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.
KeywordsDynamic moduli Multiscale theoretical approach Polymer localization Rigid fillers Rubber composites
The authors gratefully acknowledge a technical support from T. Götze, K. Scheibe, and R. Jurk (Leibniz-Institut für Polymerforschung Dresden e.V.).
We wish to thank Dr. K. W. Stöckelhuber (Leibniz-Institut für Polymerforschung Dresden e.V.) for inspiring discussions, Dr. F. Petry (Goodyear Innovation Center Luxembourg) for his outstanding support and collaboration, and the Goodyear Tire and Rubber Company for permission to publish this paper.
The authors would like to cordially express their gratitude to Prof. Dr. G. Heinrich for all the outstanding collaborations and discussions during the past years. Be it in conjunction with elastomer physics, polymer and rubber viscoelasticity, rubber friction, contact mechanics, fracture mechanics, or any other scientific subject, the discussions were always shaped by respect, honesty, integrity and an impressive level of scientific competence. Prof. Heinrich is an undisputed authority in his field, from fundamental science and polymer theory up to the tire-related applications of rubber technology. He unifies the leadership traits of a scientific director, academic teacher, and institutional manager. It has always been a great pleasure to collaborate and work with him.
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