Multiscale Modeling Approach to Dynamic-Mechanical Behavior of Elastomer Nanocomposites

Rubber composites based on an elastomeric matrix filled with rigid fillers such as carbon black or silica remain important materials for technical applications and everyday life. Targeted improvement of the mechanical properties of these materials requires a deep understanding of the molecular mobility over broad time and temperature scales. We focus here on recent studies of the dynamic properties of rubber composites with the aid of a physically motivated multiscale theoretical approach. Rubber compounds, based on a solution-polymerized styrene butadiene rubber filled with precipitated silica, have been investigated. The construction of master curves for the storage and loss moduli over more than 15 decades of frequencies is presented. The master curves over the whole frequency range are analyzed with the aid of a new multiscale approach, which includes contributions from the relaxation processes described in rigorous theoretical studies for different scales of motion. It takes into account the long-scale motions of dangling chain ends, Rouse-like dynamics and bending motions of semiflexible chain fragments in the intermediate frequency range, and the specific nonpolymeric relaxation at very high frequencies. The modification of molecular mobility of polymer chains on the surfaces of filler particles and the contribution of the percolation network built by the filler are discussed. The proposed theoretical approach allows fitting of the dynamic moduli of filled and unfilled rubbers in the linear viscoelastic regime with a limited set of parameters (relaxation times, scaling exponents, molar mass of the Kuhn segment, etc.) having reasonable values. The slowing down of the relaxation processes in the vicinity of the filler particles is demonstrated.