Critical point of electrolyte mixtures

Improving the efficiency of Monte Carlo simulations of ions using expanded grand canonical ensembles

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software.

Control of Selective Ion Transfer across Liquid-Liquid Interfaces: A Rectifying Heterojunction Based on Immiscible Electrolytes

The current rectification displayed by solid-state p-n semiconductor diodes relies on the abundance of electrons and holes near the interface between the p-n junction. In analogy to this electronic device, we propose here the construction of a purely ionic liquid-state electric rectifying heterojunction displaying an excess of monovalent cations and anions near the interface between two immiscible solvents with different dielectric properties. This system does not need any physical membrane or material barrier to show preferential ion transfer but relies on the ionic solvation energy between the two immiscible solvents. We construct a simple device, based on an oil/water interface, displaying an asymmetric behavior of the electric current as a function of the polarity of an applied electric field. This device also exhibits a region of negative differential conductivity, analogous to that observed in brain and heart cells via voltage clamp techniques. Computer simulations and mean field theory calculations for a model of this system show that the application of an external electric field is able to control the bulk concentrations of the ionic species in the immiscible liquids in a manner that is asymmetric with respect to the polarity or direction of the applied electric field. These properties make possible to enhance or suppress selective ion transport at liquid-liquid interfaces with the application of an external electric field or electrostatic potential, mimicking the function of biological ion channels, thus creating opportunities for varied applications.

Poisson-Boltzmann theory of charged colloids: limits of the cell model for salty suspensions

Thermodynamic properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions are commonly modelled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing numerical solution of the nonlinear PB equation, the cell model neglects microion-induced interactions and correlations between macroions, precluding modelling of macroion ordering phenomena. An alternative approach, which avoids the artificial constraints of cell geometry, exploits the mapping of a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interparticle interactions. In practice, effective-interaction models are usually based on linear-screening approximations, which can accurately describe strong nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions, in Donnan equilibrium with a salt reservoir, over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions from nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modelling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate for predicting osmotic pressures of deionized (counterion-dominated) suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions to the osmotic pressure grows, leading predictions from the cell and effective-interaction models to deviate. No evidence is found for a liquid-vapour phase instability driven by monovalent microions. These results may guide applications of PB theory to colloidal suspensions and other soft materials.

Phase diagrams of charged colloids from thermodynamic integration

We present full phase diagrams (including solid phases) of spherical charged colloids, using Monte Carlo sampling and thermodynamic integration of the Helmholtz free energy. Colloids and their co- and counterions are described by the primitive model for ionic systems that consists of hard-spheres with central point charges, while the solvent is taken into account solely through its dielectric constant. Two systems are considered: (i) a size-asymmetric system of oppositely charged spheres with size ratios q = 0.3 and 0.5 and (ii) a charge- and size-asymmetric system with colloid charge Q = 10 and counterions of charge -1 in the presence of monovalent added salt. In system (i), for both size ratios, the stable solid phase is equivalent to the NaCl crystal where the oppositely charged spheres take the lattice positions of Na and Cl ions. In system (ii), the phase diagram consists of gas-liquid and fluid-solid coexistence regions. We show that added salt stabilizes the fluid phase and shrinks the fluid-solid coexistence region, in agreement with experimental and theoretical results.

Electroneutrality and phase behavior of colloidal suspensions

Several statistical mechanical theories predict that colloidal suspensions of highly charged macroions and monovalent microions can exhibit unusual thermodynamic phase behavior when strongly deionized. Density-functional, extended Debye-Hückel, and response theories, within mean-field and linearization approximations, predict a spinodal phase instability of charged colloids below a critical salt concentration. Poisson-Boltzmann cell model studies of suspensions in Donnan equilibrium with a salt reservoir demonstrate that effective interactions and osmotic pressures predicted by such theories can be sensitive to the choice of reference system, e.g., whether the microion density profiles are expanded about the average potential of the suspension or about the reservoir potential. By unifying Poisson-Boltzmann and response theories within a common perturbative framework, it is shown here that the choice of reference system is dictated by the constraint of global electroneutrality. On this basis, bulk suspensions are best modeled by density-dependent effective interactions derived from a closed reference system in which the counterions are confined to the same volume as the macroions. Lower-dimensional systems (e.g., monolayers, clusters), depending on the strength of macroion-counterion correlations, may be governed instead by density-independent effective interactions tied to an open reference system with counterions dispersed throughout the reservoir, possibly explaining the observed structural crossover in colloidal monolayers and anomalous metastability of colloidal crystallites.

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.

Phase separation of charge-stabilized colloids: a Gibbs ensemble Monte Carlo simulation study

The fluid phase behavior of charge-stabilized colloidal suspensions is explored by applying a variant of the Gibbs ensemble Monte Carlo simulation method to a coarse-grained one-component model with implicit microions and solvent. The simulations take as input linear-response approximations for the effective electrostatic interactions--a hard-sphere-Yukawa pair potential and a one-body volume energy. The conventional Gibbs ensemble trial moves are supplemented by exchange of (implicit) salt between coexisting phases, with acceptance probabilities influenced by the state dependence of the effective interactions. Compared with large-scale simulations of the primitive model, with explicit microions, our computationally practical simulations of the one-component model closely match the pressures and pair distribution functions at moderate electrostatic couplings. For macroion valences and couplings within the linear-response regime, deionized aqueous suspensions with monovalent microions exhibit separation into macroion-rich and macroion-poor fluid phases below a critical salt concentration. The resulting pressures and phase diagrams are in excellent agreement with predictions of a variational free energy theory based on the same model.

Disappearance of the gas-liquid phase transition for highly charged colloids

We calculate the full phase diagram of spherical charged colloidal particles using Monte Carlo free energy calculations. The system is described using the primitive model, consisting of explicit hard-sphere colloids and point counterions in a uniform dielectric continuum. We show that the gas-liquid critical point becomes metastable with respect to a gas-solid phase separation at colloid charges Q > or =20 times the counterion charge. Approximate free energy calculations with only one and four particles in the fluid and solid phases, respectively, are used to determine the critical line for highly charged colloids up to Q=2000. We propose the scaling law T*(c) approximately Q(1/2) for this critical temperature.

Nonlinear screening and gas-liquid separation in suspensions of charged colloids

We calculate phase diagrams of charged colloidal spheres (valency Z and radius a) in a 1:1 electrolyte from multicentered nonlinear Poisson-Boltzmann theory. Our theory takes into account charge renormalization of the colloidal interactions and volume terms due to many-body effects. For valencies as small as Z = 1 and as large as 10(4) we find a gas-liquid spinodal instability in the colloid-salt phase diagram provided Z lambdaB/a > or similar 24+/-1, where lambdaB is the Bjerrum length.

Gas-liquid phase separation in oppositely charged colloids: Stability and interfacial tension

We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter sigma using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transitions using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length kappa. We find that the gas-liquid phase separation is stable for kappasigma<or=4, and that the critical temperature decreases upon increasing the screening of the interaction (decreasing the range of the interaction). In addition, we determine the gas-liquid interfacial tension using grand-canonical Monte Carlo simulations. The interfacial tension decreases upon increasing the range of the interaction. In particular, we find that simple scaling can be used to relate the interfacial tension of the YRPM to that of the restricted primitive model, where particles interact with bare Coulomb interactions.

Tracing the Critical Loci of Binary Fluid Mixtures Using Molecular Simulation

Monte Carlo simulations are used to trace the critical loci for a number of binary mixtures. In particular, we use grand canonical Monte Carlo (GCMC) simulations with histogram reweighting and mixed-field finite-size scaling to determine the mixture critical lines. Two different classes of criticality are investigated. A mixture of methane and ethane displays type I criticality, exhibiting continuous mixing between the two species across the entire composition range. A methane-water mixture shows type IIIb criticality, with a discontinuity in the critical locus. Quantitative agreement is found between simulation and experimental critical loci for the methane-ethane system using no adjustable parameters for interactions in the mixture. For the water-methane system, we investigate the effect of the combining rules for the intermolecular interaction between the two species on the mixture critical locus. We also investigate several potentials for methane: a nonpolar exponential-6, an octopolar fixed partial charge, and a polarizable fluctuating charge model. Qualitative agreement between simulations and experiments is found for all potentials, but none are able to quantitatively capture the abrupt increase in the critical temperature as methane is added to the system.

Phase behavior of the lattice restricted primitive model with nearest neighbor exclusion

The global phase behavior of the lattice restricted primitive model with nearest neighbor exclusion has been studied by grand canonical Monte Carlo simulations. The phase diagram is dominated by a fluid (or charge-disordered solid) to charge-ordered solid transition that terminates at the maximum density rho*(max)= sqrt 2 and reduced temperature T* approximately equal to 0.29. At that point, there is a first-order phase transition between two phases of the same density, one charge-ordered, and the other charge-disordered. The liquid-vapor transition for the model is metastable, lying entirely within the fluid-solid phase envelope.

Phase separation in charge-stabilized colloidal suspensions: influence of nonlinear screening

The phase behavior of charge-stabilized colloidal suspensions is modeled by a combination of response theory for electrostatic interparticle interactions and variational theory for free energies. Integrating out degrees of freedom of the microions (counterions, salt ions), the macroion-microion mixture is mapped onto a one-component system governed by effective macroion interactions. Linear response of microions to the electrostatic potential of the macroions results in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume energy, while nonlinear response modifies the effective interactions [A. R. Denton, Phys. Rev. E 70, 031404 (2004)]. The volume energy and effective pair potential are taken as input to a variational free energy, based on thermodynamic perturbation theory. For both linear and first-order nonlinear effective interactions, a coexistence analysis applied to aqueous suspensions of highly charged macroions and monovalent microions yields bulk separation of macroion-rich and macroion-poor phases below a critical salt concentration, in qualitative agreement with predictions of related linearized theories [R. van Roij, M. Dijkstra, and J.-P. Hansen, Phys. Rev. E 59, 2010 (1999); P. B. Warren, J. Chem. Phys. 112, 4683 (2000)]. It is concluded that nonlinear screening can modify phase behavior but does not necessarily suppress bulk phase separation of de-ionized suspensions.

Liquid-gas separation in colloidal electrolytes

The liquid-gas transition of an electroneutral mixture of oppositely charged colloids, studied by Monte Carlo simulations, is found in the low-temperature-low-density region. The critical temperature shows a nonmonotonous behavior as a function of the interaction range, kappa(-1), with a maximum at kappasigma approximately 10, implying an island of coexistence in the kappa-rho plane. The system is arranged in such a way that each particle is surrounded by shells of particles with alternating charge. In contrast with the electrolyte primitive model, both neutral and charged clusters are obtained in the vapor phase.

Volume terms for charged colloids: a grand-canonical treatment

We present a study of thermodynamic properties of suspensions of charged colloids on the basis of linear Poisson-Boltzmann theory. We calculate the effective Hamiltonian of the colloids by integrating out the ionic degrees of freedom grand canonically. This procedure not only yields the well-known pairwise screened-Coulomb interaction between the colloids, but also additional volume terms that affect the phase behavior and the thermodynamic properties, such as the osmotic pressure. These calculations are greatly facilitated by the grand-canonical character of our treatment of the ions and allow for relatively fast computations compared to earlier studies in the canonical ensemble. Moreover, the present derivation of the volume terms are relatively simple, make a direct connection with Donnan equilibrium, yield an explicit expression for the effective screening constant, and allow for extensions to include, for instance, nonlinear effects.

Phase separation, interface properties, and charge density waves in a simplified model for a macroion suspension

A simplified density functional theory for a macroion suspension is examined, where the correlation free energy corresponds to the macroion self-energy, treated within a linearized or Debye-Hückel approximation. The model possesses a miscibility gap (liquid-liquid phase separation) at low ionic strength. Within the gap, density profiles, electrical structure, and surface tension are calculated for the interface between coexisting phases, using a variational approximation. Additionally, structure factors are calculated for the homogeneous system. As one approaches the critical points, the structure factors can diverge at a nonzero wave vector, signaling the onset of charge density wave phases. Although the quantitative results should be treated with care, the results may be indicative of the rich phenomenology that can arise in asymmetric charged systems.

Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).