Nonexponential 2H spin-lattice relaxation as a signature of the glassy state

Combined Reduced 4D 13C Exchange and 1H Spin Diffusion Experiment for Determining the Length Scale of Dynamic Heterogeneities

“…Equilibrium is reached when the magnetization has diffused to the nearest 13 C atom over an average distance 0 . The time scale of this decay of F 4 is a measure of the length scale 0 whereas the amplitude of the decay is a measure of the distance over which 1 H magnetization can be transferred to 13 C atoms via cross polarization. If the two length scales 0 and het are significantly different the spin diffusion curve shows a two-step decay with the first decay corresponding to diffusion on the length scale 0 and the second decay corresponding to diffusion over the distance het (15).…”

“…Finally, the same filter as in the beginning of the experiments is applied again; thus, by the 4D echo experiment those components that have not changed their rates during t m2 and in the 4D-CP echo experiment the amount of magnetization that is still in the immobile regions are detected. The resulting echo decay curves F 4 (t m2 ) and F 4 (t m2 ) contain information about the exchange rate ⌫ and the length scale of dynamic heterogeneities het , respectively.…”

“…In reality D stands for the 1 H spin diffusion coefficient and a full description of the experiment is more complicated as will be discussed below. The pulse sequence used to measure F 4 (t m2 ) is given in Fig. 3b.…”

“…A number of studies on different fragile glass formers (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) has shown that the nonexponential ␣-relaxation can be attributed to the existence of dynamic heterogeneities; i.e., the macroscopically nonexponential relaxation functions are due to a superposition of different relaxation rates. Dynamic heterogeneities can be characterized by the time scale of fluctuations of relaxation rates within the rate distribution and by the spatial extension of temporary clusters of slow molecules; see Fig.…”

“…Therefore the 4D-CP echo experiment combines 13 C 2D echo filters with 1 H spin diffusion in order to achieve four-time as well as spatial correlation. The signal F 4 (t m2 ) that is recorded at the end of the pulse sequence and which is equivalent to the integral magnetization of the immobile domains is given by…”