  We study the influence of surface roughness on the adhesion of elastic
solids. Most real surfaces have roughness on many different length scales, and
this fact is taken into account in our analysis. We consider in detail the case
when the surface roughness can be described as a self affine fractal, and show
that when the fractal dimension D_f >2.5, the adhesion force may vanish, or be
at least strongly reduced. We consider the block-substrate pull-off force as a
function of roughness, and find a partial detachment transition preceding a
full detachment one. The theory is in good qualitative agreement with
experimental data.
