  Polarized emission from polycyclic aromatic hydrocarbons (PAHs) potentially
provides a new way to test basic physics of the alignment of ultrasmall grains.
In this paper, we present a new model of polarized PAH emission that takes into
account the effect of PAH alignment with the magnetic field. We first generate
a large sample of the grain angular momentum $\bf J$ by simulating the
alignment of PAHs due to resonance paramagnetic relaxation that accounts for
various interaction processes. We then calculate the polarization level of PAH
emission features, for the different phases of the ISM, including the cold
neutral medium (CNM), reflection nebulae (RN), and photodissociation regions
(PDRs). We find that a moderate degree of PAH alignment can significantly
enhance the polarization degree of PAH emission compared to the previous
results obtained with randomly oriented $\bf J$. In particular, we find that
smallest, negatively charged PAHs in RN can be excited to slightly suprathermal
rotation due to enhanced ion collisional excitation, resulting in an increase
of the polarization with the ionization fraction. Our results suggest that RN
is the most favorable environment to observe polarized PAH emission and to test
alignment physics of nanoparticles. Finally, we present an explicit
relationship between the polarization level of PAH emission and the degree of
external alignment for the CNM and RN. The obtained relationship will be
particularly useful for testing alignment physics of PAHs by future
observations.
