Bulk rheology of sticky DNA-functionalized emulsions

We measure by experiment and particle-based simulation the rheology of concentrated, non-Brownian droplet emulsions functionalized with surface-bound single-stranded (ss), ``sticky,'' DNA. In the absence of ssDNA, the emulsion viscosity increases with the dispersed phase volume fraction $\ensuremath{\phi}$, before passing through a liquid-solid transition at a critical ${\ensuremath{\phi}}_{c}$ related to random close packing. Introducing ssDNA leads to a liquid-solid transition at $\ensuremath{\phi}l{\ensuremath{\phi}}_{c}$, the onset being set by the droplet valency $N$ and the ssDNA concentration (or simulated binding strength $\ensuremath{\epsilon}$). Using insight from simulation, we identify three key behaviors: (i) jammed suspensions ($\ensuremath{\phi}g{\ensuremath{\phi}}_{c}\ensuremath{\approx}0.64$) show weak effects of functionalization, with elastic rheology instead governed by droplet stiffness; (ii) suspensions with $\ensuremath{\phi}l{\ensuremath{\phi}}_{c}$ and $N=1$, 2 always exhibit viscous rheology, regardless of functionalization; and (iii) for $\ensuremath{\phi}l{\ensuremath{\phi}}_{c}$ and $Ng3$, functionalization leads to a controllable viscous-elastic transition. We present state diagrams showing the range of rheological tuning attainable by these means.