Here we consider Langmuir model with its main assumptions:
Adsorption takes place only at specific localized sites on the surface
and the saturation coverage corresponds to complete occupancy of these
sites.
Each site can accommodate one and only one molecule or atom.
The surface is energetically homogeneous, and there is no interaction between
neighboring adsorbed molecules or atoms.
There are no phase transitions.
Next, we derive modified Langmuir adsorption isotherm on the following
additional assumptions:
We assume formation of a few adsorption layers, each layer being
adsorbed on the preceding one according to Langmuir equation. The adsorbed
molecules in one layer can act as adsorption sites for molecules in the
next layer. Clearly then, prior to complete surface coverage the formation
of second and higher layers will commence. This means that, where the surface
is covered with only one layer of adsorbate, an equilibrium exist between
that layer and the vapor, and where to layers are adsorbed, the upper one
is in equilibrium with the vapor, and so forth. Since the equilibrium is
dynamic, the actual location of the surface sites covered by one ore more
layers may vary but the number of molecules in each layer remains constant.
Adsorption energy in the first layer is a constact (E1
= constant) and in the each of the following layers the adsorption
energy En and is equal to the energy of liquefaction
(En = EL).
The effective surface area for a given layer is equal of the surface coverage
of the preceding layer.
