Melt-state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉₀/M) of cis/trans-1,4-polyisoprene, a near-atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small-angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium-based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near-monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS-based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉₀/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)-based expressions of the plateau modulus, G_N^o = kT/n_t²p³ (MPa), and the entanglement molecular weight, M_e = ρN_an_t²p³ (g mol^-1), where n_t denotes the number (∼21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and Ρ is the chain density. The product n_t²p³ is the displaced volume (V_e) of an entanglement that is also expressible as pd_t² or kT/G_N^o.