Constraining the refractive index of fractal-like aggregates from complex forward-scattering amplitudes of mass-classified aerosol particles: Application to black carbon samples

The complex refractive index m = m_r + i·m_i of black carbon (BC) aerosol governs its absorption and scattering of sunlight, yet published values remain widely scattered. At fixed particle mass and morphology, this spread leaves the mass absorption cross-section (MAC) uncertain by up to a factor of ten. We present an experimental method for inference of m jointly with the fractal dimension D_f of aerosolized BC aggregates from the complex forward-scattering amplitudes measured by a complex-amplitude sensor (CAS-v2) at three wavelengths λ ∈ {453, 638, 834} nm downstream of a differential mobility analyzer (DMA). For two BC samples (fullerene soot, FS; Jet A-1 combustion soot, J1) the inference returns compact fractal aggregates (D_f ≈ 2.6), corroborated by an independently measured mass-mobility exponent (D_m = 2.63 for both samples). The D_f posterior is bimodal, and the two modes are mutually exclusive posterior solutions — the physical refractive index is that of a single mode (low- or high-D_f), not an intermediate value. We recommend the low-D_f mode — a relative preference rather than a decisive one: for FS its simulated MAC most closely matches a reported mass-classified MAC measurement and its refractive-index posterior is markedly tighter than the high-D_f mode's, and for J1 it follows from the near-identical DMA-APM effective density and D_m of the two samples. Folding the dominant residual bias — the assumed monomer radius — into the posterior spread and propagating the instrument-calibration systematic-error uncertainty, the recommended low-D_f refractive index at the well-constrained wavelengths (midpoint ± half of the 5–95% range; wavelength in nm) is m_FS(638) = (1.85 ± 0.05) + (0.91 ± 0.03)i, m_FS(834) = (2.11 ± 0.04) + (0.99 ± 0.04)i, m_J1(638) = (2.07 ± 0.09) + (0.98 ± 0.07)i, and m_J1(834) = (2.25 ± 0.04) + (0.96 ± 0.06)i (FS 453 nm is weakly constrained, from only a few detected particles). We estimate that the constrained refractive-index range obtained here narrows the MAC uncertainty to a small fraction of its literature spread.