Unraveling Two Nonlinear Rheological Peaks in Filled Rubber: Chain-Arm Retraction and Bound-Rubber Dynamics

Carbon-black-filled nitrile butadiene rubber (NBR) exhibits two maxima in its nonlinear oscillatory response, quantified here by a Fourier-based Nonlinearity Index (NLI). The higher-strain Peak I is inherited from the neat long-chain-branched matrix, whereas the lower-strain Peak II appears only after filler addition and is markedly more sensitive to carbon-black grade. We use a molecular description that separates the intrinsic dynamics of the matrix from those of the dynamically active boundrubber population. Peak I arises from the competition between backbone orientation and delayed arm retraction; matrix–adsorbed constraints shift this maximum to lower imposed strain and attenuate its amplitude without requiring a change in the underlying arm-retraction mechanism. Peak II is assigned to collective memory carried by adsorbed polymer associated with neighboring aggregate environments. Two limiting mechanisms for the loss of this interfacial memory—controlled by local shear rate or by interfacial deformation—predict distinct frequency dependences but are indistinguishable from the available single-frequency measurements. This picture connects the two nonlinear maxima to different molecular populations and suggests direct multi-frequency tests for separating matrix and interfacial contributions in filled NBR.