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 of dense electrolytes impacting the design of technologies for energy storage and conversion.
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.…
Recent experiments and a series of subsequent theoretical studies suggest the occurrence of universal underscreening in highly concentrated electrolyte solutions. We performed a set of systematic Atomic Force Spectroscopy measurements for aqueous salt solutions in a concentration range from 1 mM to 5 M using chloride salts of various alkali metals as well as mixed concentrated salt solutions (involving both mono- and divalent cations and anions), that mimic concentrated brines typically encountered in geological formations. Experiments were carried out using flat substrates and submicrometer-s…
Recent Monte Carlo simulations of the critical point of the restricted primitive model for ionic solutions are reported. Only the continuum version of the model is considered. A finite size scaling analysis based in the Bruce-Wilding procedure gives critical exponents in agreement with those of the three-dimensional Ising universality class. An anomaly in the scaling of the specific heat with system size is pointed out.
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, $ρ^*_{max}=\sqrt2$ and reduced temperature $T^*\approx0.29$. 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 fl…
Phase separation of the ultrasoft restricted primitive model (URPM) with Gaussian charges is re-investigated in the random phase approximation (RPA)---the 'Level A' approximation discussed by Nikoubashman, Hansen and Kahl [J. Chem. Phys. 137, 094905 (2012)]. We find that the RPA predicts a region of low temperature vapour-liquid coexistence, with a critical density much lower than that observed in either simulations or more refined approximations (we also remark that the RPA critical point for a related model with Bessel charges can be solved analytically). This observation suggests that the h…
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…
Effects of charge-density fluctuations on a phase behavior of the restricted primitive model (RPM) are studied within a field-theoretic formalism. We focus on a $λ$-line of continuous transitions between charge-ordered and charge-disordered phases that is observed in several mean-field (MF) theories, but is absent in simulation results. In our study the RPM is reduced to a $ϕ^6$ theory, and a fluctuation contribution to a grand thermodynamic potential is obtained by generalizing the Brazovskii approach. We find that in a presence of fluctuations the $λ$-line disappears. Instead, a fluctuation-…
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…
The restricted primitive model with nonadditive hard-sphere diameters is shown to have interesting and peculiar clustering properties. We report accurate calculations of the cluster concentrations. Implementing efficient and ad hoc Monte Carlo algorithms we determine the effect of nonadditivity on both the clustering and the gas-liquid binodal. For negative nonadditivity, tending to the extreme case of completely overlapping unlike ions, the prevailing clusters are made of an even number of particles having zero total charge. For positive nonadditivity, the frustrated tendency to segregation o…
We investigate the liquid-vapor interface of the restricted primitive model for an ionic fluid using a density functional approach. The applied theory includes the electrostatic contribution to the free energy functional arising from the bulk energy equation of state and the mean spherical approximation for a restricted primitive model, as well as the associative contribution, due to the formation of pairs of ions. We compare the density profiles and the values of the surface tension with previous theoretical approaches.
We study the critical behavior of the systems dominated by Coulombic interaction. For this purpose we used the method of collective variables with a reference system. Starting from the Hamiltonian of the restricted primitive model (RPM), the simplest model of ionic fluids, we obtain the functional of the grand partition function given in terms of the two collective variables: the collective variables $ρ_{\mathbf{k}}$ and $c_{\mathbf{k}}$ describing fluctuations of the total number density and charge density, respectively. As the result of integration over the variables $c_{\mathbf{k}}$, the mi…
A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation functions in terms of higher-order correlation functions for the charge-density are given. It is shown that in continuum space the singularity of the charge-density correlation function associated with short-wavelength charge-ordering disappears when charge-density fluctuations are included by following the Brazovskii approach. The related singularity of th…
We study fluid-fluid equilibrium in the simplest model of ionic solutions where the solvent is explicitly included, i.e., a binary mixture consisting of a restricted primitive model (RPM) and neutral hard-spheres (RPM-HS mixture). First, using the collective variable method we find free energy, pressure and partial chemical potentials in the random phase approximation (RPA) for a rather general model that takes into consideration solvent-solvent and solvent-ion interactions beyond the hard core. In the special case of a RPM-HS mixture, we consider two regularizations of the Coulomb potential i…
We report an accurate Monte Carlo calculation of the phase diagram and clustering properties of the restricted primitive model with non-additive hard-sphere diameters. At high density the positively non-additive fluid shows more clustering than the additive model and the negatively non-additive fluid shows less clustering than the additive model, at low density the reverse scenario appears. A negative nonadditivity tends to favor the formation of neutrally charged clusters starting from the dipole. A positive nonadditivity favors the pairing of like ions at high density. The critical point of …
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…
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…
Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
We use Monte Carlo simulations to examine the simplest model of an ionic liquid, called the restricted primitive model, at a metal surface. We find that at moderately low temperatures the capacitance of the metal/ionic liquid interface is so large that the effective thickness of the electrostatic double-layer is up to 3 times smaller than the ion radius. To interpret these results we suggest an approach which is based on the interaction between discrete ions and their image charges in the metal surface and which therefore goes beyond the mean-field approximation. When a voltage is applied acro…
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…
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 co…
On the analogy between the restricted primitive model and capacitor circuits. Part II: A generalized Gibbs-Duhem consistent extension of the Pitzer-Debye-Hückel term with corrections for low and variable relative permittivity
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 …
A mesoscopic theory for the primitive model of ionic systems is developed for arbitrary size, $λ=σ_+/σ_-$, and charge, $Z=e_+/|e_-|$, asymmetry. Our theory is an extension of the theory we developed earlier for the restricted primitive model. The case of extreme asymmetries $λ\to\infty$ and $Z \to\infty$ is studied in some detail in a mean-field approximation. The phase diagram and correlation functions are obtained in the asymptotic regime $λ\to\infty$ and $Z \to\infty$, and for infinite dilution of the larger ions (volume fraction $n_p\sim 1/Z$ or less). We find a coexistence between a very …
A novel integral equations approach is applied for studying ion pairing in the restricted primitive model (RPM) electrolyte, i. e., the three point extension (TPE) to the Ornstein-Zernike integral equations. In the TPE approach, the three-particle correlation functions $g^{[3]}({\bf r}_{1},{\bf r}_{2},{\bf r}_{3})$ are obtained. The TPE results are compared to molecular dynamics (MD) simulations and other theories. Good agreement between TPE and MD is observed for a wide range of parameters, particularly where standard integral equations theories fail, i. e., low salt concentration and high io…
We discuss the first three well known moment charge-charge sum-rules for a general ionic liquid. For the special symmetric case of the Restricted Primitive Model, Das et al. [Phys. Rev. Lett. 107, 215701 (2011)] has recently discovered, through Monte Carlo simulations, that the Stillinger-Lovett or second-moment sum-rule fails at criticality. We critically discuss a possible explanation for this unexpected behavior. On the other hand the fourth-moment sum-rule turns out to be able to account for the results of the simulations at criticality.
The osmotic coefficient of solutions of rod-like polyelectrolytes is considered by comparing current theoretical treatments and simulations to recent experimental data. The discussion is restricted to the case of monovalent counterions and dilute, salt-free solutions. The classical Poisson-Boltzmann solution of the cell model correctly predicts a strong decrease in the osmotic coefficient, but upon closer look systematically overestimates its value. The contribution of ion-ion-correlations are quantitatively studied by MD simulations and the recently proposed DHHC theory. However, our comparis…
The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation is obtained and solved numerically for a totally asymmetric primitive model electrolyte around a spherical macroparticle. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential vs charge relationship, radial distribution functions, mean electrostatic potential and cumulative reduced char…
