Growth of living polymers in a good solvent

Conformation space renormalisation group theory is applied to study the size distribution of living or self-assembling polymers in good solvents. In dilute solution the aggregate size distribution is found to be of the Schulz-Zimm type. It crosses over to an (almost) exponential distribution in the semi-dilute regime. The growth exponent, describing the power law dependence of the mean aggregate size on the concentration, changes from α = ½ − (1/16) in dilute to α = ½ + (1/16) in semi-dilute solution, to first order in = 4 − d with d ⩽ 4 the dimensionality of space.