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A pulsed field gradient system for a fourier transform spectrometer
37,247-259(1980)
JOURNALOFMAGNETICRESONANCE
A Pulsed Field Gradient System for a Fourier Transform Spectrometer P. T. CALLAGHAN, Department
of Chemistry,
Biochemistry
C. M. TROTTER & Biophysics,
Massey
AND
K.
University,
W. Palmerston
.iOLLEY North,
New Zealand
Received November 16, 1978; revised February 5, 1979 The construction and performance of a pulsed field gradient system for use with a commercial high-resolution pulse-Fourier transform NMR spectrometer is described. The diffusion coefficient of benzene as measured by the system lies within 0.9% of the current literature value. The use of an external ‘H lock in conjunction with signal averaging facilitates the measurement of diffusion coefficients for solution components present in small concentrations and data are presented for a 0.5% (w/v) solution of polystyrene (M, = 110,000) in carbon tetrachloride. The ability of the system to investigate slow diffusion is demonstrated by measurements made on a 10% (w/v) solution of polystyrene (M, = 230,000) in carbon tetrachloride. Homogeneity coils in the ‘H probe enable the self-diffusion of single components in multicomponent systems to be investigated, and results for the binary system butanol-benzene are presented.
INTRODUCTION
The NMR spin-echo technique for measuring self-diffusion has been used extensively since it was first suggested by Hahn (1). The advantages associated with the technique over conventional methods have been offset by poor experimental accuracy. A recent paper, however (Z), demonstrated a reproducibility of +.z1% and an overall accuracy of *2% using a steady gradient technique to measure the self-diffusion coefficients of water in electrolyte solutions. An alternative method of studying self-diffusion in liquids is the pulsed field gradient technique. Stejskal and Tanner (3) have shown that two identical rectangular pulses applied before and after the 180” refocusing rf pulse give an echo
r.f.
gradlent
!! 1 8
G
r.f. ” 90”
gradlent G
FIG. 1. Pulsed field gradient sequence showing the times r, d, A, and 6 which can be independently set in an experiment. 0022-2364/80/020247-13902.00/O 247 Copyrrght @ 1980 by Academic Press. Inc All rights of reproduction in any form reserved. Printed m Great Rrhin
248
CALLAGHAN,
TROTTER,
I
AND
JOLLEY
I
t
+
I
S3113 QNVN AE N0113313S 3Sllld
CON32 13S3Y
3NIWl.l
L3NIN 13S3Y
I
PULSED
FIELD
GRADIENT
249
SYSTEM
b
o-
FIG.
2b. Timing pulse selection circuit.
:,,,,* pz-?ll, TRIGGER PULSE
SPIN ECHO SEQUENCE
FIG. 2c. Circuit modification required when using a two-pulse spin-echo sequence as a trigger.
attenuation
of A(G)/A(O)
= exp[-Dy2G2S2(A
-a/3)],
where A(G) and A(0) are the echo amplitudes with and without the field gradient pulses, respectively. The magnitude of the gradient in the polarizing field is G and by a suitable choice of coil may be applied as a gradient with respect to the x, y, or z direction. The quantity D is the self-diffusion coefficient of the nuclear spins along the gradient direction defined by the relationship D = f2/2t,
where r2 is the mean-square distance traveled along the gradient axis in time t. The quantity y is the magnetogyric ratio of the nuclei being observed and 6 and A are pulse spacings defined in Fig. 1. There are considerable advantages in using the pulsed field gradient technique for the measurement of self-diffusion coefficients. These include the sampling of nuclear spin echoes in the absence of a gradient (an essential requirement when frequency resolution is required), the ability to measure slower diffusion, and the detection of non-Gaussian diffusion by the use of various interpulse spacings (4,5). We describe here a pulsed field gradient system controlled by the rf gate pulse of a commercial high-resolution pulse-Fourier transform spectrometer (JEOL FX-60). THE PULSE PROGRAMMER
A digital pulse programmer has been designed so that the experimental parameters A and 8, as well as the time d (see Fig. l), may be set directly on
250
CALLAGHAN,
TROTTER,
AND
JOLLEY
BCD-coded thumbwheel switches. The circuit, which utilizes 7400 series TTL devices throughout, is shown in Fig. 2a. A l-MHz signal, derived from the JEOL spectrometer crystal clock, provides the clock pulses entering the divider chain. Timing pulses appropriate to any particular experiment may be selected using NAND gates as detailed in Fig. 2b. The precision of the output pulse timing is determined by the number of up/down counters (74190s) in cascade. Figure 2 thus represents a programmer with a precision of two digits in each of the intervals d, A, and 6. Such a precision has been found to be quite adequate for our pulsed field gradient experiments. The up/down counters are utilized in the down counting mode, and are directly programmed with the thumbwheel switches. The function of the pulse programmer is to provide the accurate, sequentially timed intervals d, S, and A. The TTL devices are used in a manner which avoids the problem of propagation delays so that the accuracy of all timed intervals is better than 1 ksec. At power turn-on, a reset pulse (> 1 ksec) must be provided to the appropriate PRE or CLR inputs (see Fig. 2b) of the 7474s to set their initial states. The trigger pulse is provided by the spectrometer pulse programmer, and as such is a two-pulse sequence for a spin-echo experiment. This two-pulse sequence is easily turned into the required single-trigger pulse by the inclusion of the circuitry shown in Fig. 2c before the trigger input. The l-MHz clock access to the divider chain is automatically disabled when the two-pulse sequence reaches completion. The appearance of the falling edge of the next trigger pulse readies the system for a new sequence, and timing proceeds from the rising edge of the trigger pulse. The circuit presented does not require the NAND gate range switches to be debounced, or to make before break, as false clocking of the counters is prevented by their inhibited CLK inputs. More details concerning the pulse programmer are given in the Appendix. CURRENT
CONTROL
The pulse programmer logic output is used to externally switch the current supplied by a commercial operational power supply (KEPCO JQE 2510M) operating in the constant current mode. This power supply was modified to give reduced response time by removal of the output capacitor, and the addition of several phase shifting networks around the error amplifier to prevent oscillation.’ Transistors in a three-stage Darlington configuration, shown in Fig. 3, are used to generate the field gradient pulses by externally switching the current path. During 6, the QA transistors are turned on and QB are off, thus allowing current to flow through the gradient coils. At all other times QA are off and QB are on, thus isolating the coils from the circuit. At all times the current magnitude is controlled by the power supply feedback amplifier. This has the advantage that the gradient pulse amplitude may be measured at any time by noting the voltage drop across the SO-W, O.ln precision resistor, Rs. The actual current pulses flowing in the coils may be monitored across resistor R using an oscilloscope with a differential input amplifier. 1 This circuitry
brings the specifications the modifications were
up to the equivalent based.
high-speed
model
OPS 25-10M
upon
whose
PULSED
FIELD
GRADIENT
251
SYSTEM
LOAD
TTL PULSE INPUT
FIG. 3. Current switching QBI), TIP 30A (QM, Qd
circuit for the field gradient and 2N3906 (QM, Qd.
coils.
The transistors
used
are TIP
36A
(QAI,
The optical isolator provides a convenient (-5 V, 0 V), to (0 V, +5 V) logic voltage level translation as well as protection for the ‘ITL pulse programmer. A 2-A fuse is included to protect the coils in the case of system failure. The current supply output transistors are protected from large voltage spikes generated during current turn-off by the high-speed rectifier diodes in parallel with the coils. The current pulses produced by this system, using the Helmholtz coils as a load, are shown in Fig. 4a. The current regulation is better than 0.02% over the operating range (100 mA to 10 A) and the pulses are precisely matched in shape. Any error in a > ‘ tr
> < tf
l-----L .
100/m
’
.rf fleM o gradmt
-4
~2
0 displacement
2 mm
4
FIG. 4. (a) Gradient pulse shape for a 1.5 T m-i pulse determined by measuring the voltage across resistor R in Fig. 3. The rise and fall times are independent of the pulse height and duration. (b) Radiofrequency field and field gradient profiles measured along the y axis of the sample space.
252
CALLAGHAN,
TROTTER,
AND
JOLLEY
measuring diffusion coefficients caused by deviation from the rectangular pulse shape is insignificant ( < 0.1%) for values of S 2 500 psec. External switching of the current to provide the gradient pulses avoids the possibility of current flowing through the coils other than during times S. Systems employing feedback amplifiers for current stabilization are susceptible to pickup on the sensing resistor during the rf pulse. This may cause small amounts of gradient current to be present during the rf pulse. We have found, by experimenting with other switching systems, that these small gradients can cause a distortion in the echo envelope and phase, effects mentioned by other authors (6, 7). Isolation of the coils during times other than 6 avoids this problem. THE
PROBE
A 60-MHz low-resolution ‘H probe was built to incorporate 0.15 T mm* A-’ field gradient coils. The entire unit was made to fit in the 32-mm gap between the polarizing magnet pole faces. The rf section of the probe consists of a single coil series resonant circuit designed according to the criteria set out by Clark and McNeil (8). The circuit diagram is shown in Fig. 5. We have used a JEOL 60-MHz FET preamplifier in the receiver stage although any other single-stage tuned preamplifier would suffice (9). Resistor Ri has been included to limit the coil Q during the ring down stage after the 60-V pp rf pulse. In order to obtain maximum power transfer the length of the 50-n coaxial transmission line was set (8) to give a load impedance, when tuned at Ci, equal to the transmitter output impedance. The sample coil, L2, was designed to give good homogeneity of the rf field and a good filling factor but with an inductance and Q limited to the desired low values. We have followed the method of Lowe and Tarr (10) and have wound a two-turn 7-mm-long, g-mm-diameter coil from 0.17-mm copper shim. After the series capacitor C1 was tuned the ‘H 90” flip time was 23 ysec under a 60-V pp rf pulse at 60 MHz. The coil was wound on the glass Dewar shown in Fig. 6 using Teflon tape to hold it in place. Sample tubes are inserted in the 5-mm-diameter cavity down the axis Ll
Dl
FIG. 5. Series resonant circuit after Clark and McNeil1 (8). Resistor RI is included to reduce ring down times to - 1.5 psec and L, is adjusted to present a 50-a load to the rf transmitter. LICI, LzCz, and L3C3 are tuned pairs. The diodes shown are high-speed silicon.
PULSED
FIELD
il
GRADIENT
+--
SYSTEM
253
thermocouple
FIG. 6. Sample space geometry. The viewing port along the axis of the Helmholtz coil allows the rf coil to be accurately centered.
of the Dewar and sample temperature is controlled using a copper-constantan thermocouple sensor in a conventional hot-air feedback system. The temperature variation over the sample volume is s 05°C. The rf profile measured along the y axis of the sample space is shown in Fig. 4b. The rf pulse strength was determined by measuring the-180” flip time in a very small water sample. The main aB,/at gradient coils for diffusion measurements are an opposed Helmholtz pair wound with 19 turns per coil using 26-swg enameled copper wire on a Teflon former. During an experiment the coils are maintained at a constant temperature by a steady stream of air directed at their base. Helmholtz coils offer good gradient uniformity over the small sample volumes employed in this system, but for extended cylindrical volumes quadrupolar coils are superior (II). The shape of the Helmholtz former follows the equation of Tanner (12) and minimizes secondorder (a2B,/k2) gradients over the sample space. The gradient uniformity in our coil is calculated to be better than 1% over the sample space 4.5 mm in diameter and 4.5 mm in length. The calculated y-axis profile has been confirmed experimentally by measuring the echo attenuation of a small water sample as a function of its position along the y axis (see Fig. 4b). We have included in the probe a set of aB,/ax, aB,/ay, and aB,/az homogeneity coils. These coils give a residual gradient, go, of 0.1 mT m-‘. This gradient is sufficiently small to resolve ‘H resonances - 60 Hz apart which allows for independent measurement of diffusion rates in some multicomponent mixtures, and provides
254
CALLAGHAN,
TROTTER,
AND
JOLLEY
a valuable increase in signal to noise when working with dilute molecular species. An excellent set of design criteria has been given by Anderson (13). Where possible we have used Teflon, laminated plastic, and Perspex as construction materials in the probe to minimize any eddy currents associated with switching on and off the field gradient pulses. These currents can distort the gradient time dependence from the desired square shape. By examining the ‘H free-induction decay in the eddy current “tail” following a maximum 1.5 T m-l gradient pulse we have determined that eddy effects contribute s 0.03 mT m-r at 500 psec following a gradient pulse and d 0.01 mT m-l at 1000 p.sec. Despite the small operating gap between the magnet pole pieces, gradients associated with eddy currents are entirely insignificant for diffusion experiments over the entire experimental range, S 2 0.5 msec, d 2 2 msec. RESULTS
‘H spin-echo signals are sampled with an AD converter and processed in the minicomputer of the JEOL spectrometer. Data are analyzed by plotting the natural logarithm of the echo attenuation versus 12S2(A -S/3) and performing a leastsquares fit to the resulting straight line. Using a water sample at 25°C and taking Mills’ value (14) for the diffusion coefficient of water at this temperature (2.266 x 10e9 m2 set-‘) we obtain a coil gradient of 0.1512 f 0.0005 T m-l A-‘, which is within 1% of that calculated from a knowledge of the coil dimensions. With this value for the field gradient the diffusion coefficient of Analar benzene at 25°C is
.-s
5
benzene
25.0 “C
.2 -
s ?i
0
2
12h2(A-
FIG. 7. Echo attenuation plot parameters, G, A, and 6, are varied.
for
Analar
benzene
8
s
4 ;a)
xl0
-1
A* s3
at 25.O”C
in which
all three
experimental
PULSED
FIELD
GRADIENT
SYSTEM
255
(2.23 f 0.02) x lo-’ m* set-‘, compared to the literature value (15) of 2.210x 1 O-’ m* set-’ . Figure 7 shows an echo attenuation plot for benzene at 25°C obtained by varying all three parameters G, A, and 6. These data are consistent with the Skejskal and Tanner formula (3), the diffusion coefficient being independent of 6 and A within experimental precision. The data intercept also agrees with the measured zero gradient amplitude. The ability to accumulate data in a signal-averaging mode is a major advantage with modern NMR spectrometers. Use of an external *H lock (JEOL NM 3900) allows for the accumulation of signals under pulsed field gradient conditions since we find that the lock signal recovers from the field gradient pulse in i 2msec. We have found that when adding successive spin echoes it is essential to remove any small
1.0
2.0 I’&‘(A
3.0 - fi
)
x
A* s3
FIG. 8. (a) Echo attenuation data for a solution of 0.5% (w/v) polystyrene (M, = 110,000) in Ccl4 at 250°C. The line shown is obtained by a linear least-squares fit. (b) 10% (w/v) polystyrene (M, = 230,000) in CC14 at 25.O”C.
2.56
CALLAGHAN,
a
TROTTER,
benzene
AND JOLLEY
butanol
100 Hz
A-15
ms
FIG. 9. (a) ‘H frequency spectrum for 5-mm-long, 4.5-mm-diameter sample consisting of an equimolar mixture of benzene and butanol at 25.o”C. (b) Echo attenuation data for pure benzene, pure butanol, and the benzene and butanol components in an equimolar mixture. Ail data were obtained at 25.O”C and the self-diffusion coefficients are respectively (2.23 k 0.02) x 10e9, (0.43 iO.01) x 10m9, (1.83 kO.02) x 10e9, and (0.90+0.01)x 10e9 m* set-‘.
PULSED
FIELD
GRADIENT
SYSTEM
251
spurious dc signal component. On our machine this is accomplished by phaseinverting successive spin-echo pulse pairs while at the same time alternating the sign of the AD converter. In Fig. 8a, the echo attenuation plot for 0.5% (w/v) polystyrene (Mr = 110,000) in carbon tetrachloride at 25°C is shown. Each data point represents 400 accumulations. Previous published diffusion measurements on polystyrene solutions using pulsed field gradient NMR have been restricted to concentrations greater than 30% (16). In conjunction with photon correlation spectroscopy methods (17) we are proceeding with comparative diffusion measurements over a wide concentration range using a variety of polystyrenes and solvents of different molecular weights. Figure 8b shows the echo attenuation plot for a 10% (w/v) solution of polystyrene (M, = 230,000) in carbon tetrachloride at 25°C. The discrepancy between the data intercept and the zero gradient amplitude is caused by slow lock signal recovery in the time 7 - S (5 msec following the long, 22-msec) gradient pulse. It is eliminated by increasing T -6. The diffusion rate of (6.8 f 0.3) x lo-l3 m2 see-i is near the slow limit for the technique and although other authors (18-20) have reported slower diffusion measurements in the vicinity of lo-l3 m2 set-‘, the present result does represent a considerable improvement in sensitivity and precision in this range. The above results were obtained by measuring the amplitude of the spin echoes directly from the time domain signal. An alternative way is to start the signal sampling at the center of the echo so that the data may be Fourier-transformed into the frequency domain. Provided that the components of a mixture have resolvable resonances it then becomes possible to measure the self-diffusion rates of the various molecular species (21). Figure 9a shows the ‘H frequency spectrum of an equimolar mixture of benzene and butanol. It can be seen that the homogeneity coils incorporated in the probe give a resolution of - 35 Hz over the sample volume and the benzene and butanol resonances are resolved. The echo attenuation data for pure butanol, pure benzene, and the equimolar mixture are shown in Fig. 9b. We intend to compare self-diffusion coefficients in various molar mixtures of this and other binary solutions with mutual diffusion rates obtained by the photon correlation spectroscopy facility in this department (17). CONCLUSION
We have shown that the pulse field gradient device described above gives excellent agreement with the accepted literature values for the diffusion coefficient of benzene (15). We have also demonstrated the advantages to be gained by interfacing such a device to a high-resolution pulse-Fourier transform spectrometer, the computer software of which facilitates spectrum accumulation and reduction. Data accumulation enables measurements to be made on dilute solutions as is demonstrated by the 0.5% polystyrene solution results, and the Fourier transform capability enables the frequency spectrum to be obtained provided sampling is commenced at the center of the echo. This allows for the measurement of diffusion coefficients for single-solution components in multicomponent systems provided their resonances are resolvable. The high-resolution magnet and the simple homogeneity coils incorporated in the
258
CALLAGHAN,
TROTTER,
AND
JOLLEY
probe provide a resolution of about 35 Hz, which is sufficient to resolve components whose chemical shift is 2 1 ppm at 60 MHz.
APPENDIX
The pulse programmer consists of three sections: the divider chain and associated pulse selection circuitry; the d, A, and S down counters; and the control circuitry. With the aid of Fig. 2, the workings of sections 1 and 2 are self-evident. However, the control circuitry, consisting of sundry D flip-flops (7474s) and several monostables, merits a little further explanation. The problem of providing sequentially timed intervals is generally complicated by the presence of propagation delays, and it is the function of the control circuitry to circumvent any inaccuracies such delays might otherwise cause. In sequential timing, the edge of a clock pulse which marks the end of an interval also marks time zero for the next interval. The second interval’s counters will always miss their time zero pulse if they are activated at the end of the first interval due to propagation delays associated with the activation process. Down counters, including the 74190 counter, often have a so-called “look ahead” feature for use in sequential timing. This is an output pin whose logic state changes upon a count of one and this change may be used to activate the next interval’s counters as the next clock pulse will mark time zero for this interval. Unfortunately the precision of the pulsed field gradient experiment often demands that there be order-of-magnitude differences in the frequencies of the clock pulses driving the A and S counters, with S having the higher-frequency pulses. Thus activation of the S counters by some “look-ahead” feature could result in 8 being incorrectly timed. In the present application these problems are overcome by inhibiting those counters not immediately concerned with timing a particular interval. This is achieved by placing a logic one at the CLK input of the initial counter in the cascade via a D flip-flop. Immediately a timed interval is completed, the next appropriate counters are activated, and the previous counters inactivated, by clocking the appropriate fiip-flops (those connected to the counters’ CLK inputs). The monostables (74123s) are also triggered at this stage and provide a pulse sequence to the divider chain which causes all outputs to go to the count of nine, then one. This reset-nine, reset-zero sequence has the effect of mimicking a timing pulse at the CLK input of any activated down counters and so time zero is restored and timing proceeds with no loss in accuracy. For the case when 1-usec pulses are selected the D flip-flop, marked as 7474” in Fig. 2a, provides the necessary zero time pulse.
ACKNOWLEDGMENTS
Mr.
The authors K. Smith
are indebted to Mr. R. C. O’Driscoll and Dr. D. N. Pinder and Mr. R. Parsons for technical assistance.
for valuable
discussions
and to
PULSED
FIELD
GRADIENT
SYSTEM
2.59
REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
16. 17. 18. 19.
20. 21.
E. HAHN, Phys. Rev. 80, 580 (1950). K.R.HARRIs,R.MILLs,P.J. BACK, AND D.S. WEBSTER, J. Map. R~SOII. 29,473 (1978). E.O.STEJSKALANDJ.E.TANNER,J. Chem.Phys.42,288 (1965). E, 0. STEJSKAL, J. Chem. Phys. 43,3597 (1965). J.E.TANNERAND E.O.STEJSKAL,J. Chem.Phys.49,1768 (1968). G. B. MATSON, Rev. Sci. Innstrum. 43, 1504 (1971). L. MCLACHLAN, Institute of Nuclear Sciences, DSIR, Wellington, N.Z., private communication. W.G.CLARKANDJ. A.McNEIL, Rev.Sci.Insrrum.44,844 (1973). D.J. ADDUCI,~. A.HORNUNG, AND D.R.TORGESON, Reo. Sci. Instrum.47,1503 (1976). J.LOWE AND C.E.TARR,J. Phys.E. 1,320(1968). D.S.WEBSTERAND K.H.MARSDEN, Rev.Sci. Insrrum.45,1232(1974). J. E. TANNER, Rev. Sci. Znsaum. 36,1086 (1965). W. A. ANDERSON, Rev. Sci. Znsrrum. 32,241(1961). R. MILLS, J. Phys. Chem. 77,687 (1973). K.R.HARRIs,C. K.N.PuA,ANDP.J.DuNLoP,J. Phys. Chem.,3524 (1970). T.COSGROVEANDR.F.WARREN, Polymer 18,255 (1977). D.N.PINDERANDR.C.O'DRISCOLL,J. Phys.E. 10,400(1977). B.D.Boss,E.O.STEJSKAL,ANDJ.D.FERRY,J. Phys.Chem. 71,1501(1967). J.E.TANNER,KANG-JEN LIU, ANDJ.E. ANDERSON, Macromolecules 4,586 (1971). J. E. TANNER, Mucromdecules 4,748 (1971). T.L.JAMEs ANDG.G.MCDONALD,J. Magn.Reson. 11,58 (1973).
JOURNALOFMAGNETICRESONANCE
A Pulsed Field Gradient System for a Fourier Transform Spectrometer P. T. CALLAGHAN, Department
of Chemistry,
Biochemistry
C. M. TROTTER & Biophysics,
Massey
AND
K.
University,
W. Palmerston
.iOLLEY North,
New Zealand
Received November 16, 1978; revised February 5, 1979 The construction and performance of a pulsed field gradient system for use with a commercial high-resolution pulse-Fourier transform NMR spectrometer is described. The diffusion coefficient of benzene as measured by the system lies within 0.9% of the current literature value. The use of an external ‘H lock in conjunction with signal averaging facilitates the measurement of diffusion coefficients for solution components present in small concentrations and data are presented for a 0.5% (w/v) solution of polystyrene (M, = 110,000) in carbon tetrachloride. The ability of the system to investigate slow diffusion is demonstrated by measurements made on a 10% (w/v) solution of polystyrene (M, = 230,000) in carbon tetrachloride. Homogeneity coils in the ‘H probe enable the self-diffusion of single components in multicomponent systems to be investigated, and results for the binary system butanol-benzene are presented.
INTRODUCTION
The NMR spin-echo technique for measuring self-diffusion has been used extensively since it was first suggested by Hahn (1). The advantages associated with the technique over conventional methods have been offset by poor experimental accuracy. A recent paper, however (Z), demonstrated a reproducibility of +.z1% and an overall accuracy of *2% using a steady gradient technique to measure the self-diffusion coefficients of water in electrolyte solutions. An alternative method of studying self-diffusion in liquids is the pulsed field gradient technique. Stejskal and Tanner (3) have shown that two identical rectangular pulses applied before and after the 180” refocusing rf pulse give an echo
r.f.
gradlent
!! 1 8
G
r.f. ” 90”
gradlent G
FIG. 1. Pulsed field gradient sequence showing the times r, d, A, and 6 which can be independently set in an experiment. 0022-2364/80/020247-13902.00/O 247 Copyrrght @ 1980 by Academic Press. Inc All rights of reproduction in any form reserved. Printed m Great Rrhin
248
CALLAGHAN,
TROTTER,
I
AND
JOLLEY
I
t
+
I
S3113 QNVN AE N0113313S 3Sllld
CON32 13S3Y
3NIWl.l
L3NIN 13S3Y
I
PULSED
FIELD
GRADIENT
249
SYSTEM
b
o-
FIG.
2b. Timing pulse selection circuit.
:,,,,* pz-?ll, TRIGGER PULSE
SPIN ECHO SEQUENCE
FIG. 2c. Circuit modification required when using a two-pulse spin-echo sequence as a trigger.
attenuation
of A(G)/A(O)
= exp[-Dy2G2S2(A
-a/3)],
where A(G) and A(0) are the echo amplitudes with and without the field gradient pulses, respectively. The magnitude of the gradient in the polarizing field is G and by a suitable choice of coil may be applied as a gradient with respect to the x, y, or z direction. The quantity D is the self-diffusion coefficient of the nuclear spins along the gradient direction defined by the relationship D = f2/2t,
where r2 is the mean-square distance traveled along the gradient axis in time t. The quantity y is the magnetogyric ratio of the nuclei being observed and 6 and A are pulse spacings defined in Fig. 1. There are considerable advantages in using the pulsed field gradient technique for the measurement of self-diffusion coefficients. These include the sampling of nuclear spin echoes in the absence of a gradient (an essential requirement when frequency resolution is required), the ability to measure slower diffusion, and the detection of non-Gaussian diffusion by the use of various interpulse spacings (4,5). We describe here a pulsed field gradient system controlled by the rf gate pulse of a commercial high-resolution pulse-Fourier transform spectrometer (JEOL FX-60). THE PULSE PROGRAMMER
A digital pulse programmer has been designed so that the experimental parameters A and 8, as well as the time d (see Fig. l), may be set directly on
250
CALLAGHAN,
TROTTER,
AND
JOLLEY
BCD-coded thumbwheel switches. The circuit, which utilizes 7400 series TTL devices throughout, is shown in Fig. 2a. A l-MHz signal, derived from the JEOL spectrometer crystal clock, provides the clock pulses entering the divider chain. Timing pulses appropriate to any particular experiment may be selected using NAND gates as detailed in Fig. 2b. The precision of the output pulse timing is determined by the number of up/down counters (74190s) in cascade. Figure 2 thus represents a programmer with a precision of two digits in each of the intervals d, A, and 6. Such a precision has been found to be quite adequate for our pulsed field gradient experiments. The up/down counters are utilized in the down counting mode, and are directly programmed with the thumbwheel switches. The function of the pulse programmer is to provide the accurate, sequentially timed intervals d, S, and A. The TTL devices are used in a manner which avoids the problem of propagation delays so that the accuracy of all timed intervals is better than 1 ksec. At power turn-on, a reset pulse (> 1 ksec) must be provided to the appropriate PRE or CLR inputs (see Fig. 2b) of the 7474s to set their initial states. The trigger pulse is provided by the spectrometer pulse programmer, and as such is a two-pulse sequence for a spin-echo experiment. This two-pulse sequence is easily turned into the required single-trigger pulse by the inclusion of the circuitry shown in Fig. 2c before the trigger input. The l-MHz clock access to the divider chain is automatically disabled when the two-pulse sequence reaches completion. The appearance of the falling edge of the next trigger pulse readies the system for a new sequence, and timing proceeds from the rising edge of the trigger pulse. The circuit presented does not require the NAND gate range switches to be debounced, or to make before break, as false clocking of the counters is prevented by their inhibited CLK inputs. More details concerning the pulse programmer are given in the Appendix. CURRENT
CONTROL
The pulse programmer logic output is used to externally switch the current supplied by a commercial operational power supply (KEPCO JQE 2510M) operating in the constant current mode. This power supply was modified to give reduced response time by removal of the output capacitor, and the addition of several phase shifting networks around the error amplifier to prevent oscillation.’ Transistors in a three-stage Darlington configuration, shown in Fig. 3, are used to generate the field gradient pulses by externally switching the current path. During 6, the QA transistors are turned on and QB are off, thus allowing current to flow through the gradient coils. At all other times QA are off and QB are on, thus isolating the coils from the circuit. At all times the current magnitude is controlled by the power supply feedback amplifier. This has the advantage that the gradient pulse amplitude may be measured at any time by noting the voltage drop across the SO-W, O.ln precision resistor, Rs. The actual current pulses flowing in the coils may be monitored across resistor R using an oscilloscope with a differential input amplifier. 1 This circuitry
brings the specifications the modifications were
up to the equivalent based.
high-speed
model
OPS 25-10M
upon
whose
PULSED
FIELD
GRADIENT
251
SYSTEM
LOAD
TTL PULSE INPUT
FIG. 3. Current switching QBI), TIP 30A (QM, Qd
circuit for the field gradient and 2N3906 (QM, Qd.
coils.
The transistors
used
are TIP
36A
(QAI,
The optical isolator provides a convenient (-5 V, 0 V), to (0 V, +5 V) logic voltage level translation as well as protection for the ‘ITL pulse programmer. A 2-A fuse is included to protect the coils in the case of system failure. The current supply output transistors are protected from large voltage spikes generated during current turn-off by the high-speed rectifier diodes in parallel with the coils. The current pulses produced by this system, using the Helmholtz coils as a load, are shown in Fig. 4a. The current regulation is better than 0.02% over the operating range (100 mA to 10 A) and the pulses are precisely matched in shape. Any error in a > ‘ tr
> < tf
l-----L .
100/m
’
.rf fleM o gradmt
-4
~2
0 displacement
2 mm
4
FIG. 4. (a) Gradient pulse shape for a 1.5 T m-i pulse determined by measuring the voltage across resistor R in Fig. 3. The rise and fall times are independent of the pulse height and duration. (b) Radiofrequency field and field gradient profiles measured along the y axis of the sample space.
252
CALLAGHAN,
TROTTER,
AND
JOLLEY
measuring diffusion coefficients caused by deviation from the rectangular pulse shape is insignificant ( < 0.1%) for values of S 2 500 psec. External switching of the current to provide the gradient pulses avoids the possibility of current flowing through the coils other than during times S. Systems employing feedback amplifiers for current stabilization are susceptible to pickup on the sensing resistor during the rf pulse. This may cause small amounts of gradient current to be present during the rf pulse. We have found, by experimenting with other switching systems, that these small gradients can cause a distortion in the echo envelope and phase, effects mentioned by other authors (6, 7). Isolation of the coils during times other than 6 avoids this problem. THE
PROBE
A 60-MHz low-resolution ‘H probe was built to incorporate 0.15 T mm* A-’ field gradient coils. The entire unit was made to fit in the 32-mm gap between the polarizing magnet pole faces. The rf section of the probe consists of a single coil series resonant circuit designed according to the criteria set out by Clark and McNeil (8). The circuit diagram is shown in Fig. 5. We have used a JEOL 60-MHz FET preamplifier in the receiver stage although any other single-stage tuned preamplifier would suffice (9). Resistor Ri has been included to limit the coil Q during the ring down stage after the 60-V pp rf pulse. In order to obtain maximum power transfer the length of the 50-n coaxial transmission line was set (8) to give a load impedance, when tuned at Ci, equal to the transmitter output impedance. The sample coil, L2, was designed to give good homogeneity of the rf field and a good filling factor but with an inductance and Q limited to the desired low values. We have followed the method of Lowe and Tarr (10) and have wound a two-turn 7-mm-long, g-mm-diameter coil from 0.17-mm copper shim. After the series capacitor C1 was tuned the ‘H 90” flip time was 23 ysec under a 60-V pp rf pulse at 60 MHz. The coil was wound on the glass Dewar shown in Fig. 6 using Teflon tape to hold it in place. Sample tubes are inserted in the 5-mm-diameter cavity down the axis Ll
Dl
FIG. 5. Series resonant circuit after Clark and McNeil1 (8). Resistor RI is included to reduce ring down times to - 1.5 psec and L, is adjusted to present a 50-a load to the rf transmitter. LICI, LzCz, and L3C3 are tuned pairs. The diodes shown are high-speed silicon.
PULSED
FIELD
il
GRADIENT
+--
SYSTEM
253
thermocouple
FIG. 6. Sample space geometry. The viewing port along the axis of the Helmholtz coil allows the rf coil to be accurately centered.
of the Dewar and sample temperature is controlled using a copper-constantan thermocouple sensor in a conventional hot-air feedback system. The temperature variation over the sample volume is s 05°C. The rf profile measured along the y axis of the sample space is shown in Fig. 4b. The rf pulse strength was determined by measuring the-180” flip time in a very small water sample. The main aB,/at gradient coils for diffusion measurements are an opposed Helmholtz pair wound with 19 turns per coil using 26-swg enameled copper wire on a Teflon former. During an experiment the coils are maintained at a constant temperature by a steady stream of air directed at their base. Helmholtz coils offer good gradient uniformity over the small sample volumes employed in this system, but for extended cylindrical volumes quadrupolar coils are superior (II). The shape of the Helmholtz former follows the equation of Tanner (12) and minimizes secondorder (a2B,/k2) gradients over the sample space. The gradient uniformity in our coil is calculated to be better than 1% over the sample space 4.5 mm in diameter and 4.5 mm in length. The calculated y-axis profile has been confirmed experimentally by measuring the echo attenuation of a small water sample as a function of its position along the y axis (see Fig. 4b). We have included in the probe a set of aB,/ax, aB,/ay, and aB,/az homogeneity coils. These coils give a residual gradient, go, of 0.1 mT m-‘. This gradient is sufficiently small to resolve ‘H resonances - 60 Hz apart which allows for independent measurement of diffusion rates in some multicomponent mixtures, and provides
254
CALLAGHAN,
TROTTER,
AND
JOLLEY
a valuable increase in signal to noise when working with dilute molecular species. An excellent set of design criteria has been given by Anderson (13). Where possible we have used Teflon, laminated plastic, and Perspex as construction materials in the probe to minimize any eddy currents associated with switching on and off the field gradient pulses. These currents can distort the gradient time dependence from the desired square shape. By examining the ‘H free-induction decay in the eddy current “tail” following a maximum 1.5 T m-l gradient pulse we have determined that eddy effects contribute s 0.03 mT m-r at 500 psec following a gradient pulse and d 0.01 mT m-l at 1000 p.sec. Despite the small operating gap between the magnet pole pieces, gradients associated with eddy currents are entirely insignificant for diffusion experiments over the entire experimental range, S 2 0.5 msec, d 2 2 msec. RESULTS
‘H spin-echo signals are sampled with an AD converter and processed in the minicomputer of the JEOL spectrometer. Data are analyzed by plotting the natural logarithm of the echo attenuation versus 12S2(A -S/3) and performing a leastsquares fit to the resulting straight line. Using a water sample at 25°C and taking Mills’ value (14) for the diffusion coefficient of water at this temperature (2.266 x 10e9 m2 set-‘) we obtain a coil gradient of 0.1512 f 0.0005 T m-l A-‘, which is within 1% of that calculated from a knowledge of the coil dimensions. With this value for the field gradient the diffusion coefficient of Analar benzene at 25°C is
.-s
5
benzene
25.0 “C
.2 -
s ?i
0
2
12h2(A-
FIG. 7. Echo attenuation plot parameters, G, A, and 6, are varied.
for
Analar
benzene
8
s
4 ;a)
xl0
-1
A* s3
at 25.O”C
in which
all three
experimental
PULSED
FIELD
GRADIENT
SYSTEM
255
(2.23 f 0.02) x lo-’ m* set-‘, compared to the literature value (15) of 2.210x 1 O-’ m* set-’ . Figure 7 shows an echo attenuation plot for benzene at 25°C obtained by varying all three parameters G, A, and 6. These data are consistent with the Skejskal and Tanner formula (3), the diffusion coefficient being independent of 6 and A within experimental precision. The data intercept also agrees with the measured zero gradient amplitude. The ability to accumulate data in a signal-averaging mode is a major advantage with modern NMR spectrometers. Use of an external *H lock (JEOL NM 3900) allows for the accumulation of signals under pulsed field gradient conditions since we find that the lock signal recovers from the field gradient pulse in i 2msec. We have found that when adding successive spin echoes it is essential to remove any small
1.0
2.0 I’&‘(A
3.0 - fi
)
x
A* s3
FIG. 8. (a) Echo attenuation data for a solution of 0.5% (w/v) polystyrene (M, = 110,000) in Ccl4 at 250°C. The line shown is obtained by a linear least-squares fit. (b) 10% (w/v) polystyrene (M, = 230,000) in CC14 at 25.O”C.
2.56
CALLAGHAN,
a
TROTTER,
benzene
AND JOLLEY
butanol
100 Hz
A-15
ms
FIG. 9. (a) ‘H frequency spectrum for 5-mm-long, 4.5-mm-diameter sample consisting of an equimolar mixture of benzene and butanol at 25.o”C. (b) Echo attenuation data for pure benzene, pure butanol, and the benzene and butanol components in an equimolar mixture. Ail data were obtained at 25.O”C and the self-diffusion coefficients are respectively (2.23 k 0.02) x 10e9, (0.43 iO.01) x 10m9, (1.83 kO.02) x 10e9, and (0.90+0.01)x 10e9 m* set-‘.
PULSED
FIELD
GRADIENT
SYSTEM
251
spurious dc signal component. On our machine this is accomplished by phaseinverting successive spin-echo pulse pairs while at the same time alternating the sign of the AD converter. In Fig. 8a, the echo attenuation plot for 0.5% (w/v) polystyrene (Mr = 110,000) in carbon tetrachloride at 25°C is shown. Each data point represents 400 accumulations. Previous published diffusion measurements on polystyrene solutions using pulsed field gradient NMR have been restricted to concentrations greater than 30% (16). In conjunction with photon correlation spectroscopy methods (17) we are proceeding with comparative diffusion measurements over a wide concentration range using a variety of polystyrenes and solvents of different molecular weights. Figure 8b shows the echo attenuation plot for a 10% (w/v) solution of polystyrene (M, = 230,000) in carbon tetrachloride at 25°C. The discrepancy between the data intercept and the zero gradient amplitude is caused by slow lock signal recovery in the time 7 - S (5 msec following the long, 22-msec) gradient pulse. It is eliminated by increasing T -6. The diffusion rate of (6.8 f 0.3) x lo-l3 m2 see-i is near the slow limit for the technique and although other authors (18-20) have reported slower diffusion measurements in the vicinity of lo-l3 m2 set-‘, the present result does represent a considerable improvement in sensitivity and precision in this range. The above results were obtained by measuring the amplitude of the spin echoes directly from the time domain signal. An alternative way is to start the signal sampling at the center of the echo so that the data may be Fourier-transformed into the frequency domain. Provided that the components of a mixture have resolvable resonances it then becomes possible to measure the self-diffusion rates of the various molecular species (21). Figure 9a shows the ‘H frequency spectrum of an equimolar mixture of benzene and butanol. It can be seen that the homogeneity coils incorporated in the probe give a resolution of - 35 Hz over the sample volume and the benzene and butanol resonances are resolved. The echo attenuation data for pure butanol, pure benzene, and the equimolar mixture are shown in Fig. 9b. We intend to compare self-diffusion coefficients in various molar mixtures of this and other binary solutions with mutual diffusion rates obtained by the photon correlation spectroscopy facility in this department (17). CONCLUSION
We have shown that the pulse field gradient device described above gives excellent agreement with the accepted literature values for the diffusion coefficient of benzene (15). We have also demonstrated the advantages to be gained by interfacing such a device to a high-resolution pulse-Fourier transform spectrometer, the computer software of which facilitates spectrum accumulation and reduction. Data accumulation enables measurements to be made on dilute solutions as is demonstrated by the 0.5% polystyrene solution results, and the Fourier transform capability enables the frequency spectrum to be obtained provided sampling is commenced at the center of the echo. This allows for the measurement of diffusion coefficients for single-solution components in multicomponent systems provided their resonances are resolvable. The high-resolution magnet and the simple homogeneity coils incorporated in the
258
CALLAGHAN,
TROTTER,
AND
JOLLEY
probe provide a resolution of about 35 Hz, which is sufficient to resolve components whose chemical shift is 2 1 ppm at 60 MHz.
APPENDIX
The pulse programmer consists of three sections: the divider chain and associated pulse selection circuitry; the d, A, and S down counters; and the control circuitry. With the aid of Fig. 2, the workings of sections 1 and 2 are self-evident. However, the control circuitry, consisting of sundry D flip-flops (7474s) and several monostables, merits a little further explanation. The problem of providing sequentially timed intervals is generally complicated by the presence of propagation delays, and it is the function of the control circuitry to circumvent any inaccuracies such delays might otherwise cause. In sequential timing, the edge of a clock pulse which marks the end of an interval also marks time zero for the next interval. The second interval’s counters will always miss their time zero pulse if they are activated at the end of the first interval due to propagation delays associated with the activation process. Down counters, including the 74190 counter, often have a so-called “look ahead” feature for use in sequential timing. This is an output pin whose logic state changes upon a count of one and this change may be used to activate the next interval’s counters as the next clock pulse will mark time zero for this interval. Unfortunately the precision of the pulsed field gradient experiment often demands that there be order-of-magnitude differences in the frequencies of the clock pulses driving the A and S counters, with S having the higher-frequency pulses. Thus activation of the S counters by some “look-ahead” feature could result in 8 being incorrectly timed. In the present application these problems are overcome by inhibiting those counters not immediately concerned with timing a particular interval. This is achieved by placing a logic one at the CLK input of the initial counter in the cascade via a D flip-flop. Immediately a timed interval is completed, the next appropriate counters are activated, and the previous counters inactivated, by clocking the appropriate fiip-flops (those connected to the counters’ CLK inputs). The monostables (74123s) are also triggered at this stage and provide a pulse sequence to the divider chain which causes all outputs to go to the count of nine, then one. This reset-nine, reset-zero sequence has the effect of mimicking a timing pulse at the CLK input of any activated down counters and so time zero is restored and timing proceeds with no loss in accuracy. For the case when 1-usec pulses are selected the D flip-flop, marked as 7474” in Fig. 2a, provides the necessary zero time pulse.
ACKNOWLEDGMENTS
Mr.
The authors K. Smith
are indebted to Mr. R. C. O’Driscoll and Dr. D. N. Pinder and Mr. R. Parsons for technical assistance.
for valuable
discussions
and to
PULSED
FIELD
GRADIENT
SYSTEM
2.59
REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
16. 17. 18. 19.
20. 21.
E. HAHN, Phys. Rev. 80, 580 (1950). K.R.HARRIs,R.MILLs,P.J. BACK, AND D.S. WEBSTER, J. Map. R~SOII. 29,473 (1978). E.O.STEJSKALANDJ.E.TANNER,J. Chem.Phys.42,288 (1965). E, 0. STEJSKAL, J. Chem. Phys. 43,3597 (1965). J.E.TANNERAND E.O.STEJSKAL,J. Chem.Phys.49,1768 (1968). G. B. MATSON, Rev. Sci. Innstrum. 43, 1504 (1971). L. MCLACHLAN, Institute of Nuclear Sciences, DSIR, Wellington, N.Z., private communication. W.G.CLARKANDJ. A.McNEIL, Rev.Sci.Insrrum.44,844 (1973). D.J. ADDUCI,~. A.HORNUNG, AND D.R.TORGESON, Reo. Sci. Instrum.47,1503 (1976). J.LOWE AND C.E.TARR,J. Phys.E. 1,320(1968). D.S.WEBSTERAND K.H.MARSDEN, Rev.Sci. Insrrum.45,1232(1974). J. E. TANNER, Rev. Sci. Znsaum. 36,1086 (1965). W. A. ANDERSON, Rev. Sci. Znsrrum. 32,241(1961). R. MILLS, J. Phys. Chem. 77,687 (1973). K.R.HARRIs,C. K.N.PuA,ANDP.J.DuNLoP,J. Phys. Chem.,3524 (1970). T.COSGROVEANDR.F.WARREN, Polymer 18,255 (1977). D.N.PINDERANDR.C.O'DRISCOLL,J. Phys.E. 10,400(1977). B.D.Boss,E.O.STEJSKAL,ANDJ.D.FERRY,J. Phys.Chem. 71,1501(1967). J.E.TANNER,KANG-JEN LIU, ANDJ.E. ANDERSON, Macromolecules 4,586 (1971). J. E. TANNER, Mucromdecules 4,748 (1971). T.L.JAMEs ANDG.G.MCDONALD,J. Magn.Reson. 11,58 (1973).