The sticking probability is the probability that molecules are trapped on surfaces and adsorb chemically. From Langmuir's adsorption isotherm, molecules cannot adsorb on surfaces when the adsorption sites are already occupied by other molecules, so the sticking probability can be expressed as follows:

${\displaystyle S=S_{0}(1-\theta )}$

where ${\displaystyle S_{0}}$ is the initial sticking probability and ${\displaystyle \theta }$ is the surface coverage fraction ranging from 0 to 1.

Similarly, when molecules adsorb on surfaces dissociatively, the sticking probability is

${\displaystyle S=S_{0}(1-\theta )^{2}}$

The square is because a disassociation of 1 molecule into 2 parts requires 2 adsorption sites. These equations are simple and can be easily understood but cannot explain experimental results.

In 1958, P. Kisliuk^[1] presented an equation for the sticking probability that can explain experimental results. In his theory, molecules are trapped in precursor states of physisorption before chemisorption. Then the molecules meet adsorption sites that molecules can adsorb to chemically, so the molecules behave as follows.

If these sites are not occupied, molecules do the following (with probability in parentheses):

1. adsorb on the surface chemically (${\displaystyle P_{a}}$)
2. desorb from the surface (${\displaystyle P_{b}}$)
3. move to the next precursor state (${\displaystyle P_{c}}$)

and if these sites are occupied, they

1. desorb from the surface (${\displaystyle P_{b}'}$)
2. move to the next precursor state (${\displaystyle P_{c}'}$)

Note that an occupied site is defined as one where there is a chemically bonded adsorbate so by definition it would be ${\displaystyle P_{a}'=0}$. Then the sticking probability is, according to equation (6) of the reference,^[1]

${\displaystyle S=S_{0}\left(1+{\frac {\theta }{1-\theta }}K\right)^{-1}=S_{0}{\frac {1-\theta }{1+(K-1)\theta }}}$

${\displaystyle K={\frac {P_{b}'}{P_{a}}}+P_{b}}$

When ${\displaystyle K=1}$, this equation is identical in result to Langmuir's adsorption isotherm.

• The constitution and fundamental properties of solids and liquids. part i. solids. Irving Langmuir; J. Am. Chem. Soc. 38, 2221-95 1916 Langmuir, I. (1916). "The Constitution and Fundamental Properties of Solids and Liquids. Part I. Solids". Journal of the American Chemical Society. 38 (11): 2221–2295. doi:10.1021/ja02268a002.