Non-linear Poisson-Boltzmann Theory for Swollen Clays

The non-linear Poisson-Boltzmann equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving the latter iteratively. This method proves efficient, robust, and can be readily generalized to other problems based on cell models, treated within non-linear Poisson-like theory. The solution to the PB equation is computed over a wide range of physical conditions, and the resulting osmotic equation of state is shown to be in fair agreement with recent experimental data for Laponite clay suspensions, in the concentrated gel phase.Comment: 13 pages, 4 postscript figure

Correlation functions in ionic liquid at coexistence with ionic crystal. Results of the Brazovskii-type field theory

Correlation functions in the restricted primitive model are calculated within a field-theoretic approach in the one-loop self-consistent Hartree approximation. The correlation functions exhibit damped oscillatory behavior as found before in the Gaussian approximation [Ciach at. al., J. Chem. Phys. {\bf 118}, 3702 (2003)]. The fluctuation contribution leads to a renormalization of both the amplitude and the decay length of the correlation functions. The renormalized quantities show qualitatively different behavior than their mean-field (MF) counterparts. While the amplitude and the decay length both diverge in MF when the $\lambda$-line is approached, the renormalized quantities remain of order of unity in the same dimensionless units down to the coexistence with the ionic crystal. Along the line of the phase transition the decay length and the period of oscillations are independent of density, and their values in units of the diameter of the ions are $\alpha_0^{-1}\approx 1$ and $2\pi/\alpha_1\approx 2.8$ respectively.Comment: 21 pages including 9 figure

Charge Oscillations in Debye-Hueckel Theory

The recent generalized Debye-Hueckel (GDH) theory is applied to the calculation of the charge-charge correlation function G_{ZZ}(r). The resulting expression satisfies both (i) the charge neutrality condition and (ii) the Stillinger-Lovett second-moment condition for all T and rho_N, the overall ion density, and (iii) exhibits charge oscillations for densities above a "Kirkwood line" in the (rho_N,T) plane. This corrects the normally assumed DH correlations, and, when combined with the GDH analysis of the density correlations, leaves the GDH theory as the only complete description of ionic correlation functions, as judged by (i)-(iii), (iv) exact low-density (rho_N,T) variation, and (v) reasonable behavior near criticality.Comment: 6 pages, EuroPhys.sty (now available on archive), 1 eps figur

Effective Magnetic Hamiltonian and Ginzburg Criterion for Fluids

We develop further the approach of Hubbard and Schofield (Phys.Lett., A40 (1972) 245), which maps the fluid Hamiltonian onto a magnetic one. We show that all coefficients of the resulting effective Landau-Ginzburg-Wilson (LGW) Hamiltonian may be expressed in terms of the compressibility of a reference fluid containing only repulsive interactions, and its density derivatives; we calculate the first few coefficients in the case of the hard-core reference fluid. From this LGW-Hamiltonian we deduce approximate mean-field relations between critical parameters and test them on data for Lennard-Jones, square-well and hard-core-Yukawa fluids. We estimate the Ginzburg criterion for these fluids.Comment: 4 pages, LaTeX, To appear in Phys.Rev.

The liquid-vapor interface of an ionic fluid

We investigate the liquid-vapor interface of the restricted primitive model (RPM) for an ionic fluid using a density-functional approximation based on correlation functions of the homogeneous fluid as obtained from the mean-spherical approximation (MSA). In the limit of a homogeneous fluid our approach yields the well-known MSA (energy) equation of state. The ionic interfacial density profiles, which for the RPM are identical for both species, have a shape similar to those of simple atomic fluids in that the decay towards the bulk values is more rapid on the vapor side than on the liquid side. This is the opposite asymmetry of the decay to that found in earlier calculations for the RPM based on a square-gradient theory. The width of the interface is, for a wide range of temperatures, approximately four times the second moment correlation length of the liquid phase. We discuss the magnitude and temperature dependence of the surface tension, and argue that for temperatures near the triple point the ratio of the dimensionless surface tension and critical temperature is much smaller for the RPM than for simple atomic fluids.Comment: 6 postscript figures, submitted to Phys. Rev.

Density Fluctuations in an Electrolyte from Generalized Debye-Hueckel Theory

Near-critical thermodynamics in the hard-sphere (1,1) electrolyte is well described, at a classical level, by Debye-Hueckel (DH) theory with (+,-) ion pairing and dipolar-pair-ionic-fluid coupling. But DH-based theories do not address density fluctuations. Here density correlations are obtained by functional differentiation of DH theory generalized to {\it non}-uniform densities of various species. The correlation length $\xi$ diverges universally at low density $\rho$ as $(T\rho)^{-1/4}$ (correcting GMSA theory). When $\rho=\rho_c$ one has $\xi\approx\xi_0^+/t^{1/2}$ as $t\equiv(T-T_c)/T_c\to 0+$ where the amplitudes $\xi_0^+$ compare informatively with experimental data.Comment: 5 pages, REVTeX, 1 ps figure included with epsf. Minor changes, references added. Accepted for publication in Phys. Rev. Let

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

Effective Interactions and Volume Energies in Charged Colloids: Linear Response Theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out from the partition function the degrees of freedom of all microions, and assuming linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the DLVO screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy -- a natural consequence of the one-component reduction -- contributes to the total free energy and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.Comment: 14 pages, including 3 figure

Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the {\em universal} character of the Casimir force in systems with short-ranged interactions. The effects due to dispersion forces are discussed for systems with periodic or realistic boundary conditions. In contrast to systems with short-ranged interactions, for $L/\xi \gg 1$ one observes leading finite-size contributions governed by power laws in $L$ due to the subleading long-ranged character of the interaction, where $L$ is the finite system size and $\xi$ is the correlation length.Comment: 11 pages, revtex, to appear in Phys. Rev. E 68 (2003