Entangled polymer dynamics through the lens of density self-correlation function

The real-space signature of entangled polymer dynamics is characterized via the density self-correlation function G_s(r,t). Using coarse-grained molecular dynamics simulations, it is shown that the self-correlation function of an entangled polymer melt deviates strongly from the Gaussian distribution, exhibiting a stretched tail at large distances. Such a tail can be approximated by an exponential function, G_s(r,t) ~ exp[-r/λ(t)], with λ being a characteristic length that depends on the correlation time t. For unconstrained Rouse dynamics, the characteristic length scales with the correlation time as: λ ~ t^1/4; when the molecular motions become constrained by entanglements, a much weaker time dependence is revealed: λ ~ t^1/8; eventually the behavior of t^1/4 reemerges in the reptation regime. These scalings further suggest a close relation between the exponential tail at large distances and the mean-squared displacement (MSD) that is largely determined by the self-correlation at small distances for the studied polymer melts. Specifically, it is found that λ ~ MSD^1/2. This relation bears some apparent resemblance to the non-Gaussian dynamics observed in other soft materials.