When a chain, tethered at one end, is immersed in a fixed entanglement network, the mobile tip of the chain encounters an entropic potential barrier that penalizes deep fluctuations needed to bring the tip close to the tethering point. Using the tube model, Doi and Kuzuu [J. Polym. Sci., Polym. Lett. Ed. 18, 775 (1980)] estimated that this potential, which is crucial to describe the rheology of branched polymers in fixed networks and melts, has a quadratic form with a prefactor $\nu =1.5$. Later calculations based on regular lattices indicated that the potential is nonquadratic, and its steepness depends on the lattice coordination number. In this Letter, we analyze the primitive paths obtained using the bond-fluctuation model for chains with up to 12.5 entanglements. Our simulations confirm a quadratic form for the potential with a prefactor close to the Doi-Kuzuu value, $\nu \approx 1.5$.

• Received 20 September 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.076001