Abstract
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.