Diffusion of a Polymer Tracer in an Unentangled Matrix

It has been recognized for some years but remains controversial that hydrodynamic interactions are in fact not screened beyond the monomeric scale in polymer melts. This study adapts the so-called viscoelastic hydrodynamic interaction (VHI) effect to explain the center-of-mass (c.m.) diffusion of a polymer tracer of length Ntra diluted in an unentangled matrix of the same chemistry but different chain length Nmat, which disproves the classic Rouse model from the existing experimental data. The theory of the matrix effect on the tracer’s c.m. diffusion is introduced, which decouples the total diffusion into the localized and hydrodynamic parts. The localized contribution is described from the diffusion of a monomer tracer in the same matrix. The time-dependent generalized Oseen tensor is used to predict the hydrodynamic contribution. The theory predicts that before the Fickian diffusion regime, the profile of the transient hydrodynamic diffusion constant relies on the parameter Nmat/Ntra1/3. Subdiffusion is predicted to occur when Nmat/Ntra1/3 ≫ 1 until the matrix relaxation time. The total diffusion constant in the Fickian regime superposes Rouse-like and Zimm-like processes. Momentum-conserving molecular dynamics simulations that cover the entire range of unentangled polymers are performed, and they show excellent agreement with theoretical predictions. The tracer’s monomeric diffusion and a discussion on the nonmomentum-conserving dynamics coupled with a Langevin damping effect further support the VHI theory.