Correlation of primary relaxations and high-frequency modes in supercooled liquids. I. Theoretical background of a nuclear magnetic resonance experiment.

The question regarding a possible correlation of the time scales of primary and secondary relaxations in supercooled liquids is formulated quantitatively. It is shown how this question can be answered using spin-lattice relaxation weighted stimulated-echo experiments, which are presented in an accompanying paper [A. Nowaczyk, B. Geil, G. Hinze, and R. Böhmer, Phys. Rev. E 74, 041505 (2006)]. General theoretical expressions relevant for the description of such experiments in the presence of correlation effects are derived. These expressions are analyzed by Monte Carlo integration for various correlation scenarios also including exchange processes, which are the hallmark of dynamical heterogeneity. The results of these numerical simulations provide clear signatures that allow one to distinguish uncorrelated from differently correlated cases. Since modified spin-lattice relaxation effects occur in the presence of nonexponential magnetization recovery, it is shown how to correct for them to a good approximation.

Correlation of primary and secondary relaxations in a supercooled liquid.

The widespread assumption that primary and secondary relaxations in glass-forming materials are independent processes is scrutinized using spin-lattice relaxation weighted stimulated-echo spectroscopy. This nuclear magnetic resonance (NMR) technique is simultaneously sensitive to the dynamics on well-separated time scales. For the deeply supercooled liquid sorbitol, which exhibits a strong secondary relaxation, the primary relaxation (that is observable using NMR) can be modified by suppressing the contributions of those subensembles which are characterized by relatively slow secondary relaxations. This is clear evidence for a correlation between primary and secondary relaxation times. In the disordered crystal orthocarborane high-frequency processes are absent and consequently no such modifications could be achieved.

Rotational correlation functions of single molecules.

Single molecule rotational correlation functions are analyzed for several reorientation geometries. Even for the simplest model of isotropic rotational diffusion our findings predict nonexponential correlation functions to be observed by polarization sensitive single molecule fluorescence microscopy. This may have a deep impact on interpreting the results of molecular reorientation measurements in heterogeneous environments.

Simple modeling of dipolar coupled 7Li spins and stimulated-echo spectroscopy of single-crystalline beta-eucryptite.

Stimulated-echo spectroscopy has recently been applied to study the ultra-slow dynamics of nuclear spin-3/2 probes such as 7Li and 9Be in solids. Apart from the dominant first-order quadrupolar interaction in the present article also the impact of the homonuclear dipolar interactions is considered in a simple way: the time evolution of a dipole coupled pair of spins with I = 3/2 is calculated in an approximation, which takes into account that the satellite transitions usually do not overlap. Explicit analytical expressions describing various aspects of a coupled quadrupolar pair subjected to a Jeener-Broekaert pulse sequence are derived. Extensions to larger spin systems are also briefly discussed. These results are compared with experimental data on a single-crystalline Li ion conductor.

Microscopic origin of the nonexponential dynamics in a glassy crystal.

The origin of the slow relaxation and of the dynamic heterogeneity is studied for an orientation-ally disordered crystal, orthocarborane, composed of quasi-icosahedrally shaped molecules. Multidimensional deuteron magnetic resonance reveals that large jump angles dominate their complex, anisotropic reorientational motion. It involves a sequence of small-angle tilts about locally preferred axes as well as symmetry adapted threefold jumps. The intrinsic dynamics of this glassy crystal is nonexponential and can be fully accounted for in terms of the tilt and jump motion.

Experimental Determination of Four-Time Stimulated Echoes in Liquids, Colloidal Suspensions, and Crystals

Four-time stimulated echo experiments have been used to monitor the temporal evolution of the reorientation rates of deuterated molecules or colloidal suspensions. We present extended phase cycles for this seven-pulse experiment. In order to test its performance three vastly different materials are chosen. These include a crystal in which the molecules carry out well-defined 180 degrees flips and a supercooled liquid characterized by a distribution of jump angles centered around 10 degrees. As an example for rotational diffusion, data on a concentrated suspension of polystyrene spheres in a viscous medium are presented. Copyright 1998 Academic Press.