  Critical lateral pressure for a pore formation and phase diagram of porous
membrane are derived analytically as functions of the microscopic parameters of
the lipid chains. The derivation exploits path-integral calculation of the free
energy of the ensembles of semi-flexible strings and rigid rods that mimic the
hydrophobic tails of lipids in the lipid bilayers and bolalipid membranes
respectively. Analytical expressions for the area stretch/compressibility
moduli of the membranes are derived in both models.
