  The TRAPPIST-1 planetary system is an excellent candidate for study of the
evolution and habitability of M-dwarf planets. Transmission spectroscopy
observations performed with the Hubble Space Telescope (HST) suggest the
innermost five planets do not possess clear hydrogen atmospheres. Here we
reassess these conclusions with recently updated mass constraints and expand
the analysis to include limits on metallicity, cloud top pressure, and the
strength of haze scattering. We connect recent laboratory results of particle
size and production rate for exoplanet hazes to a one-dimensional atmospheric
model for TRAPPIST-1 transmission spectra. Doing so, we obtain a
physically-based estimate of haze scattering cross sections. We find haze
scattering cross sections on the order of 1e-26 to 1e-19 cm squared are needed
in hydrogen-rich atmospheres for TRAPPIST-1 d, e, and f to match the HST data.
For TRAPPIST-1 g, we cannot rule out a clear hydrogen-rich atmosphere. We also
modeled the effects an opaque cloud deck and substantial heavy element content
have on the transmission spectra. We determine that hydrogen-rich atmospheres
with high altitude clouds, at pressures of 12mbar and lower, are consistent
with the HST observations for TRAPPIST-1 d and e. For TRAPPIST-1 f and g, we
cannot rule out clear hydrogen-rich cases to high confidence. We demonstrate
that metallicities of at least 60xsolar with tropospheric (0.1 bar) clouds
agree with observations. Additionally, we provide estimates of the precision
necessary for future observations to disentangle degeneracies in cloud top
pressure and metallicity. Our results suggest secondary, volatile-rich
atmospheres for the outer TRAPPIST-1 planets d, e, and f.
