Short-time elasticity of polymer melts: Tobolsky conjecture and heterogeneous local stiffness

An extended molecular-dynamics study of the short- time “glassy” elasticity exhibited by a polymer melt of linear fully-flexible chains above the glass transition is presented. The focus is on the infinite-frequency shear modulus G1 manifested in the picosecond time scale and the relaxed plateau Gp reached at later times and terminated by the structural relaxation. The local stiffness of the interactions with the first neighbors of each monomer exhibits marked distribution with average value given by G1. In particular, the neighborhood of the end monomers of each chain are softer than the one of the inner monomers, so that G1 increases with the chain length. Gp is not affected by the chain length and is largely set by the nonbonding interac- tions, thus confirming for polymer melts the conjecture formu- lated by Tobolsky for glassy polymers.