Volume-fraction dependence of elastic moduli and transition temperatures for colloidal silica gels

Colloidal silica spheres bearing grafted octadecyl chains dispersed in hexadecane undergo a sol-gel transition with decreasing temperature. The gelation temperature depends on the volume fraction φ and, perhaps, the particle size. For φ>${\mathrm{\phi }}_{gel}$(T), the value at the transition, the elastic modulus varies as (φ-${\mathrm{\phi }}_{gel}$ ${)}^{\mathit{s}}$ with the prefactor and exponent independent of temperature. This form resembles prediction from static percolation theories, but the exponent s=3.0±0.5 lies significantly below those expected and the transition volume fraction varies with temperature. The relationship of the gelation transition to dynamic percolation and phase transitions predicted by equilibrium statistical mechanics has also been addressed. Matching the calculated structure factor for adhesive spheres with that measured by static light scattering yields the unknown strength of the interparticle attraction as a function of temperature. Though an imperfect fit introduces considerable uncertainty, this empirical relationship distinguishes the gel transition from both the dynamic percolation threshold and the spinodal associated with the fluid-fluid transition for adhesive spheres. Thus we conclude that gelation in this colloidal dispersion corresponds to a metastable state lying between the fluid-solid phase boundary and the spinodal.