Quantum Deviations in Two-Dimensional Gases

The second virial coefficient, correct to the fourth power in Planck's constant, is derived for a two-dimensional gas in an external potential field. The molecules of the gas are assumed to interact via either a renormalized (12,6) potential or the Sinanoǧlu–Pitzer (12,6,3) potential, where the inverse cube term accounts for the perturbation of the gas–gas interactions by the field. As the magnitude of the perturbation increases the quantum defects at a given temperature are enhanced. The models are applied to data for CH4, CD4, H2, and D2 on a uniform graphitic surface. The results are inconclusive, since uncertainties in the data for the hydrogens preclude a (12,6,3) analysis for these gases.