Nuclear magnetic resonance studies of multi-site chemical exchange. I. Matrix formulation of the Bloch equations

Abstract

A concise matrix formulation of chemical exchange effects on a nuclear magnetic resonance (n.m.r.) spectrum using the Bloch equations is described. The method accommodates many-site exchange processes, site-dependent relaxation times, differing site populations, and saturation effects in a steady-state first-order spectrum. The simple two-site exchange system is analyzed in detail and saturation effects in this system are studied numerically. Alternative forms of the basic lineshape equation are derived, all of which are readily adapted to efficient computer calculations for complete lineshape fitting to obtain kinetic data for complicated chemical exchange processes.