A reptation-based model to the dynamics and rheology of linear entangled polymers reinforced with nanoscale rigid particles

Abstract

A reptation-based model, that incorporates transient polymer–nanoparticle surface interactions, is proposed to describe the dynamics and rheological behaviors of linear entangled polymers filled with isotropic rigid nanoscale particles. Dispersed nanoparticles are sufficiently small such that even at low volume fractions, the average particle wall-to-wall distance is on the order of the chain size. The model predicts a scaling law in the form, τ d , e f f ∼ τ d ( ϕ a d N + 1 ) 2 , where τ d, eff is the effective reptation time of a chain in the presence of attractive nanoparticles, τ d is its reptation time in the neat polymer, ϕ ad is the fraction of attached monomers per chain, and N is the number of monomers per chain. Hence, the overall relaxation is extremely retarded by attractive nanoparticles in the limit of strongly adsorbed chains. Also, it is found that the effective reptation time, τ d, eff , can be controlled through five main parameters, i.e., the molecular weight of the polymer chain, N, the size of the nanoparticles, d f , the density of attractive site on the nanoparticle surface, n as , the monomer–nanoparticle energetic interaction, ɛ, and the nanoparticle volume fraction, ϕ f . The nonequilibrium dynamics of detachment/re-attachment of monomers from/to nanoparticle surfaces under flow conditions is incorporated in the model to elucidate the effect of monomer–surface interactions on the nonlinear viscoelastic behavior. The resulting model correctly captures the linear dynamical properties and shear rheological behaviors of nanocomposite systems studied. Under very slow shear flow conditions, these filled systems exhibit a strong non-Newtonian behavior and a large enhancement in the viscosity as a certain number of monomers in the chain are attached to nanoparticle surfaces, while at very high shear rates, the neat polymer dominates the shear thinning behavior, suggesting that addition of nanoparticles contributes negligible to the viscosity in strong flows. A picture that is based on transient polymer–particle surface interactions, i.e., the detachment/re-attachment dynamics of monomers from/to nanoparticle surfaces is proposed to interpret the observed huge alteration in rheological properties.