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The Langevin Equation for cooperative dynamics represents the dynamics ofpolymer melts with chains of increasing degree of polymerization, covering thefull range of behavior from the unentangled to the entangled regime. Thisequation describes the motion of a group of interpenetrating polymers that areinteracting through an effective potential resulting from the many-bodycoupling of the inter polymer potential inside the macromolecular liquid. Theconfinement of the dynamics due to the presence of entanglements is accountedfor by an effective inter-monomer potential which is zero until the distancebetween two monomers belonging to different chains reaches a characteristicvalue, d. At that distance a constraint is applied through an effectivehard-core repulsion that represents the effect of entanglements in the slowingdown of the relative diffusion of the monomers. As the time evolves theconstraint relaxes due to the chain interdiffusion. The same potential acts onboth unentangled and entangled polymer chains, but short chains are notaffected as they relax faster than they experience the presence of thepotential. The comparison with Neutron Spin Echo experiments of polyethylenemelts shows quantitative agreement of the theory with the time dependentincoherent scattering function for a variety of samples in both the unentangledand the entangled regimes.

Microscopic Theory for the Dynamics of Unentangled and Entangled Polymer Melts