The Static Magnetic Field Dependence of Chemical Exchange Linebroadening Defines the NMR Chemical Shift Time Scale

The static magnetic field dependence of chemical exchange linebroadening in NMR spectroscopy is investigated theoretically and experimentally. Two-site exchange (A ⇆ B) is considered with site A more highly populated than site B (pa > pb), a shift difference between sites equal to Δω, and an exchange rate constant given by kex. The exchange contribution to the transverse relaxation rate constant for the more highly populated site is denoted Rex. The dependence of Rex on the static magnetic field strength is characterized by a scaling parameter α = d ln Rex/d ln Δω, in which 0 ≤ α ≤ 2 for pa > 0.7. The value of α depends on the NMR chemical shift time scale for the exchange process:  for slow exchange (kex/Δω 1), 1 < α ≤ 2. Consequently, the static magnetic field dependence of Rex defines the chemical shift time scale for an exchange process even if the populations are so highly skewed (pa ≫ pb) that the minor r...