A simulation method for highly entangled polymer nanocomposites: scaling exponents of slip-spring age among free and grafted chains, grafting density and nanoparticle/polymer interaction dependence on particle dispersion†

We present an extension of the SLIPLINK technology introduced by A. Likhtman to polymer nanocomposites in order to model explicitly free and grafted chains. Entanglements are explicitly modeled by slip-springs (SS) and follow the constraint release algorithm of destruction/recreation when reaching the chain end. Following the birth/death process, one can compute the age of slip-springs and the entire population age pyramid. We varied nanoparticle volume fraction, grafting density, and polymer/particle interactions to determine structural and dynamic properties of the nanocomposite materials. Scaling laws for slip-springs average age versus chain length have been obtained. While the dynamics of slip-springs between free chains in the nanocomposite is almost identical to that of a pure polymer melt, a characteristic exponent close to 3.7 has emerged governing the average age of slip-springs between grafted chains. The number of inter-particle graft–graft entanglements and their increased average lifetimes have a strong impact on the viscoelastic response of the material and the nanoparticle cluster formation. The emergence of polymer network elasticity will be discussed for high grafting density and high-volume fraction.