Probing matrix/filler interphase with ultrasonic waves

Sound propagation velocities in rod-shaped samples of epoxy-graphene nanocomposites with varying concentrations of multi-layered graphene fillers are measured experimentally and numerically simulated using the effective medium approximation (EMA). A notable discrepancy between theory and experiment is observed, which tends to increase with increasing the filling degree. A generalized effective medium approach is therefore proposed to account for the observed discrepancy. It employs modified elastic constants of the polymer matrix not only within a local neighborhood of the filler particle but also far away from the matrix/filler interface. It appears that exploiting this approach the interphase region in the epoxy-graphene nanocomposites would be as large as hundreds of nanometers away from the matrix/filler interface in order to maintain a reasonable agreement between the experimental and predicted velocities of ultrasonic waves. The size of the interphase region deduced from ultrasonic measurements is in excellent agreement with the one predicted by the Brownian motions of the nanoparticles during the curing process. Graphical Abstract