Ion association in low-polarity solvents: comparisons between theory, simulation, and experiment

The association of ions in electrolyte solutions at very low concentration and low temperature is studied using computer simulations and quasi-chemical ion-pairing theory. The specific case of the restricted primitive model (charged hard spheres) is considered. Specialised simulation techniques are employed that lead to efficient sampling of the arrangements and distributions of clusters and free ions, even at conditions corresponding to nanomolar solutions of simple salts in solvents with dielectric constants in the range 5-10, as used in recent experimental work on charged-colloid sus- pensions. A direct comparison is effected between theory and simulation using a variety of clustering criteria and theoretical approximations. It is shown that conventional distance-based cluster criteria can give erroneous results. A reliable set of theoretical and simulation estimators for the degree of association is proposed. The ion-pairing theory is then compared to experimental results for salt solutions in low-polarity solvents. The agreement is excellent, and on this basis some calculations are made for the screening lengths which will figure in the treatment of colloid-colloid interactions in such solutions. The accord with available experimental results is complete

Liquid-liquid interfacial tension of electrolyte solutions

It is theoretically shown that the excess liquid-liquid interfacial tension between two electrolyte solutions as a function of the ionic strength I behaves asymptotically as O(- I^0.5) for small I and as O(+- I) for large I. The former regime is dominated by the electrostatic potential due to an unequal partitioning of ions between the two liquids whereas the latter regime is related to a finite interfacial thickness. The crossover between the two asymptotic regimes depends sensitively on material parameters suggesting that, depending on the actual system under investigation, the experimentally accessible range of ionic strengths can correspond to either the small or the large ionic strength regime. In the limiting case of a liquid-gas surface where ion partitioning is absent, the image chage interaction can dominate the surface tension for small ionic strength I such that an Onsager-Samaras limiting law O(- I ln(I)) is expected. The proposed picture is consistent with more elaborate models and published measurements.Comment: Accepted for publication in Physical Review Letter

Stability of additive-free water-in-oil emulsions

We calculate ion distributions near a planar oil-water interface within non-linear Poisson-Boltzmann theory, taking into account the Born self-energy of the ions in the two media. For unequal self-energies of cations and anions, a spontaneous charge separation is found such that the water and oil phase become oppositely charged, in slabs with a typical thickness of the Debye screening length in the two media. From the analytical solutions, the corresponding interfacial charge density and the contribution to the interfacial tension is derived, together with an estimate for the Yukawa-potential between two spherical water droplets in oil. The parameter regime is explored where the plasma coupling parameter exceeds the crystallization threshold, i.e. where the droplets are expected to form crystalline structures due to a strong Yukawa repulsion, as recently observed experimentally. Extensions of the theory that we discuss briefly include numerical calculations on spherical water droplets in oil, and analytical calculations of the linear PB-equation for a finite oil-water interfacial width.Comment: 9 pages, 4 figures, accepted by JPCM for proceedings of LMC

Sedimentation of binary mixtures of like- and oppositely charged colloids: the primitive model or effective pair potentials?

We study sedimentation equilibrium of low-salt suspensions of binary mixtures of charged colloids, both by Monte Carlo simulations of an effective colloids-only system and by Poisson-Boltzmann theory of a colloid-ion mixture. We show that the theoretically predicted lifting and layering effect, which involves the entropy of the screening ions and a spontaneous macroscopic electric field [J. Zwanikken and R. van Roij, Europhys. Lett. {\bf 71}, 480 (2005)], can also be understood on the basis of an effective colloid-only system with pairwise screened-Coulomb interactions. We consider, by theory and by simulation, both repelling like-charged colloids and attracting oppositely charged colloids, and we find a re-entrant lifting and layering phenomenon when the charge ratio of the colloids varies from large positive through zero to large negative values

Computer simulations of the restricted primitive model at very low temperature and density

The problem of successfully simulating ionic fluids at low temperature and low density states is well known in the simulation literature: using conventional methods, the system is not able to equilibrate rapidly due to the presence of strongly associated cation–anion pairs. In this paper we present a numerical method for speeding up computer simulations of the restricted primitive model (RPM) at low temperatures (around the critical temperature) and at very low densities (down to 10−10σ −3, where σ is the ion diameter). Experimentally, this regime corresponds to typical concentrations of electrolytes in nonaqueous solvents. As far as we are aware, this is the first time that the RPM has been equilibrated at such extremely low concentrations. More generally, this method could be used to equilibrate other systems that form aggregates at low concentrations

Curvature dependence of the electrolytic liquid-liquid interfacial tension

The interfacial tension of a liquid droplet surrounded by another liquid in the presence of microscopic ions is studied as a function of the droplet radius. An analytical expression for the interfacial tension is obtained within a linear Poisson–Boltzmann theory and compared with numerical results from nonlinear Poisson–Boltzmann theory. The excess liquid-liquid interfacial tension with respect to the pure salt-free liquid-liquid interfacial tension is found to decompose into a curvature-independent part due to short-ranged interfacial effects and a curvature-dependent electrostatic contribution. Several curvature-dependent regimes of different scalings of the electrostatic excess interfacial tension are identified. Symmetry relations of the interfacial tension upon swapping droplet and bulk liquid are found to hold in the low-curvature limit, which, e.g., lead to a sign change of the excess Tolman length. For some systems a low-curvature expansion up to the second order turns out to be applicable if and only if the droplet size exceeds the Debye screening length in the droplet, independent of the Debye length in the bulk