A dispersion of PMMA spheres at is left undisturbed for one year at and shows no…
PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Non-equilibrium statistical mechanics and stochastic thermodynamics
Soft Matter at the Thermal Scale, Ch Brownian particles, sedimentation and the hard-sphere fluid
Problem
A dispersion of PMMA spheres at ϕ=0.60 is left undisturbed for one year at 298K and shows no Bragg reflections throughout; it remains amorphous. Particle tracking by video microscopy over the same year shows each sphere rattling inside the cage of its neighbours, with no long-time diffusion through the sample. A colleague argues: "The equilibrium phase diagram for hard spheres says the stable state between freezing (ϕ=0.494) and melting (ϕ=0.545) is a fluid-crystal mixture, and above ϕ=0.545 it should be a crystal, right up to close packing. Since this sample has not crystallised after a year, either the equilibrium phase diagram is wrong at high ϕ, or these spheres are not really behaving as hard spheres." Explain what is wrong with this reasoning, and state what actually determines whether a hard-sphere dispersion at ϕ=0.60 reaches its equilibrium crystal within a given observation time.