 
Summary: Clustering of Binary ColloidalSuspensions: Theory
JUN LIU, WAN Y. SHIH, RYOICHI KIKUCHI, AND ILHAN A. AKSAY
Department ofMaterials Science and Engineering and Advanced Materials Technology Center,
Washington Technology Centers, University of Washington, Seattle, Washington 98195
Received November 3, 1988;accepted May 23, 1989
Recent experiments on binary colloidal suspensions have shownthat particles of the first kind (e.g.,
alumina) can be induced to flocculateby the presenceofparticlesofthe second kind (e.g.,polyacrylate),
within a certain range of the density of the second species of particles. This is similar to the depletion
flocculation and depletion stabilization of polymercolloidal systems. We have thoroughly examined
the binaryparticlesystemswithnumericalsimulations(Monte Carlo)aswellaswithanalyticalequilibrium
calculations [cluster variation method (CVM)]. The simulations show a peak in the flocculation rate
as the number density of the second speciesparticles is varied, in agreement with the experiments. The
CVMcalculationsshowa monotonic increasein clustersizeasthe particle2 densityisincreased.Moreover,
the simulations show an aging phenomenon at high particle 2 densities, i.e., the growth of the cluster
sizein the initially restabilized region, which has also been wellobservedin the experiment. We further
show from freeenergy calculations that the flocculated state, including the seeminglyrestabilizedstate
at high particle 2 densities, is metastable and the underlying thermodynamically stable state is phase
separation. Therefore,the restabilizationat highparticle2 densitiesisdue to kinetics,namelythe slowdown
in particlemovements,but not to thermodynamic reasons.Our calculationstogetherwiththe experiments
on binary colloids may shed some light on the understanding of polymercolloidal systems. © 1991
