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Gray, Peter (1962) A contribution to the study of linear dissipative processes in liquids on the basis of relaxation times. Doctoral thesis, Sir John Cass College.
Kirkwood has shown that, under certain circumstances, the action of single molecules in a liquid obeys the Langevin equation. The expression for the friction constant which he obtained resembles an expression which can be derived from the conventional theory of Brownian Movement. This resemblance is analysed by means of the conventional theory, and a criterion is established which indicates the conditions under which the two expressions are the same. It is pointed out that Kirkwood’s hypothesis that the autocorrelation integral of the total force acting on a molecule possesses a non-zero plateau value is inconsistent with dynamical principles, however. His method is reformulated in such a way that it leads to explicit expressions for non linear contributions to the dissipative term in the Langevin equation. It is found that the dissipative term is linear if the previously established criterion is satisfied. An attempt is made to construct a simple, qualitatively satisfactory, statistical mechanical theory of liquid transport processes, in which the pair distribution function satisfies a relaxation equation. This model is found to correspond closely to the small-step diffusion model of Rice and Kirkwood, and also has a close connection with the theory of rigid sphere fluids. Good order of magnitude agreement is obtained with experimental data for the transport coefficients of liquid argon. The average molecular velocity is found to satisfy a second order linear differential equation in general, and satisfies the Langevin equation only in the special case that the mass of the diffusing particle is large compared to the mass of a liquid molecule. The diffusive motion of a molecule in liquid argon has, according to the empirically determined values of the friction constant and the relaxation time, the nature of a quasi-random walk in steps of average length 0.25Å, the motion for each step being oscillatory.
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