Collectiive Properties of Adsorption-Desorption Processes

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{$1-\rho(t)\sim 1/\log(t)$}.