Restraints on bi-exponential fitting of inversion-recovery data involved in two-site exchange

The recovery of the inverted magnetization in two-site exchange systems gen erally follows a bi-exponential law, C(+)e (-lambda +t) + C(-)e (-lambda -t ) with lambda (+)> lambda (-). With the assumption R-1A < R-1B (R-1 denotes the relaxation rate), however, bi-exponential fitting should be performed under the restraints: one of the four coefficients in the AB system, CA+, M ust be positive, while the other three, CA- CB+, and CB-, must be negative. The bi-exponential law can be approximated to a mono-exponential law only when one of the following conditions is satisfied. (1) k(AB) + k(BA) much l ess than \R-1A - R-1B\ (slow exchange limit); (2) k(AB) + k(BA) much greate r than \R-1A - R-1B\ (fast exchange limit); (3) k(AB) + k(BA) can be any va lue, but R-1A approximate to R-1B (small relaxation-difference limit); (4) P-A much greater than P-B (large population-difference limit), where k and P denote the exchange rate and population, respectively. The last condition is suitable only to the more populated spin. (C) 2001 John Wiley & Sons, I nc.