On the Definitions of Entanglement Spacing and Time Constants in the Tube Model
R.G. Larson (1), T. Sridhar (2), L.G. Leal (3), G.H. McKinley (4), A.E.Likhtman (5) and T.C.B.McLeish (5)
(1) Dept. of Chemical Engineering, University of Michigan, USA
(2) Dept. of Chemical Engineering, Monash University, Australia
(3) Dept. of Chemical Engineering, University of California – Santa Barbara, USA
(4) Dept. of Mechanical Engineering, Massachusetts Institute of Technology, USA
(5) Physics Department, University of Leeds, UK
Numerous papers have recently appeared in the literature presenting quantitative comparisons of experimental linear viscoelastic data to the most recent versions of “tube” models for entangled polymer melts and solutions. Since these tube models are now being used for quantitative, rather than just qualitative, predictions, it has become important that numerical pre-factors for the time constants that appear in these theories be evaluated correctly using literature data for the constants (i.e., density, plateau modulus, etc.) that go into the theories. However, in the literature two definitions of the entanglement spacing in terms of plateau modulus have been presented, and confusion between these has produced numerous errors in the recent literature. In addition, two different definitions of the “equilibration time,” a fundamental time constant, have also appeared, creating additional potential for confusion. We therefore carefully review the alternative definitions and clarify the values of the pre-factors that must be used for the different definitions, in the hope of helping future authors to avoid such errors.