Flocculation in Elastomeric Polymers Containing Nanoparticles: Jamming and the New Concept of Fictive Dynamic Strain

Understanding the physics of the particle network in filled rubber is key to developing reduced energy loss compounds for automobile tires and other applications.  Progress toward that goal is evident in the recent literature which reveals some fascinating parallels between the effect of temperature on traditional glassy materials and the role of deformation on the behavior of granular solids, foams, and particle-filled polymers and pastes.  The phenomenological treatment of structural relaxation (physical aging) in the nonequilibrium state of glasses, which includes the characteristic features of nonexponentiality and nonlinearity, is extended in the present work to model the progressive structural arrest (jamming) that occurs during the filler flocculation process in uncrosslinked elastomers.  A new concept of fictive dynamic strain is developed for nanoparticle-reinforced rubbery polymers by drawing an analogy to the use of fictive temperature in nonequilibrium glasses.  The fictive strain converges toward the actual strain as the system approaches steady state.  The utility of the approach is demonstrated using literature data for the filler flocculation process of nanoparticle-filled elastomers.