  We present the results of modeling dust SEDs across the SMC with the aim of
mapping the distribution of PAHs in a low-metallicity environment. Using
Spitzer Survey of the SMC (S3MC) photometry from 3.6-160 um over the main
star-forming regions of the Wing and Bar along with spectral mapping from 5-38
um from the Spitzer Spectroscopic Survey of the SMC (S4MC) in selected regions,
we model the dust SED and emission spectrum to determine the fraction of dust
in PAHs across the SMC. We use the regions of overlapping photometry and
spectroscopy to test the reliability of the PAH fraction as determined from SED
fits alone. The PAH fraction in the SMC is low compared to the Milky Way and
variable--with relatively high fractions (q_PAH~1-2%) in molecular clouds and
low fractions in the diffuse ISM (<q_PAH>=0.6%). We use the map of PAH fraction
across the SMC to test a number of ideas regarding the production, destruction
and processing of PAHs in the ISM. We find weak or no correlation between the
PAH fraction and the distribution of carbon AGB stars, the location of
supergiant H I shells and young SN remnants, or the turbulent Mach number. We
find that the PAH fraction is correlated with CO intensity, peaks in the dust
surface density and the molecular gas surface density as determined from 160 um
emission. The PAH fraction is high in regions of active star-formation, as
predicted by its correlation with molecular gas, but is suppressed in H II
regions. Because the PAH fraction in the diffuse ISM is generally very low--in
accordance with previous work on modeling the SED of the SMC--and the PAH
fraction is relatively high in molecular regions, we suggest that PAHs are
destroyed in the diffuse ISM of the SMC and/or PAHs are forming in molecular
clouds. We discuss the implications of these observations for our understanding
of the PAH life cycle, particularly in low-metallicity galaxies.
