Neutron Scattering of Residual Hydrogen in 1,4-Dioxane-d₈ Liquid: Understanding Measurements with Molecular Dynamics Simulations

That incoherent scattering from protiated molecular liquids adds a constant background to the measured scattering intensity is well-known, but less appreciated is the fact that coherent scattering is also induced by the presence of hydrogen in a deuterated liquid. In fact, the scattering intensity can be very sensitive, in the small-q region, with respect to the amounts and distribution of residual H in the system. We used 1,4-dioxane liquid to demonstrate that the partial structure factors of the HD and DD atom pairs contribute significantly to intermolecular scattering and that uncertainty in the extent of deuteration account for discrepancies between simulations and measurements. Both contributions to uncertainty have similar magnitudes: scattering interference of the hydrogen-deuterium pair, and complementary interference from the deuterium-deuterium pair by virtue of chemical inhomogeneity. This situation arises in practice since deuteration of liquids is often 99% or less. A combined experimental and extensive computational study of static thermal neutron scattering of 1,4-dioxane demonstrates the foregoing. We show, through simulations, that the reason for the differences is the content of protiated dioxane (vendors quote 1%). We estimate that up to 5% (at 298 K and at 343 K) protiated molar fraction may be involved in generating the scattering differences. Finally, we find that the particular distribution of hydrogen in the protiated molecules affects the results significantly; here, we considered molecules to be either fully protiated or fully deuterated. This scenario best reconciles the computational and experimental results, and leads us to speculate that the deuteration synthesis process tends to leave a molecule either fully deuterated or fully protiated. Although we have used 1,4-dioxane as a model liquid, the effects described in this study extend to similar liquids, and similar systematic experimental/computational studies can be performed to either understand measurements or calibrate/validate molecular dynamics models.