Quantitative examination of a fundamental assumption in small-angle neutron scattering studies of deformed polymer melts

It has long been established that the coherent scattering intensity of neutrons by isotropic mixtures of hydrogenous and deuterated polymers of matching molecular weights is, to the first approximation, proportional to the single-chain structure factor of the polymer chain. The validity of this fundamental relation for equilibrium, undeformed polymer melts is well supported by the extensive experimental and theoretical investigations over the past several decades. The generalization of this relation to the case of nonequilibrium, deformed polymer melts, however, is not a trivial one. Despite its widespread usage in small-angle neutron scattering (SANS) studies of deformed polymer melts, the assumed proportionality between coherent scattering intensity and single-chain structure factor has received very little experimental scrutiny. This work quantitatively examines this issue through spherical harmonic expansion analysis of the anisotropic SANS spectra of deformed polystyrene melts of different levels of deuterium labeling. It is shown that the classical assumption works extremely well over a wide range of scattering wavevectors, where the isotropic component of the SANS spectrum and the leading term of structural anisotropy vary by more than two orders of magnitude.