The Influence of Carbon Black Colloidal Properties on the Parameters of the Kraus Model

The Payne Effect (also known as the Fletcher–Gent Effect) has a fundamental impact on the behavior of filled rubber composites and therefore must be considered during their design. This study investigates the influence of carbon black (CB) surface area and structure on the observed Payne Effect and builds on the existing models of Kraus and Ulmer to explain this phenomenon. Dynamic strain sweeps were carried out on natural rubber (NR) compounds containing eight different grades of CB at equivalent volume fractions. The loss and storage moduli were modeled according to the Kraus and Ulmer equations, using a curve optimization tool in SciPy. Subsequent regression analysis provided strong correlations between the fitting parameters and the CB structure and surface area. Using this regression analysis, this work provides further insight into the physical meaning behind the Kraus and Ulmer models, which are phenomenological in nature.