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

A Monte Carlo 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){∝}(l/L)^γeff-1exp(-l/L), with an effective exponent γeff, reflecting the crossover from dilute to semidilute regime. Beyond the crossover density φ* the distribution function gradually reduces to a purely exponential form C(l,T)={φ}/L²exp(-l/L) known from mean-field approximation treatments. In the case of numerical simulation the determination of φ* can be done by seeking the maximum of γeff.