Primitive Model Electrolyte Research Articles

Comment on "Binding Debye-Hückel theory for associative electrolyte solutions" [J. Chem. Phys. 159, 154503 (2023)

It is argued that the Binding Debye-Hückel (BiDH) model proposed by Naseri Boroujeni et al. [J. Chem. Phys. 159, 154503 (2023)] might not be appropriate for the description of Monte Carlo simulation data obtained for primitive model electrolytes. The first reason is that the original Debye-Hückel (DH) theory is of low accuracy for describing deviations from ideality in concentrated solutions of strong salts. The DH framework is thus a poor basis for building a model including association. The second reason is that the mean-spherical approximation, without assumption of association, apparently predicts Monte Carlo (MC) data for primitive electrolytes better than BiDH. Thus, the BiDH model seems to be simply a way of compensating for the deficiencies of DH theory by assuming association.

Cluster Formation Induced by Local Dielectric Saturation in Restricted Primitive Model Electrolytes.

Experiments using the Surface Force Apparatus (SFA) have found anomalously long-ranged charge-charge underscreening in concentrated salt solutions. Meanwhile, theory and simulations have suggested ion clustering to be a possible origin of this behavior. The popular Restricted Primitive Model of electrolyte solutions, in which the solvent is represented by a uniform relative dielectric constant, εr, is unable to resolve the anomalous underscreening seen in experiments. In this work, we modify the Restricted Primitive Model to account for local dielectric saturation within the ion hydration shell. The dielectric "constant" in our model locally decreases from the bulk value to a lower saturated value at the ionic surface. The parameters for the model are deduced so that typical salt solubilities are obtained. Our simulations for both bulk and slit geometries show that our model displays strong cluster formation and these give rise to long-ranged density correlations between charged surfaces, at distances similar to what has been observed in SFA measurements. An electrolyte model wherein the dielectric constant remains uniform does not display similar clusters, even with εr equal to the low saturated value at ion contact. Hence, the observed behaviors are not simply due to an enhanced Coulomb interaction. In the latter case, cluster growth is counteracted by long-ranged repulsions between like-charged ions within clusters; this is an effect that is considerably reduced when the dielectric response drop is local. Our results imply that long-ranged interactions in these systems are mainly due to cluster-cluster correlations, rather than large electrostatic screening lengths.

Surface Tension of Simple Molten Salts: Insight from a Charged Hard Sphere Model.

Surface tension of molten salts is rooted in many important phenomena in physical chemistry. We develop an analytical theory for the surface tension of molten salts, where the molten salt is described by a restricted primitive model electrolyte consisting of charged hard spheres, and surface tension is related to the formation of a cavity in the electrolyte. The integral equation theory is applied to the restricted primitive model electrolyte to derive an analytical formula of the cavity formation energy. The scaling relation of the cavity formation energy is further combined with morphological thermodynamics theory to determine the formula for surface tension. According to our formula, surface tension consists of a positive hard sphere contribution and a negative electrostatic contribution. Using the molar mass, interionic distance, density, and temperature as the input, our theory leads to a good prediction of surface tension of more than 16 molten salts at their melting point without introducing any adjustable parameters.

Effect of Counterion Size on Knotted Polyelectrolyte Conformations.

Using Langevin dynamics simulations and a coarse-grained primitive model of electrolytes, we show that the behavior of knotted circular strong polyelectrolytes (PEs) in diluted aqueous solution is largely affected by the diameter of the counterions (CIs), σCI. Indeed, we observe that both gyration radius and knot length vary nonmonotonically with σCI, with both small and bulky CIs favoring knot localization, while medium-sized ones promote delocalized knots. We also show that the conformational change from delocalized to tight knots occurs via the progressive coalescence of the knot's essential crossings. The emerging conformers correspond to the minima of the free energy landscape profiled as a function of the knot length or PE size. We demonstrate that different conformational states can coexist, the transition between them appearing first-order-like and controlled by the enthalpic and entropic trade-off of the amount of CIs condensed on the PE. Such balance can be further altered by varying CI concentrations, thus providing an additional and more convenient tuning parameter for the system properties. Our results lay the foundation for achieving broader and more precise external adjustability of knotted PE size and shape by choosing the nature of its CIs. Thus, they offer new intriguing possibilities for designing novel PE-based materials that are capable of responding to changes in ionic solution properties.

An efficient method to establish electrostatic screening lengths of restricted primitive model electrolytes.

We present a novel, and computationally cheap, way to estimate electrostatic screening lengths from simulations of restricted primitive model (RPM) electrolytes. We demonstrate that the method is accurate by comparisons with simulated long-ranged parts of the charge density, at various Bjerrum lengths, salt concentrations and ion diameters. We find substantial underscreening in low dielectric solvent, but with an "aqueous" solvent, there is instead overscreening, the degree of which increases with ion size. Our method also offers a possible path to (future) more accurate classical density functional treatments of ionic fluids.

Application of the symmetric Poisson-Boltzmann theory to equilibrium thermodynamic properties of primitive model electrolyte mixtures

A symmetric Poisson-Boltzmann theory is applied to a primitive model electrolyte solution containing 7 different ion species. Only 7 coupled equations need to be solved for the mean electrostatic potential around the ions once the uncharged hard sphere radial distribution function is specified. Comparison is made with the individual activity and osmotic coefficients of a simulation study of a sea water mixture. Good overall agreement is found with the simulation results.

Confined Electrolytes Show Bulk Dynamics Modulated by Hydrodynamic Couplings with the Walls

We use numerical simulations at the mesoscopic scale, namely, multiparticle collision dynamics (MPCD), to investigate the properties of electrolyte solutions in a charged slit pore. The solution is described within the primitive model of electrolytes, where ions are charged hard spheres embedded in a dielectric medium. Hydrodynamic couplings between ions and with the charged walls are precisely accounted for by the MPCD algorithm. We show that the dynamic properties of ions in this situation strongly differ from the behavior at infinite dilution (ideal case), contrary to what is usually assumed in the usual Poisson-Nernst-Planck description of this kind of systems. As a consequence of confinement, the diffusion coefficients of ions unexpectedly increase with the average ionic density in the systems. This is due to a decrease of the proportion of ions that are slowed down by the wall. Moreover, nonequilibrium simulations are used to estimate the electrical conductivity of these confined electrolytes. We show that the simulation results can be accounted for quantitatively by combining bulk descriptions of the electrical conductivity of electrolytes with a simple description of the hydrodynamics of ions in a slit pore.

Algebraic infection of charge correlations at the ionic critical point

AbstractWe consider a classical two‐component plasma analog of the restricted primitive model of electrolyte, where the hard‐core interaction is replaced by a soft differentiable potential. Within the Born–Green–Yvon hierarchy for the equilibrium distribution functions, we shed light on an infection mechanism where the charge correlations are polluted by the density correlations at the critical point of the liquid–gas transition. This should imply an algebraic decay of critical charge correlations, consistently with the violation of the Stillinger–Lovett sum rule observed in Monte Carlo simulations. In connection with this effect of density correlations on the charge correlations, we also provide a discussion on an extended version of the Debye–Hückel theory that calculates charge correlations in the restricted primitive model for an externally imposed spatial fluctuation of charges.PACS Numbers: 05.30.‐d, 05.70.Ce, 52.25.Kn.

Entropy of electrolytes with off-centre charge cations. Monte Carlo studies

Monte Carlo techniques including Inverse Grand Canonical Monte Carlo simulations are utilized to calculate the entropy of a restricted primitive model electrolyte with the caveat that the cation charge centre is displaced from the geographical centre of the cation sphere towards the surface of the sphere. Calculations have been performed for symmetric valency (1:1) and asymmetric valency (2:1) electrolytes at 298.15 K for a range of electrolyte concentrations. The cation charge centre displacement accompanied by an increase of temperature leads to an increase of entropy. For the 2:1 valency system the entropy as a function of the square root of concentration reveals a broad inflexion region that separates the domains of deformation due to the electrostatic and steric interactions. When the central ion is an anion, and the charge centres of the surrounding cations are oriented towards the anion then the electrostatic interactions are stronger than in the standard restricted primitive model and the entropy decreases, while a central cation deforms the ionic atmosphere surrounding it and the entropy increases. In the low concentration regime good agreement is seen between the results from the Debye-Hückel limiting law and the corresponding simulations.

Entropy characteristics in an electric double layer with off-centre charge ions. A statistical thermodynamics approach

Statistical thermodynamics methods are utilised to characterise aspects of the entropy of formation of a planar electric double layer. The model system consists of a primitive model electrolyte but with off-centre charge cations and centro-symmetric anions, next to a planar, uniformly charged electrode. An expression is developed for the entropy of off-centre charge ions. The theoretically predicted results of this entropy as a function of the electrode surface charge are compared with those from the corresponding Monte Carlo simulations. The entropy change with respect to the absolute value of the surface charge density is seen to be negative (or normal) if the displacement of the cation charge centre is zero or is independent of temperature. However, if the displacement is temperature dependent, the entropy can be positive (or anomalous). In each situation, the simulation data are well reproduced by the predicted results.

Reactive Monte Carlo simulations for charge regulation of colloidal particles.

We use a reactive Monte Carlo simulation method and the 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 numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.

Underscreening and hidden ion structures in large scale simulations of concentrated 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. We measure the decay of the charge-charge correlation among ions in the bulk and compare it against scaling trends found experimentally and determined in certain weak coupling theories of ion-ion correlation. Moreover, we find that additional large scale ion structures emerge at high concentrations. In this regime, the frequency of oscillations computed from the charge-charge correlation function is not dominated by electrostatic interactions but rather by excluded volume interactions and with oscillation periods on the order of the ion diameter. We also find the nearest neighbor correlation of ions sharing the same charge transitions from negative at small concentrations to positive at high concentrations, representing the formation of small, like-charge ion clusters. We conclude that the increase in local charge density due to the formation of these clusters and the topological constraints of macroscopic charged surfaces can help explain the degree of underscreening observed experimentally.

The differential capacitance as a probe for the electric double layer structure and the electrolyte bulk composition.

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 behavior for high electrode potentials. In this study, we consider primitive model electrolytes and not only use the standard definition of the differential capacitance but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte-electrode interface as well as the (composition of the) bulk electrolyte.

On the modified Poisson–Boltzmann closure for primitive model electrolytes at high concentration

The modified Poisson-Boltzmann closure is applied to the Kirkwood hierarchy of integral equations to investigate high concentration primitive model electrolytes. Two approximations are considered in the two sphere fluctuation potential problem. The derived damped oscillatory mean electrostatic potentials suggest that this closure should be of use in providing a basis for understanding the large experimental decay lengths found at high electrolyte concentrations.

Seeking the origins of a mysteriously large decay length in electrolytes

Researchers aim to corroborate experimental evidence of long-range decay with theory and simulations of primitive model electrolytes.

Primitive model electrolytes in the near and far field: Decay lengths from DFT and simulations

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 is based on the simplest mean-field treatment of Coulomb interactions (MFC), while 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 are in excellent agreement 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.

Ionic structure and decay length in highly concentrated confined electrolytes

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 concentrations, interfacial separations, surface charge densities, and ion sizes. The investigations are inspired by recent experiments that have directly measured the increase in the decay length for highly concentrated electrolytes with an increase in concentration. The behavior of ions in the nanoconfinement created by the interfaces is probed by evaluating the ionic density profiles, net charge densities, integrated charges, and decay lengths associated with the screening of the charged interface. The results show the presence of two distinct regimes of screening behavior as the concentration is changed from 0.1M to 2.5M for a wide range of electrolyte systems generated by tuning the interfacial separation, surface charge density, and ionic size. For low concentrations, the integrated charge exhibits a monotonic decay to 0 with a decay length that decreases sharply with increasing concentration. For high concentrations (≳1M), the integrated charge has a non-monotonic behavior signaling charge inversion and formation of structured layers of ions near the interfaces. The decay length under these conditions rises with increasing concentration. To complement the simulation results, a variational approach is developed that produces charge densities with characteristics consistent with those observed in simulations. The results demonstrate the relation between the rise in the strength of steric correlations and the changes in the screening behavior.

Effective electrostatic potential between two oppositely charged cylinder rods in primitive model and extended primitive model electrolytes

The classical density functional theory, combined with a fundamental measure functional and a second order functional perturbation truncation, is employed to study effective electrostatic potential between two oppositely and asymmetrically or symmetrically charged cylinder rods in electrolyte solution modeled by the primitive model and extended primitive model, respectively. We investigate how strength and distance of a peculiar repulsion peak are modulated by the influencing factors such as rod charge strength, rod charge strength asymmetry, salt concentration, interionic neutral and non-hard sphere interactions, and ion electric valence and size. We acquire a dozen change patterns of the repulsion peak strength and peak distance with system parameters and draw out normative as well as raw empirical implications of the repulsion mechanism based on the idea of excess adsorption-induced osmotic pressure difference by augmenting the abstract idea by the electric neutrality principle and concepts such as tightness or compression of the ion layer, crowding of the surface region, and multiplayer in the ion distribution. The observed rich diversity of the possible effective electrostatic potential between the two oppositely and asymmetrically or symmetrically charged rods increases the options to optimize the interactions for specific purposes.

Modeling selective ion adsorption into cylindrical nanopores

Ion selectivity by cylindrical pores has been investigated using the primitive model of electrolytes and the classical density functional theory. It is found that a neutral pore always exhibits the preferential adsorption of large ions, regardless of the pore size and the bulk electrolyte composition. For a charged nanopore, however, the pore selectivity depends not only on the ion size but also on the pore radius as well as the surface electrical potential. While a nanopore prefers adsorption of small counterions when its radius is sufficiently large, it can be large-ion selective when its size becomes comparable to the ion diameters.

Thermodynamics of primitive model electrolytes in the symmetric and modified Poisson-Boltzmann theories. A comparative study with Monte Carlo simulations

Osmotic coefficients, individual and mean activity coefficients of primitive model electrolyte solutions are computed at different molar concentrations using the symmetric Poisson-Boltzmann and modified Poisson-Boltzmann theories. The theoretical results are compared with an extensive series of Monte Carlo simulation data obtained by Abbas et al. [Fluid Phase Equilib., 2007, 260, 233; J. Phys. Chem. B, 2009, 113, 5905]. The agreement between modified Poisson-Boltzmann predictions with the "exact" simulation results is almost quantitative for monovalent salts, while being semi-quantitative or better for higher and multivalent salts. The symmetric Poisson-Boltzmann results, on the other hand, are very good for monovalent systems but tend to deviate at higher concentrations and/or for multi-valent systems. Some recent experimental values for activity coefficients of HCl solution (individual and mean activities) and NaCl solution (mean activity only) have also been compared with the symmetric and modified Poisson-Boltzmann theories, and with the Monte Carlo simulations.