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 $N^{ u}$, where $ uapprox3/4$, in agreement with the Flory theory in 2D. The chain diffusion coefficient $D$ approximately scales as $Dpropto N^{- u}$, as predicted by the Zimm model. Unlike molecular polymers, colloidomers can be repeatedly assembled and disassembled under temperature cycling, allowing for reconfigurable, responsive matter.
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