Raymond M. Fuoss

Anomalous Dispersion and Dielectric Loss in Polar Polymers

A theory of dielectric loss of polar polymers at high dilution in a nonpolar plasticizer is developed. The theory leads to a broad distribution in relaxation times, associated with the internal rotatory Brownian motion of the hydrocarbon chain. An approximate relation between the degree of polymerization, the frequency of maximum loss, and the viscosity coefficient of a polar plastic is obtained. The loss factor is calculated from the theoretical relaxation time distribution for a mono‐disperse polymer and for a poly‐disperse polymer with an exponential distribution in chain length. The theoretical loss factor is compared with the experimental loss factor of polyvinyl chloride plasticized with diphenyl. The agreement with experiment is semi‐quantitative.

Conductance in isodielectric mixtures. III.i-butyronitrile with chlorobenzene,o-dichlorobenzene,p-dichlorobenzene, 1,2-dichloroethane, andn-pentanol

The conductance of tetrabutylammonium tetraphenylboride, picrate, perchlorate, and nitrate has been measured at 25°C in mixtures ofi-butyronitrile with chlorobenzene,o-dichlorobenzene,p-dicholorobenzene, 1,2-dichloroethane, andn-pentanol covering the range of dielectric constants 10≤D≤20. In these mixtures of polar solvents, both association constants and ionic mobilities depend on ion-solvent interaction energies and on free volume in a manner that is specific for each system. This failure of the primitive model (rigid charged spheres in a continuum) is shown to be the consequence of short-range spatial and energetic interactions between ions and adjacent solvent molecules.

Conductance of potassium lodide in mixed solvents

The conductance of potassium iodide has been measured in the solvents ethylene carbonate, water, methyl ethyl ketone, and pairwise mixtures of these solvents at 40°C; and ethylene carbonate-water, tetramethylene sulfone-water, dimethyl sulfoxide-water, tetrahydrofuran-water, ethylene carbonate-tetramethylene sulfone-water, ethylene carbonate-tetramethylene sulfone, and tetrahydrofuran-dimethyl sulfoxide at 25°C. For dielectric constants greater than about 60, the pairing constants KA are in the range 0.3–2.0; no correlation between KA and solvent properties could be established. For lower dielectric constants, KA increases exponentially with decreasing dielectric constant. Addition of a proton, acceptor to water initially decreases KA regardless of whether the dielectric constant of the mixture is higher or lower than that of water, suggesting that ion pairs in water may be stabilized by cage structures. The Walden product Aoη is also decreased by the addition of proton acceptors.

Review of the theory of electrolytic conductance

The Ostwald dilution law, based on the Arrhenius hypothesis of electrolytic dissociation, was the first theoretical formulation of the dependence of conductance on concentration. While it adequately described the conductance of weak electrolytes, it could not account for the observation by Kohlrausch that, at low concentrations, the equivalent conductance Λ of strong electrolytes approached linearity inc1/2, the square root of concentration. Debye and Hückel (1923) assumed complete dissociation and calculated the theoretical behavior of rigid charged spheres moving in a continuum (the primitive model); the result was prediction of the Kohlrausch result. Onsager (1927) predicted the exact numerical value of the limiting slope for the Λ vs.c1/2 curves. Bjerrum (1926) suggested association of ions to pairs which would not contribute to the long-range interionic effects considered by Debye and Hückel. Fuoss and Kraus (1933) corrected the Ostwald dilution law for the DHO square-root terms and obtained a Λ(c) function which satisfactorily accounted for conductance curves which lay below the limiting tangent. Investigations of the effects of higher terms which had been neglected in the classical DHO treatment of the primitive model led to Λ(c) functions which lay above the limiting tangent for completely dissociated electrolytes. By combining these higher-term equations with Bjerrum pairing, a generally useful conductance function was obtained (Fuoss-Hsia, 1957). In order to eliminate a number of inconsistencies between the properties of real systems and those of the primitive model, a new model (Fuoss, 1975) was proposed: Ion pairs are defined as those whose center-to-center distance lies in the rangea≤r≤R, whereR is the diameter of the Gurney cosphere. Later (1977) the paired ions were divided into two categories: ions which have only solvent molecules as nearest neighbors, and ions which have one ion of opposite charge as a member of the inner shell. The latter contribute only to charging current.

Conductance in isodielectric mixtures. II.i-butyronitrile with benzene, carbon tetrachloride, dioxane, and tetrahydrofuran

The conductance of tetrabutylammonium nitrate, perchlorate, and picrate and of tetraethyl-, tetrapropyl-, and tetrabutylammonium tetraphenylborides has been measured at 25°C ini-butyronitrile and in mixtures of this solvent with benzene, carbon tetrachloride, dioxane, and tetrahydrofuran, covering the range of dielectric constants 10–23.81. The association constant for a given salt is the same in isodielectric mixtures ofi-butyronitrile with the nonpolar liquids; association is greater at a given dielectric constant for the mixtures with tetrahydrofuran. Single-ion mobilities are specific for any ion-solvent combination and therefore cannot be described in terms of the radius of an equivalent sphere and the bulk dielectric constant and viscosity of the solvent.

Conductance in isodielectric mixtures. I.n-butyronitrile with dioxane, benzene, and carbon tetrachloride

The conductance of tetrabutylammonium tetraphenylboride, picrate, nitrate, and bromide has been measured at 25°C inn-butyronitrile and in mixtures of this solvent with dioxane, benzene, and carbon tetrachloride covering the range of dielectric constants from 10–24.26. For the picrate, nitrate, and bromide, the association constants at a given dielectric constant are independent of the chemical composition of the solvent. The changes of Walden products with solvent composition, however, are different, depending on which other solvent is mixed with the butyronitrile.

Association constants for ion pairs

The isodielectric rule is a corollary of the theoretical equation KΛ=(4πNa3/3000) exp (e2/aDkT) derived for primitive model electrolytes. Real systems, especially those involving small ions in structured solvents, do not follow the rule because energies of short range system-specific interactions contribute to Δg, the difference in free energy between paired and unpaired ions. Δg=−kT ln (KΛ/Vm), where VM is the molar volume (in liters) of the solvent. The thermodynamic constant Ka=ap/(a±)2, where ap is the Lewis activity of the pairs and a± that of cation and anion; for ideal solutes, activity=mole fraction. Incidentally, ln KΛ calls for an undefinable operation: only pure numbers have logarithms.

Ion pairing of quaternary salts in solvent mixtures

Conductances at 25.00°C are reported for the following systems: tetrabutylammonium bromide in dimethyl sulfoxide-acetone mixtures (Bu4NBr in Me2SO−Me2CO); tetraphenylphosphonium bromide (Ph4PBr) in water Me2SO, Me2CO, and in the mixtures H2O−Me2SO, Me2SO−Me2CO and Me2CO−H2O; Ph4PCl in Me2SO, Me2CO, H2O−Me2SO, and Me2SO−Me2CO; and tetrapropylammonium bromide (Pr4NBr) in Me2SO and Me2CO. The data were analyzed using the Fuoss 1978 equation which is based on the coupled equilibria: (unpaired ions)⇌(solvent-separated pairs)⇌(contact pairs). The conductimetric pairing constantKA=KR(l+Ks) is the product of two factors:KR, which describes the first (diffusion controlled) equilibrium andKs=exp(−Es/kT), which describes the second (system-specific) equilibrium. Ions with overlapping cospheres (of diameterR) are defined as paired: their center-to-center distancer lies in the rangea≤r≤R; contact pairs (r=a) are ions which have one ion of opposite charge as a nearest neighbor, all other nearest and next nearest neighbors being solvent molecules. The quantityEs is the difference in free energy between the states defined byr=R andr=a. For the Me2SO−Me2CO systems,Es is positive for solutions in Me2SO and decreases through zero to negative values as the fraction of the less polarizable acetone increases. For solutions in waterEs is also positive. On addition of Me2SO or Me2CO,Es initially increases, goes through a maximum, and then decreases to negative values as the fraction of the less polarizable component increases. The decrease is an electrostatic effect, common to all the systems. The initial increase inEs appears when the small water molecules surrounding solvent-separated pairs are replaced by organic molecules which have greater volumes than water.

The conductance of lithium-7 fluoride in dioxane-water mixtures at 25°C

Conductance data for lithium-7 fluoride in dioxane-water mixtures covering the range 78.35>D>36 in dielectric constant are presented. These data and other previous data on lithium-7 chloride and lithium-7 iodide were analyzed by the Fuoss 1980 conductance equation in order to find the limiting conductance Δo, the pairing distance R and the conductometric association constant Kλ. Setting Ka=Kλ/VM (where VM is the molar volume of the solvent), the thermodynamic pairing constant and the corresponding change of the free energy Δg were calculated. Correlation among the values found for R and Δg=Δh−TΔs and the properties characteristic of the ions and solvents are discussed.

Ion pairing in solutions of sodium tetraphenylborate

AbstractConductance data are presented for sodium tetraphenylborate (NaBPh4) in three solvent systems: water-dimethyl sulfoxide, water-acetone, and acetone-dimethyl sulfoxide. These and other data from the literature were first analyzed by the three-parameter equation Λ′=Λ0+Aτ2+Bτ3, where