  Spectropolarimetry enables us to measure the geometry and chemical structure
of the ejecta in supernova explosions, which is fundamental for the
understanding of their explosion mechanism(s) and progenitor systems. We
collected archival data of 35 Type Ia Supernovae (SNe Ia), observed with FORS
on the Very Large Telescope at 127 epochs in total. We examined the
polarization of the Si II $\lambda$6355 $\AA$ line (p$_{\rm Si II}$) as a
function of time which is seen to peak at a range of various polarization
degrees and epochs relative to maximum brightness. We reproduced the
$\Delta$m$_{15}$-p$_{\rm Si II}$ relationship identified in a previous study,
and show that subluminous and transitional objects display polarization values
below the $\Delta$m$_{15}$-p$_{\rm Si II}$ relationship for normal SNe Ia. We
found a statistically significant linear relationship between the polarization
of the Si II $\lambda$6355 $\AA$ line before maximum brightness and the Si II
line velocity and suggest that this, along with the $\Delta$m$_{15}$-p$_{\rm Si
II}$ relationship, may be explained in the context of a delayed-detonation
model. In contrast, we compared our observations to numerical predictions in
the $\Delta$m$_{15}$-v$_{\rm Si II}$ plane and found a dichotomy in the
polarization properties between Chandrasekhar and sub-Chandrasekhar mass
explosions, which supports the possibility of two distinct explosion
mechanisms. A subsample of SNe display evolution of loops in the $q$-$u$ plane
that suggests a more complex Si structure with depth. This insight, which could
not be gleaned from total flux spectra, presents a new constraint on explosion
models. Finally, we compared our statistical sample of the Si II polarization
to quantitative predictions of the polarization levels for the
double-detonation, delayed-detonation, and violent-merger models.
