Self-assembly and dynamics of freely-jointed emulsion polymers

We present the self-assembly process of emulsion polymers, which differ from colloidosomes, or colloidal polymers, in that they are flexible and deformable. When two emulsion droplets labeled with complementary DNA meet, the balance of DNA hybridization energy and droplet deformation energy yields an equilibrium patch size\footnote{Feng \textit{et. al}. (2013). Soft Matter, 9(41).}. Varying the concentration of DNA allows us to tune the number of droplet-droplet bonds to assemble dimers, polymers, or even cross-linked networks. A random combinatoric model for picking binding partners, given an input valency distribution, is in quantitative agreement with the statistics of the observed droplet configurations, suggesting the system achieves the steady-state limit. Under tailored assembly conditions, we find that ~96\% of droplets assemble into either linear or branched polymers. Analyzing the dynamics of only the linear chains, we find that they are freely-jointed and that the end-to-end length fluctuations follow the 2D Flory model of polymer scaling. These polymers are then collapsed into compact clusters via secondary interactions, allowing us to monitor the distribution of folded structures for a given chain length $N$.