Ergodicity and efficiency of cross-polarization in NMR of static solids

A 14-spin simulation showing that the thermodynamic limit of magnetization cannot be fully transferred from a static proton bath to a nitrogen spin in a single cross-polarization contact. [Display omitted] ► Thermodynamic limit cannot be transferred from high to low spins in one CP contact. ► The thermodynamic limit can nevertheless be achieved through multiple contacts. ► The effect of dynamics on CP build up in many-spin systems is considered. Cross-polarization transfer is employed in virtually every solid-state NMR experiment to enhance magnetization of low-gamma spins. Theory and experiment is used to assess the magnitude of the final quasistationary magnetization amplitude. The many-body density matrix equation is solved for relatively large (up to N = 14) spin systems without the spin-temperature assumption for the final spin states. Simulations show that about 13% of the thermodynamic limit is still retained within the proton bath. To test this theoretical prediction, a combination of a reverse cross-polarization experiment and multiple contacts is employed to show that the thermodynamic limit of magnetization cannot be transferred from high- to low-gamma nuclei in a single contact. Multiple contacts, however, fully transfer the maximum magnetization. A simple diffusion on a cone model shows that slow dynamics can affect the build up profile for the transferred magnetization.