TUNABLE FRACTAL SHAPES IN SELF-AVOIDING POLYGONS AND PLANAR VESICLES

The shapes of self-avoiding continuum and lattice polygons of N monomers in a plane are studied using Monte Carlo simulations and exact enumeration. To model vesicles, a pressure increment p=pin-pout, is included. For N1 and p=0, the usual universal fractal shapes appear; but for p 0, continuously variable fractal shapes are found controlled by the variable xpN2 where =1/DF=3/4. Thus, the ratio of principal radii of gyration (x)=RG,min2/RG,max2 changes smoothly from (+)=1, for circles, through (0) 0.39, to (-) 0.23, which corresponds to branched polymers. © 1990 The American Physical Society.