Fluorescent contacts measure the coordination number and entropy of a 3D jammed emulsion packing

Abstract

Jammed matter is by definition impenetrable to light, rendering the characterization of the 3D geometry difficult. Confocal microscopy of a dyed, refractive index matched emulsion nevertheless allows one to image the jammed system. Here we explain the origin of the mechanism of enhanced fluorescence at the contacts of jammed emulsion droplets in terms of a blue-shifted fluorescence emission band due to the change in the polarity of the interfacial environment. We then use this information to determine the contact network in the emulsion, which models a frictionless jammed system. This enables the experimental determination of the average coordination number, $<Z >$ giving the theoretically predicted value of $<Z > \approx 6$. Furthermore, the method enables the experimental measurement of the entropy of the packing from the network of contacts.