LETTER TO THE EDITOR Mean end-to-end distance of branched polymers

Abstract. We use Monte Carlo methods to calculate the mean end-to-end distance of randomly branched polymer molecules. Molecular realisations are brown on the square and simple cubic lattices, and consist of N bifunctional monomers and N, polyfunctional branching units of functionality f. We treat three cases in which the monomer branches are either random walks, self-avoiding walks (saw), or SAW'S except that different branches may join at their end points to form closed loops. For the first case, we find that the mean end-to-end distance L varies with N as L- for fixed branching probability p, consistent with previous theoretical predictions. For the latter two cases we find that for fixed p. L-Nu, where Y = 0.57 i 0.06 on the square lattice and 0.45 *0.06 on the simple cubic lattice. Although the number of closed loops formed per realisation is quite small, it does appear possible that loop formation may play a dominant role in the N+oo limit. An important class of polymer configurations is formed when N bifunctional monomers and Nf polyfunctional branching units of functionality f connect in a random way to form a branched structure (see figure 1). The theoretical treatment of such randomly branched polymer configurations was initiated by Zimm and Stockmayer (1949), wh