Rheological Scaling Relation for an Out-of Equilibrium Colloidal Solid

We explore scaling relations for the slow ripening of an out-of-equilibrium model colloidal solid that consists of clay particles that swell and exfoliate into randomly oriented clay sheets through the action of end-functionalized (``sticky'') polymer molecules. A freshly mixed sample quickly forms a sample-spanning network structure that gradually approaches its equilibrium. The ripening process accelerates at elevated temperature. After rescaling (Rheol Acta 45:331-338, 2006), the complex modulus data $G$',$G$''(\textit{$\omega $}, $t_{r})$ from time-resolved mechanical spectroscopy (Rheol Acta 33:385-397, 1994) shows that, surprisingly, the growth function of the elastic modulus is the inverse of the decaying characteristic relaxation time. Parameter of the isothermal ripening process is the ``ripening time'', $t_{r}$. A single scaling function with two pronounced powerlaw regions, a fast ripening process ($\sim \quad t_{r}^{-2})$ followed by slow ripening ($\sim \quad t_{r}^{-1/2})$, defines the state of ripening and projects the time necessary to reach equilibrium.