The dynamic structure factor in non-entangled polymer melts-theoretical results for real chains and the stretched exponential approximation

摘要

The dynamic structure factor S(Q,t) measured in quasi-elastic scattering experiments (Q being the momentum transfer) is calculated for real poly(dimethyl siloxane) (PDMS) and polyethylene (PE) chains in the molten state at high Q, where chain entanglements are irrelevant. The theoretical lineshapes, obtained within the rotational isomeric states approach, are empirically fitted with the stretched exponential function S(Q,t) = exp[-(t/τ)~β]. We find that the stretching exponent β increases with chain stiffness, in keeping with our previous results for coarse-grained chain models. In particular, for high molar-mass polymers PE has a somewhat larger β exponent than PDMS, in fair agreement with experimental results. Moreover, the theory predicts a marginal decrease of β with increasing temperature, due to the increased conformational flexibility. Additionally, the β exponent for PE is predicted to slightly increase in oligomers at a given T, in qualitative agreement with recent experimental results.