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Superlattice formation of the type AB in an adsorbed layer

Published online by Cambridge University Press:  24 October 2008

T. S. Chang
T. S. Chang
Affiliation:
Fitzwilliam HouseCambridge
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Extract

The possibility, pointed out in a previous paper, of superlattice formation in an adsorbed layer when the adsorbed atoms tend to repulse each other is developed in detail. Both Bragg and Williams's approximation and Bethe's approximation are used, but restricted to superlattices of the type AB. In a range of θ, the fraction of surface covered, a superlattice is found to be possible. Bragg and Williams's approximation shows further that the state with the lowest free energy is the one with a superlattice when the latter is possible. Rough kinetic expressions are also given. The equations derived from the principle necessary to preserve equilibrium are found to reduce to those of detailed balancing, and they also agree with the formula obtained statistically. As expected, all the corresponding results obtained from the two methods become the same when the number of nearest neighbours of a site approaches infinity, provided that the product of this number and the interaction potential of two adsorbed atoms occupying two neighbouring sites remains finite.

The only significant result is the large value of the slope of isotherms (the rate of change of the pressure with respect to the fraction of adsorption) when there is a nearly complete superlattice.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 35 , Issue 1 , January 1939 , pp. 70 - 83
Copyright
Copyright © Cambridge Philosophical Society 1939

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References

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* Some of these results are exactly those given in the previous paper. We may point out that in that paper, the second formula on p. 236 should be

the extra ½(z − 2) x 2/z 2(x 2 − 1) being a misprint. The long-distance order S on p. 231 should be defined as half so much, and the two subsequent formulae should be divided on the right-hand side by 2 and 4 respectively. The curves are unaffected.

* Benton, and White, , J. Amer. Chem. Soc. 52 (1930), 2325CrossRefGoogle Scholar; 53 (1931), 2807, 3301.

† Allamand, Burrage and Chaplin, Discussion of Faraday Society, January, 1932; Allamand, A. J. and Chaplin, , Proc. Roy. Soc. 130 (1930), 197.CrossRefGoogle Scholar