  We have constructed a model for the kinetics of rupture of membranes under
tension, applying physical principles relevant to lipid bilayers held together
by hydrophobic interactions. The membrane is characterized by the bulk
compressibility (for expansion), the thickness of the hydrophobic part of the
bilayer, the hydrophobicity and a parameter characterizing the tail rigidity of
the lipids. The model is a lattice model which incorporates strain relaxation,
and considers the nucleation of pores at constant area, constant temperature,
and constant particle number. The particle number is conserved by allowing
multiple occupancy of the sites. An equilibrium ``phase diagram'' is
constructed as a function of temperature and strain with the total pore surface
and distribution as the order parameters. A first order rupture line is found
with increasing tension, and a continuous increase in proto-pore concentration
with rising temperature till instability. The model explains current results on
saturated and unsaturated PC lipid bilayers and thicker artificial bilayers
made of diblock copolymers. Pore size distributions are presented for various
values of area expansion and temperature, and the fractal dimension of the pore
edge is evaluated.
