Field-theoretic approach to ionic systems: Criticality and tricriticality (original) (raw)
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Critical behaviour of ionic fluids
Molecular Physics, 1993
Recently we proposed a microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures. It was based on the method of collective variables (CV) with a reference system. The approach allowed us to obtain the functional of the Ginzburg-Landau-Wilson (GLW) Hamiltonian expressed in terms of the CV (fluctuating densities). The corresponding set of CV included the variable connected with the order parameter. In this paper we use this approach to the study of the critical behaviour of ionic fluids. For the restricted primitive model (RPM) we obtain the functional of the grand partition function in the phase space of the two fluctuating fields conjugate to the fluctuating densities. First we calculate the phase diagram of the RPM in the mean-field (MF) approximation and then we do this calculation taking into account the terms of the higher orders in the effective Hamiltonian. In the both cases the phase diagrams demonstrate the gas-liquid (GL) and charge ordering phase instabilities. In the latter case, the obtained value for the GL critical temperature is in good agreement with the MC simulation data whereas the critical density is underestimated. The explicit expression found for the grand thermodynamic potential in the vicinity of the GL critical point implies a classical critical behaviour of the RPM.
The Journal of Chemical Physics, 2001
A Landau-Ginzburg-Wilson functional of two order-parameters-the density of charge and the density of mass -is constructed for ionic systems in which the positions of ions are either in the Euclidean space or are restricted to the lattice sites. We find two phase-transitions: ͑i͒ a line of continuous transitions to the charge-ordered phase, induced by the fluctuations (r)ϰcos(r•k) with 2/k of molecular size, which terminates at a tricritical point and ͑ii͒ a transition between two uniform, ion-poor and ion-rich phases, induced by the whole spectrum of the charge fluctuations. Due to the dominant role of the short-wavelength charge fluctuations, the positions of the transitions depend significantly on the short-distance properties of the system. In different systems ͑continuous or on different lattices͒ one or the other transition may be preempted by the occurrence of the other, by which qualitatively different phase diagrams are obtained.
Gas–liquid critical point in ionic fluids
Journal of Physics: Condensed Matter, 2006
Based on the method of collective variables we develop the statistical field theory for the study of a simple charge-asymmetric 1 : z primitive model (SPM). It is shown that the well-known approximations for the free energy, in particular DHLL and ORPA, can be obtained within the framework of this theory. In order to study the gas-liquid critical point of SPM we propose the method for the calculation of chemical potential conjugate to the total number density which allows us to take into account the higher order fluctuation effects. As a result, the gas-liquid phase diagrams are calculated for z = 2 − 4. The results demonstrate the qualitative agreement with MC simulation data: critical temperature decreases when z increases and critical density increases rapidly with z.
Ionic fluids: charge and density correlations near gas–liquid criticality
Journal of Physics: Condensed Matter, 2005
The correlation functions of an ionic fluid with charge and size asymmetry are studied within the framework of the random phase approximation. The results obtained for the charge-charge correlation function demonstrate that the secondmoment Stillinger-Lovett (SL) rule is satisfied away from the gas-liquid critical point (CP) but not, in general, at the CP. However in the special case of a model without size assymetry the SL rules are satisfied even at the CP. The expressions for the densitydensity and charge-density correlation functions valid far and close to the CP are obtained explicitely.
Criticality and tricriticality in ionic systems
Physica A: Statistical Mechanics and its Applications, 2002
The origin of the tricritical point (tcp) in ionic solutions and its dependence on the short-range e ective free energies (SR) are studied within a Landau-Ginzburg-Wilson approach. The tcp is associated with a continuous transition to a charge-ordered phase, in which the charge density oscillates in space. SR interactions a ect signiÿcantly the charge ordering and the position of the tcp depends sensitively on the strength, shape and state dependence of the SR potentials. The tcp can be located close to the coulombic critical point or close to the solvophobic critical point. For particular forms of the SR interactions either the tricritical or the critical point can be preempted by the occurrence of the other transition.
Structure and criticality of ionic fluids
Pure and Applied Chemistry, 2000
Two properties render electrolyte theories difficult, namely the long-range nature of the Coulomb interactions and the high figures of the Coulomb energy at small ion separations. In solvents of low dielectric constant, where the Coulomb interactions are particularly strong, electrical conductance and dielectric spectra suggest that the ion distribution involves dipolar ion pairs, which then interact with the free ions and with other dipolar pairs. The dipole-dipole interactions between ion pairs lead to an increase of the dielectric constant, which in turn stabilizes the free ions, thus leading to redissociation at high salt concentrations. An equation of state that accounts for ion pairing, ion-ion pair, and ion pair-ion pair interactions rationalizes the basic features of the ion distribution. It also predicts a fluid-phase transition at low reduced temperatures, which closely corresponds to simulation results and to experimentally observed liquid-liquid phase transitions. The long-range nature of the Coulomb potential driving these transitions raises questions concerning their universality class. Experiments suggest that the Ising universality class applies, but there is cross-over to mean-field behavior rather close to the critical, not yet well explained by theory.
Mesoscopic Field Theory of Ionic Systems
International Journal of Modern Physics B, 2005
A mesoscopic field theory for the primitive model of ionic systems with additional, shortrange interactions is presented. Generic models in continuum space and with positions of the ions restricted to lattice sites of various lattices are described in detail. We describe briefly the field-theoretic methods and review the foundations of the mesoscopic description. The types of phase diagrams predicted by our theory for different versions of the model are presented and discussed. They all agree with recent simulations. On the quantitative level our theory yields an RPM tricritical-point location on the sc lattice which is in good agreement with the simulation results. Arguments indicating that the critical point in the RPM belongs to the Ising universality class are given.
The moment sum-rules for ionic liquids at criticality
Physica A: Statistical Mechanics and its Applications
We discuss the first three well known moment charge-charge sum-rules for a general ionic liquid. For the special symmetric case of the Restricted Primitive Model, Das et al. [Phys. Rev. Lett. 107, 215701 (2011)] has recently discovered, through Monte Carlo simulations, that the Stillinger-Lovett or second-moment sum-rule fails at criticality. We critically discuss a possible explanation for this unexpected behavior. On the other hand the fourth-moment sum-rule turns out to be able to account for the results of the simulations at criticality.
Gas-liquid critical parameters of asymmetric models of ionic fluids
Physical review. E, Statistical, nonlinear, and soft matter physics, 2010
The effects of size and charge asymmetry on the gas-liquid critical parameters of a primitive model (PM) of ionic fluids are studied within the framework of the statistical field theory based on the collective variables method. Recently, this approach has enabled us to obtain the correct trends of the both critical parameters of the equisize charge-asymmetric PM without assuming ionic association. In this paper, we focus on the general case of an asymmetric PM characterized by the two parameters: hard-sphere diameter, lambda=sigma+/sigma-, and charge, z=q+/|q-|, ratios of the two ionic species. We derive an explicit expression for the chemical potential conjugate to the order parameter which includes the effects of correlations up to the third order. Based on this expression we consider the three versions of PM: a monovalent size-asymmetric PM (lambda not equal 1, z=1) , an equisize charge-asymmetric PM (lambda=1, z not equal 1) and a size- and charge-asymmetric PM (lambda not equal...