Monte Carlo study of the molecular-weight distribution of living polymers

Monte CarIo simulation in two dimensions shows that the distribution of chain lengths in a system of living polymers is well described by a Schultz molecular-weight distribution C(l,T)proportional to(l/L)(gamma eff-1)exp(-l/L), with an effective exponent gamma(eff), reflecting the crossover from dilute to semidilute regime. Beyond the crossover density phi* the distribution function gradually reduces to a purely exponential form C(I,T) = phi/L(2)exp(-l/L) known from mean-field approximation treatments. In the case of numerical simulation the determination of phi* can be done by seeking the maximum of gamma(eff).