The diffusion coefficient of a reptating polymer

The dynamics of a polymer in a network of entanglements is studied. The viscosity has been examined for chains up to 50 links and is found to scale with chain length L as L3.41±0.14 in agreement with previous theoretical work, that attributes this anomalous exponent as a finite size effect because of the finite tube length. Numerical results for chains up to 100 links give that the diffusion coefficient D, scales as L−2.50±0.04. This result differs from theoretical predictions based on tube fluctuations which claim finite length effects are unimportant for diffusion and therefore imply a −2 power law dependence for D. The reason for this discrepancy is examined. Previous work used a one-dimensional rather than a three-dimensional diffusion coefficient as the starting point of analysis. By deriving the correct procedure for calculating the three-dimensional D, one sees that it has corrections to its asymptotic behavior which are quite large, of order L−1/2, rather than L−1 as was thought previously. This suggests that fluctuations in the tube length cannot provide an adequate explanation for the experimental data.