Macromolecules, Vol.34, No.13, 4580-4590, 2001
A length scale dependent model for stress relaxation in polymer melts
A model for the plateau in the relaxation modulus is presented. This model treats the relaxation on successively longer length Scales. The extent of relaxation in the strain-induced excess fi ee energy for each length scale is evaluated by minimizing the free energy through motions on that length scale, while constraining the system such that there is no relaxation on all longer length scales. The extent of relaxation is determined by the number of other chain segments in contact with a relaxing chain segment. The residual excess free energy, which remains after the relaxation on a length scale, is further reduced by the subsequent relaxation on the longer length scales. This analysis predicts that the entanglement chain length for relaxation should scale as N-e similar to rho (-2)b(-3)b(1)(-3), where rho is the monomer density, b is the monomer bond length, and b(1) is the Kuhn length. Two methods for the evaluation of the time dependent relaxation modulus, which are based on this length scale dependent analysis of the relaxation, are proposed and compared.