Physisorption at temperatures below the critical temperature Tc and in the complete wetting regime leads to the development of multilayer adsorption by approaching the saturation pressure Po. The BET theory describes adsorption of the first two or three layers in a satisfying way, but fails to assess correctly the range of the adsorption isotherm, which is associated with the development of thick multilayer films.

Beyond a film thickness of two or three molecular layers, the effect of surface structure is largely smoothed out and close to the saturation pressure the adsorbed layer has a thickness, which allows to consider the adsorbed film as a slab of liquid. It is assumed that here the adsorbed film has the same properties (i.e., density etc.) as the bulk liquid would have at this temperature. This is the basic assumption of the slab approximation, which was first proposed by Frenkel and was later also derived independently by Halsey and Hill. The only modification to its free energy of the adsorbed liquid slab arises from the interaction with the solid, i.e., the adsorption forces (dispersion forces). The interaction energy Us(z) of a gas molecule at distance z from a solid surface is approximately given as

(1)

where Csf is a measure for the strength of attractive fluid-wall interactions and ps represents the solid density.

Within the spirit of the FHH approach, the chemical potential difference between an adsorbed, liquid-like film (Ua) of thickness Z=l and the value (Uo) at gas-liquid coexistence of the bulk fluid is given by

(2)

The more general equation (2) is known as the Frenkel-Halsey-Hill (FHH) equation:

（3）

where a is an empirical parameter, characteristic for the gas-solid interaction. For non-retarded van-der-Waals' interactions (i.e., dispersion forces), one expects m = 3 (as expected from equation (2)). According to equation 3, the FHH-equation predicts that the thickness of a film  adsorbed on a solid surface is expected to increase without limit for    i.e. by approaching P/Po = 1.

(a) Chemical potential difference of an adsorbed film as function of distance z (i.e. film thickness l) from the adsorbent surface. The film thickness diverges by approaching U0. which corresponds to a relative pressure P/Po =1. 

(b) Corresponding adsorption isotherm revealing the diverging of the film thickness (and Vads for P/Po --- 1).

In the case of low temperature adsorption (e.g. adsorption of nitrogen and argon at their boiling temperatures) the adsorption can be analyzed in terms of a two-phase model in which a clearly defined adsorbed phase coexists with a bulk gas phase of low density. In this case the thickness of the adsorbed liquid-like multilayer, L, can be related to the volume Vliq of the adsorbed phase, viz

(4)

where S is the total surface area. Inserting this expression into the equation (3) gives

(5)

The validity of the FHH equation can be tested by plotting loglog (P/Po) against log(Vliq/S) (the classical FHH plot). In the multilayer region of the sorption isotherm a straight line should be obtained; the slope is indicative of Frenkel-Halsey-Hill exponent m. Experimental values usually found for m are often significantly smaller than the theoretical values of 3, i.e., values of m = 2.5-2.7 are found even for strongly attractive adsorbents like graphite, as well as for samples with oxidic surfaces like silica, alumina, rutile etc.. The deviations from the theoretical value m = 3 were often attributed to interparticle condensation, which overlaps with multilayer adsorption, as well as to surface roughness and fractality of the adsorbent surface. In addition it was found that the relative pressure range over which a linear FHH plot is achieved seems to depend on the nature of the adsorbent-adsorbate interaction. Please note also that the FHH theory is only applicable in the regime of high relative pressures, where the assumption that the adsorbate can be considered as slab of liquid with bulk-like properties can be indeed justified.  Accordingly, when the FHH theory is applied to the low or middle range of isotherms the values obtained for m etc. can only be considered as empirical.

The temperature dependence of the FHH-equation was tested by Findenegg and co-workers over a large temperature up to the critical temperature Tc. In the region of higher temperatures and pressures the relative pressure P/Po has to be replaced by the ratio of appropriate fugacities f/f0. The correspondent FHH equation can then be written in the form:  and it could be concluded that the simple FHH equation remains indeed applicable up to nearly the critical point.