Size of an inflated vesicle in two dimensions

A two-dimensional vesicle of N monomers of diameter a (or a closed, planar, self-avoiding walk of N links) subject to an internal pressure increment {Δ}p{≥}0 is analyzed. In the large-inflation scaling limit x{∝}{Δ}pa²{N}^{2{ν}}$/${k}BT1, the mean area and mean-square radius of gyration vary as Δ{p}^{2{{ω}}}N^2ν+ with {ω}=(1-{ν})/(2{ν}-1)=1/2 and ν⁺={ν}/(2{ν}-1)=3/2, where {ν}=3/4 is the self-avoiding-walk size exponent. The results are related to Pincus's expression for the size of a stretched polymer chain. Monte Carlo simulations confirm the behavior and yield the corresponding scaling functions.