Restraints on bi-exponential fitting of inversion-recovery data involved in two-site exchange
✍ Scribed by Mao, Xi-An ;Zhang, Yong-Hong
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 153 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1043-7347
- DOI
- 10.1002/cmr.1016
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✦ Synopsis
Abstract
The recovery of the inverted magnetization in two‐site exchange systems generally follows a bi‐exponential law, C~+~e+C~−~e with λ~+~>λ~−~. With the assumption R~1__A__~<R~1__B__~ (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, C~A+~, must be positive, while the other three, C~A−~, C~B+~, and C~B−~, 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~≪|R~1__A__~−R~1__B__~| (slow exchange limit); (2) k~AB~+k~BA~≫|R~1__A__~−R~1__B__~| (fast exchange limit); (3) k~AB~+k~BA~ can be any value, but R~1__A__~≈R~1__B__~ (small relaxation‐difference limit); (4) P~A~≫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. © 2001 John Wiley & Sons, Inc. Concepts Magn Reson 13: 326–333, 2001