Inspired by recent experimental observations of anomalously large decay lengths in concentrated electrolytes, we revisit the Restricted Primitive Model (RPM) for an aqueous electrolyte. We investigate the asymptotic decay lengths of the one-body ionic density profiles for the RPM in contact with a planar electrode using classical Density Functional Theory (DFT), and compare these with the decay lengths of the corresponding two-body correlation functions in bulk systems, obtained in previous Integral Equation Theory (IET) studies. Extensive Molecular Dynamics (MD) simulations are employed to complement the DFT and IET predictions. Our DFT calculations incorporate electrostatic interactions between the ions using three different (existing) approaches: one based on the simplest mean field treatment of Coulomb interactions (MFC), whilst the other two employ the Mean Spherical approximation (MSA). The MSAc invokes only the MSA bulk direct correlation function whereas the MSAu also incorporates the MSA bulk internal energy. Although MSAu yields profiles that agree best with MD simulations in the near field, in the far field we observe that the decay lengths are consistent between IET, MSAc, and MD simulations, whereas those from MFC and MSAu deviate significantly. Using DFT we calculated the solvation force, which relates directly to surface force experiments. We find that its decay length is neither qualitatively nor quantitatively close to the large decay lengths measured in experiments and conclude that the latter cannot be accounted for by the primitive model. The anomalously large decay lengths found in surface force measurements require an explanation that lies beyond primitive models.
The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using temperature-density, (T, rho), loci of inflections, Q = <m^2>^2/<m^4> maxima, canonical and C_V criticality, yield estimates of (T_c, rho_c) to +- (0.04, 3)%. Extrapolated exponents and Q-ratio are (gamma, nu, Q_c) = [1.24(3), 0.63(3); 0.624(2)] which support Ising (n = 1) behavior with (1.23_9, 0.630_3; 0.623_6), but exclude classical, XY (n = 2), SAW (n = 0), and n = 1 criticality with po…
Structure and thermodynamics in restricted primitive model electrolytes are examined using three recently developed versions of a linear form of the modified Poisson-Boltzmann equation. Analytical expressions for the osmotic coefficient and the electrical part of the mean activity coefficient are obtained and the results for the osmotic and the mean activity coefficients are compared with that from the more established mean spherical approximation, symmetric Poisson-Boltzmann, modified Poisson-Boltzmann theories, and available Monte Carlo simulation results. The linear theories predict the the…
Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding o…
Approximate theories for the restricted primitive model electrolyte are compared in the light of Totsuji's lower bound for the energy (an improvement over Onsager's), Gillan's upper bound for the free energy, and thermal stability requirements. Theories based on the Debye-Hueckel (DH) approach and the mean spherical approximation (MSA), including extensions due to Bjerrum, Ebeling, Fisher and Levin, and Stell, Zhou, and Yeh (PMSA1,2,3) are tested. In the range T* = (k_B T)Da/q^2 \lesssim 10 T*_c \simeq 0.5, all DH-based theories satisfy Totsuji's bound, while the MSA possesses a significant re…
We compared the results of the Madden-Glandt (MG) integral equation approximation for partly-quenched systems with the commonly accepted formalism of Given and Stell (GS). The system studied was a +1:-1 restricted primitive model (RPM) electrolyte confined in a quenched +1:-1 RPM matrix. A renormalization scheme was proposed for a set of MG replica Ornstein-Zernike equations. Long-ranged direct and total correlation functions, describing the interactions between the annealed electrolyte species within the same replicas and between the annealed and matrix particles, appeared to be the same for …
In this study the Singlet Reference Interaction Site Model (SRISM) is employed to the study of the electrode charge dependence of the capacitance of a planar electric double layer using the primitive model of the double layer for a high density electrolyte that mimics an ionic liquid. The ions are represented by charged hard spheres and the electrode is a uniformly charged flat surface. The capacitance of this model fluid is calculated with the SRISM approach with closures based on the hypernetted chain (HNC) and Kovalenko-Hirata (KH) closures and compared with simulations. As long as the magn…
The constant-volume heat capacity, C_V(T, rho), of the restricted primitive model (RPM) electrolyte is considered in the vicinity of its critical point. It is demonstrated that, despite claims, recent simulations for finite systems do not convincingly indicate the absence of a divergence in C_V(T, rho)--which would point to non-Ising-type criticality. The strong qualitative difference between C_V for the RPM and for a Lennard-Jones fluid is shown to result from the low critical density of the former. If one considers the theoretically preferable configurational heat-capacity density, C_V/V, th…
We study, using Density Functional theory and Monte Carlo simulations, aqueous electrolyte solutions between charged infinite planar surfaces, in a contact with a bulk salt reservoir. In agreement with recent experimental observations [Z. Luo et al., Nat. Comm. 6, 6358 (2015)], we find that the confined electrolyte lacks local charge neutrality. We show that a Density Functional Theory (DFT) based on a bulk- HNC expansion properly accounts for strong electrostatic correlations and allows us to accurately calculate the ionic density profiles between the charged surfaces, even for electrolytes c…
The pair-correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model, all ions are approximated as non-overlapping hyperspheres with Coulomb interactions. Our spectral HNC solver is based on a Fourier-Bessel transform introduced by Talman [J. Comput. Phys., 29, 35 (1978)], with logarithmically spaced computational grids. Numeric efficiency for arbitrary spatial dimensions is a commonly exploited virtue of this transform method. Here, we highlight another advantage of logarithmic grids, consisting i…
Accuracy of the mean activity coefficient expression (Hansen-Vieillefosse-Belloni equation), valid within the hypernetted chain (HNC) approximation, was tested in a wide concentration range against new Monte Carlo (MC) data for +1:-1 and +2:-2 primitive model electrolytes. The expression has an advantage that the excess chemical potential can be obtained directly, without invoking the time consuming Gibbs-Duhem calculation. We found the HNC results for the mean activity coefficient to be in good agreement with the machine calculations performed for the same model. In addition, the thermodynami…
The Debye charging method is generalized to study the linear response properties of the asymmetric primitive model for electrolytes. Analytic results are obtained for the effective charge distributions of constituent ions inside the electrolyte, from which all static linear response properties of system follow. It is found that, as the ion density increases, both the screening length and the dielectric constant receive substantial renormalization due to ionic correlations. Furthermore, the valence of larger ion is substantially renormalized upwards by ionic correlations, whilst that of smaller…
The structures of dilute electrolyte solutions close to non-uniformly charged planar substrates are systematically studied within the entire spectrum of microscopic to macroscopic length scales by means of a unified classical density functional theory (DFT) approach. This is in contrast to previous investigations, which are applicable either to short or to long length scales. It turns out that interactions with microscopic ranges, e.g., due to the hard cores of the fluid molecules and ions, have negligible influence on the formation of non-uniform lateral structures of the electrolyte solution…
The structure of dilute electrolyte solutions close to a surface carrying a spatially inhomogeneous surface charge distribution is investigated by means of classical density functional theory (DFT) within the approach of fundamental measure theory (FMT). For electrolyte solutions the influence of these inhomogeneities is particularly strong because the corresponding characteristic length scale is the Debye length, which is large compared to molecular sizes. Here a fully three-dimensional investigation is performed, which accounts explicitly for the solvent particles, and thus provides insight …
In this work we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical Density Functional Theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly, and also how small ions dominate its behaviour for high electrode potentials. In this study, we consider primitive model electrolytes, and not only use the standard …
We study the adsorption of primitive model electrolytes into a layered slit system using grand canonical Monte Carlo simulations. The slit system contains a series of charged membranes. The ions are forbidden from the membranes, while they are allowed to be adsorbed into the slits between the membranes. We focus on the electrical properties of the slit system. We show concentration, charge, electric field, and electrical potential profiles. We show that the potential difference between the slit system and the bulk phase is mainly due to the double layers formed at the boundaries of the slit sy…
The purpose of this study is to provide data for the primitive model of the electrical double layer, where ions are modeled as charged hard spheres, the solvent as an implicit dielectric background (with dielectric constant $ε= 78.5$), and the electrode as a smooth, uniformly charged, hard wall. We use canonical and Grand Canonical Monte Carlo simulations to compute the concentration profiles, from which the electric field and electrostatic potential profiles are obtained by solving Poisson's equation. We report data for an extended range of parameters including 1:1, 2:1, and 3:1 electrolytes …
The electrostatic screening length predicted by Debye-Hückel theory decreases with increasing ionic strength, but recent experiments have found that the screening length can instead increase in concentrated electrolytes. This phenomenon, referred to as underscreening, is believed to result from ion-ion correlations and short-range forces such as excluded volume interactions among ions. We use Brownian Dynamics to simulate a version of the Restrictive Primitive Model for electrolytes over a wide range of ion concentrations, ionic strengths, and ion excluded volume radii for binary electrolytes.…
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 manuscript 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 $10^{-10}σ^{-3}$, where $σ$ is the ion diameter). Experimentally, this regime corresponds to typical concentra…
We use molecular dynamics simulations of the primitive model of electrolytes to study the ionic structure in aqueous monovalent electrolyte solutions confined by charged planar interfaces over a wide range of electrolyte concentration, interfacial separation, surface charge density, and ion size. The investigations are inspired by recent experiments that have directly measured the increase in the decay length for highly-concentrated electrolytes with increase in concentration. The behavior of ions in the nanoconfinement created by the interfaces is probed by evaluating the ionic density profil…
A Grand-canonical Monte-Carlo simulation method extended to simulate a mixture of salts is presented. Due to charge neutrality requirement of electrolyte solutions, ions must be added to or removed from the system in groups. This leads to some complications compared to regular Grand Canonical simulation. Here, a recipe for simulation of electrolyte solution of salt mixture is presented. It is then implemented to simulate solution of 1:1, 2:1 and 2:2 salts or their mixtures at different concentrations using the primitive ion model. The osmotic pressures of the electrolyte solutions are calculat…
Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, …
We use a reactive Monte Carlo simulation method and primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different number of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium …
Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
Machine-Learned Many-Body Potentials for Charged Colloids reveal Gas-Liquid Spinodal Instabilities only in the strong-coupling regime of Primitive Models
The ongoing scientific interest in the properties and structure of electric double layers (EDLs) stems from their pivotal role in (super)capacitive energy storage, energy harvesting, and water treatment technologies. Classical density functional theory (DFT) is a promising framework for the study of the in- and out-of-plane structural properties of double layers. Supported by molecular dynamics simulations, we demonstrate the adequate performance of DFT for analyzing charge layering in the EDL perpendicular to the electrodes. We discuss charge storage and capacitance of the EDL and the impact …
Simulations of the Lebowitz length, $ξ_{\text{L}}(T,ρ)$, are reported for t he restricted primitive model hard-core (diameter $a$) 1:1 electrolyte for densi ties $ρ\lesssim 4ρ_c$ and $T_c \lesssim T \lesssim 40T_c$. Finite-size eff ects are elucidated for the charge fluctuations in various subdomains that serve to evaluate $ξ_{\text{L}}$. On extrapolation to the bulk limit for $T\gtrsim 10T_c$ the low-density expansions (Bekiranov and Fisher, 1998) are seen to fail badly when $ρ> {1/10}ρ_c$ (with $ρ_c a^3 \simeq 0.08$). At highe r densities $ξ_{\text{L}}$ rises above the Debye length, $ξ_{\tex…
