in press Phys. Rev.