Often molecules do form multilayers, that is, some are adsorbed on already adsorbed molecules, and the Langmuir isotherm is not valid. In 1938 Stephen Brunauer, Paul Emmett, and Edward Teller developed a model isotherm that takes that possibility into account. Their theory is called BET theory, after the initials in their last names. They modified Langmuir's mechanism as follows:
:A + S ⇌ AS,
:A + AS ⇌ AS,
:A + AS ⇌ AS and so on.
The derivation of the formula is more complicated than Langmuir's (see links for complete derivation). We obtain:
where x is the pressure divided by the vapor pressure for the adsorbate at that temperature (usually denoted ), v is the STP volume of adsorbed adsorbate, v is the STP volume of the amount of adsorbate required to form a monolayer, and c is the equilibrium constant K we used in Langmuir isotherm multiplied by the vapor pressure of the adsorbate. The key assumption used in deriving the BET equation that the successive heats of adsorption for all layers except the first are equal to the heat of condensation of the adsorbate.
The Langmuir isotherm is usually better for chemisorption, and the BET isotherm works better for physisorption for non-microporous surfaces.