THE NONLINEARITY INDEX: A NEW FINGERPRINT FOR POLYMER–FILLER INTERACTIONS IN FUNCTIONALIZED SBR

ABSTRACT This study investigates the transition from linear to nonlinear viscoelastic behavior in polymers and rubber compounds under cyclic sinusoidal shear deformation. By using Fourier series decomposition, we define the generalized elastic modulus and viscous modulus to capture critical aspects of the material’s response. The is further divided into two components: the first harmonic, representing linear elasticity, and a nonlinear modulus , derived from higher harmonic contributions. To quantify the degree of nonlinearity, we introduce the nonlinearity index (NLI), defined as the ratio of the nonlinear modulus to the first harmonic elastic modulus and , providing a precise metric for nonlinear viscoelastic behavior. We demonstrate the high sensitivity and utility of NLI in distinguishing different polymer topologies, particularly to differentiate between linear and branched macrostructures. Furthermore, we explore the influence of silica loading in silica-filled tread solution SBR (s-SBR) compounds, revealing the pronounced nonlinearity induced by filler content and the sensitivity of NLI in detecting filler–rubber interactions. The study also examines functionalized s-SBR in silica-based tread formulations for high-performance tires, emphasizing the critical role of polymer–filler interactions in dynamic reinforcement. Our findings establish NLI as a robust analytical tool for characterizing viscoelastic properties, offering valuable insight into molecular architecture and rubber–filler interactions for functionalized s-SBR compound.