Figure 8.

Normalized terminal particle diffusion coefficient D_t/D_s in polymer melt. Solid circles are data from ref. 46 for diffusion of a particle with diameter d = 6σ in melts of polymers with degree of polymerization N ranging from 10 (unentangled) to 200 (entangled). Here σ corresponds to Lennard–Jones length.⁴⁷N_d ≃ 24 represents the crossover degree of polymerization, below which the particle diffusion coefficient is reciprocally proportional to the degree of polymerization (see eq. 33) and above which it is independent of the degree of polymerization (see eq. 35). The root-mean-square end-to-end distance of polymer chains with degree of polymerization N_d is R ≃ √6R_g ≃ 6σ, which is equal to the particle size d.