EFFECTS OF POLYDISPERSITY ON HARD-SPHERE CRYSTALS

We use simple models and molecular dynamics simulations to determine t he effects of polydispersity delta on the equation of state for hard s phere crystals. Experiments show that the osmotic pressure for poly-(m ethyl methacrylate) (PMMA) spheres with a poly-(12-hydroxy stearic aci d) (PHSA) layer with a 5% polydispersity exceeds the value expected fo r hard spheres as the volume fraction phi increases, particularly for phi>0.60. Mean field theory predicts a higher osmotic pressure with in creasing polydispersity, but the effects are only significant for delt a>0.10. Molecular dynamics simulations with delta=0.05 bound the equat ion of state between-a metastable disordered upper limit and a crystal line organized polydisperse (possibly) lower limit. The pressure for t he PMMA-PHSA spheres lies close to the organized polydisperse limit, i ndicating a preference, for;a crystalline ordered arrangement where-sm aller particles surround larger ones. Thus, the higher osmotic pressur e seen in the equation of State of PMMA-PHSA spheres isa direct effect of polydispersity, manifest as a pronounced reduction in the crystall ine close packed volume fraction from phi(max)(FCC, delta=0)=0.7404 to phi(max)(FCC, delta=0.1)=0.665. The random close packing phi(max)(RCP ) is almost independent of polydispersity. This leads to a crossing of values of phi(max)(FCC) and phi(max)(RCP) and hence a possible termin al polydispersity of 0.12+/-0.01, consistent with other simulations, t heories, and experiments. Since our results do not include size fracti onation of the liquid and solid, the exact meaning of this crossing is unclear and its agreement with previously reported terminal polydispe rsities may be coincidental. (C) 1998 American Institute of Physics.