Virial expansion of the second layer in physical adsorption. An ab initio calculation for helium on argon crystal

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Abstract
A theory of localized and nonlocalized adsorption is given by applying the virial expansion theorem to the second layer. An ab initio calculation of the thermodynamic functions is carried out for the system of helium on an argon crystal. The gas‐solid interaction potential is calculated using lattice summation. The periodic potential along the directions parallel to the solid surface is described by a polynomial φn (x/d)/V0 = 1−[1−(2x/d)2]n within a site spacing d, where V0 is the height of potential barrier and n is an integer to be determined from the minimum potential surface. The values of n used for the first and second layers in the present work are 7 and 4, respectively. The second virial coefficient under the external potential is very well approximated by that of the two dimensional gas in free space. The Boyle temperature is 16.3°K for the system which is close to the experimental temperatures (10–20°K) of Ross and Steele. The deviation from the ideality due to the second virial coefficient is small in the experimental temperature ranges; in the isosteric heat, the contribution coming from the second virial coefficient is less than 10% of the total heat. The theory is in excellent agreement with experiment of Ross and Steele.