  Biomimetic membranes in contact with a planar substrate or a second membrane
are studied theoretically. The membranes contain specific adhesion molecules
(stickers) which are attracted by the second surface. In the absence of
stickers, the trans--interaction between the membrane and the second surface is
assumed to be repulsive at short separations. It is shown that the interplay of
specific attractive and generic repulsive interactions can lead to the
formation of a potential barrier. This barrier induces a line tension between
bound and unbound membrane segments which results in lateral phase separation
during adhesion. The mechanism for adhesion--induced phase separation is rather
general, as is demonstrated by considering two distinct cases involving: (i)
stickers with a linear attractive potential, and (ii) stickers with a
short--ranged square--well potential. In both cases, membrane fluctuations
reduce the potential barrier and, therefore, decrease the tendency of phase
separation.
