N. B. Slater

Aspects of a theory of unimolecular reaction rates

A uniform gas of polyatomic molecules is treated as an assembly of classical vibrating systems, which dissociate when one internal co-ordinate q reaches a critically high value qo which is related to the dissociation energy E0. The unimolecular velocity constant at temperature T is found to be K = v exp (— EJkT), where the ‘frequency factor’ v lies in the range of molecular vibration frequencies. The factor v may be interpreted (i) as a weighted average of the noi nal vibration frequencies, or (ii) as the ratio of the product of the normal frequencies to the product of the frequencies with q fixed, or (iii) in the case where dissociation is due to the rupture of an isolated bond, as the vibration frequency of an imaginary diatomic molecule consisting merely of the two bonded atoms connected by the original bond-force. The dissociation rate is formulated in several ways, which represent different aspects of the physical picture. The main contrast is between (a) the rate as the average frequency with which the normal-mode vibrations come sufficiently into phase to carry q to the critical value q0, and (b) ‘transition state’ formulations, giving the rate as the product of the relative concentration of activated complexes (molecules with q near q0) and the mean transition frequency. The mathematical equivalence of these methods is shown by a study of the asymptotic distribution of values of sums of harmonic vibrations. The present model is used to illustrate some concepts of transition state or activated complex theory, such as the ‘effective mass’ in the reaction co-ordinate, and the partition function of the activated complex. The relation of the model to Kassel’s theory is shown by calculating the dissociation rates of molecules of specified total energy.

GASEOUS UNIMOLECULAR REACTIONS: THEORY OF THE EFFECTS OF PRESSURE AND OF VIBRATIONAL DEGENERACY

A theory which gave the high-pressure unimolecular reaction rate as K8 = v exp ( — E0/kT) is extended to find the decline of rate with pressure; the gas molecule is again a classical vibrating system which dissociates at a critical extension of an internal co-ordinate. The general rate K is found to be approximately... where n is the effective number of normal modes of vibration; d is proportional to pT~^n, but depends also on the molecular structure and size. For n < 13, this integral is tabulated, and the pressures at which the rate declines from first order are estimated. The pressure tends to decrease as n increases; for E0/k T ~ 40, it is estimated that only molecules with six or more atoms should show rates approaching KCX) at normal pressures. The table of K/K;a is not carried as far as the ‘bimolecular’ range, but a precise technique is developed for this region. The theory is compared with Kassel’s classical theory of a molecule of s ‘oscillators’. The lowpressure activation energy, and the shape of the curve of log K against log p, are similar in the two theories if n = 2s — 1; the absolute values of p for a given rate are also roughly comparable. Two results are proved, for the present severely classical model, concerning special cases. (i) A pair or triplet of degenerate modes with equal frequencies counts as one in assessing ‘n’ for the general rate K. (ii) If the dissociation co-ordinate q relates atoms ml, and mx is replaced by an isotope m*, the high-pressure rate changes in the ratio d{m1(m*+ m2)/m^(m1+m2)}; for this, the internal potential energy V need not be quadratic, nor need q be isolated in V from other co-ordinates.

On Two-Server Poisson Queues with Two Types of Customers

This paper considers two schemes for a steady-state queue with two types of customers served by two desks, the customers arriving mixed in a Poisson stream and having negative-exponential service-time distributions, with different means characterizing the two types of customers. In Scheme I each type has a particular desk, for which he queues on arrival. In Scheme II all customers keep in a single queue and proceed indifferently to either desk. Numerical remits indicate that Scheme II reduces mean queue size and queuing times, generally with advantage to both types of customers.

Cubic Potential Surfaces in the Transition‐State Theory of Unimolecular Reactions

The frequency factor of a unimolecular dissociation rate is enhanced if the molecular vibrations are loosened during the approach to the activated state; this loosening may be regarded as affecting the partition function or entropy in the nonreactive degrees of freedom. These ideas are illustrated here in terms of cubic potential surfaces, with examples of linear molecules and of the effect of freeing an internal rotation. As a more general but related point, the uniqueness of the reaction coordinate of transition‐state theory is discussed with some reference to isotope effects.

Eddington's Fundamental Theory

Alrthur Stanley Eddington (1882–1944) has an unassailable reputation as a founder of astrophysics. His work on the combination of relativity and quantum theory and on the calculation of physical constants has a less secure reputation, but is likely to prove of equal pioneer importance. In sketching the genesis and development of this work in its historical setting, I shall perhaps overemphasize the importance of numbers in physics ; this is because interest has been attracted to Eddingtons theory mainly by his calculated numbers.