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:

s=s_{0}(1c)
where s_{0} is the initial sticking probability and c is the coverage.
Similarly, when molecules adsorb on surfaces dissociatively, the sticking probability is

s=s_{0}(1c)^{2}
Although these equations are simple and can be easily understood, they cannot explain experimental results. Their simple explanation is not enough.
In 1958, P. Kisliuk^{[1]} presented an equation that can explain experimental results. In his theory, molecules are trapped in precursor states (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

desorb from the surface (pd: probability)

move to the next precursor state (pm: probability)

adsorb on the surface chemically (pa: probability)
and if these sites are occupied, they

desorb from the surface (pd': probability)

move to the next precursor state (pm': probability)
Then the sticking probability is

s=s_{0}(1+cK/(pa+pd)1

(K=pd'/(pa+pd))
When K=1, this equation equals Langmuir's adsorption isotherm.
Notes

^ Kisliuk, Paul (1957). "The sticking probabilities of gases chemisorbed on the surfaces of solids". Journal of Physics and Chemistry of Solids 3: 95–101.
References

The constitution and fundamental properties of solids and liquids. part i. solids. Irving Langmuir;
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