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Deuterium NMR relaxation times of specifically deuterated block terpolymers of 2-vinyl pyridine (VP), styrene (S), and deuterostyrene (DS) were measured for the polymers in solution and on silica as a function of temperature and solvent. The block polymers were attached to the silica through the VP segments; the S and DS segments were extended into the solution. In a thermodynamically poor solvent, such as carbon tetrachloride, the relaxation times were consistent with the S segments on the surface-bound polymer being less mobile than their counterparts in solution. This is in contrast with their behavior in toluene (previously reported), where the styrene segments of the surface-bound polymer appeared to be more mobile than in solution. The results demonstrate that the solvent quality may have a dramatic effect on the dynamics of the chain segments of the surface-bound polymer. In a mixture of solvents, namely carbon tetrachloride and methanol there was evidence for more mobile S segments in the surface-bound polymer, however, the VP units also had additional mobility due to the presence of the methanol. The relaxation times were also used, along with the model of Hall and Helfand, to determine the motional parameters and spectral densities for the polymers in the different systems.