Direct Calculation of the Tube Potential Confining Entangled Polymers

We directly compute, for the first time, a confining “tube” potential acting on a flexible or semiflexible polymer chain entangled with like chains using equilibrium molecular dynamics simulations and compare these results to the conventional tube diameter inferred from the plateau in the time-dependent relaxation modulus G(t) and to an apparent tube diameter inferred from the crossover time τe from t1/2 to t1/4 scaling in the time-dependent monomer diffusivity g2(t). We find that the “narrow” tube diameter obtained at the equilibration time τe, where the monomer first “feels” that it is in a tube, widens with time as the tube potential softens and develops a nonquadratic tail. Our results help explain why the value of the entanglement spacing inferred by measurements at time scale τe is only half the conventional value obtained by measurements of the plateau modulus in the vicinity of the Rouse time τR.