Nonexponential ²H spin-lattice relaxation and slow translational exchange in disordered systems

We present an analysis of ²H spin-lattice relaxation of deuterated benzene in the glass former tricresyl phosphate. Whereas pronounced nonexponential relaxation is observed well below the glass transition temperature T_g (181 K), a crossover to exponential relaxation is found at T ≅ T_g. By assuming a certain distribution of barriers for the rotational jump process of benzene in the glassy matrix, we are able to describe all relaxation curves in the temperature range 20 K < T < 160 K. The crossover from nonexponential to exponential relaxation is described by additionally assuming translational exchange processes of benzene molecules between sites with different barriers for the rotational jumps. Within a simple model we are able to determine exchange rates over more than two decades. Comparing the results with diffusion data, we conclude that the obtained rates correspond to diffusion coefficients in the range 10^-18 < D/m² s^-1 < 10^-16 and that translational rotational coupling does not hold near T_g. The further potential of the method in order to determine very slow exchange processes is discussed.