Multiple-quantum dynamics in solid state NMR

Abstract

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.

Silica Surface Features and Their Role in the Adsorption of Biomolecules: Computational Modeling and Experiments

“…154 In the solid state, MQ (multiplequantum) methods for spin counting have been developed since 1985. 155 On silica, proton MQ-NMR could be used in principle to count the number of silanols interacting in a « silanols cluster ». This technique has been applied to silica catalyst supports 156 but with rather trivial results, namely that all 1 H spins exist in clusters of less than seven silanols.…”

Multiple-quantum NMR studies of spin clusters in liquid crystals and zeolites

“…One of the concepts used to describe multiple-quantum spin counting experiments is 'growth' of a spin network [37][38]. This terminology is misleading, To differentiate between growth of the spin network and an increase in the measured size of the spin network, the size of the spin network measured as a function of excitation time will be referred to as the apparent spin network size, Napp, with the assumption:…”

“…Napp is determined by performing a two parameter least squares gaussian fit of I(n), with the assumption that Napp accurately reflects the size of a coupled spin network only when the evolution of the density matrix reaches the statistical limit. Indeed, I(n) generally will not be closely approximated by a gaussian distribution before p has reached the -statistical limit [37][38], due to the differing weights of each transition in the multiple-quantum spectrum. Experimentally, N is determined by:…”

“…The number of spins present in an isolated cluster can be found by comparing -the relative intensities of multiple-quantum transitions summed by order n. Once the spectrum no longer changes with increased preparation time the density matrix is assumed to have reached the statistical limit, with each element Pij permissible under the selection rules being equal in amplitude [37]. To illustrate the density matrix evolution from the initial condition to the statistical limit, consider p for an isolated cluster of four Initially, ali spin polarization is localized along the diagonal in the population terms of p [16].…”

“…First for consideration is the eight pulse sequence of Baum, et al [37], which is an adaptation of an earlier sequence [21]. The sequence is designed to create an even order selective propagator during the preparation period and its time reversed compliment during the mixing period by utilization of homonuclear dipole-dipole couplings.…”