Describing NMR chemical exchange by effective phase diffusion approach

Abstract: This paper proposes an effective phase diffusion method to analyze chemical exchange in nuclear magnetic resonance (NMR). The chemical exchange involves spin jumps around different sites where the spin angular frequencies vary, which leads to a random phase walk viewed from the rotating frame reference. Therefore, the random walk in phase space can be treated by the effective phase diffusion method. Both the coupled and uncoupled phase diffusions are considered; additionally, it includes normal diffusion as well as fractional diffusion. Based on these phase diffusion equations, the line shape of NMR exchange spectrum can be analyzed. By comparing these theoretical results with the conventional theory, this phase diffusion approach works for fast exchange, ranging from slightly faster than intermediate exchange to very fast exchange. For normal diffusion models, the theoretically predicted curves agree with those predicted from traditional models in the literature, and the characteristic exchange time obtained from phase diffusion with a fixed jump time is the same as that obtained from the conventional model. However, the phase diffusion with a monoexponential time distribution gives a characteristic exchange time constant which is half of that obtained from the traditional model. Additionally, the fractional diffusion obtains a significantly different line shape than that predicted based on normal diffusion.