  We analyze the uncertainty in grain size estimation of pure methane (CH4) and
nitrogen saturated with methane (N2:CH4) ices, the most abundant volatile
materials on trans-Neptunian objects (TNOs) and Kuiper belt objects (KBOs). We
compare the single scattering albedo, which determines the grain size
estimation of outer solar system regolith (Hansen, 2009), of these ices using
the Mie scattering model and two other Hapke approximations (Hapke, 1993) in
radiative transfer scattering models (RTM) at near-infrared (NIR) wavelengths
(1-5 $\mu$m). The equivalent slab (Hapke Slab) approximation model predicts
results much closer to Mie scattering over the NIR wavelengths at a wide range
of grain sizes. In contrast, even though the internal scattering model (ISM)
predicts an approximate particle diameter close to the Mie model for particles
with a 10 $\mu$m radii, it exhibits higher discrepancies in the predicted
estimation for larger grain sizes (e.g., 100 and 1000 $\mu$m radii). Owing to
the Rayleigh effect on single-scattering properties, neither Hapke approximate
models could predict an accurate grain size estimation for the small particles
(radii $\leq$ 5 $\mu$m). We recommend that future studies should favor the
equivalent slab approximation when employing RTMs for estimating grain sizes of
the vast number of TNOs and KBOs in the outer solar system.
