A statistical approach for analyzing the development of 1H multiple-quantum coherence in solids

Abstract

A novel statistical approach for analyzing ¹H multiple-quantum (MQ) spin dynamics in so-called spin-counting solid-state NMR experiments is presented. 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 present approach can thus be used to determine ¹H arrangement in solids.