Thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) particles of a nearly constant swelling ratio and with polydispersity indices (PDIs) varying over a wide range (7.4% - 48.9%) are synthesized to study the effects of polydispersity on the dynamics of suspensions of soft PNIPAM colloidal particles. The PNIPAM particles are characterized using dynamic light scattering (DLS) and scanning electron microscopy (SEM). The zero shear viscosity ($eta_{0}$) data of these colloidal suspensions, estimated from rheometric experiments as a function of the effective volume fraction $phi_{eff}$ of the suspensions, increases with increase in $phi_{eff}$ and shows a dramatic increase at $phi_{eff}=phi_{0}$. The data for $eta_{0}$ as a function of $phi_{eff}$ fits well to the Vogel-Fulcher-Tammann (VFT) equation. It is observed that increasing PDIs results in increasingly fragile supercooled liquid-like behavior, with the parameter $phi_{0}$, extracted from the fits to the VFT equation, shifting towards higher $phi_{eff}$. The observed increase in fragility is attributed to the prevalence of dynamical heterogeneities (DHs) in these polydisperse suspensions, while the simultaneous shift in $phi_{0}$ is ascribed to the decoupling of the dynamics of the smallest and largest particles. Finally, it is observed that the intrinsic nonlinearity of these suspensions, estimated at the third harmonic near $phi_{0}$ in Fourier transform oscillatory rheological experiments, increases with increase in PDIs. Our results are in agreement with theoretical predictions and simulation results for polydisperse hard sphere colloidal glasses and clearly demonstrate that jammed suspensions of polydisperse colloidal particles can be effectively fluidized with increasing PDIs.
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