Elastic and yield behavior of strongly flocculated colloids

We have investigated theoretically the elastic and yield behaviors of stron gly flocculated colloids by first examining the yield forces between two pa rticles within the framework of Derjaguin-Landau-Verwey-Overbeck (DLVO) int eractions. Under highly attractive conditions, i,e,, in the absence of the secondary minimum in the DLVO potential, the radial (tensile) motion betwee n particles is nonelastic because of the lack of an inflection point in the DLVO potential. However, the lateral (shear) motion is shown to be elastic up to a distance y(max), providing a mechanism for the observed elasticity in colloidal gels. If r(0) and s(0) are, respectively, the closest center- to-center and surface-to-surface distances between two particles, y(max) proportional to (1- 0.5 alpha zeta(2))(s(0)r(0))(1/2) where zeta is the zeta potential of the particles and a a defined constant. Moreover, the yield force between two particles is much smaller in the lat eral direction than in the radial direction. These results suggest that yie lding of a particulate network is likely to occur through the lateral movem ents between particles. The yield strain can be approximated as that at whi ch all the bonds in a certain direction have a perpendicular displacement > y(max), resulting in epsilon(yield) = y(max)/r(0) proportional to (1 - 0.5 alpha zeta(2))(s(0)/r (0))(1/2) The shear modulus of the network, G', can be deduced by combining the elast ic constant of the lateral movement with the existing elastic theory of a p articulate network. The yield stress can be approximated as sigma(yield) approximate to G'epsilon(yield) proportional to (1 - 1.5 alpha zeta(2))A/24s(0)(3/2) 1/Rd-3/2 where A is the Hamaker constant and R the particle radius. These prediction s are shown to compare favorably with existing experiments.