Karl F. Herzfeld

Vibrational Relaxation Times in Gases (Three‐Dimensional Treatment)

The calculations previously made by Schwartz, Slawsky, and Herzfeld are extended to three dimensions. As before, an exponential repulsion is fitted to the Lennard‐Jones potential, with constants found from viscosity data. While the transition probability is determined directly by the short range repulsion forces, the attractive forces and the effect of the centrifugal quasi‐potential modify the effective velocity of the colliding molecules. The agreement with experiment is fairly good, although high up on the repulsion curve (O2,N2) the Lennard‐Jones 6—12 curve seems to be not quite steep enough.

Gas Bubbles with Organic Skin as Cavitation Nuclei

The hypothesis discussed that the cavitation nuclei consist in gas bubbles. Due to surface tension, small bubbles would dissolve in a very short time. If the bubbles are larger than 5×10−3 cm, or if the liquid is supersaturated, they may last longer or even be stable, but then no cavitation threshold exists.The hypothesis expressed that the nuclei are very small bubbles, stabilized by an organic skin, which mechanically prevents loss of gas by diffusion. The cavitation occurs when the skin breaks and the threshold is determined by the breaking strength of the film and the size of the bubble.

Deactivation of Vibrations by Collision in the Presence of Fermi Resonance

The rate of vibrational deactivation by collision of polyatomic molecules is discussed. Previous calculations for CO2 by the author are corrected. A systematic method to find the steric factor in complex collisions is proposed, and the best procedure for evaluation of such collisions is discussed. Mixture of vibrational wavefunctions may increase the rate appreciably, particularly in the presence of Fermi resonance. The agreement with experiment is good for the deactivation of the transversal vibration and for the effect of CO2 admixture on O2 deactivation, but the experimental rate of deactivation of the asymmetric longitudinal CO2 vibration is much greater (60 to 90 times) then the calculated one.

On the States of Aggregation

The problem of investigating systematically the possible states of aggregation has not yet been attacked. It has been approached here in the hope of getting a deeper insight into the nature of the liquid state. After a discussion of the general methods, a simplified one‐dimensional model is introduced. It was possible to find the exact equation of state. However, it turned out that in this case a single (gaseous) state exists. This is due to the presence of aggregates of all sizes. It is found that the existence of at least one condensed state is possible only if the change in free energy that occurs when an atom is added to a large aggregate is higher than the change that occurs in the addition of this atom to a small molecule. No progress could be made in the understanding of the liquid state.

On the Theory of Energy Exchange in Liquids by Isolated Binary Encounters

Litovitz and Herzfeld have given reasons for the belief that the exchange of internal vibrational and of external energy in Kneser liquids is determined by isolated binary encounters. Fixman and Zwanzig have raised objections against their calculations, Fixman by introducing Brownian motion type forces, Zwanzig by emphasizing the interference between subsequent events. The present paper tries to show that these objections are not justified in most cases.

On the Absorption Spectrum of Some Polymethine Dyes

The energy levels of certain polymethine dyes are calculated approximately. The dyes consist of a chain of conjugated double bonds, with end groups which might or might not differ from each other. Ions and neutral molecules are treated. The calculations are performed both with the valence bond method (resonance between different structures) and the LCAO method, but without antisymmetrization and without taking electronic interaction into account. The effect of chain length and of the nature of the end groups is discussed.

The Origin of the Absorption of Ultrasonic Waves in Liquids

It seems now experimentally certain that the absorption of sound waves in water, benzene, carbon tetrachloride and methyl alcohol is strictly proportional to the square of the frequency up to 50 megacycles, but considerably larger than can be explained by viscosity and heat conduction. It is shown here that an explanation of this increased absorption by slowness of energy exchange between internal and external degrees of freedom is not in disagreement with the facts for the three last named liquids, while the absorption in water must have a different origin.

The Mechanism of Some Chain Reactions

The effect of the new values of the heats of activation on the mechanism of the ethane decomposition is discussed. A modification of the original scheme has been put forward by Kuchler and Theile which is examined here in detail.

An Attempted Theory of Photosynthesis

An attempt is made to explain quantitatively many observations described in the literature on the photosynthetic production of oxygen in its dependence on light intensity, time of irradiation, etc. Four photochemical steps and two dark reactions are assumed, in which among others, a peracid, formic acid and a peraldehyde occur. These are the same intermediate compounds as in auto‐oxydation processes, so that the similarity between these two inverse processes is striking. Light saturation is explained by back chain reactions initiated by photolytical decomposition of the per‐compounds. The agreement between observations and calculations is good. The picture gained for the photosynthesis of CO2 can be applied in the same way for that of plant acids but the plant acids can also be photooxidized in a reaction sensitized by chlorophyll.

The Origin of the Ultrasonic Absorption in Liquids. II

Excess absorption in nonassociated liquids has been explained by the same mechanism as is responsible for molecular absorption in gases, namely, slow exchange of energy between internal and external degrees of freedom.In this paper the rate of energy exchange is calculated for benzene and found to be three times too rapid. The Lennard‐Jones interaction potential and model of the liquid are used; the fourth‐order terms in the interaction provide the coupling between internal vibrations and Debye waves.