Local dynamics of polyethylene and its oligomers: A molecular dynamics interpretation of the incoherent dynamic structure factor

We present a detailed study of the local dynamics of short polyethylene (PE) chains using molecular dynamics (MD) simulations and quasi-elastic neutron scattering (QENS) data. QENS measurements were carried out on two samples having different chain lengths: C₄₄H₉₀ and PE2K (M_w = 2150 g/mol). The incoherent dynamic structure factors obtained from experiments at T = 450 K and MD simulations carried out at the same temperature are compared in the range 0.5 = Q = 2.0 Å^-1. Agreement between experimental data and simulations is quantitative. Attempts are made to characterize the momentum transfer and the chain length dependence of the I(Q,t) and S(Q,?) data on the basis of the Kohlrausch-Williams-Watts (KWW) function and two exponentials relaxation functions in time. As MD simulation data cover a broader frequency window and have a very low statistical noise, a more refined analysis of the intermediate scattering functions in terms of a continuous linear combination of exponentials weighted by a distribution of relaxation times has been performed. This analysis shows a systematic evolution of the shape of the distribution of relaxation times going from a two-process situation at low Q toward a single merged process at higher Q. This allows us to point out in a well-defined case the limitations of both the KWW and two exponentials descriptions which approximate the distribution of relaxation times either as one broad and asymmetric distribution or as a conjugation of two delta distributions.