John G. Kirkwood

Statistical Mechanics of Fluid Mixtures

Expressions for the chemical potentials of the components of gas mixtures and liquid solutions are obtained in terms of relatively simple integrals in the configuration spaces of molecular pairs. The molecular pair distribution functions appearing in these integrals are investigated in some detail, in their dependence upon the composition and density of the fluid. The equation of state of a real gas mixture is discussed, and an approximate molecular pair distribution function, typical of dense fluids, is calculated. Applications of the method to the theory of solutions will be the subject of a later article.

The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics

The equations of hydrodynamics—continuity equation, equation of motion, and equation of energy transport—are derived by means of the classical statistical mechanics. Thereby, expressions are obtained for the stress tensor and heat current density in terms of molecular variables. In addition to the familiar terms occurring in the kinetic theory of gases, there are terms depending upon intermolecular force. The contributions of intermolecular force to the stress tensor and heat current density are expressed, respectively, as quadratures of the density and current density in the configuration space of a pair of molecules.

The Dielectric Polarization of Polar Liquids

An extension of the Onsager theory of dielectric polarization is presented. The local dielectric constant is approximated by the macroscopic dielectric constant of the fluid in a region outside a molecule and its first shell of neighbors rather than in the entire region exterior to the molecule. In addition to the molecular dipole moment, the average value 〈cosγ〉Av of the cosine of the angle between neighbor dipoles is a determining factor. Hindered relative rotation of neighboring molecules produces a correlation between their orientations and prevents 〈cosγ〉Av from vanishing. The theory is applied to liquid water under the assumption of tetrahedral coordination and directed bonds between neighboring molecules.

Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions

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 Statistical Mechanical Theory of Solutions. I

A general statistical mechanical theory of solutions is developed with the aid of the theory of composition fluctuations in the grand canonical ensemble. It is shown that the derivatives of the chemical potentials and osmotic pressure with respect to concentrations, the partial molar volumes, and compressibility may be expressed in terms of integrals of the radial distribution functions of the several types of molecular pairs present in the solution. Explicit coefficients of a q‐fraction expansion of the thermodynamic variables are presented in a detailed treatment of the two‐component system.

The Statistical Mechanical Theory of Surface Tension

A general statistical mechanical theory of interfacial phenomena is developed and expressions are derived relating the surface tension and other superficial thermodynamic functions to the potential of intermolecular force and molecular distribution functions. On the basis of a reasonable approximation to the superficial density of molecular pairs, the Lennard‐Jones potential and the Eisenstein‐Gingrich radial distribution function, the surface tension, surface energy, and the superficial density of matter, referred to the surface of tension, are calculated for liquid argon at 90°K and compared with experiment. The positive value which is obtained for the superficial density, referred to the surface of tension, confirms the results of Tolmans quasi‐thermodynamic theory and leads to the conclusion the surface tension of small drops decreases with increasing curvature.

Statistical Mechanical Theory of Transport Processes. VII. The Coefficient of Thermal Conductivity of Monatomic Liquids

A molecular theory of the coefficient of thermal conductivity is developed from the general theory of transport processes presented in the first article of this series. The thermal conductivity of liquid argon at its normal boiling point is evaluated using the Lennard‐Jones intermolecular potential and a theoretically determined radial distribution function. The theory leads to an explicit expression for the product of the thermal conductivity and the friction constant of the theory of Brownian motion. With a reasonable estimate of the friction constant, the results of the theory agree satisfactorily with experiment.

On the Theory of Optical Rotatory Power

The Born theory of optical activity in quantum‐mechanical form is simplified with the aid of certain approximations. It leads to a simple expression for the rotatory parameter of an active molecule in terms of the geometrical configuration and the polarizability tensors of its constituent groups. Optical anisotropy of the component groups and inhibited internal rotation are found to play an important role in determining rotatory power. The proposed theory has points of similarity both with the polarizability theories of Gray, de Mallemann, and Boys and also with Kuhns specialization of Borns classical theory of optical activity. To illustrate its use, the absolute configuration and the specific rotation of d‐secondary butyl alcohol are calculated.

The Electrostatic Influence of Substituents on the Dissociation Constants of Organic Acids. II

Bjerrums theory of the influence of substituents on dissociation constants has been extended and amplified. The molecules and ions entering into the ionization equilibria are treated as cavities of low dielectric constant, rather than as structureless regions of the same dielectric constant as the solvent. The theory gives better results than the simple Bjerrum formulation, especially for the short chain dicarboxylic acids, and in the fact that it permits a satisfactory treatment of the influence of dipolar substituents on dissociation constants.

On the Theory of Dielectric Polarization

The polarization of a nonpolar dielectric in a homogeneous field is investigated from a molecular point of view. A statistical calculation of the average local field in a molecule shows that fluctuations in the induced molecular moment give rise to a deviation from the Lorentz field. As a result, small but significant deviations from the Clausius‐Mosotti formula are to be expected. A series expansion for (e—1)v/3 of the following form is obtained (e−1)v/3=P0[1+(1+γ+σ)P0/v+···], where e is the dielectric constant, v the molal volume and P0 the molecular polarization. The coefficients in the corresponding expansion of the Clausius‐Mosotti formula are all equal to unity. The correction γ, arising from translational fluctuations, is about 0.1 for most substances. The correction σ depends upon the optical anisotropy of the molecule and its shape.