Shape asymmetry of star‐branched random walks and nonreversal random walks

Abstract

AbstractStar‐branched random walks with 3, 4, 6, 8 and 12 arms (the total chain‐length ranging from N = 49 to 1925) have been produced and analysed with respect to their instantaneous shape. The short‐chain behaviour of nonreversal random walk stars (NRRWs) embedded in various lattices is compared to that of star‐branched freely jointed (off‐lattice) chains (RWs). While for all types of NRRW‐stars examined as well as for RW‐stars with bonds of constant length shape‐asymmetry increases with increasing chain‐lengths, the opposite behaviour is found for RW‐stars with Gaussian‐distributed bond‐lengths. The amount of short‐chain effects is strongly dependent on the number of arms and on the lattice type used. In the limit of infinitely large molecules, however, quantities characteristic of the shape converge to common values for all types of RWs and NRRWs examined.