  Limited-valency colloidal particles can self-assemble into polymeric
structures analogous to molecules. While their structural equilibrium
properties have attracted wide attention, insight into their dynamics has
proven challenging. Here, we investigate the polymerization dynamics of
semiflexible polymers in two dimensions (2D) by direct observation of
assembling divalent particles, bonded by critical Casimir forces. The
reversible critical Casimir force creates living polymerization conditions with
tunable chain dissociation, association and bending rigidity. We find that
unlike dilute polymers that show exponential size distributions in excellent
agreement with Flory theory, concentrated samples exhibit arrest of rotational
and translational diffusion due to a continuous isotropic-to-nematic transition
in 2D, slowing down the growth kinetics. These effects are circumvented by
addition of higher-valency particles, cross-linking the polymers into networks.
Our results connecting polymer flexibility, polymer interactions and the
peculiar isotropic-nematic transition in 2D offer insight into polymerization
processes of synthetic two-dimensional polymers, and biopolymers at membranes
and interfaces.
