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RECEIVEDfor review January 22,1979. Accepted July 23,1979. This research was supported by the Natural Sciences and Engineering Research Council of Canada and by the Research Corp.
Simulation of Nuclear Magnetic Resonance Spin Lattice Relaxation Time Measurements for Examination of Systematic and Random Error Effects T. Phil Pitner" and Jerry F. Whidby" Philip Morris USA Research Center, P.O.
Box 26583, Richmond, Virginia 2326 1
Systematic and random errors in NMR spin lattice relaxation time ( T , ) measurements are investigated by simulating relaxation data using various experimental parameters: pulse width, recovery delay, waiting times, and signal-to-noise. T,'s are calculated from the hypothetical data by linear least squares, two-parameter exponential, three-parameter exponential, and four-parameter exponential analyses to explore the suitability of these analyses. The computed T,'s and standard deviations are discussed in terms of random and systematk errors. Experimental data are presented to illustrate the applicability of the calculations.
When faced with measuring spin lattice relaxation times
(T,),the NMR spectroscopist is confronted by a myriad of confusing opinions, almost amounting to myth and folklore, as to the proper choice of measurement method, experimental parameters, and data analysis method. Several studies have appeared in the literature, aimed at delineating and clarifying this problem (1-19). The need in this laboratory for accurate and reproducible T , measurements led us to investigate some of the various methods by simulating experimental relaxation data and subjecting these data to several analyses to determine how well the calculated Tl's compare with 5"''s used in generating the data. We hope the results presented in this paper will aid and give insight to experimentalists who desire to have a reasonable degree of confidence in the Tl's they measure.
EXPERIMENTAL 'H (12.29 MHz) NMR spectra were obtained with a Bruker WP-80 spectrometer at ambient probe temperature. T,'s were measured for the 2H resonance of a 5% solution of DzO(Merck & Co.) in HzO doped with a trace of copper sulfate.
RESULTS AND DISCUSSION The most common method of measuring T,'s involves applying a perturbing rf pulse to the nuclear spins, waiting for a range of times 7 to allow the spins to relax, and sampling 0003-2700/79/035 1-2203$01 .OO/O
the extent of relaxation with an observing pulse. The peak intensity A , after waiting time 7 is given for steady-state conditions by
A, = A , sin /3
1 - [I - cos
cy
(1- e-D/T1)]e-r/T1
1 - [cos cy cos /3 e-D/T1]e-.IT1
(1)
(2, 14, 18) where A , is the equilibrium intensity; a , the perturbing pulse flip-angle; p, the observing pulse flip-angle; and D , the recovery delay between the observing pulse and the next perturbing pulse. For the standard inversion-recovery experiment a = 180" and /3 = 90" (1.2). Equation 1 assumes rf homogeneity, no offset effects (Le., (pulse width)
