Strain Hardening of Fractal Colloidal Gels

Abstract

We report on experiments on the rheology of gels formed by diffusion-limited aggregation of neutrally buoyant colloidal particles. These gels form very weak solids, with the elastic modulus, $G^{\prime }\left(\omega \right)$, larger than the loss modulus, $G^{\prime \prime }\left(\omega \right)$, and with both $G^{\prime }\left(\omega \right)$ and $G^{\prime \prime }\left(\omega \right)$ exhibiting only a very weak frequency dependence. Upon small but finite strains $\gamma <0.45\mathrm{}$ the elastic modulus increases roughly exponentially with ${\gamma }^2$. We explain the observed strain hardening with the highly nonlinear elastic response of the rigid backbone of the gel to elongational deformation.