Freely Jointed Polymers Made of Droplets

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 statistics reveal that the chains are freely jointed, so that the Kuhn length is close to one bead diameter. The end-to-end length scales with the number of bonds $N$ as $N^{\nu }$, where $\nu \approx 3/4$, in agreement with the Flory theory in two dimensions. 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.

Figure 1

(a) A schematic of the DNA-lipid construct grafted on the droplet. (b) Mixing emulsions with complementary DNA strands leads to their binding to form a trimer. (c) A bright-field image overlayed with a fluorescence image shows adhesions in self-assembled droplet chains. Scale bar is $5\mu \mathrm{m}$.

Figure 2

Bright-field [(a),(b),(c)] and fluorescence [(d),(e),(f)], images of droplet structures show an increase in valence as a function of $C_{\mathrm{DNA}}$. Attaching DNA via fluorescent streptavidin [26] in panels (d),(e),(f) instead of the chemistry described in the main text does not change our results. Scale bars are $5\mu \mathrm{m}$. (g) The number of bonds per droplet $B_n$ increases with $C_{\mathrm{DNA}}$, as shown by the average and the mode of the distributions in the inset.

Figure 3

Distribution of structure sizes for linear chains (a) and all clusters (b) for the indicated given loadings. The solid lines are predictions of the RBM, while dashed lines are the results of a Monte Carlo simulation. The horizontal error bars in (b) indicate monomer bin size.

Figure 4

Evolution of the bond number distribution of a sample as a function of time under the temperature ramp shown in red. The corresponding images of the droplet structures are shown above. Scale bar is $5\mu \mathrm{m}$.

Figure 5

(a) A histogram of the explored angular configurations of 876 trimers, corrected for out of plane motion. Angles above $(\pi /3)$ and below $(5\pi /3)$ are allowed. (b) The measured angular diffusion coefficient for the bond reorganization as a function of the DNA loading density. There is no correlation between DNA loading density and bond viscosity.

Figure 6

Plots of the (a) $R_e$, (b) $R_g$, and (c) $D$, normalized by the diffusion of a single monomer $(0.12\mu {\mathrm{m}}^2{\mathrm{s}}^{-1})$, for linear colloidomers as a function of the number of bonds $N$, where $N+1$ is the number of droplets in the chain. Error bars are the standard error from measurements of many polymers and time points. (a) and (b) are derived from an analysis of 22 096 different polymers, while (c) is derived from an analysis of 7119 polymers. Insets show the scaling relations on a log-log plot.