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 thermodynamic consistency of the HNC approximation was tested. The mean activity coefficients, calculated via the Gibbs-Duhem equation, seem to follow the MC data slightly better than the Hansen-Vieillefosse-Belloni expression. For completeness of the calculation, the HNC excess internal energies and osmotic coefficients are also presented. These results are compared with the calculations based on other theories commonly used to describe electrolyte solutions, such as the mean spherical approximation, Pitzer's extension of the Debye-Hückel theory, and the Debye-Hückel limiting law.
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…
The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study
针对球形大颗粒周围的完全不对称原始模型电解质，获得了超网链/平均球近似（HNC/MSA）积分方程并进行了数值求解。随后的径向分布函数显示出非常好的协议相比，我们的Monte Carlo和分子动力学模拟的球形几何形状和相对于以前的各向异性参考HNC计算在平面极限。我们报告的电位与电荷的关系，径向分布函数，平均静电势和累积减少电荷的1：1和2：2盐的大小不对称比为2的代表性情况下的分析。我们的结果整理与修改的Gouy-Chapman（MGC）和不等半径修改的Gouy-Chapman（URMGC）理论和HNC/MSA的限制原始模型（RPM）的大小不对称的影响的重要性进行评估。发现的最显著的特征之一是，\textit{contrary to the general belief}，远离零电荷点，非对称双电层（EDL）的性质不是对应于具有电荷的对称电解质的性质，即\textit{counterions do not always dominate}。这种行为表明存在一个新的现象学的EDL，真正属于一个更现实的尺寸不对称的模型，空间相关性考虑一致。这些新的特征不能用传统的平均场论如MGC、URMGC，甚至不能用基于RPM的增强形式化如HNC/MSA来描述。
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…
Effective interactions between like-charged particles immersed in an electrolyte solution were calculated using two integral equation theories, hypernetted-chain (HNC)-Ornstein--Zernike (OZ) and ionic Percus--Yevick 2 (IPY2)-OZ. When the HNC-OZ theory was adopted, the electrolyte concentration dependence of the effective interaction showed a reentrant behavior. By contrast, the IPY2-OZ theory did not indicate the behavior. Monte Carlo simulations were performed for one of the model systems, and the results agreed qualitatively with those calculated using the HNC-OZ theory.
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 …
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…
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…
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…
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…
We revisit the role of the local solvent structure on the activity coefficient of electrolytes with a general non-local dielectric function approach. We treat the concentrated electrolyte as a dielectric medium and suggest an interpolated formula for the dielectric response. The pure water limit is calibrated based on MD simulations and experimental data. Solving our model around a central ion, we find strong over-screening and oscillations in the potential, which are absent in the standard "primitive model" predictions. We obtain mathematically tractable closed-form expressions for the activi…
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 …
An elementary statistical observation identifies generalizations of the Fuoss approximation for the probability distribution function that describes ion clustering in electrolyte solutions. The simplest generalization, equivalent to a Poisson distribution model for inner-shell occupancy, exploits measurable inter-ionic correlation functions, and is correct at the closest pair distances whether primitive electrolyte solutions models or molecularly detailed models are considered, and for low electrolyte concentrations in all cases. With detailed models these generalizations includes non-ionic in…
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 …
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…
