Conformations of Polymers with Random Branches of Constant Number in Athermal Isolated Condition

Abstract

Computer simulations were carried out for self-avoiding walk conformations of randomly branched polymers on a simple cubic lattice. The number of segments (N) and branching points (m) are set constant. The maximum N and fi examined are 500 and 5, respectively. No attractive energy among the segments is considered. The standard success-walk number is 100000 for every condition. A critical exponent (v) on N for the root of the mean square radius of gyration ((s 2 ) 1/2 ) is found to be 0.598. This vis the same value as those of both linear and star-branched polymers reported in other papers. The g-values (= s 2 ) branch / linear obtained are nearly equal to those of the random walk in the m-range of this work. Generalization of the conclusion is speculated. v of the case where m distributes statistically is estimated to be 0.35 which is smaller by about 0.1 than that of other randomly-branched polymers. The difference, 0.1, might be attributed to that of the distribution of branching points. The above description assumes the polymers long and flexible.