# Stress Enhancement in the Delayed Yielding of Colloidal Gels

## Summary

Networks of weakly aggregated colloidal particles, or colloidal gels, exhibit a solidlike behavior: their elastic modulus G' is nearly independent of frequency <math>\omega</math> and significantly larger than their viscous modulus G". Interestingly, G" exhibits a feature common to many soft materials; it is largely frequency-independent but nevertheless displays a weak but noticeable increase at the lowest <math>\omega</math> typically measured. This rise suggests the presence of an ultraslow relaxation mechanism in the material. Such relaxation could reflect the ultimate fluid like behavior of the gel at frequencies so low they cannot be probed with oscillatory rheology. Alternatively it could result from aging, which leads to irreversible fluidization of the gel that cannot even be correctly measured with oscillatory rheological measurements. Instead, the mechanics of such soft solid materials can be probed with creep measurements. At low applied stress <math>\sigma</math>, the creep response of colloidal and polymeric gels typically displays the characteristics of a mechanically stable solid, with the deformation reaching a time-independent plateau that reflects the elasticity of the material. However, this solidlike stability persists only for a finite time, whereupon the gel suddenly and catastrophically yields. For polymer networks, the time between the application of a load and the time of yield, <math>\tau_d</math>, exhibits an exponential dependence on the applied stress; this results from stress enhancement of the thermal relaxation of individual bonds within the network. The yielding of colloidal gels also exhibits a strong dependence on stress, but the origin of this behavior has never been fully established.