Molecular ordering is important for physical and electrical properties of materials such as polymers and liquid crystals. For these non-crystalline/amorphous materials, multiple-quantum (MQ) spin-counting solid-state NMR is a powerful tool for structural analysis as it permits to get insight into the spatial distribution of spins in such disordered solid yet the quantitative analysis of size and shape of spin clusters by the density matrix approach remains very difficult. Here we presents a novel stochastic approach for analyzing MQ spin dynamics. The statistical approach is based on the percolation theory with Monte Carlo methods and is examined by applying it to the experimental results of three solid samples having unique hydrogen arrangement for 1–3 dimensions: the n-alkane–d-urea inclusion complex as a one-dimensional (1D) system, whose 1H nuclei align approximately in 1D, and magnesium hydroxide and adamantane as a two-dimensional (2D) and a three-dimensional (3D) system, respectively. Four lattice models, linear, honeycomb, square and cubic, are used to represent the 1H arrangement of the three samples. It is shown that the MQ dynamics in adamantane is consistent with that calculated using the cubic lattice and that in Mg(OH)2 with that calculated using the honeycomb and the square lattices. For n-C20H42–d-urea, these 4 lattice models fail to express its result. It is shown that a more realistic model representing the 1H arrangement of n-C20H42–d-urea can describe the result. The approach is then applied to investigate 1H distribution in various inorganic materials, for example, tobermorite and appetite. Application to MQ among spins other than 1H will also be presented.
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 Y. Mogami, Y. Noda, H. Ishikawa and K. Takegoshi, Phys. Chem. Chem. Phys. 15 (2013) 7403-7410.