Distinguishing Gas-Phase and Nanoparticle Contributions to Small-Angle X‑ray Scattering in Reacting Aerosol Flows

We have developed
a strategy for distinguishing between small-angle
X-ray scattering (SAXS) from gas-phase species and newly formed nanoparticles
in mixed gas- and particle-phase reacting flows. This methodology
explicitly accounts for temperature-dependent scattering from gases.
We measured SAXS in situ in a sooting linear laminar
partially premixed co-flow ethylene/air diffusion flame. The scattering
signal demonstrates a downward curvature as a function of the momentum
transfer (q) at q values of 0.2–0.57
Å–1. The q-dependent curvature
is consistent with the Debye equation and the independent-atom model
for gas-phase scattering. This behavior can also be modeled using
the Guinier approximation and could be characterized as a Guinier
knee for gas-phase scattering. The Guinier functional form can be
fit to the scattering signal in this q range without
a priori knowledge of the gas-phase composition, enabling estimation
of the gas-phase contribution to the scattering signal while accounting
for changes in the gas-phase composition and temperature. We coupled
the SAXS measurements with in situ temperature measurements
using coherent anti-Stokes Raman spectroscopy. This approach to characterizing
the gas-phase SAXS signal provides a physical basis for distinguishing
among the contributions to the scattering signal from the instrument
function, flame gases, and nanoparticles. The results are particularly
important for the analysis of the SAXS signal in the q range associated with particles in the size range of 1–6
nm.