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Sodium-based rechargeable battery technologies are being pursued as an alternative to lithium, in part due to the relative abundance of sodium compared to lithium. Despite their low dielectric constant, glyme-based electrolytes are particularly attractive for these sodium-based batteries due to their ability to chelate with the sodium ion and their high electrochemical stability. While the glyme chain length is a parameter that can be tuned to modify solvation properties, charge transport behavior, reactivity, and ultimately battery performance, anion identity provides another tunable variable. Trifluoromethanesulfonate (triflate/OTf) and bis(trifluoromethane)sulfonamide (TFSI) are chemically similar anions, which are often used in battery electrolytes for lithium-based batteries. In this paper, molecular simulations are used to examine the differences in ion association and charge transport between sodium salts of these two anions at different salt concentrations in glymes with the increasing chain length. The use of the modified force field developed for NaOTf in glymes for the NaTFSI electrolytes was validated by comparing the TFSI-sodium ion radial distribution functions to the results from ab initio molecular dynamics simulations on 1.5 M NaTFSI in diglyme. While the ion association behavior as a function of salt concentration showed similar trends for both NaOTf and NaTFSI in tetraglyme and triglyme electrolytes, the dominant solvation structures for the two sets of electrolytes are distinctly different in the monoglyme and diglyme cases. The conductivity is impacted by both the ion association behavior in these electrolytes and the non-vehicular or hopping transport of the anions in these systems.

The semimicroscopic model separates the electronic and reorientational components of the solvent dielectric response. The former is accounted for by embedding the computational system in an electrical background that describes the high-frequency (optical) contributions to the dielectric constant (e∼2). The latter is treated by means of the force field. We use this decomposition to describe the solvation of simple monovalent ions in water. The free energy of solvation is composed of two terms: one Born-like, describing the transfer of the ion from vacuum to the electrical background and the other describing the shielding free energy due to interaction between the ion and the surrounding solvent. We employ a highly simplified model: ions are hard spheres with crystal radii and water is a hard sphere with an embedded (gas-phase) multipole. Absolute ionic hydration energies cannot be directly measured. They hinge on the value accepted for the absolute potential of the standard hydrogen electrode. Using the mo...

Structural properties and energies of solvation are simulated for alkali and halide ions. The solvation structure is discussed in terms of various site–site distribution functions, of solvation numbers, and of orientational correlation functions of the solvent molecules around the ions. The solvent polarizability has notable effects which cannot be intuitively predicted. In particular, it is necessary to reproduce the experimental solvation numbers of small ions. The changes of solvation properties are investigated along the alkali and halide series. By comparing the solvation of ions in acetone to that in acetonitrile, it is shown that the spatial correlations among the solvent molecules around an ion result in a strong screening of the ion–solvent direct intermolecular potential and are essential to understand the changes in the solvation structures and energies between different solvents. The solvation properties derived from the simulations are compared to earlier predictions of the hypernetted chain ...

We investigate the ion–ion pair association equilibrium in the hard sphere ionic fluid as predicted by several Debye–Huckel-based theories. The degree of dissociation is examined in a pairing theory based on Ebeling’s definition of the association constant, and in extensions of this theory for ion pair–free ion interactions by Fisher and Levin, and ion pair–ion pair interactions by Weiss and Schroer. The effect of an increase of the dielectric constant on the degree of dissociation is studied. In all cases, minima of the density-dependent degree of dissociation along isotherms are found at low ionic density, at least over part of the temperature range. The loci of these minima in the temperature-density plane are calculated. The results are compared with conductivity data. We discuss a possible resemblance of the system’s behavior in a region in which the degree of association changes rapidly with a tricritical scenario, in which a line of second-order insulator–conductor phase transitions intersects the coexistence curve.

Monte Carlo simulations have been used to investigate condensation and ion association in primitive models of electrolyte solutions. We have examined models in which the ions have equal diameter, the cation charge is +Zq, and the anion charge is −q, with Z=1, Z=2, and Z=4. Z=1 corresponds to the familiar restricted primitive model. Rough estimates of the critical temperatures have been obtained. In all cases the vapor phase is highly associated, with the ions forming electroneutral pairs, triples, and quintuples for Z=1, Z=2, and Z=4, respectively. Ion association has been investigated using a nearest-neighbor distribution function. For each value of Z the onset of ion dissociation in the low-density vapor is shown to occur at a temperature very close to the critical temperature. This raises the possibility of ion association affecting the critical behavior of ionic fluids. We have compared the simulation results for the restricted primitive model with the predictions of Debye–Huckel-based theories and the pairing mean spherical approximation. All of the theories perform well in the vapor phase, but are less successful in the liquid phase.

The solvation energy of a pair of ions in polar media is exactly calculated within the framework of the dielectric continuum model. The product ions are modeled as either conducting spheres with charges on their surfaces or spherical vacuum cavities with point charges at their centers. The results show that, if the two ions are close to each other, the solvation energy is different from the results known in the literature.

A recently published ion association theory which includes the formation of trimers and tetramers has been further developed by accounting for density-dependent properties. This theory is developed in the framework of a primitive model and based on the completely dissociated reference system. The association constants of the equilibria between the ions and the clusters are related to an integral over the pair distribution function of the ionic fluid by an association balance. In order to calculate the fraction of trimers and larger ion clusters use has been made of the Kirkwood superposition approximation. For all calculations the dielectric constant of the pure solvent has been employed. In this paper an extension of the theory has been accomplished by replacing properties of the low density limit by density-dependent properties. The exponential low density pair correlation function has been replaced by the analytically available general mean spherical approximation expression. The covolumes of the clusters have been approximated with a perturbation approach for an effective Bjerrum distance. The ion clusters are modeled as hard spherocylinders. For the charged clusters the Coulomb interaction is described with the mean spherical approximation expression. Finally, the model is applied to some 1–1 electrolyte solutions in water. In the applications the dielectric constant of pure water has been used at a given temperature.

The first part of this paper reviews the theory of the calculation of the frequency-dependent dielectric properties (i.e., conductivity and dielectric constant) of ionic solutions from computer simulations. Based on a 2.2-ns molecular dynamics simulation, the second part presents a detailed analysis of the various contributions to the frequency-dependent conductivity of a saturated solution of ZnBr2 in water. We find evidence for two separate relaxation channels in the frequency-dependent conductivity, and a very low value for the static (i.e., zero frequency) conductivity, which is consistent with the high degree of ion association and the prevalence of electrically neutral ion clusters that we observe in this system.

We describe atomistic simulations of the free energy and entropy of hydration of ions in aqueous solution at 25 °C using a simple point charge model (SPC/E) for water and charged spherical Lennard-Jones solutes. We use a novel method with an extended Lagrangian or Hamiltonian in which the charge and the size of the ions are considered as dynamical variables. This enables us to determine thermodynamic properties as continuous functions of solute size and charge and to move smoothly from hydrophilic to hydrophobic solvation conditions. On passing between these extremes, the entropy of solvation goes through maxima. For example it shows a double maximum as a function of charge at constant size and a single maximum as a function of size at constant (non-zero) charge. These maxima correspond to extremes of structure-breaking and are associated with the disappearance of the second solvation shell in the radial distribution function; no anomalies are seen in the first shell. We also present direct evidence of th...

The phenomenon of electrical conductivity maxima of molten salts versus temperature during orthobaric (closed-vessel) conditions is further examined via ab initio simulations. Previously, in a study of molten BiCl3, a new theory was offered in which the conductivity falloff at high temperatures is due not to traditional ion association, but to a rise in the activation energy for atomic ions hopping from counterion to counterion. Here this theory is further tested on two more inorganic melts which exhibit conductivity maxima: another high-conducting melt (SnCl2, σmax = 2.81 Ω(-1) cm(-1)) and a low-conducting one (HgBr2, σmax = 4.06 × 10(-4) Ω(-1) cm(-1)). First, ab initio molecular dynamics simulations were performed and again appear successful in reproducing the maxima for both these liquids. Second, analysis of the simulated liquid structure (radial distributions, species concentrations) was performed. In the HgBr2 case, a very molecular liquid like water, a clear Grotthuss chain of bromide transfers was observed in simulation when seeding the system with a HgBr(+) cation and HgBr3 (-) anion. The first conclusion is that the hopping mechanism offered for molten BiCl3 is simply the Grotthuss mechanism for conduction, applicable not just to H(+) ions, but also to halide ions in post-transition-metal halide melts. Second, it is conjectured that the conductivity maximum is due to rising activation energy in network-covalent (halide-bridging) melts (BiCl3, SnCl2, PbCl2), but possibly a falling Arrhenius prefactor (collision frequency) for molecular melts (HgBr2).

The luminescence of Eu3+ in a salt–polymer complex, poly(propylene oxide) containing Eu(CF3SO3)3 salt, was studied using broad band and site‐selective excitation. Two distinctly different types of local structure around Eu3+ were detected. To investigate and compare the local structure around the SO3CF−3 anions with that around the Eu3+ cations, a Raman scattering study of the SO3 symmetric stretch vibration was performed in the same system. The vibrational data clearly reveal that also the anions are subject to two types of local environment. It is found that neither of the two states can be attributed to ‘‘free’’ (completely solvated) ions, which implies the existence of two different anion–cation configurations. Temperature and concentration dependent studies of the site‐selective Eu3+ luminescence and the SO3 vibrational spectrum show that the relative amount of ions in the two states is, within the experimental accuracy, constant. However at elevated temperatures there is a rapid exchange between the...

Ion association in a 1–3 electrolyte is studied using an asymmetrically charged soft‐sphere model. The ions in this model have identical size, and the aqueous solvent is treated as a structureless dielectric continuum. The fraction of monomers, dimers, and trimers in the electrolyte are predicted by an extension of Wertheim’s associating liquids integral equation theory. Over the range of concentrations from 0.002 to 1.5M, the predictions for the thermodynamic quantities such as the reduced excess energy and the osmotic coefficient, are compared with existing molecular dynamics simulations of a ‘‘hard‐core’’ model of 1–3 electrolytes. The influence of charge asymmetry on ion association is examined by comparing the 1–3 predictions with those for 1–1, 1–2, and 2–2 model electrolytes with the same Debye screening length.

Raman spectra of poly(propylene oxide) (PPO) complexed with LiClO4 and NaCF3SO3, respectively, reveal the presence of both ion pairs and solvated ions. The amount of dissociated and paired ions has been calculated using a two‐component band analysis of the ν1(A1) anion vibration. The degree of dissociation is approximately constant in the low concentration range of monomer (i.e., oxygen) repeating unit to salt ratio O:M=1000–30. For larger concentrations, it gradually decreases with increasing salt content. Association constants for the two systems are estimated from the concentration quotients at low salt contents using the Debye–Huckel theory. Extrapolation to zero concentration indicates a dissociation minimum at concentrations lower than O:M=1000. Large and positive values of ΔS0 (100±40 and 120±40 Jmol−1 K−1 for PPO–NaCF3SO3 and PPO–LiClO4, respectively) are obtained for the ‘‘free’’ ion–ion pair equilibria, which may reflect the increasing configurational freedom of polymer chains upon forming ion p...

A simple estimating formula is derived for rate coefficients of three-body ion atom association in gases and compare its predictions to experimental data on ion association and three-body radiative charge transfer reactions of singly- and doubly-charged rare-gas ions. The formula appears to reproduce most experimental data quite well. It may be useful for estimating the rates of reactions that have not been studied in the laboratory.

Tailoring the nature of individual segments within ion containing block co-polymers is one critical design tool to achieve desired properties. The local structure including the size and distribution of the ionic blocks, as well as the long range correlations, are crucial for their transport ability. Here, we present molecular dynamics simulations on the effects of varying the concentrations of the ionizable groups on the conformations of pentablock ionomer that consist of a center block of ionic sulfonated styrene tethered to polyethylene and terminated by a bulky substituted styrene in dilute solutions. Sulfonation fractions f (0 ≤ f ≤ 0.55), spanning the range from ionomer to polyelectrolytes, were studied. Results for the equilibrium conformation of the chains in water and a 1:1 mixture of cyclohexane and heptane are compared to that in implicit poor solvents with dielectric constants e = 1.0 and 77.73. In water, the pentablock collapses with the sulfonated groups on the outer surface. As f increases, the ionic, center block increasingly segregates from the hydrophobic regions. In the 1:1 mixture of cyclohexane and heptane, the flexible blocks swell, while the center ionic block collapses for f > 0. For f = 0, all blocks swell. In both implicit poor solvents, the pentablock collapses into a nearly spherical shape for all f. The sodium counterions disperse widely throughout the simulation cell for both water and e = 77.73, whereas for e = 1.0 and mixture of cyclohexane and heptane, the counterions largely condense onto the collapsed pentablock.

We show that in the framework of the Poisson-Nernst-Planck model, where the ions are assumed point-like particles, the dielectric constant of the electrolyte coincides with that of the solvent in which the ions are dispersed. Only in the case where the ions are considered polarizable particles, their presence can contribute to the effective dielectric constant of the electrolyte and can play a role in the non-linear version of the Poisson-Nernst-Planck model. From this observation, it follows that generalizations of the linear Poisson-Nernst-Planck model in which the dielectric constant of the solution is considered depending on the ionic distributions are questionable.

The long-known observations that dc conductivity sigma(dc) of an ultraviscous liquid varies nonlinearly with the dielectric relaxation time tau, and the slope of the log sigma(dc) against log tau plot deviates from -1 are currently seen as two of the violations of the Debye-Stokes-Einstein equation. Here we provide a formalism using a zeroth order Bjerrum description for ion association to show that in addition to its variation with temperature T and pressure P, impurity ion population varies with a liquid's equilibrium dielectric permittivity. Inclusion of this electrostatic effect modifies the Debye-Stokes-Einstein equation to log(sigma(dc)tau)=constant+log alpha, where alpha is the T and P-dependent degree of ionic dissociation of an electrolytic impurity. Variation of a liquid's shear modulus with T and P would add to the nonlinearity of sigma(dc)-tau relation, as would a nonequivalence of the shear and dielectric relaxation times, proton transfer along the hydrogen bonds, or occurrence of another chemical process. This is illustrated by using the data for ultraviscous acetaminophen-aspirin liquid.

In this Response, answers are given, respectively, to the questions raised in the Comment by Buchner et al. [J. Chem. Phys.(to be published)]. We believe that, in the analysis of vibrational spectra in the liquid phase, dynamic viewpoints are necessary in order to fully understand their band shapes.

The “dynamic exchange” model of ion association proposed by Watanabe and Hamaguchi, [J. Chem. Phys.123, 034508 (2005)] for aqueous solutions of MgSO4 is shown to be inconsistent with the extensive information available from Raman, relaxation, and thermodynamic studies, all of which can be explained by the Eigen equilibrium model.

A new perspective is shown on the interaction between the sulfate ion and its counter cation in aqueous solutions. We propose the dynamic exchange model of ion association instead of the conventional static equilibrium model. The concentration dependence of the Raman band shape of the totally symmetric (a(1)) SO stretch mode of the sulfate ion is investigated systematically for four sulfate ions, MgSO(4), (NH(4))(2)SO(4), K(2)SO(4), and Li(2)SO(4). The concentration dependence of the a(1) Raman band shape in the MgSO(4) system is successfully reproduced by the analysis based on the dynamic exchange model. As a result, quantitative information about the extremely dynamic nature of the ion association has been obtained: the mean time between associations is a few picoseconds and the mean lifetime of association is several hundred femtoseconds.

The sticky electrolyte model (SEM) is solved analytically in the mean spherical approximation (MSA) for binding between oppositely charged ions of a symmetrical electrolyte at a distance L=σ/4 and σ/5, where σ is the atomic diameter, extending earlier analytic studies for L=σ, σ/2, and σ/3. The excess energy of a fluid of dipolar dumbbells of elongation L

In this paper, molecular‐structure data derived from recent quantum‐chemical studies are used in conjunction with the Mandel–Mazur theory of the static dielectric constant to estimate the importance of intermolecular polarization contributions to the static dielectric constant of water. A scalar expression for the static dielectric constant is identified and then investigated via a multibody decomposition in which the effects of 2‐, 3‐, ... n‐body interactions are displayed and then analyzed numerically. Our main conclusion is that the intermolecular polarization contribution is of crucial importance in determining the static dielectric constant of water. Further, our calculations show that the predicted dielectric constant is extraordinarily sensitive to the geometry of the first hydration shell; thus, the use of a slightly inaccurate potential function may lead to a predicted dielectric constant in significant disagreement with the experimental value.

The method of molecular dynamics is applied to a solvent‐averaged model of electrolyte solutions, described by a generalized Langevin equation. For Brownian motion without solute–solute interactions, we recover the characteristic features of an infinitely dilute solution. For interacting brownons, the results exhibit a noticeable dependence of the calculated self‐diffusion coefficients on the influence of the Coulomb forces. The model system exhibits ion association when the Coulomb forces are made strong enough.

We extend an earlier analytic study of a sticky electrolyte model (SEM) to the case L=σ/3, where L is the distance at which positive and negative ions bind to each other, using the hypernetted chain (HNC) approximation within the spherical core and the mean spherical approximation (MSA) outside. We also present numerical solutions to the HNC approximation alone for σ/3 ≤L≤σ/2. The average number of bonded pairs is found to be essentially the same for the two approximations but the ion–ion correlation functions are very different except at high concentrations when the shielding is large. Small amounts of tetramers are also observed in the HNC correlation functions for σ/3

The sticky electrolyte model in a dipolar solvent is studied in this paper. A detailed separation of the Ornstein–Zernike (OZ) equations and their solution in the mean spherical (MS) approximation for binding (or stickiness) at L=σ are given. The results derived earlier by Adelman and Deutch, Blum et al. and by Ho/ye et al. in this approximation are reproduced when the stickiness is switched off. Also when the density of the solvent goes to zero, the results reduce to those of the sticky electrolyte model (SEM) in a continuum solvent. It is found that the PY/MS approximation gives negative solutions for the association parameter λ, while the HNC/MS approximation works in a narrow interval of the sticky potential well depth e2 between the positive and negative ions. As expected, the ion association increases when sticky potential well becomes deeper, but the dipole moment of the solvent is found to have a strong screening effect on this association. The study of the radial distribution functions of this sy...

In an earlier study of the reactions (1) COH++CO+H2=(CO)2H++H2 and (2) N2H++N2+H2=(N2)2H++H2 it was observed that (1) was much faster than (2). On theoretical grounds the reactions are expected to have similar rates. A closer investigation of the reactions reveals that over a wide temperature and concentration range the products (CO)2H+ [respectively, (N2)H+] are not formed by the normal three body reaction but by a parallel sequence (the chaperone sequence), i.e., COH++2H2=COH3++H2 followed by COH3++CO=(CO)2H++H2 for the COH+ case. Significantly, for a wide range of conditions the chaperone complex COH3+ (respectively, N2H3+) is at too low concentrations to be detected, and the rate law is the same as that for the direct three body reactions. Unraveling the kinetics of the reactions led to determination of the rate constants for the direct and chaperone reactions.

The β coefficients in the equation T1−1—T10−1=Σβscs, which represents the nuclear relaxation rate of 23Na+ in dilute aqueous solutions at 25° as a function of solute molarity, have been determined for a variety of ionic solutes and separated into cationic and anionic contributions. For many species β is simply expressed in terms of viscosity and volume effects. Large additional contributions to β are found for a group of symmetrical, singly charged oxy and fluoro anions of which ClO4=, studied in the previous paper, is typical. The same is true for ions such as SO4= and PO4−3 for which extra interaction (such as association) with Na+ has been deduced from other types of measurements. For some solutes, including sucrose, nonlinear contributions to T1−1 dominate at concentrations as low as 0.2M. In the case of SO4= the observed nonlinearity may be attributed to ion association, in which case a dissociation constant (molar scale) of 0.2, in agreement with the result of Davies may be deduced from the data if ...

The molar activity coefficients of uni‐univalent electrolytes may be predicted on the basis of conductivity data with an accuracy of at least 1 percent up to concentrations of the order of 0.01 M in solvents of dielectric constant as low as 10. The method is based on Bjerrum's theory of ion association,1 with the ion pair dissociation constant evaluated from conductivity data.4–6 The success of the method depends on the use of expressions for y′, the quasi‐activity coefficient of the dissociated fraction, and for Λ, the equivalent conductivity, which go beyond the limiting law approximations of the interionic attraction theory. Equations (6), (8), (10), (12), and (13) have been developed for this purpose. In solvents of dielectric constant 10–40 the prediction involves no adjustable parameters characteristic of the electrolyte. The equations have been tested by comparing the conductivity‐predictedy values for hydrochloric acid with those determined from emf measurements. To insure the significance of this comparison, new emf data for the cell Pt–H2(g)/HCl AgCl–Ag have been obtained for 82.00 wt percent dioxane (D=10.56) in the concentration range 0.0001–0.01 M.

The Poisson‐Boltzmann equation for a penetrable spherical polyelectrolyte ion in the presence of smaller ions has been solved precisely by numerical integration methods using a high‐speed computer. The polyelectrolyte ion was assumed in one case to be immersed in a sea of simple electrolyte and in another case to be surrounded by an appropriate volume of solution containing only the polyelectrolyte's counter ions. Since the absolute value of the electrostatic potential energy of a small ion in the center of a polyelectrolyte ion is found to be several times kT, the nonlinear differential equation cannot justifiably be rendered linear by the Debye‐Huckel type of approximation. The fraction of the counter ions held within the sphere of the polyelectrolyte ion is calculated from the solution to the differential equation. The extent of such ion association is found, for reasonable values of the molecular parameters, to range between 50 and 75% in substantial agreement with experimental observations based on transference studies. The results of the numerical computations are for the most part presented graphically.

Results of dielectric constant and loss measurements on a range of aqueous and alcoholic electrolytes at wavelengths of 1.25, 3.2, 9.9, 17, and 51.5 cm from 3°C to 25°C are analyzed in terms of dielectric constant depression, relaxation time depression and spread, and conductivity elevation. The small relaxation time spread (α∼0.02) is interpreted as being due to hydrogen bond bending, the relaxation time depression as bond breaking, and the dielectric constant depression as restriction of dipole rotation by the ions. The conductivity elevation is believed to be an effect of the same type as that observed by Little and Smith.It is shown that the alcohol dielectric constant depression is too large to be interpreted in terms of dipole restriction by solvation so that the ion must have a marked effect on the alcohol structure.

New equations for the excess sound absorption per wavelength and the relaxation frequency have been derived. These equations are derived on the assumption that a dissociation process of the type (AB)⇌(A)+(B) is irreversibly perturbed by the sound field due to assumed pressure dependence of the equilibrium. These equations are applied to the problem of excess sound absorption in dilute magnesium sulfate solutions.By using mixtures of dioxane and water to vary the dielectric constant of the solvent the effect of varying the ion Coulombic interaction forces of the ions in solution has been studied experimentally. This work and the work of other investigators on the excess sound absorption in dilute magnesium sulfate solutions is explained quantitatively.The specific rates of dissociation and ion association for magnesium sulfate in solutions of water and water‐dioxane have been determined. Good agreement is found between values of the mass action equilibrium constant determined by acoustic means and values d...

Measurements of the static dielectric constant and the density of o‐methylanisole, m‐methylanisole, p‐methylanisole, 2,6‐dimethylanisole, and 3,5‐dimethylanisole from 20° to 60°C, are reported. These data are combined with estimates of the limiting dielectric constant at high frequency in order to obtain information about the interaction of a dipolar molecule with its neighbors. The dielectric constant and loss at 2‐mm wavelength are also reported. These data are used to provide a partial characterization of the dielectric relaxation. The dielectric constants permit more accurate estimates of the high‐frequency dielectric constants than possible previously.

The effect of the addition of ``inert'' salts on ionic reaction rates is discussed. For reactions between ions of the same charge sign, the effect is caused almost exclusively by the concentration and character of salt ions of charge sign opposite to that of the reactants. The rate is not dependent upon the ionic strength of the solutions. In reactions between ions of opposite charge sign, both salt ions may affect the rate, but the effect of one type may be dominant. The effects are quantitatively interpretable in terms of an ion association constant and specific rate constants for the associated and non‐associated reactants. The further introduction of activity coefficients is not necessary. The reactions upon which the Livingston Diagram is based have been explored from this viewpoint and found to be in quantitative accord.

The electrical contribution to the chemical potential of an ion having an arbitrary charge distribution is calculated with the aid of the Debye‐Huckel theory. The calculation is based upon a general solution in polar coordinates of the approximate Debye‐Huckel equation, Δψ—κ2ψ=0. In addition, the Born relation between the free energy of solvation of a spherical ion and the dielectric constant of the solvent, is generalized to include ions of arbitrary charge distribution. Application of the theory to a study of the influence of simple electrolytes, and of the dielectric constant of the solvent on the solubilities of the aliphatic amino‐acids in alcohol water mixtures, is discussed.

The conductance of LiI has been measured in p‐dioxane—water mixtures at 25° over the composition range 0%—95% dioxane. The data were analyzed using the Fuoss—Onsager theory to give Λ0, aJ, and KA parameters. Although aJ remains constant over the whole composition range, the Walden product decreases monotonically. Both the Stokes radius and the association constant show markedly different behavior in the range over 80% dioxane.

The Np(V)—Np(VI) electron exchange reaction has been found to be independent of the composition and of the gross properties, dielectric constant, refractive index, viscosity, etc., of two mixed solvents. To account for these phenomena, the critical complex is assumed to consist of a region containing the reactant ions and the solvent component of highest dielectric constant. This component preferentially solvates the ionic reactants. In this region, complete dielectric saturation is also assumed.

(13s) - 2.918 890 - 2.943 038 - 2.968178 (13s7p)/[13s2p] - 2.932 810 - 2.974135 - 2.978 528 (13s7pld)/[ 13s2pld] - 2.933 063 - 2.977 655 - 2.978 668 H+b 3 (13s) - 1.280604 - 1.311 589 - 1.324986 (13s3p)/[ IOs1p] - 1.300052 - 1.336955 - 1.343357 (13s3p)/[10s2p] - 1.300052 -1.340628 - 1.343500

The separation between the isotropic and the anisotropic component of some Raman bands of polar molecules is studied as a function of concentration in different solvents. It is found that it depends linearly on the ratio between the volume fraction and the static dielectric constant of the solution, and becomes zero at a finite concentration. It is suggested that this concentration threshold is related to the relaxation time of the vibrational energy. An explanation is proposed for the observed dependence on the dielectric constant.