Microgel crystals

The phase behavior of charged, soft microgel suspensions is profoundly influenced by ions. In the colloidal-liquid state, despite particle charge, hard sphere models often describe the structure well; counterions guarantee electroneutrality, and their associated osmotic pressure can cause microgel deswelling, renormalizing the suspension volume fraction. At high particle-number densities, colloidal crystals form. By analyzing vibrational modes accessed through confocal microscopy, we construct dispersion relations via the equipartition theorem, fit them to a dynamical matrix, and extract inter-particle force constants. From the long-wavelength limit, we derive crystal elastic constants and find that the Cauchy relation, indicative of central interactions, is violated. This indicates a metal-like behavior suggesting that ions delocalize within the suspension, presumably in our case for entropic reasons, altering inter-particle interactions in non-trivial ways, and ultimately confirming the role of the ions in contributing to the suspension osmotic pressure and crystal elastic properties.