  We compute the desorption rate of icy mantles on dust grains as a function of
the size and composition of both the grain and the mantle. We combine existing
models of cosmic ray (CR) related desorption phenomena with a model of CR
transport to accurately calculate the desorption rates in dark regions of
molecular clouds. We show that different desorption mechanisms dominate for
grains of different sizes, and in different regions of the cloud. We then use
these calculations to investigate a simple model of the growth of mantles,
given a distribution of grain sizes. We find that modest variations of the
desorption rate with grain size lead to a strong dependence of mantle thickness
on grain size. Furthermore, we show that freeze-out is almost complete in the
absence of an external UV field, even when photodesorption from CR produced UV
is taken into consideration. Even at gas densities of $10^4$ ${\rm cm^{-3}}$,
less than 30\% of the CO remains in the gas phase after $3\times 10^5$ years
for standard values of the CR ionization rate.

Astrophysics of Galaxies