The proton spin-lattice and spin-spin relaxation times (T//1 and T//2) of the liquid crystal BBOA have been measured at frequencies between 2. 5 MHz and 25 MHz. A sharp break in the temperature dependence of the spin-lattice relaxation rate was found at the transition temperature T//A//B between smectic A and smectic B phases. Further, at a temperature 2 degree C above T//A//B a second sharp break in the temperature dependence of T//1 was discovered. The temperature, frequency, and angle dependence of T//1 outside this interval of temperature can be associated with diffusion induced order-director-fluctuations. Within the 2 degree C interval, T//1 monotonically increases with decreasing temperature indicating an increase in the Frank elastic constants. From T//2 data we deduce that the r. m. s. molecular misorientation in the smectic phase is approximately 1 degree and that this misorientation changes with temperature and time in this same temperature interval.
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