Julius L. Jackson

The self-diffusion of ions in a polyelectrolyte solution is investigated both with respect to the average time an ion is associated with a particular polyelectrolyte molecule and with respect to the effect of the electrostatic field of the macro-ions on the macroscopic self-diffusion constant. The results on the macroscopic self-diffusion constant are shown to be generally compatible with experiments on self-diffusion of counterions in polyelectrolyte solutions. On the other hand, the study of the time of association of a counterion with a particular macro-ion yields results which cannot be reconciled with the common interpretation of transference experiments on the same solutions.

The fluctuation-dissipation theorem relating spontaneous equilibrium fluctuations to the conductance in a dissipative thermodynamic system is extended to the case of several variables, using a quantum statistical analysis. The conductance matrix is shown to be subject to certain symmetry relations, providing a generalization of the Onsager reciprocity theorem. The susceptance matrix is also shown to be subject to similar symmetries. The symmetries apply to all frequency components, and hence to arbitrary transient processes.

A general theory of the effective diffusion constant of ions in a periodic electric field is presented. The predictions of the theory are compared with the results of experiments on the diffusion of labeled sodium in a sodium hydroxide—polyacrylic acid solution.

A general statistical mechanical relationship between the chemical potential and the probability distribution function of the micropotential in a fluid at equilibrium is derived. It is applied to a plasma and a hard-sphere gas.