Linear Response Theory for Hard and Soft Glassy Materials

Despite qualitative differences in their underlying physics, both hard and soft glassy materials exhibit almost identical linear rheological behaviors. We show that these nearly universal properties emerge naturally in a shear-transformation-zone theory of amorphous plasticity, extended to include a broad distribution of internal thermal-activation barriers. The principal features of this barrier-height distribution are predicted by nonequilibrium, effective-temperature thermodynamics. Our theoretical loss modulus $G^{\prime \prime }(\omega )$ has a peak at the $\alpha$ relaxation rate, and a power law decay of the form ${\omega }^{-\zeta }$ for higher frequencies, in quantitative agreement with experimental data.

Figure 1

Experimental data for Vitreloy 4 and theoretical comparisons for the storage modulus $G^{\prime }(\omega )$ (red squares) and the loss modulus $G^{\prime \prime }(\omega )$ (blue circles). The data points were extracted from Fig. 2 in 1, where very similar curves for oxide and polymeric glasses can be found.

Figure 2

Experimental data and theoretical comparisons for the storage modulus $G^{\prime }(\omega )$ (red squares) and the loss modulus $G^{\prime \prime }(\omega )$ (blue circles) for two different suspensions of thermosensitive particles, as reported in 13. The values of the parameters for the top and bottom panels, respectively, are $\rho =0.04,3\times {10}^{-4}$; ${\nu }^{*}=0.001,{10}^{-3}\rho$; $\zeta =1.0,0.5$; $\overline{\Lambda }=200,40$; $\mu =12,35\mathrm{Pa}$; and ${\tau }_K=0.004,0.002\sec$. In all cases, ${\zeta }_1=1$ and $c=0.1$.