The stretched-exponential approximation to the dynamic structure factor in non-entangled polymer melts

Abstract

The coherent and incoherent dynamic structure factor S(Q,t) measured in neutron scattering experiments (Q being the momentum transfer) provides invaluable information about the intramolecular dynamics of polymer chains. Here we report an analysis of the calculated S(Q,t) for low-molar-mass chains in the molten state with no entanglements. The theoretical results from coarse-grained and realistic models are empirically fitted with the Kohlrausch–Williams–Watts (KWW) stretched-exponential function exp[−(t/τ)^β]. Both the characteristic time τ and the β exponent (β < 1) are allowed to depend on Q. The KWW function fit is shown to be adequate down to S(Q,t)/S(Q,0) ≈ 0.05, but to become increasingly poorer at longer times, much earlier than the diffusive regime sets in, due to the breadth of the spectrum of relaxation times. Results are discussed in terms of τ and β, which are tentatively correlated with the stiffness of the model chains, and compared both with recent experimental results and with theoretical approaches.