  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.
