mean square of the signal alone. For an alternating waveform, the mean square value is directly proportional to the power of the alternating waveform. Thus the signal-to-noise power ratio can be calculated from the mean square of the signal divided by the difference between the 7 = 0 value (S N) and the mean square of the signal. On this basis the signal-to-noise power ratio in the original noisy sine wave calculated from its autocorrelation function (Figure 8u) is about 0.2.
+
CONCLUSIONS This autocorrelator was not directly applied to a chemical signal. The primary aim of this study was to point out the availability and applicability of devices such as the serial analog memory to correlation measurements. Hieftje (6) has shown that correlation techniques can be advantageously applied to measurements where lock-in amplifiers are typically employed. Since lock-in amplification is widely used in analytical instrumentation, the correlation approach has potential wide applicability as instrumentation becomes more readily available to implement correlation analysis. Devices such as the SAM are sure to promote this development. In addition, the autocorrelation approach to processing a noisy periodic signal does not require a reference signal as is necessary for lock-in detection. Application of the SAM to chemical measurements is by no means limited to autocorrelation. Both transient recorders and cross-correlation instruments could be constructed using serial analog memories. The construction of a transient recorder using a device related to the SAM, a serial analog delay (SAD), has already been reported (14).Many additional applications are outlined in literature available from Reticon. Reticon also has available a tapped analog delay line (TAD-
12). This device can be thought of as an analog shift register with serial electrical input and parallel electrical outputs. The TAD-12 has 24 storage cells and 12 taps. It is potentially a very powerful device for matched filtering, real-time correlation filtering, and pattern recognition (9).Many filter characteristics can be implemented that are difficult or even impossible to implement using conventional approaches. Work is presently under way in our laboratory to evaluate the application of tapped analog delay lines to the real-time correlation processing of chemical signals.
LITERATURE CITED (1) Y. W. Lee, T. P. Cheatham, Jr., and J. B. Wiesner, Roc. IRE, 38, 1165 (1950). (2) Y. W. Lee, "Statistical Theory of Communication", John Wiley 8 Sons, New York, N.Y., 1960. (3) F. H. Lange, "Correlation Techniques", D. Van Nostrand, Princeton, N.J., 1967. (4) W. A. Rosenbleth, "Processing Neuroelectric Data", The M.I.T. Press, Cambridge, Mass., 1959. (5) J. S. Barlow, IRE Trans. Med. Electron., 6, 179 (1959). (6) G. M. Hieftje, R. J. Bystroff, and R. Lim, Anal. Cbem., 45, 253 (1973). (7) Gary Horlick, Anal. Cbem., 45, 319 (1973). (8)Gary Horlick and Gary M. Hieftje in "Computers in Chemical and Biochemical Research", Vol. 3, C. Klopfenstein and C. L. Wilkins, Ed., Academic Press, New York, N.Y. (in press). (9) Gary Horlick, Anal. Cbem., 48, 783A (1976). (IO) G. M. Hieftje, Anal. Cbem., 44(7), 69A (1972). (11) P. W. Fry, J. Phys. E, 8, 337 (1975). (12) Gary Horlick, Appl. Spectrosc., 30, 113 (1976). (13) H. V. Malmstadt, C. G. Enke, S. R. Crouch, and Gary Horlick, "Optimization of Electronic Measurements", W. A. Benjamin, Menlo Park, Calif., 1974. (14) T. A. Last and C. G. Enke, Anal. Chem. (submitted for publication).
RECEIVEDfor review March 29, 1976. Accepted July 27,1976. Financial support by the University of Alberta and the National Research Council of Canada is gratefully acknowledged.
Automated Measurement of Spin-Lattice Relaxation Times: Optimized Pulsed Nuclear Magnetic Resonance Spectrometry D. MI. Cantor* and Jiri Jonas Department of Chemistry, School of Chemical Sciences and Materials Research Laboratory, University of Illinois, Urbana, Ill. 6 180 1
An automated system for the measurement of the spin-lattice relaxationtimes, T1, has been developed using the pulsed NMR technique. The system automatically generates and optlmlres the pulse sequences and carries out the measurement of T1. There are three major advantages of thls system: a) substantially improved precision; b) reduction of measurement time; c) more accurate optimlzation of pulse lengths and phases than for manual operation. The performance of the system has been tested on several NMR samples.
Measurement of spin-lattice relaxation times ( T I )has assumed considerable importance to physical chemists and biochemists, since these measurements can provide detailed information about molecular motions in solids, liquids, and solutions. In biological systems, TI can also be used to help make assignments of lines in complicated spectra (1,2),and to detect the presence ( 3 )of paramagnetic ions near the active sites of enzymes. A number of computerized systems have been reported (4-7) which can generate pulse sequences, collect data, and perform the necessary calculations, and there is at least one 1904
e
commercially available system (8).There are no pulsed NMR systems, however, which can automatically optimize experimental parameters. This fact was noted with some surprise in a review article in this journal (9). For some time, this laboratory has measured T I under conditions of extreme pressure and temperature (10).Changes in those conditions lead to subsequent changes of electrical parameters in the NMR sample probe, which in turn lead to variations in the effective radiofrequency field felt by the sample, and in its phase. Thus, frequent reoptimization of pulse lengths and phase is necessary, and it was decided to automate these optimizations as much as possible.
MEASUREMENT TECHNIQUE Details of the measurement of T I by pulsed methods may be found elsewhere ( I I ) , so only a brief discussion of the 180°-r-900 pulse sequence technique, which is the most common, will be presented here. Application of a pulse of radiofrequency energy of the appropriate frequency causes the magnetic moment to tip away from its equilibrium position by an angle 6, which is approximately given by
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
I
1'
PDPB/E COMPUTER
Figure 2. Automated NMR system block diagram
COMPUTER OR FRONT PANEL SWITCH REGISTER
Figure 1. Timing relationships in the inversion-recovery pulse sequence
6'
P
?Hit,
(1)
where y is the magnetogyric ratio, H I is the radiofrequency magnetic field strength, and t , is the pulse length. HIis typically in the range 1-50 gauss. After such a pulse, a signal is produced (the so-called free-induction decay, FID) which is proportional to the projection of the magnetic moment vector into the x-y plane. A diagram of the timing relations in the 18Oo-~-9O0sequence is shown in Figure 1, where tp, is the 180" pulse length, t,, that of the 90° pulse. The magnetization after such a sequence is given by (11): In
- M ) = ln 2
~ -0I
(2) T1 where M o is the equilibrium magnetization. Thus, by measuring the magnetization for several values of 7 and plotting In (Mo - M ) vs. 7 , a linear plot with slope - 1/T1is obtained. Mo is measured by using a sequence with only a single 90' pulse. An equilibration period, typically 5T1 or more, must be allowed between pulse sequences. For samples with a single resonance, the magnetization may be determined directly from the height of the FID. If several lines are present, the FID must be Fourier transformed and peak heights or areas are used. In this work, samples with single-line spectra are used exclusively. The measurement requires control over the pulse lengths, the phase of the pulses, and T . Pulse lengths range typically from 1 to 50 ps, depending on the power of the transmitter used, and T is comparable to TI, which ranges between 1ms and 60 s for most liquids. In Fourier transform measurements, the phase adjustment is performed by software after transformation. For single-line spectra, experimental adjustment of the phase is necessary. Optimization of pulse lengths and phase is achieved through a modification of the UNIPLEX algorithm of King and Deming (12).This is a one-dimensional sequential search, which uses information from previous measurements to determine where the next measurement should be made. For details, see the original paper (12). A 90" pulse represents a maximum in the height of the FID. To reduce the influence of noise, a function proportional to the magnetization, of the form (MO
m = J bM ( t ) d t
(3)
is used, where M ( t ) is the FID height as a function of time. The lower limit is chosen large enough that averaging takes place beyond any ringing in the detector. The upper limit is made small enough to minimize the effects of field drift. Typically, a = 0.5 ms, and b = 2.5 ms. The net magnetization is zero for a 180" pulse. Since the FID can have either positive or negative values, the optimum
-
L
TRANSMITTER
1
Figure 3. Block diagram of the computer-controlled pulse programmer
is defined as the maximum in the function - [ m 1. This requires an accurate knowledge of the baseline, which is determined by measuring the FID a long time after the pulse. It is possible to use other functions to optimize the 180" pulse, e.g., the initial slope of the FID, but these are unduly complicated by field inhomogeneity, drift, and detector ringing. Phase optimization does not require accurate pulse lengths, and so is normally performed first. Pulse lengths approxi. mating a 90" pulse are used, and the function m in Equation 3 is maximized to give the optimum phase. The initial point chosen has little or no effect on the optimum found for any of the procedures, but the speed of convergence depends quite strongly on this guess. Since the optimum values change relatively little during the course of the experiment, the previous optimum is normally used as the starting point for subsequent optimization. The measurement program has been designed for maximum flexibility by using a task-oriented structure. This does not impose any restrictions on the order in which tasks are performed.
EXPERIMENTAL The NMR system used has been described elsewhere (IO).The major change made in this work is substitution of the pulse programmer which can be controlled by the computer for the manually operated pulse programmer previously used. A block diagram of the system is shown in Figure 2. The computer is a Digital Equipment Corporation PDP 8/e with 16k of core. Software was written in FORTRAN and SABR assembly language. The transient recorder is a Biomation Model 610B, which has a 6-bit analog-to-digital converter, and 256 words of storage. A block diagram of the computer-controlled pulse programmer is shown in Figure 3. All functions of this programmer may be controlled by the computer, or through a front-panel switch register. The disable circuits shown in the figure allow the programmer to generate single pulses during optimizations. Otherwise, a pulsel-T-pulsez sequence is generated. Each pulse length is determined by a 12-bit presettable downcounter. The counter is clocked a t 10 MHz, so pulse lengths are available in 0.1-ps increments, to a maximum of 409.6 ps. It was not possible to measure any propagation error, which must be less than 0.1 p s . Any pulse length instability was not detectable. The time between pulses, T , is determined in a similar manner. Since a broad range of values is needed, only the lowest 8 bits of the 12-bit word are used to load the down-counter. The upper 4 bits are used to gate a frequency divider at the input to the counter. The pulses
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Table I. Comparison of Measured and Literature Values of TI
Sample T I ,s Lit. T I ,s Reference Hz0-0.050 M NiClz 0.0286 0.0260 (13) Hz0.0.020 M NiClz 0.0658 0.0650 (13) Hz0-0.005M NiClz 0.263 0.260 (13) CF4 @ 4250 psi 0.697 0.720a ... CF4 @ 6040 psi 0.881 0.870" ... CF4 @ 7550 psi 0.979 0.960a ... HzO @ 5 "C 2.00 2.02 (15) HzO @ 10 "C 2.35 2.37 (15) a Unpublished results from our laboratory (Ref. 14).
may be separated by times between 51.2 f i s and 63.7 s. The propagation error was significant, on the order of 0.5 count, but very reproducible. This allows the computer to calculate corrected values of T , which are accurate to within 5 ppm. Values of T are chosen to give equally spaced FID's, in the range of 0.3 to 2.4 times an estimate of 2'1 made by the operator. Phase control is achieved by means of two latched digital-to-analog converters which provide control signals for a pair of voltage-variable phase shifters (Merrimac Corp., Model PSEF-BE). These provide 180" of phase shift, and are inserted after the variable delay lines in the transmitter. Since the phase shifters have relatively narrow bandwidths, plug-in modules with the appropriate shifters are provided for each NMR frequency used. Detailed schematics and software are available from the authors upon request.
SYSTEM PERFORMANCE The precision of the system was tested by replicate measurements of T I for several samples. Typical values were in the range of 1 4 % RSD. This is comparable to earlier systems, and represents a substantial improvement over manual measurements in this laboratory. The precision is limited primarily by two factors: Lack of resolution in the 6-bit ADC of the transient recorder, and drift in the main magnetic field, which can be more than 100 Hz over the course of the experiment. Plans are being made to substitute a transient recorder with an 8-bit ADC, and to implement a field-frequency lock to remove the drift. It is estimated that this should improve the precision by a t least a factor of two. Replicate optimizations of the pulse lengths showed reproducibilities of better than f 0 . 2 ys. A measure of the success in pulse length optimization is the ratio of magnetizations for 90" and 180' pulses. For this system r n ~ o o l r n 1 ~ o o > 250. Phase optimization reproduced to within 5%, which compares very favorably to manual adjustments (-15%). Normally, the last several iterations were visually indistinguishable on the oscilloscope. The optimizations required on the order of 11measurements, depending on the initial point chosen. Barring severe field drift, false optima were not a problem. Accuracy of the measurements was checked by a comparison with literature values for a number of samples with TI'S
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in the range 25 ms to 2.5 s. This comparison is shown in Table I. The average error between the measured TI'Sand the literature values was 2.6%. For system with short T1 (
