We study the conformation and scaling properties of a self-avoiding fluid membrane, subject to an osmotic pressure $p$, by means of Monte Carlo simulations. Using finite size scaling methods in combination with a histogram reweighting techniques we find that the surface undergoes an abrupt conformational transition at a critical pressure $p^ast$, from low pressure deflated configurations with a branched polymer characteristics to a high pressure inflated phase, in agreement with previous findings cite{gompper,baum}. The transition pressure $p^{ast}$ scales with the system size as $p^ast propto N^{-alpha}$, with $alpha = 0.69 pm 0.01$. Below $p^ast$ the enclosed volume scales as $V propto N$, in accordance with the self-avoiding branched polymer structure, and for $psearrow p^{ast}$ our data are consistent with the finite size scaling form $V propto N^{beta_{+}}$, where $beta_{+} = 1.43 pm 0.04$. Also the finite size scaling behavior of the radii of gyration and the compressibility moduli are obtained. Some of the observed exponents and the mechanism behind the conformational collapse are interpreted in terms of a Flory theory.
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