INFLATED VESICLES - A LATTICE MODEL

A three-dimensional vesicle model on the cubic lattice with fixed surface area N subject to an internal pressure increment p greater-than-or-equal-to 0 is analyzed using a Monte Carlo method and finite size scaling. At the branching point p = 0, the conformations are of branched-polymer-like structures and the mean volume and the mean-square radius of gyration vary as [V(b)] approximately [R(b)2] approximately N. In the large-inflation scaling regime, 100 < pN < 20N1/2, the surface of the vesicle is stretched with [V+]2/3 approximately [R+2] approximately N(nu+)p2omega and nu+ almost-equal-to 6/5 and omega = 1/5. The Pincus-Fisher stretching exponent is chi almost-equal-to 1/3. At the crumpling point x(c) = p(c)N almost-equal-to 100, separating the branched and the stretched regime, the conformations are crumpled with [V(c)]2/3 approximately [R(c)2] approximately N(nuc) and nu(c) almost-equal-to 4/5. The transition between stretched and crumpled conformations is continuous, whereas the transformation between branched and crumpled shapes is discontinuous. The various regimes are discussed in terms of simple Flory-type arguments.