We report studies of the frequency dependent shear modulus, $G^*(omega)=G(omega)+iG(omega)$, of the liquid crystal octylcyanobiphenyl (8CB) confined in a colloidal aerosil gel. With the onset of smectic order, $G$ grows approximately linearly with decreasing temperature, reaching values that exceed by more than three orders of magnitude the values for pure 8CB. The modulus at low temperatures possesses a power-law component, $G^*(omega) sim omega^alpha$, with exponent $alpha$ that approaches zero with increasing gel density. The amplitude of $G$ and its variation with temperature and gel density indicate that the low temperature response is dominated by a dense population of defects in the smectic. In contrast, when the 8CB is isotropic or nematic, the modulus is controlled by the elastic behavior of the colloidal gel.
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