Estimation of incoherent backgrounds in SANS studies of polymers

Small- and intermediate-angle neutron scattering studies have been undertaken on mixtures of deuterated and protonated poly(ethylene terephthalate) (PET) molecules with a wide range of concentration. The samples were converted to random copolymers by transesterifying in the melt, thus removing the coherent component of the intensity associated with single-chain scattering. The transesterified samples were used to determine the level of incoherent scattering associated with each isotopic mixture which was compared with estimates from established background-correction techniques based on extra-polating from the scattering of fully protonated or deuterated blanks. Scaling via the measured sample transmission works well for predominantly protonated mixtures but fails when the fraction of deuterated polymer exceeds φ_D ~0.6. Scaling via the component of the sample transmission attributable to the incoherent scattering from H nuclei works well over the whole concentration range. This method involves calculations of the sample transmission via the bound-atom cross section and this is a good approximation at the wavelength employed (λ ~4.75 Å), where the hydrogen incoherent cross section is close to the bound-atom cross section (σ_H ~80 × 10⁻²⁸ m²). However, σ_H is a strong function of wavelength and the method cannot be used where the measured and calculated transmissions diverge. A recently developed theory describing the scattering from random copolymers was used to analyze the residual coherent cross section of the copolymers and led to a statistical segment length b = 14.3 ± 1 Å, in good agreement with existing values for PET.