Recently developed solid state multiple-quantum NMR methods are applied to extended coupling networks, where direct dipole-dipole interactions can be used to create coherences of very high order ( -1(0). The progressive development of multiple-quantum coherence over time depends upon the formation of multiple-spin correlations, a phenomenon which also accompanies the normal decay to equilibrium of the free induction signal in a solid. Both the time development and the observed distributions of coherence can be approached statistically, with the spin system described by a time-dependent density operator whose elements are completely uncorrelated at sufficiently long times. With this point of view, we treat the distribution of coherence in a multiple-quantum spectrum as Gaussian, and characterize a spectrum obtained for a ~iven preparation time by its variance. The variance of the distribution is associated roughly wIth the number of coupled spins effectively interacting, and its steady growth with time reflects the continual expansion of the system under the action of the dipolar interactions. The increase in effective system "size" is calculated for a random walk model for the time development of the density operator. Experimental results are presented for hexamethylbenzene, adamantane, and squaric acid. The formation of coherence in systems containing physically isolated clusters is also investigated, and a simple method for estimating the number of spins involved is demonstrated.

No abstract

No abstract

No abstract

An approach to spin dynamics in systems with many degrees of freedom, based on a recognition of the constraints common to all large systems, is developed and used to study the excitation of multiple-quantum coherence under a nonsecular dipolar Hamiltonian. The exact equation of motion is replaced by a set of coupled rate equations whose exponential solutions reflect the severe damping expected when many closely spaced frequency components are superposed. In this model the evolution of multiple-quantum coherence under any bilinear Hamiltonian is treated as a succession of discrete hops in Liouville space, with each hop taking the system from a K-spin/n-quantum mode to a K′-spin/n′-quantum mode. In particular, for a pure double-quantum Hamiltonian the selection rules are ΔK=±1 and Δn=±2. The rate for each move depends on the number of Liouville states at the origin and destination, and on the total number of spins present. All rates are scaled uniformly by a factor dependent on the properties of the material, such as the dipolar linewidth, but otherwise the behavior predicted is universal for all sufficiently complicated systems. Results derived by this generic approach are compared to existing multiple-quantum data obtained from solids and liquid crystals.