Kenneth G. Lawrence

Transition state treatment of the relative viscosity of electrolytic solutions. Applications to aqueous, non-aqueous and methanol + water systems

A transition-state treatment of the relative viscosity of electrolyte solutions is described. The following expression is found for the viscosity B-coefficient: B=(text-decoration:overlineV°1–text-decoration:overlineV°2)/1000 +text-decoration:overlineV°1[(Δµ°[graphic omitted]2–Δµ°[graphic omitted]1)/1000 RT]. text-decoration:overlineV°1 and text-decoration:overlineV°2 are the partial molal volumes of the solvent and solute respectively; Δµ°[graphic omitted]1 is the activation energy for viscous flow of the solvent, and Δµ°[graphic omitted]2 the “ionic activation energy” at infinite dilution.For aqueous solutions, at 25°C, the term (text-decoration:overlineV°1–text-decoration:overlineV°2)/1000 accounts completely, in the case of ammonium chloride, and partially in the case of potassium, rubidium and caesium chlorides, for the negative sign of the B-coefficient. When solutions in different solvents are compared, the well-known tendency for B to increase with text-decoration:overlineV°1 is at least partly explained by the form of the above expression; changes in µ°[graphic omitted]2 from water to methanol, for example, are less dramatic than changes in B. B-coefficients in the methanol + water system are consistent with a maximum in solvent structure around 20% methanol (w/w) at 25°C; whilst the µ°[graphic omitted]2-values support this interpretation, it is noted that solvent structure can influence B twice over, in µ°[graphic omitted]2 and (trivially) in µ°[graphic omitted]1.

Relative viscosities and quasi-thermodynamics of solutions of tert-butyl alcohol in the methanol–water system: a different view of the alkyl–water interaction

Viscosity B coefficients for tert-butyl alcohol (TBA) in water, methanol and mixtures of the two have been obtained at 25 and 35 °C. Hence solute contributions to the activation parameters for viscous flow of the solutions have been calculated, as well as the Gibbs energy, enthalpy and entropy of transfer from the ground-state solvent to the hypothetical viscous ‘transition-state solvent’. The enthalpies of mixing of the two transition-state solvents and their relative partial molar enthalpies L′1 and L′2 are also given.In water, B is large and positive and dB/dT large and negative; in methanol B is small and dB/dT near zero. The classical explanation of these observations, which is solely in terms of water–water (1,1) interactions in an ‘iceberg’ around the alkyl group, is inconsistent with the Compensation Principle because B is proportional to a Gibbs energy function, and this requires that solute–solvent (3, 1) interactions must determine B.It is proposed that in water the alkyl group occupies a ‘cage’ in which the strength of the bonding with respect to the pure solvent is of minor importance. The ‘caging’ of the alkyl group enhances its van der Waals interactions with its nearest neighbours. The expected dependence of such interactions on distance leads to energy–reaction coordinate diagrams in the form required to explain the inversion in sign of the solvation energies from ground-state solvent to transition-state solvent in highly aqueous media.These results are consistent with, though independent of, recent structural studies by neutron diffraction with isotopic substitution.

The viscosity and structure of solutions. Part 1.—A new theory of the Jones–Dole B-coefficient and the related activation parameters: application to aqueous solutions

For many years the lowering of the viscosity of water by certain electrolytes has been attributed to the action of their ions in breaking down its special three-dimensional structure. In this paper, the familiar viscosity B-coefficients for the alkali-metal chlorides in aqueous solutions and the related ionic molar contributions to the free energy, enthalpy and entropy of activation, namely Δµ°[graphic omitted]3, Δtext-decoration:overlineH°3 and ΔS°[graphic omitted]3, are re-examined. Particular attention is paid to the nature of the solvent in the transition state.The application of the compensation principle is first explored. If compensation between enthalpic and entropic contributions from solute-induced structural changes occurs in both ground- and transition-state solvents, Δµ°[graphic omitted]3, and hence B cannot by influenced by changes in the structure of the solvent of the type proposed, say, by Frank and Wen. Instead it is suggested that, in aqueous solution, an ion can coordinate more solvent molecules in the more weakly bonded transition-state solvent than in the ground-state solvent. This is particularly important for solutions containing the larger alkali-metal and halide ions, whose enhanced fluidity thus stems not from solvent–solvent bond-breaking in the ground state, but from ion–solvent bond-making in the transition state. Even if the compensation principle is not accepted, this explanation removes structurel changes in the solvent as a unique explanation of the observed trends in B-coefficients.

Ionic viscosity B coefficients in dimethyl sulphoxide at 25, 35 and 45°C

The relative viscosities of solutions of lithium, rubidium and caesium bromides, sodium chloride, sodium tetraphenylborate and tri-isopentylbutylammonium tetraphenylborate in dimethyl sulphoxide have been measured at 25, 35 and 45°C thus making, with earlier work, a complete study of the alkali metal halides, with the exception of fluoride. Ionic viscosity B coefficients for the alkali metal and halide ions have been obtained, as well as the transition state parameters for viscous flow.

Ionic contributions to the viscosity B coefficients of the Jones–Dole equation. Part 5.—Acetonitrile

The B coefficients of the Jones–Dole viscosity equation are a measure of the size of the ions and of the interaction between the ions and the solvent. The B coefficients have been determined for the electrolytes Bu4NBu4B, Bu4NBr, Bu4NI, Ph4PBr, Ph4PI, NaI and NaPh4B, and for the homologous series from Et4NBr to Hept4NBr in acetonitrile at 25 and 35 °C. Ionic B values for the bromide and iodide ions have been calculated from the B coefficients for the tetra-alkylammonium solutions and are compared with those obtained from the tetraphenylphosphonium solutions. The transition-state treatment has been applied to the results, and the thermodynamic activation parameters for viscous flow have been calculated. These are compared with those found previously for solutions of dimethyl sulphoxide, hexamethylphosphoric triamide and N,N-dimethylformamide, and are discussed in terms of the new theory of B coefficients proposed by Feakins.

The viscosity and structure of solutions. Part 2.—Measurement of the B coefficient of viscosity for alkali-metal chlorides in propan-1-ol–water mixtures at 25 and 35 °C

Measurements of the B coefficients of viscosity in the Jones–Dole equation ηr= 1 +Ac½+Bc are reported for the alkali-metal chlorides in the propan-1-ol–water system at 25 and 35 °C; they extend to 85%(w/w) propanol for Cs+Cl– to 70%(w/w) propanol for Na+Cl– and K+Cl– and 30%(w/w) propanol for Li+Cl–. Photoelectric timing and high-precision density measurements were used in determining the relative viscosities, ηr, of the solutions. Conductivity measurements of intermediate precision gave values of the limiting equivalent conductivities of the electrolytes for use in the calculation of A, above. To 50% alcohol, the equivalent conductances of the ions could be established accurately using transport numbers from another investigation. To 30% alcohol the Jones–Dole equation was obeyed by all the electrolytes except Li+Cl–, where an additional term Dc2, with small positive values of D, was required. For mixtures containing 50%(w/w) alcohol or more, the Jones–Dole equation was of the correct form to represent the ηr, but the values of A required were larger than the theoretical ones; the conductivity measurements indicated that the electrolytes were associated in these mixtures. The values of the ion-pair dissociation constants, determined from the conductivity measurements, were about those expected from Bjerrum theory; they were used to calculate the degree of dissociation α of the ion pairs. Values of Bi, referring to the free ions, were obtained by fitting the ηr to the equation ηr= 1 +A(αc)½+Biαc+Bp(1 –α)c in which Bp is the corresponding coefficient for the ion pairs. Values of the partial molal volumes of the electrolytes at infinite dilution in the various solvent mixtures were obtained from the density measurements. The densities and viscosities of the mixtures are recorded.

Density, refractive index, viscosity and 1H nuclear magnetic resonance measurements of dimethyl sulphoxide at 2 °C intervals in the range 20–60 °C. Structural implications

The density, refractive index, kinematic viscosity and 400 MHz 1H n.m.r. spectra of pure DMSO have been measured very accurately at two degree intervals in the range 20–60 °C. The measurements were analysed statistically to detect marked changes in these physical properties that might indicate a liquid structural transition temperature previously suggested to occur between 40 and 60 °C. Over the temperature range studied it was found that the measurements of density and refractive index varied linearly with temperature, whereas smooth, curved plots were obtained for measurements of kinematic viscosity and 1H n.m.r. chemical shifts with temperature. There is no evidence from these results that the intermolecular-association structure of DMSO breaks down over the temperature range studied.

The viscosity and structure of solutions. Part 3.—Interpretation of the thermodynamic activation parameters for propan-1-ol–water–electrolyte systems

The molar contributions of the electrolyte Δµ⊖≠3, Δtext-decoration:overlineH⊖≠3 and Δtext-decoration:overlineS⊖≠3 to the activation parameters for viscous flow of the ternary systems propan-1-ol-water–electrolyte are analysed in terms of the new approach given in the first part of this series. The thermodynamic activation parameters for the binary solvent system are first briefly discussed. The excess enthalpy for the transition state is calculated and resolved into the corresponding partial molar enthalpies; these functions are compared with the corresponding ground-state functions. The thermodynamics and quasi-thermodynamics are consistent with the retention of an aqueous structure as propanol is added to water, up to a volume fraction ϕ2 of ca. 0.25, followed by a breakdown to a structure of lower order. The mean entropy of activation Δtext-decoration:overlineS≠12 passes through a maximum at ϕ2 of ca. 0.25 and is taken as a measure of the extent to which the transition-state mixtures are in turn broken down with respect to the ground state. Minima in Δµ⊖≠3 near ϕ2≈ 0.25 are observed for all the salts at both temperatures. In solvents having an aqueous type of structure, coordination of the ions is incomplete in the ground state but increases in the less strongly bonded transition state; the increase in coordination is a maximum and Δµ⊖≠3 a minimum when the transition-state mixed solvent is most broken up with respect to the ground-state solvent. The minima are least pronounced and at lowest ϕ2 for the chloride of the strongly coordinating Li+. For ϕ2 > 0.25 the Δµ⊖≠3 increase to the values characteristic of typical non-aqueous solvents, in which ground-state coordination is complete and formation of the transition state is characterised by breaking rather than making ion–solvent bonds. The enthalpies of transfer of the electrolytes in the transition state, ΔH⊖′t, are related to the thermodynamics of the transition-state solvent by the theory of de Valera, Feakins and Waghorne. Though crude, the approach shows why the minima in Δtext-decoration:overlineH⊖≠3, unlike those in Δµ⊖≠3, occur at widely different ϕ2 for different electrolytes, and demonstrates the power of considering the special properties of the solvent in the transition state.

The thermodynamics of solvation of ions. Part 3.—The heat capacity for solvation of gaseous ions in methanol at 298.15 K

Literature values of the standard partial molar heat capacities of 1:1 electrolytes in methanol have been divided into ionic contributions using the assumption that [graphic omitted]. Combination with Cop values for gaseous ions then leads to single-ion values for the solvation of gaseous ions in methanol, ΔsolvCop. These latter values are then broken down into a neutral term N, an electrostatic term E and a configurational term C. It is shown that the above single-ion division leads to configurational single-ion quantities that agree well with other single-ion parameters. Using this division, all the inorganic cations and anions can be regarded as structure-makers that decrease the fluidity of the solvent. The tetra-alkylammonium ions are also structure-makers, but exhibit ‘solvophobic solvation’, analogous to, but quantitatively much smaller than, the corresponding hydrophobic hydration in water.

Separation of viscosity B coefficients into ionic contributions. Part 4.—Extrapolation methods using tetra-alkylammonium bromides in dimethyl sulphoxide and hexamethylphosphoric triamide

Viscosity B coefficients of the Jones–Dole equation have been determined with a high degree of precision for Pr4NBr, Bu4NBr, Pe4NBr, Hex4NBr and Hept4NBr in dimethyl sulphoxide and hexamethylphosphoric triamide at 25 and 35 °C. The B coefficients were plotted as functions of the van der Waals volumes, Stokes radii and formula weights of the cations, and the linear portions of the graphs were extrapolated to the zero value of each property tested. The intercepts thus obtained are discussed and compared with the ionic B(Br–) values reported previously using Bu4NBu4B and Ph4PPh4B as reference salts. The reference-salt method is considered to give the best division into ionic contributions.