An interface model for the prediction of Young's modulus of layered silicate-elastomer nanocomposites

Recent experiments on layered silicate-elastomer nancomposites by Burnside and Giannelis have shown that there is a discrepancy between theoretical modulus predictions and experimental modulus measurements. A theory is proposed to explain this discrepancy. We hypothesize that the discrepancy is due to imperfect bonding between the matrix/inclusion interface which effectively reduces the aspect ratio and the volume fraction of the inclusion. We use a simple interface model to quantify the imperfect interfacial bonding, From this model, we introduce the concept of the effective aspect ratio and effective volume fraction of the inclusions. These effective quantities depends on a single material parameter, namely, the constant interfacial shear stress, tau. The interfacial shear stress for the elastomer-silicate nanocomposites is found by fitting the theory to the experimentally measured modulus of Burnside and Giannelis. The interfacial shear stress is in the range of thousands of Pascals. For the elastomer-silicate nanocomposite systems considered here, the interfacial shear stress can be decomposed into two parts; intrinsic shear stress tau(i) and frictional shear stress tau(f). The intrinsic interfacial shear stress tau(i) depends only on the volume fraction of inclusions and decreases with increasing volume fraction of inclusions. On the other hand, the frictional shear stress tau(f) is found to increase linearly with the applied strain. Since the mean stress is also proportional to the applied strain, this gives rise to an effective coefficient of friction, which is found to be 0.0932 for the nanocomposite system considered here.