Remarks on the theory of diffusion in electrolyte solutions

The assumptions usually made that the ionic atmosphere has spherical symmetry in the diffusion of binary electrolytes and that the electrophoretic effect is negligible in the tracer diffusion of ions are pointed out to be incorrect when terms up to order κ² ln κ (κ is the Debye-Hückel parameter) are considered.     

On a new approximation in the theory of electrolyte solutions

We compare the results of a new approximation for the interionic radial distribution function developed previously by Olivares and McQuarrie to those from the nonlinear Poisson—Boltzmann equation for the highly-charged system of the spherical protein bearing a charge as 20 in an aqueous electrolyte solution. In particular, we use both approximations to predict the experimental results for protein titration, which are the experimental data to which the results of the Poisson—Boltzmann equation had been directed.     

Molecular dynamics and theory for the contact values of the radial distribution functions of hard-disk fluid mixtures

We report molecular dynamics results for the contact values of the radial distribution functions of binary additive mixtures of hard disks. The simulation data are compared with theoretical predictions from expressions proposed by Jenkins and Mancini [J. Appl. Mech. 54, 27 (1987)] and Santos et al. [J. Chem. Phys. 117, 5785 (2002)]. Both theories agree quantitatively within a very small margin, which renders the former still a very useful and simple tool to work with. The latter (higher-order and self-consistent) theory provides a small qualitative correction for low densities and is superior especially in the high-density domain.     

Thermodynamic properties of strong electrolyte solutions from correlation functions

General relations are presented to relate the fluctuation thermodynamic properties of multicomponent electrolyte solutions (concentration derivatives of the chemical potential, partial molar volume, and compressibility) to integrals of the total correlation function (Kirkwood-Buff solution theory) and of the nondivergent portion of the direct correlation function. Detailed expressions are given for the single-salt, single-solvent system. It appears that the direct correlation function expressions may be of more practical use in developing correlations for solution properties because, unlike the total correlation functions, terms exist which distinguish between cation and anion interactions with water and with other ions.     

Effect of available volumes on radial distribution functions

The traditional method of analyzing solution structuring properties of solutes using atom–atom radial distribution functions (rdfs) can give rise to misleading interpretations when the volume occupied by the solute is ignored. It is shown by using the examples of O(4) in α- and β-D-allose that a more reliable interpretation of rdfs can be obtained by normalising the rdf using the available volume, rather than the traditional volume of a spherical shell. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 363–367, 1998     

New evaluation of reconstructed spatial distribution function from radial distribution functions

Although three dimensional (3D) solvation structure is much more informative than one dimensional structure, its evaluation is difficult experimentally and theoretically. In our previous Communication [Yokogawa et al., J. Chem. Phys. 123, 211102 (2005)], we proposed a new method to present reconstructed spatial distribution function (RC-SDF) from a set of radial distribution functions (RDFs). In this article, we successfully extended the method more accurately with new basis sets. This new method was applied to two liquid solvation structures, methanol and dimethyl sulfoxide, as examples. Their RC-SDFs evaluated here clearly show that the former solvation structure is well defined while the latter one is broad, which agrees well with the SDFs calculated directly from molecular dynamics simulations. These results indicate that the method can reproduce well these 3D solvation structures in reasonable computational cost.     

The McMillan–Mayer framework and the theory of electrolyte solutions

In electrolyte thermodynamics one often speaks of two thermodynamic frameworks; the Lewis–Randall framework (characterised by temperature, pressure, and mole numbers) and the McMillan–Mayer framework (characterised by temperature, total volume, solute mole numbers, and solvent chemical potential). However, there is only one framework in thermodynamics; the apparent difference between the two ‘frameworks’ is, in electrolyte thermodynamics, due to the change in the pressure caused by the charging process at constant volume and solvent chemical potential.The so-called McMillan–Mayer framework is set in the context of the classical thermodynamics and the use of it is examplified by the Debye–Hckel theory. The so-called McMillan–Mayer framework is superfluous when the thermodynamics of the electrolyte solutions is described by the Helmholtz energy functions.     

Force-field parametrization based on radial and energy distribution functions

We propose a novel force-field-parametrization procedure that fits the parameters of potential functions in a manner that the pair distribution function (DF) of molecules derived from candidate parameters can reproduce the given target DF. Conventionally, approaches to minimize the difference between the candidate and target DFs employ radial DFs (RDF). RDF itself has been reported to be insufficient for uniquely identifying the parameters of a molecule. To overcome the weakness, we introduce energy DF (EDF) as a target DF, which describes the distribution of the pairwise energy of molecules. We found that the EDF responds more sensitively to a small perturbation in the pairwise potential parameters and provides better fitting accuracy compared to that of RDF. These findings provide valuable insights into a wide range of coarse graining methods, which determine parameters using information obtained from a higher-level calculation than that of the developed force field. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

微扰理论非原始模型用于1:1价单一电解质水溶液

本文采用微扰理论非原始模型, 以带电硬球混合物为参考体系, 考虑粒子间各种作用能(色散、静电、偶极、四极、诱导), 首次取相对介电常数为1, 拟合了12处1:1价电解质水溶液的渗透系数, 获得了成功, 得到了7种1价离子Na^+,K^+, Rb^+, Cs^+, Cl^-, Br^-, I^-的微观参数(软球直径σ和色散能常数ε/k)。计算得到的电解质水溶液渗透系数的总平均绝对偏差是0.041。这些离子的微观参数在不同体系中维持不变。计算中未引入混合参数。     

Perturbation theory for the radial distribution function for simple polar fluids

The radial distribution function for a fluid whose molecules interact according to the Stockmayer potential was calculated by means of thermodynamic perturbation theory using two different approximations for the perturbation term and was compared with computer simulation results. The approximation based on the Percus-Yevick equation was found to be in much better agreement with the simulations than was the “simplified superposition approximation” to the perturbation term.     

Structure of electrolyte solutions sorbed in carbon nanospaces, studied by the replica RISM theory

The replica RISM theory is used to investigate the structure of electrolyte solutions confined in carbonized polyvinylidene chloride (PVDC) nanoporous material, compared to bulk electrolyte solution. Comparisons are made between the models of electrolyte solution sorbed in the carbonized PVDC material and a single carbon nanosphere in bulk electrolyte solution. Particular attention is paid to the chemical potential balance between the species of the sorbed electrolyte solution and the bulk solution in contact with the nanoporous material. As a result of the strong hydrophobicity of the carbonized PVDC material in the absence of activating chemical groups, the densities of water and ions sorbed in the material are remarkably low compared to those in the ambient bulk solution. The interaction between water molecules and cations becomes strong in nanospaces. It turns out that, in carbon nanopores, a cation adsorbed at the carbon surface is fully surrounded by the hydration shell of water molecules which separates the cation and the surface. Distinctively, an anion is adsorbed in direct contact with the carbon surface, which squeezes a part of its hydration shell out. The tendency increases toward smaller cations, which are characterized as "positive hydration" ions. In the bulk, cations are not hydrated so strongly and behave similarly to anions. The results suggest that the specific capacitance of an electric double-layer supercapacitor with nanoporous electrodes is intimately related to the solvation structure of electrolyte solution sorbed in nanopores, which is affected by the microscopic structure of the nanoporous electrode.     

Blip function calculation of the radial distribution functions for a binary liquid mixture

It is shown that the use of the high temperature approximation to blip function theory together with a two-component hard sphere reference fluid leads to reasonably accurate predictions for the radial distribution functions in a moderate temperature, moderate density, binary Lennard-Jones mixture.     

The changes in free energies and entropies from analytical radial distribution functions

The changes in Helmholtz free energies and entropies in dense fluids have been evaluated using three known analytical expressions for radial distribution functions (RDFs) of Lennard–Jones (L-J) fluid. This method provides a simpler and a more expeditious way for the calculation of free energy and entropy in L-J dense fluids through statistical mechanics. Previously, integral equations or perturbation theories were used for this purpose. Such approach not only tests the power of analytical distribution functions in predicting the changes in Helmholtz free energies and entropies, but also specifies better expressions in determining these properties. The results are compared with experimental data and an accurate analytic equation of state for the L-J fluid. It is shown if an expression properly presents RDFs as a function of interparticle distance, density and temperature, it is possible to calculate the changes in Helmholtz free energies and entropies from analytical distribution functions.     

Symmetrical and localized solutions of the equations of the multiconfigurational theory of a self-consistent field for even polyenes

Theoretical and Experimental Chemistry -     

The effective fragment potential: small clusters and radial distribution functions

The effective fragment potential (EFP) method for treating solvent effects provides relative energies and structures that are in excellent agreement with the analogous fully quantum [i.e., Hartree-Fock (HF), density functional theory (DFT), and second order perturbation theory (MP2)] results for small water clusters. The ability of the method to predict bulk water properties with a comparable accuracy is assessed by performing EFP molecular dynamics simulations. The resulting radial distribution functions (RDF) suggest that as the underlying quantum method is improved from HF to DFT to MP2, the agreement with the experimental RDF also improves. The MP2-based EFP method yields a RDF that is in excellent agreement with experiment.     

Thermochemistry of electrolyte solutions

The results of calorimetric investigations of electrolyte solutions in the mixtures of water, methanol, N,N-dimethylformamide, and acetonitrile with numerous organic cosolvents are discussed with regard to the intermolecular interactions that occur in the solution. Particular attention is given to answer the questions how and to what extent the properties of the systems examined are modified by the cosolvent added and how much the properties of the cosolvent are revealed in the mixtures with the solvents mentioned above. To this goal, the analysis of the electrolyte dissolution enthalpies, single ionic transfer enthalpies, and enthalpic pair interaction coefficients as well as the preferential solvation (PS) model are applied. The analysis performed shows that in the case of the dissolution enthalpies of simple inorganic electrolytes in water–organic solvent mixtures, the shape of the dependence of the standard dissolution enthalpy on the mixed solvent composition reflects to a large extent the hydrophobic properties of the organic cosolvent. In the mixtures of methanol with organic cosolvents, the ions are preferentially solvated either by methanol molecules or by molecules of the cosolvent, depending on the properties of the mixed solvent components. The behavior of inorganic salts in the mixtures containing N,N-dimethylformamide is mostly influenced by the DMF which is a relatively strongly ion solvating solvent, whereas in acetonitrile mixtures, the thermochemical behavior of electrolyte solutions is influenced to a large extent by the properties of the cosolvent particularly due to the PS of cation by the cosolvent molecules.     

A study of a nonprimitive model for electrolyte solutions based on perturbation theory

The equation for the Helmholtz free energy for systems of small anisotropic molecules and ions is deduced by substituting the complete expression for various potential energies (including repulsive, dispersive, electrostatic, and induced energies) into the perturbation expansion. The equation is applied to pure water. The relative dielectric constant is set at unity. Based on the equal chemical potentials of equilibrated vapor and liquid phases, the molecular parameters of water are regressed from the densities of saturated vapor in the temperature range of 0 to 370°C. The ARD of regression is 1.16%. These parameters are used to predict the heat of vaporization and densities of saturated vapor and liquid phases of water in the same temperature range. The ARDs of prediction are 4.5% and 9.8%, respectively. The equation is used to correlate the osmotic coefficients of twelve 1:1 electrolyte solutions. The relative dielectric constant is set at unity. The parameters (Soft-sphere diameter and dispersive constant) of seven ions (Na⁺, K⁺, Rb⁺, Cs⁺, Cl^–, Br^–, and I^–) are obtained. The total average absolute deviation between calculated and experimental values of the osmotic coefficient is 0.041. The parameters of ions can keep constant in different systems.     

Hall voltage in electrolyte solutions

Abstract

Hall coefficient for CuSO₄ liquid electrolyte has been measured and found to be positive. Detection of Hall signal was limited to de methods although ac techniques were also investigated. The Hall coefficient increases with decreasing concentration of solute and for distilled water approaches 5 × 10⁵ cm³/coul. Calculations of H⁺ ion mobility using the two carrier expression for Hall coefficient show the charge carrier in a liquid electrolyte to be the H⁺ ion. Mobility of the proton in water is of the order of 1 cm² voltsec, which is near the value in ice