  Photometric and polarimetric observations toward type Ia supernovae (SNe Ia)
frequently report an unusually low total-to-selective extinction ratio ($R_{\rm
V} < 2$) and small peak wavelength of polarization ($\lambda_{\rm max}< 0.4 \mu
m$). Recently, Hoang et al. proposed that the increase in the abundance of
small grains relative to large grains near SNe Ia due to RAdiative Torque
Disruption (RATD) can explain this puzzle. To test this scenario, we will
perform detailed modeling of dust extinction and polarization of SNe Ia
accounting for grain disruption by RATD and grain alignment by RAdiative
Torques (RATs). For dust clouds at distance $d< 4$ pc from the source, we find
that $R_{\rm V}$ decreases rapidly from the standard value of $3.1$ to $\sim
1.5$ after a disruption time $t_{\rm disr}\le 40$ days. We then calculate the
observed SNe Ia light curve and find that the colors of SNe Ia would change
with time due to time-varying extinction for dust clouds at distance of $d<4$
pc. We also calculate the wavelength-dependence polarization produced by grains
aligned with the magnetic fields by RATs. We find that $ \lambda_{\rm max}$
decreases rapidly from $\sim 0.55 \mu$m to $\sim 0.15 \mu$m over an alignment
time of $t_{\rm align}< 10$ days due to the enhanced alignment of small grains.
By fitting the theoretical polarization curve with the Serkowski law, we find
that the parameter $K$ from the Serkowski law increases when large grains are
disrupted by RATD which can explain the $K$ vs. $\lambda_{\rm max}$ data
observed for SNe Ia. Finally, we discover an anti-correlation between $K$ and
$R_{\rm V}$ which might already be supported by SNe Ia observational data. Our
results demonstrate the important effect of rotational disruption of dust
grains by radiative torques on the time-dependent extinction, polarization, and
colors of SNe Ia.
