S 1-An(1-a)"n
o,r = o0 (A(l1-a)) +a eqn 2.3
The steady-state solution for the entering fractional coverage can be determined by taking
the limit of this function as the number of cycles approaches infinity, given by eqn 2.4.
=01.,in a eqn 2.4
1- (1- a),.
This expression agrees with steady-state expressions developed previously by
Sawyer and Blanchet [17]. The adsorption ratio a can be found from the Langmuir
solution for vapor adsorption, which states that the rate of adsorption is a product of the
adsorption coefficient (v), the gas pressure (P), and the nascent surface area fraction
(1-0).
dO
S= vP(l -) eqn 2.5
dt
From this, the change in fractional coverage for any cycle is given by eqn 2.6, where tcis
the time the element is exposed to the environment between exiting the contact and re-
entry. The adsorption fraction is then given by eqn 2.7.
0,,,, = 1 (- O- ,)e-' eqn 2.6
a=1-e (-v''c) eqn 2.7
The derivation of the adsorption fraction from the Langmuir model can be seen in
Appendix A. Substituting this expression fora into eqn 2.3 and simplifying gives eqn
2.8, which is a cycle-dependent solution for the entering fractional coverage.
O,, = o ("n (e-"P' )) + (1- e-' )1-~(eVP) eqn 2.8