Sticking probability
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: formula_1 where formula_2 is the initial sticking probability and formula_3 is the surface coverage fraction ranging from 0 to 1. Similarly, when molecules adsorb on surfaces dissociatively, the sticking probability is formula_4 The square is owing to the fact that 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 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): and if these sites are occupied, they Note that an occupied site is defined as one where there is a chemically bonded adsorbate so by  definition it would be formula_10. Then the sticking probability is, according to equation (6) of the reference, formula_11 formula_12 When formula_13, this equation is identical in result to Langmuir's adsorption isotherm.