The quantum mechanical derivation of the physical adsorption isotherm is reviewed and explained. The method starts by making a separation of variables into the direction normal to the surface and parallel to the surface. The normal to the surface is calculated using a Leonard-Jones potential. However, this is not the most important calculation. The wave function in the direction parallel to the surface is model using QM analog of Fuller’s Auto-Shielded Physisorption (ASP) model, that is the adsorbed molecules are treated as a perturbation on the surface, which may be treated as a “particle in the box” with a perturbing energy due to other adsorbate molecules. The derived isotherm equation for a non-porous plane surface has a simple form: θ = ΔχUΔχ where Δχ = χ - χc , χc = -ln(Eads/RT) and χ = -ln(-ln(P/Pvap)) Where U is the unit step function and Eads (&lt; 0) is the energy of adsorption for the first adsorbate molecule. For non-porous surfaces with one Eads a plot of nads, moles adsorbed, versus χ yields the Eads , as the abscissa intercept, and nm, the monolayer equivalent moles from the slope, since θ := nads/nm. Comparisons to “standard adsorption isotherms” will be presented along with experimental evidence of the threshold pressure predicted by this theory. This latter effect is support by Dubinin’s “Thermodynamic criterion” and the isotherms that use this concept, and by the disjoining pressure theory. Additional implications include: For porous adsorbents and surfaces with more than one Eads the plot’s first and second derivative with respect to nads yields the Eads distributions, and both the micropore and the mesopore dimensions and distributions as well as the extermal surface area. The expanded theory in terms of two adsorbates has also been successful in determining the binary adsorption phase diagram with a minimum of measurements.

Quantum mechanical derived description of physical adsorption

256th National Meeting (2018)

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