Electrostatic interactions mediated by polarizable counterions: weak and strong coupling limits

We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between charged dielectric interfaces.Comment: 25 pages, 7 figure

Nonlinear screening of charged macromolecules

We present several aspects of the screening of charged macromolecules in an electrolyte. After a review of the basic mean field approach, based on the linear Debye-Huckel theory, we consider the case of highly charged macromolecules, where the linear approximation breaks down and the system is described by full nonlinear Poisson-Boltzmann equation. Some analytical results for this nonlinear equation give some interesting insight on physical phenomena like the charge renormalization and the Manning counterion condensation

All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas

We develop an all-electron path integral Monte Carlo (PIMC) method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend PIMC studies beyond hydrogen and helium to elements with core electrons. PIMC pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics (DFT-MD) at temperatures of (2.5-7.5)$\times10^5$ K and both methods together form a coherent equation of state (EOS) over a density-temperature range of 3--12 g/cm$^3$ and 10$^4$--10$^9$ K

Lattice Models of Ionic Systems

A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye-Huckel theory with ion-pairing and dipole-ion solvation, specific calculations being performed for 3D lattices. As for continuum electrolytes, low-density results for sc, bcc and fcc lattices indicate the existence of gas-liquid phase separation. The predicted critical densities have values comparable to those of continuum ionic systems, while the critical temperatures are 60-70% higher. However, when the possibility of sublattice ordering as well as Debye screening is taken into account systematically, order-disorder transitions and a tricritical point are found on sc and bcc lattices, and gas-liquid coexistence is suppressed. Our results agree with recent Monte Carlo simulations of lattice electrolytes.Comment: 25 pages, 3 figures, ReVTeX 4, Submitted to J. Chem. Phy

Aging of rotational diffusion in colloidal gels and glasses

We study the rotational diffusion of aging Laponite suspensions for a wide range of concentrations using depolarized dynamic light scattering. The measured orientational correlation functions undergo an ergodic to non-ergodic transition that is characterized by a concentration-dependent ergodicity-breaking time. We find that the relaxation times associated with rotational degree of freedom as a function of waiting time, when scaled with their ergodicity-breaking time, collapse on two distinct master curves. These master curves are similar to those previously found for the translational dynamics; The two different classes of behavior were attributed to colloidal gels and glasses. Therefore, the aging dynamics of rotational degree of freedom provides another signature of the distinct dynamical behavior of colloidal gels and glasses.Comment: 12 pages, 7 figure

Rescaling Relations between Two- and Three-dimensional Local Porosity Distributions for Natural and Artificial Porous Media

Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensional plane-section through the medium are generally different. However, for homogeneous and isotropic media having finite correlation-lengths, a good degree of correspondence between the two sets of local porosity distributions can be obtained by rescaling lengths, and the mapping associating corresponding distributions can be found from two-dimensional observations alone. The agreement between associated distributions is good as long as the linear extent of the measurement cells involved is somewhat larger than the correlation length, and it improves as the linear extent increases. A simple application of the central limit theorem shows that there must be a correspondence in the limit of very large measurement cells, because the distributions from both sets approach normal distributions. A normal distribution has two independent parameters: the mean and the variance. If the sample is large enough, LPDs from both sets will have the same mean. Therefore corresponding distributions are found by matching variances of two- and three-dimensional local porosity distributions. The variance can be independently determined from correlation functions. Equating variances leads to a scaling relation for lengths in this limit. Three particular systems are examined in order to show that this scaling behavior persists at smaller length-scales.Comment: 15 PostScript figures, LaTeX, To be published in Physica

Where the linearized Poisson-Boltzmann cell model fails: (I) spurious phase separation in charged colloidal suspensions

We perform a linearization of the Poisson-Boltzmann (PB) density functional for spherical Wigner-Seitz cells that yields Debye-H\"uckel-like equations agreeing asymptotically with the PB results in the weak-coupling (high-temperature) limit. Both the canonical (fixed number of microions) as well as the semi-grand-canonical (in contact with an infinite salt reservoir) cases are considered and discussed in a unified linearized framework. In the canonical case, for sufficiently large colloidal charges the linearized theory predicts the occurrence of a thermodynamical instability with an associated phase separation of the homogeneous suspension into dilute (gas) and dense (liquid) phases. In the semi-grand-canonical case it is predicted that the isothermal compressibility and the osmotic-pressure difference between the colloidal suspension and the salt reservoir become negative in the low-temperature, high-surface charge or infinite-dilution (of polyions) limits. As already pointed out in the literature for the latter case, these features are in disagreement with the exact nonlinear PB solution inside a Wigner-Seitz cell and are thus artifacts of the linearization. By using explicitly gauge-invariant forms of the electrostatic potential we show that these artifacts, although thermodynamically consistent with quadratic expansions of the nonlinear functional and osmotic pressure, may be traced back to the non-fulfillment of the underlying assumptions of the linearization.Comment: 32 pages, 3 PostScript figures, submitted to J. Chem. Phy

The Nonlinear Debye-Onsager Relaxation Effect in Weakly Ionized Plasmas

A weakly ionized plasma under the influence of a strong electric field is considered. Supposing a local Maxwellian distribution for the electron momenta the plasma is described by hydrodynamic equations for the pair distribution functions. These equations are solved and the relaxation field is calculated for an arbitrary field strength. It is found that the relaxation effect becomes lower with increasing strength of the electrical field.Comment: 4 pages, 1 figur

Nonlinear effects in charge stabilized colloidal suspensions

Molecular Dynamics simulations are used to study the effective interactions in charged stabilized colloidal suspensions. For not too high macroion charges and sufficiently large screening, the concept of the potential of mean force is known to work well. In the present work, we focus on highly charged macroions in the limit of low salt concentrations. Within this regime, nonlinear corrections to the celebrated DLVO theory [B. Derjaguin and L. Landau, Acta Physicochem. USSR {\bf 14}, 633 (1941); E.J.W. Verwey and J.T.G. Overbeck, {\em Theory of the Stability of Lyotropic Colloids} (Elsevier, Amsterdam, 1948)] have to be considered. For non--bulklike systems, such as isolated pairs or triples of macroions, we show, that nonlinear effects can become relevant, which cannot be described by the charge renormalization concept [S. Alexander et al., J. Chem. Phys. {\bf 80}, 5776 (1984)]. For an isolated pair of macroions, we find an almost perfect qualitative agreement between our simulation data and the primitive model. However, on a quantitative level, neither Debye-H\"uckel theory nor the charge renormalization concept can be confirmed in detail. This seems mainly to be related to the fact, that for small ion concentrations, microionic layers can strongly overlap, whereas, simultaneously, excluded volume effects are less important. In the case of isolated triples, where we compare between coaxial and triangular geometries, we find attractive corrections to pairwise additivity in the limit of small macroion separations and salt concentrations. These triplet interactions arise if all three microionic layers around the macroions exhibit a significant overlap. In contrast to the case of two isolated colloids, the charge distribution around a macroion in a triple is found to be anisotropic.Comment: 10 pages, 9 figure

Field theory fo charged fluids and colloids

A systematic field theory is presented for charged systems. The one-loop level corresponds to the classical Debye-H\"uckel (DH) theory, and exhibits the full hierarchy of multi-body correlations determined by pair-distribution functions given by the screened DH potential. Higher-loop corrections can lead to attractive pair interactions between colloids in asymmetric ionic environments. The free energy follows as a loop-wise expansion in half-integer powers of the density; the resulting two-phase demixing region shows pronounced deviations from DH theory for strongly charged colloids.Comment: 4 pages, 2 ps figs; new version corrects some minor typo