Scale-free power-law distribution of branched polymers formed in a continuously stirred tank reactor: Simple relationship for the exponent

The high-molecular-weight tail of the molecular weight distribution (MWD) of branched polymers formed via free-radical polymerization involving polymer transfer reactions conducted in a continuously stirred tank reactor (CSTR) follows a power-law distribution. The exponent, alpha, of the weight fraction distribution W(M)similar toM(-alpha) is determined by the P(b) value, which represents the probability that the chain end is connected to a backbone chain, with the simple relationship, alpha=1/P(b). Since alpha>1, the number-average molecular weight will always reach a stationary-state value but the weight-average and higher-order averages of molecular weights may continue to increase without limit under ideal CSTR conditions. Because it takes an infinitely long time for the second or a higher moment of the MWD to go to infinity, the kinetic behaviour is significantly different from usual gelation phenomena. The i-th moment of the MWD goes to infinity for P(b)greater than or equal to1/i.