Mobile DNA linkers mediate the multi-stage melting and valence hierarchy of emulsion droplets

Using single-stranded DNA to mediate the interactions between colloidal particles is a promising approach to program the assembly of functional materials. In contrast to solid particles, liquid droplets offer a unique design space that more closely resembles biological matter due to the mobile nature of the DNA linkers on the surface of the droplets. While the programmability of this type of matter hinges on the ability to turn on and off specific DNA interactions, usually via a temperature protocol, even a qualitative understanding of the effect of mobile linkers on the phase behavior of colloidal droplets is lacking. Here, we systematically probe the effect of the linker properties on the melting transition of DNA-coated PDMS droplets in water. Below the melting transition, the droplets bind via the formation of patches of condensed DNA linkers between the droplet surfaces. By varying the density and sequence of the single-stranded DNA on the droplets’ surfaces, we show that the droplets undergo a multi-stage melting process whereby the droplets with the highest valence (the most patches) melt first and those with fewer patches melt at higher temperatures. This valence-dependent melting hierarchy is due to the distribution of a fixed amount of DNA into different numbers of patches, thereby lowering the binding energy of droplets with more patches. In combination with simulations, we elucidate how the statistics of reversible DNA binding relative to the entropic costs of patch formation underlies these trends.