Two-stage feature of Hartmann-Hahn cross relaxation in magic-angle sample spinning

In magic-angle sample-spinning experiments the Hartmann-Hahn cross relaxation between protonated ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and protons usually proceeds in two stages, except in fast internal rotating ${}_{}{}^{13}{}_{}{}^{}\mathrm{CH}_3^{}{}_{}{}^{}$. The protonated ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ magnetization of powder samples changes very rapidly during the first tens of microseconds due to the fast energy exchange between each protonated ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and its directly bonded ${}_{}{}^1{}_{}{}^{}\mathrm{H}$ spins; then it approaches at a much slower rate to a quasiequilibrium value via the energy exchange between these ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}{\mathrm{H}}_n$ subsystems and the remaining ${}_{}{}^1{}_{}{}^{}\mathrm{H}$ spins. This fact means that the whole ${}_{}{}^1{}_{}{}^{}\mathrm{H}$ spin system is not in a quasiequilibrium state and is not describable by a single spin temperature at least during the first stage of the cross relaxation. The two-stage feature has been obviously revealed by the depolarization experiment for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ magnetization. The expression for protonated ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ magnetization as a function of depolarization time has been deduced, which reaches agreement with the experiments semiquantitatively. The depolarization experiment offers a reliable approach to distinguishing between ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$H and ${}_{}{}^{13}{}_{}{}^{}\mathrm{CH}_2^{}{}_{}{}^{}$ signals in organic solids.