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

Abstract

Abstract 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.