Diffusion and brownian motion of polymeric liquids

The dynamics of dense model systems of pearl-necklace polymer chains, consisting of up to N = 98 hard spheres each, has been investigated using Monte Carlo methods. Excluded volume conditions as well as entanglement constraints have been taken into account. The time-dependent displacement of a single monomer on the chain follows the classic Rouse equation gr(t) α t^1/2 until the monomer equilibrates, whereas the diffusion constant for the center-of-mass motion is in agreement with the reptation law D α N^−2±0.2. The equilibration time for conformational fluctuations is given by the Rouse equation T_e α N², whereas the disengagement time, after which the motion of the monomers is dominated by the center-of-mass motion, is given by T_d, α N^3.4±0.2.