Relaxation Dynamics of Nano Particles Embedded in a Soft Glassy Matrix

Using x-ray photon correlation spectroscopy, we have studied slow, wave vector and temperature dependent microrheology of nano particles embedded in glassy matrix with unique viscoelastic properties. The measurements were done for a polymer matrix (PMMA) using gold nanoparticles as probe. The intensity auto-correlation function exhibits a cross-over from compressed to stretched relaxation behavior on cooling from above the glass transition temperature (T$_{g})$ of PMMA. Although stretched exponential relaxation is expected in the glassy state one would expect simple exponential relaxation above the T$_{g}$. We also find that the relaxation time ($\tau)$, follows $\tau \sim $ q$^{-1}$ dependence indicating super-diffusive motion of nanoparticles. Interestingly, we have also observed subtle effects like length scale dependence of the stretching exponent. This points to the importance of the nanoparticles in modifying the viscoelastic property of the polymer matrix and highlights the strength of this technique in extracting their micro-rheological properties.