  An important goal of self-assembly is to achieve a preprogrammed structure
with high fidelity. Here, we control the valence of DNA-functionalized
emulsions to make linear and branched model polymers, or `colloidomers'. The
distribution of cluster sizes is consistent with a polymerization process in
which the droplets achieve their prescribed valence. Conformational dynamics
reveals that the chains are freely-jointed, such that the end-to-end length
scales with the number of bonds $N$ as $N^{\nu}$, where $\nu\approx3/4$, in
agreement with the Flory theory in 2D. The chain diffusion coefficient $D$
approximately scales as $D\propto N^{-\nu}$, as predicted by the Zimm model.
Unlike molecular polymers, colloidomers can be repeatedly assembled and
disassembled under temperature cycling, allowing for reconfigurable, responsive
matter.
