  We present a comparison of barstrength Qb and circumnuclear dust morphology
for 75 galaxies in order to investigate how bars affect the centers of
galaxies. We trace the circumnuclear dust morphology and amount of dust
structure with structure maps generated from visible-wavelength HST data,
finding that tightly wound nuclear dust spirals are primarily found in weakly
barred galaxies. While strongly barred galaxies sometimes exhibit grand design
structure within the central 10 percent of D25, this structure rarely extends
to within ~10 pc of the galaxy nucleus. In some galaxies, these spiral arms
terminate at a circumnuclear starburst ring. Galaxies with circumnuclear rings
are generally more strongly barred than galaxies lacking rings. Within these
rings, the dust structure is fairly smooth and usually in the form of a loosely
wound spiral. These data demonstrate that multiple nuclear morphologies are
possible in the most strongly barred galaxies: chaotic central dust structure
inconsistent with a coherent nuclear spiral, a grand design spiral that loses
coherence before reaching the nucleus, or a grand design spiral that ends in a
circumnuclear ring. These observations may indicate that not all strong bars
are equally efficient at fueling material to the centers of their host
galaxies. Finally, we investigate the longstanding hypothesis that SB(s)
galaxies have weak bars and SB(r) galaxies have strong bars, finding the
opposite to be the case: namely, SB(r) galaxies are less strongly barred and
have less dust structure than SB(s) galaxies. In general, more strongly barred
galaxies tend to have higher nuclear dust contrast.
