## Collectiive Properties of Adsorption-Desorption Processes

### P. L. Krapivsky and E. Ben-Naim

A reversible adsorption-desorption parking process in one dimension is
studied. An exact solution for the equilibrium properties is
obtained. The coverage near saturation depends logarithmically on the
ratio between the adsorption rate, $\k_+$, and the desorption rate,
$\k_-$, \hbox{$\req\cong 1-1/\log(k_+/k_-)$}, when $\k_+\gg\k_-$. A
time dependent version of the reversible problem with immediate
adsorption ($k_+=\infty$) is also considered. Both heuristic arguments
and numerical simulations reveal a logarithmically slow approach to
the completely covered state, \hbox{$1-\rho(t)\sim 1/\log(t)$}.

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