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A quantum mechanical theory of energy exchanges between inert gas atoms and a solid surface

Published online by Cambridge University Press:  24 October 2008

J. M. Jackson
J. M. Jackson
Affiliation:
Trinity College
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Extract

The interaction between gas atoms and solid surfaces has been studied experimentally for many years. The first detailed study of the nature of this interaction was perhaps due to Knudsen, who in his classical researches introduced the idea of the accommodation coefficients for energy or momentum exchanges between gas atoms and a solid surface, when the gas atoms and the solid are at different temperatures or possess different mass motions. Knudsen and other investigators have given numerical values for these accommodation coefficients for various gases and solid surfaces, which seem to indicate that the accommodation coefficients are never small and are often of the order unity. This means that the gas molecules before reflection accommodate themselves almost completely to equilibrium with the temperature or motion of the wall. Before the recent work of Roberts referred to below, which has inspired this paper, no special precautions had been taken in the preparation of the wall surface, and as we now know the walls used by all previous investigators must have been completely covered with at least a mono-molecular film of gas. Thus the old observations of the accommodation coefficient do not determine it under precise conditions, and find in fact a value many times larger than that found by Roberts for the energy exchanges between the gas and a clean tungsten surface. For helium and metal with a dirty surface the value of the accommodation coefficient is some 6 times as large as the true value for the clean surface. The older values of the coefficients were so large that there were apparently grave difficulties in the way of any simple theory, but this is so no longer.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 1 , January 1932 , pp. 136 - 164
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

* Roberts, J. K., Proc. Roy. Soc., A, vol. 129, p. 146 (1930).CrossRefGoogle Scholar

† Lennard-Jones, and Dent, , Trans. Faraday Soc., vol. 24, p. 92 (1928)CrossRefGoogle Scholar; also Fowler, R. H., Statistical Mechanics, Ch. x, pp. 261–3.Google Scholar

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* Roberts, personal communication.

* §§ 2 and 3 have been developed from some MSS. notes by Mr R. H. Fowler, in which he suggested the model of a solid surface used in the present paper and in which he showed how might be calculated.

† This method of calculating transition probabilities has been given in greater detail by Born, , Zeitschrift für Physik, vol. 58, p. 306 (1929)CrossRefGoogle Scholar. The validity of the method is discussed by Dirac, , Quantum Mechanics, § 54, pp. 169–171.Google Scholar

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* Aldis, S. W., Proc. Roy. Soc., vol. 64, p. 219 (1898)CrossRefGoogle Scholar; also Watson, G. N., Bessel Functions, Table II, p. 698Google Scholar; and Jahnke-Emde, , Funktionentafeln, Table 14, p. 135.Google Scholar

* Fowler, R. H., Statistical Mechanics, Ch. XVII, pp. 431–36.Google Scholar

* It is readily found that the number of gas atoms crossing unit area in unit time inside the attractive potential step is

in the limit T 1 → T 2 → T. This corresponds to an adsorbed gas density N(e Φ/(kT) − 1). We see that this result is independent of the quantum transition by which it is reached. It is the adsorbed gas density which we should expect when we consider a simple adsorption theory in which there is no upper limit to the density of adsorbed gas on the surface.

† Physikalische Zeitschrift, vol. 11, p. 609 (1910).Google Scholar

* 1 electron volt = mean energy of gas atoms, at temperature T = 7740°K.

* See note, p. 162.

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