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.     

Corrections for volume changes in describing diffusion in electrolyte solutions

It is possible to avoid certain difficulties in describing the diffusion in electrolyte solutions by taking into account the process of spatial rearrangement of species that accompanied the concentration variations and was recently introduced into consideration. The experimental substantiation of taking into account this process is the different concentrations of solvent, i.e., water, observed in solutions of different concentrations.     

External transverse magnetic field effect on electrolyte diffusion in alkali chloride-water solutions

The observed external transverse magnetic field effect on electrolyte diffusion in diamagnetic alkali chloride (LiCl, NaCl; KCl and CsCl)-water solutions, expressed as the fractional arithmetic average integral diffusion coefficient, $\text{D}$*=[(?$\text{D}$⁰_H > -<$\text{D}$⁰ > )/<$\text{D}$⁰ > ;]×10²; has been correlated with structural (hydration number, viscosity and ionic limiting equivalent conductance) and microdynamical (proton nuclear magnetic relaxation times and proton nuclear magnetic resonance shifts) parameters expressing the configurational rearrangement modes of the solvent and solute molecules forming the aqueous solution.     

Symmetrical radial distribution functions in the potentially theory of electrolyte solutions

A symmetrical radial distribution function g_ij in electric double layer theory has been proposed by Féat and Levine. We adopt their work to the electrolyte bulk to show how a symmetrical g_ij may be obtained in the potential theory of electrolyte solutions.     

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.     

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。     

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.     

Comparison of theory and experiment for diffusion in dilute polymer solutions

Results from a number of theories for the concentration dependence of the mutual diffusion coefficient in dilute polymer solutions are examined, and clarifications are made as to what forms of the equations for these theories should be used in comparisons with experimental diffusivity data. An evaluation of the available theories for the concentration dependence of the diffusivity under theta conditions is carried out using experimental diffusivity data taken using sharp fractions of polystyrene. It is concluded that the Pyun—Fixman theory appears to provide the most promising method for estimating the concentration dependence of the mutual diffusion coefficient in dilute polymer solutions at the present time.     

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.     

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.     

Semi-ideal solution theory. 2. Extension to conductivity of mixed electrolyte solutions

Conductivities were measured for the ternary systems NaCl-LaCl(3)-H(2)O and KCl-CdCl(2)-H(2)O and their binary subsystems NaCl-H(2)O, KCl-H(2)O, CdCl(2)-H(2)O, and LaCl(3)-H(2)O at 298.15 K. The semi-ideal solution theory for thermodynamic properties of aqueous solutions of electrolyte mixtures was used together with the Eyring absolute rate theory to study conductivity of mixed electrolyte solutions. A novel simple equation for prediction of the conductivity of mixed electrolyte solutions in terms of the data of their binary solutions was established. The measured conductivities and those reported in literature were used to test the newly established equation and the generalized Young's rule for conductivity of mixed electrolyte solutions. The comparison results show that the deviation of a ternary solution from the new conductivity equation is closely related to its isopiestic behavior and that the deviations are often within experimental uncertainty if the examined system obeys the linear isopiestic relation. While larger deviations are found in the system with large ion pairing effect, the predictions can be considerably improved by using the parameters calculated from its isopiestic results. These results imply that the previous formulation of the thermodynamic properties of aqueous solutions of electrolyte mixtures has a counterpart for transport properties.     

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     

Overcharging of nanoparticles in electrolyte solutions

Monte Carlo simulations are performed to investigate the effects of salt concentration, valence and size of small ions, surface charge density, and Bjerrum length on the overcharging of isolated spherical nanoparticles within the framework of a primitive model. It is found that charge inversion is most probable in solutions containing multivalent counterions at high salt concentrations. The maximum strength of overcharging occurs near the nanoparticle surface where counterions and coions have identical local concentrations. The simulation results also suggest that both counterion size and electrostatic correlations play major roles for the occurrence of overcharging.     

Remarks on projection operators used in the theory of intermolecular interactions

In the theory of intermolecular forces some authors used the inverse of the antisymmetrizer. The non-existence of this operator is pointed out and the use of a different type of projection operator is suggested.     

Anomalous nanoparticle diffusion in polymer solutions and melts: a mode-coupling theory study

Mode-coupling theory is employed to study diffusion of nanoparticles in polymer melts and solutions. Theoretical results are directly compared with molecular dynamics simulation data for a similar model. The theory correctly reproduces the effects of the nanoparticle size, mass, particle-polymer interaction strength, and polymer chain length on the nanoparticle diffusion coefficient. In accord with earlier experimental, simulation, and theoretical work, it is found that when the polymer radius of gyration exceeds the nanoparticle radius, the Stokes-Einstein relation underestimates the particle diffusion coefficient by as much as an order of magnitude. Within the mode-coupling theory framework, a microscopic interpretation of this phenomenon is given, whereby the total diffusion coefficient is decomposed into microscopic and hydrodynamic contributions, with the former dominant in the small particle limit, and the latter dominant in the large particle limit. This interpretation is in agreement with previous mode-coupling theory studies of anomalous diffusion of solutes in simple dense fluids.     

Thermochemistry of nonaqueous electrolyte solutions

Heats of solution and specific heats have been measured for NaI and KI in methanol at 25 and 50 for the full range of concentrations; the integral heat of solution of NaI or KI in methanol has a positive temperature coefficient, whereas the heats of solution of these salts and all strong electrolytes in water have negative temperature coefficients. The thermal capacity of an aqueous electrolyte is less than the sum of the thermal capacities of the components, whereas the result for methanol is the reverse. In addition, the integral heat of solution has a concentration coefficient much larger than that found for water, mainly because water has a dielectric constant about 2.5 times that of methanol. This leads to stronger interactions between ions in methanol, which contains ion pairs.     

Acidity of frozen electrolyte solutions

Ice is selectively intolerant to impurities. A preponderance of implanted anions or cations generates electrical imbalances in ice grown from electrolyte solutions. Since the excess charges are ultimately neutralized via interfacial (H(+)/HO(-)) transport, the acidity of the unfrozen portion can change significantly and permanently. This insufficiently recognized phenomenon should critically affect rates and equilibria in frozen media. Here we report the effective (19)F NMR chemical shift of 3-fluorobenzoic acid as in situ probe of the acidity of extensively frozen electrolyte solutions. The sign and magnitude of the acidity changes associated with freezing are largely determined by specific ion combinations, but depend also on solute concentration and/or the extent of supercooling. NaCl solutions become more basic, those of (NH(4))(2)SO(4) or Na(2)SO(4) become more acidic, while solutions of the 2-(N-morpholino)ethanesulfonic acid zwitterion barely change their acidity upon freezing. We discuss how acidity scales based on solid-state NMR measurements could be used to assess the degree of ionization of weak acids and bases in frozen media.     

Surface tension of electrolyte solutions

A simple analytic expression is derived for the excess surface tension of electrolyte solutions, which is in good agreement with the experimental data on NaCl in the concentration range up to as high as 1 M. This expression is consistent with the following two theories: (i) The recent theory of Levin and Flores-Mena (Europhys Lett (2001) 56:187), who demonstrated the important contribution of the formation of an ion free layer at the air–electrolyte solution interface, and (ii) the Onsager–Samaras theory (J Chem Phys (1934) 2:528) modified by taking into account the ion-free layer effect. It is shown that the excess surface tension consists of three parts: the contributions of the ion-free layer, the image interaction between the electrolyte ions and the ion-free layer, and the image interaction between the electrolyte ions and air.     

A view of electrolyte solutions

The uncertainties in the route to infinite dilution for 2–2 electrolytes are discussed in relation to the practical difficulties of determining the standard emf's of simple reversible cells containing ZnSO₄ in H₂O and D₂O solutions. These difficulties are due to uncertainties in the theory of highly charged ions in aqueous solution. Recent developments in theories of electrolytes, especially those for which numerical results are available, are critically evaluated for their accuracy and adaptability to changes in the solute potential. Simple refinements to the model (i.e., the solute potential) are described, and the changes are interpreted, in terms of the molecular interactions between sets or pairs of ions in the pure solvent. Recent work on the effect of solvent granularity and other molecular properties of the solvent (e.g., dipole moment) on the solute potential is reviewed.This paper was presented at the symposium, The Physical Chemistry of Aqueous Systems, held at the University of Pittsburgh, Pittsburgh, Pennsylvania, June 12–14, 1972, in honor of the 70th birthday of Professor H. S. Frank.