Direct Determination of the Phase Diagram of a Depletion-Mediated Colloidal System

Depletion is one widely used potential to modulate colloidal interaction because it enables the production of a wide variety of crystalline and glassy phases of spherical and shape-tailored colloids. The attractive depletion potential gives rise to qualitatively new behavior. However, depletion-mediated phase behaviors have never been systematically investigated experimentally regarding pair potentials for aqueous suspensions. In this work, we implement three distinct phases of fluid, crystal, and glass by adjusting the concentrations of depletant and salt in the aqueous suspension of polystyrene particles. To define the phase boundary between the fluid and crystal, we calculate pair potential with a superposition of van der Waals, electrostatic, and depletion interactions. Two unknown parameters in the pair potential─the concentration of ionic impurities and the ratio of the molar concentration of depletant to osmolarity─are experimentally determined from sets of reflectance spectra. The interparticle spacing in the crystalline phase is extracted from the peak wavelength originating from Bragg diffraction, which corresponds to the interparticle separation at energy minimum in the pair potential. The boundary between the fluid and crystal is well defined with the depth of the energy well of 3k_BT. By contrast, the onset of glass formation is better characterized by not the well depth but the assembly rate, which is estimated from the slope of the pair potential from force balance. Glasses are produced as the speed exceeds 300 μm/s. That is, crystals are produced by enthalpy gain overwhelming entropy loss, whereas glasses are kinetically produced due to fast jamming.