- Email: [email protected]
Nuclear spin-lattice relaxation time measurements in solids by dispersion signal decay
JOURNAL
OF MAGNETIC
RESONANCE
12, 276-279 (1973)
Nuclear Spin-Lattice Relaxation Time Measurements in Solids by Dispersion Signal Decay* W. R.
JANZEN?
Department of Chemistry, The University of British Columbia, Vancouver 8, British Columbia, Canada
ReceivedJuly 5, 1973 Decay curvesof the lock-in NMR dispersionsignal at the center of resonance u,(O)have beenused to measurenuclear spin-lattice relaxation times in solids.The maximum lock-in absorption signal v,(max) which has been used by previous authors, on the other hand, yieldedspurious Tl values.This wasnot surprisingsince ~~(0)saturatesnormally, whereas,v,(max) doesnot. INTRODUCTION
In a recent paper (1) the author has shown that the nuclear magnetic resonance lock-in dispersion signal at the center of resonance u,(O) appears to saturate normally in solids, i.e., u,(O)/H, is proportional to the BPP (2) saturation factor
Z(A) = [I + y2H12 7cg(A)TJ’,
VI
with A = 0, as predicted by Goldman’s (3) extension of Provotorov theory (4). In Eq. [I] y is the nuclear gyromagnetic ratio, HI the amplitude of the rf field, g(A) the absorption line shape function, A the distance in rad/sec from the center of resonance, and Tl is the usual Zeeman spin-lattice relaxation time. It is, therefore, possible to obtain true Tl values by measuring the progressive
saturation of the dispersion signal u,(O)-provided certain conditions are satisfied (I). Similar measurements have also been recently reported by Trontelj et al. (5). The saturation behavior of lock-in NMR signals in solids when A # 0 is more complicated (I, 3). In this paper we report Tl measurements made by a cw technique we have called
dispersion signal decay (DSD). When the rf field is strong enough to partially saturate a nuclear spin system, the steady state difference in populations between a pair of adjacent Zeeman energy levels is n, =&Z(A), where n, is the thermal equilibrium population difference before application of the rf field. We are interested in the rate of approach to this steady state which is described (6) by the following equation: n(t) - n, = (n, - n,)exp[-t/TJ(A)].
PI
The signal decay technique to measure Tl in solids appears to have originated with Linder (7) and has been used by Smith (8). These authors allowed the sample to equilibrate in a magnetic field corresponding to one of the extrema v,(max) of itsabsorption * Researchsupported by the National ResearchCouncil of Canada via grants to ProfessorB. A. Dunell. f Presentaddress:16-1111 Kendall Ave., Port Albemi, B.C., Canada. 276 Copyright 0 1973 by Academic Press, Inc. All rights of reproduction Printed in Great Britain
in any form reserved.
DISPERSION
SIGNAL
DECAY
277
derivative (lock-in) spectrum. A partially saturating rf field was then switched on and v,(max) recorded as a function of time. If BPP theory applies, Eq. [2] says that this signal should decay exponentially with time constant T,Z(d). This particular method, however, can yield spurious Tl values since we now know that BPP saturation theory is only valid in solids at the center of resonance (1,4). The lock-in absorption signal at this point, however, is zero. We have, therefore, used the dispersion signal u,(O) in our signal decay measurements. EXPERIMENTAL
The potassium caproate (KC,) and lithium stearate (LiC& samples were in sealed thin-wall 5 mm diam Pyrex tubes and have been described before (1). The NMR spectrometer was a Varian Associates model DP-60 operating at a ratio frequency of 56.4 MHz. The rf field was gated by a coaxial switch made from an Amphenol type 83-IT “T” adapter (9). Room temperature decay curves were recorded on a Sanborn model 151 thermal strip-chart recorder; the curves for LiCiB in liquid nitrogen (where Tl is long), on a Varian model G-10 strip-chart recorder. The field modulation frequency used was 200 Hz = 1256 set-i. The equation for the decay curve is
a(t) - a,= (a0- a,)exWlTA0)1,
[31
where a(t) is the amplitude of the dispersion signal, a, is the initial amplitude corresponding to no saturation, a, is the steady-state amplitude with saturation. A semilogarithmic plot of a(t) -a, versus time t yields T,Z(O) and a,,. Tl can then be obtained since Z(0) = as/a,. The conditions that must be satisfied are expected to be the same as those for progressive saturation of dispersion (1) namely: (i) H, < HLr the local field which is related to the second moment of the unsaturated absorption line by the expression Ht, = *(AH*), (ii) l/T, < s2 < yH,, where Q is the angular frequency of the modulation field of amplitude Hm, (iii) H,,, much less than the line width, and (iv) y’Hfng(O) + s2in order to avoid modulation saturation. RESULTS
AND
DISCUSSION
Typical dispersion signal decay (DSD) curves for potassium caproate and lithium stearate at room temperature are shown in Fig. 1. The recorder was run at a slow speed for some time before and after the signal decay in order to establish a good base line, it was also switched to the slow speed to measure a,. The small circles mark a,, values obtained from the semilog plots. The results from several curves obtained at room temperature are listed in Table 1. The normal absorption line width at room temperature is 8.5 gauss for KC. and 14 gauss for LiCls, yHLr values are 5.0 x lo4 and 7.3 x lo4 set-‘, respectively. The average Tl for KC6 is 4.01 set with a standard deviation of 0.13 sec. This agrees well with the progressive saturation of dispersion (PSD) result of 4.1 set (I). The average of the DSD Tl values for LiC,, is 16.3 set with a standard deviation of 0.6 sec. The PSD result was 17.4 set (2). We expect the DSD results to be the more accurate ones since they depend on only one calibration, i.e., the recorder time base.
278
JANZEN KC6
Lic18
trace
119
trace
406
HI = 7.2 mG
H, = 6.4 mG
FIG. 1 Typical lock-in dispersion signal ~~(0) decay curves for potassium caproate and lithium stearate. The curve for KC6 yields a TI of 3.83 set, the curve for LiC,, a TI of 16.4 sec.
TABLE SIGNAL
DECAY
RESULTS
1
AT ROOM TEMPERATURE
Potassium caproate
Lithium stearate
HI mG
HIIS gauss
z
Tl set
HI mG
KN gauss
Z
T, set
7.2 7.2 9.1 9.1 9.1
1.06 0.51 1.06 1.06 0.51
0.308 0.315 0.214 0.198 0.232
3.83 3.99 3.96 4.19 4.08
6.4 6.4 6.4 6.4 6.4 14.3
1.06 1.06 2.11 2.11 1.06 1.06
0.210 0.205 0.202 0.194 0.498” 0.342”
16.4 15.4 16.4 16.9 23.0” 18.9”
E From decay curves of the absorption signal q(max).
The results from two absorption signal u,(max) decay curves for LiC,, are also listed in Table 1. One of them was obtained with the same HI as the DSD curves, however, both the Tl and 2 values found are larger. The increase in 2 can be expected from BPP theory since it depends on g(d), but Tl should not. Also, the decrease in the absorption Z value on increasing HI from 6.4 to 14.3 mG does not agree with Eq. [ 11. On the other hand, the change in Z(0) with HI for KC6 (obtained by DSD) agrees quite well.
DISPERSION
SIGNAL
279
DECAY
DSD has also been used to measure T1 in LiCr, at 77 K, where it is too long to measure accurately by progressive saturation. The results from two decay curves are 95 and 96 set (H, = 4.5 mG, H,,, = 1.06 gauss, 2 = 0.0806 and 0.0817). In conclusion, the dispersion signal decay technique is particularly suitable for measuring long spin-lattice relaxation times in solids (at least with our simple apparatus) and, therefore, complements the progressive saturation method. Its other advantages are that H, does not have to be calibrated, the absorption spectrum is not needed, and it is faster to perform. With a faster recording device (such as an oscillograph or Computer of Average Transients) and an electronic rf gate, the technique should be useful for short T1 values as well. ACKNOWLEDGMENT The support and interest of Professor B. A. Dune11 in this work is greatly appreciated. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. Y.
W. R. JANZEN,
J. Magn. Resonance 10,263 (1973). N. BLOEMBERGEN, E. M. PURCELL, AND R. V. POUND, Phys. Rev. 73,679 (1948). M. GOLDMAN, J. Physique 25,843 (1964). B. N. PROVOTOROV,~. I?ksper. Teoret. Fiz. 41,1582 (1961); Soviet Physics JEPT14,1126 2. TRONTELJ, J. L. BJORKSTAM, AND R. JOHNSTON, J. Magn. Resonance 8,35 (1972). E. R. ANDREW, “Nuclear Magnetic Resonance,” p. 21, Cambridge University Press, S. LINDER, J. Chem. Phys. 26,900 (1957). G. W. SMITH, J. Chem. Phys. 36,308l (1962). G. W. SMITH, private communication.
(1962). London, 1955.
OF MAGNETIC
RESONANCE
12, 276-279 (1973)
Nuclear Spin-Lattice Relaxation Time Measurements in Solids by Dispersion Signal Decay* W. R.
JANZEN?
Department of Chemistry, The University of British Columbia, Vancouver 8, British Columbia, Canada
ReceivedJuly 5, 1973 Decay curvesof the lock-in NMR dispersionsignal at the center of resonance u,(O)have beenused to measurenuclear spin-lattice relaxation times in solids.The maximum lock-in absorption signal v,(max) which has been used by previous authors, on the other hand, yieldedspurious Tl values.This wasnot surprisingsince ~~(0)saturatesnormally, whereas,v,(max) doesnot. INTRODUCTION
In a recent paper (1) the author has shown that the nuclear magnetic resonance lock-in dispersion signal at the center of resonance u,(O) appears to saturate normally in solids, i.e., u,(O)/H, is proportional to the BPP (2) saturation factor
Z(A) = [I + y2H12 7cg(A)TJ’,
VI
with A = 0, as predicted by Goldman’s (3) extension of Provotorov theory (4). In Eq. [I] y is the nuclear gyromagnetic ratio, HI the amplitude of the rf field, g(A) the absorption line shape function, A the distance in rad/sec from the center of resonance, and Tl is the usual Zeeman spin-lattice relaxation time. It is, therefore, possible to obtain true Tl values by measuring the progressive
saturation of the dispersion signal u,(O)-provided certain conditions are satisfied (I). Similar measurements have also been recently reported by Trontelj et al. (5). The saturation behavior of lock-in NMR signals in solids when A # 0 is more complicated (I, 3). In this paper we report Tl measurements made by a cw technique we have called
dispersion signal decay (DSD). When the rf field is strong enough to partially saturate a nuclear spin system, the steady state difference in populations between a pair of adjacent Zeeman energy levels is n, =&Z(A), where n, is the thermal equilibrium population difference before application of the rf field. We are interested in the rate of approach to this steady state which is described (6) by the following equation: n(t) - n, = (n, - n,)exp[-t/TJ(A)].
PI
The signal decay technique to measure Tl in solids appears to have originated with Linder (7) and has been used by Smith (8). These authors allowed the sample to equilibrate in a magnetic field corresponding to one of the extrema v,(max) of itsabsorption * Researchsupported by the National ResearchCouncil of Canada via grants to ProfessorB. A. Dunell. f Presentaddress:16-1111 Kendall Ave., Port Albemi, B.C., Canada. 276 Copyright 0 1973 by Academic Press, Inc. All rights of reproduction Printed in Great Britain
in any form reserved.
DISPERSION
SIGNAL
DECAY
277
derivative (lock-in) spectrum. A partially saturating rf field was then switched on and v,(max) recorded as a function of time. If BPP theory applies, Eq. [2] says that this signal should decay exponentially with time constant T,Z(d). This particular method, however, can yield spurious Tl values since we now know that BPP saturation theory is only valid in solids at the center of resonance (1,4). The lock-in absorption signal at this point, however, is zero. We have, therefore, used the dispersion signal u,(O) in our signal decay measurements. EXPERIMENTAL
The potassium caproate (KC,) and lithium stearate (LiC& samples were in sealed thin-wall 5 mm diam Pyrex tubes and have been described before (1). The NMR spectrometer was a Varian Associates model DP-60 operating at a ratio frequency of 56.4 MHz. The rf field was gated by a coaxial switch made from an Amphenol type 83-IT “T” adapter (9). Room temperature decay curves were recorded on a Sanborn model 151 thermal strip-chart recorder; the curves for LiCiB in liquid nitrogen (where Tl is long), on a Varian model G-10 strip-chart recorder. The field modulation frequency used was 200 Hz = 1256 set-i. The equation for the decay curve is
a(t) - a,= (a0- a,)exWlTA0)1,
[31
where a(t) is the amplitude of the dispersion signal, a, is the initial amplitude corresponding to no saturation, a, is the steady-state amplitude with saturation. A semilogarithmic plot of a(t) -a, versus time t yields T,Z(O) and a,,. Tl can then be obtained since Z(0) = as/a,. The conditions that must be satisfied are expected to be the same as those for progressive saturation of dispersion (1) namely: (i) H, < HLr the local field which is related to the second moment of the unsaturated absorption line by the expression Ht, = *(AH*), (ii) l/T, < s2 < yH,, where Q is the angular frequency of the modulation field of amplitude Hm, (iii) H,,, much less than the line width, and (iv) y’Hfng(O) + s2in order to avoid modulation saturation. RESULTS
AND
DISCUSSION
Typical dispersion signal decay (DSD) curves for potassium caproate and lithium stearate at room temperature are shown in Fig. 1. The recorder was run at a slow speed for some time before and after the signal decay in order to establish a good base line, it was also switched to the slow speed to measure a,. The small circles mark a,, values obtained from the semilog plots. The results from several curves obtained at room temperature are listed in Table 1. The normal absorption line width at room temperature is 8.5 gauss for KC. and 14 gauss for LiCls, yHLr values are 5.0 x lo4 and 7.3 x lo4 set-‘, respectively. The average Tl for KC6 is 4.01 set with a standard deviation of 0.13 sec. This agrees well with the progressive saturation of dispersion (PSD) result of 4.1 set (I). The average of the DSD Tl values for LiC,, is 16.3 set with a standard deviation of 0.6 sec. The PSD result was 17.4 set (2). We expect the DSD results to be the more accurate ones since they depend on only one calibration, i.e., the recorder time base.
278
JANZEN KC6
Lic18
trace
119
trace
406
HI = 7.2 mG
H, = 6.4 mG
FIG. 1 Typical lock-in dispersion signal ~~(0) decay curves for potassium caproate and lithium stearate. The curve for KC6 yields a TI of 3.83 set, the curve for LiC,, a TI of 16.4 sec.
TABLE SIGNAL
DECAY
RESULTS
1
AT ROOM TEMPERATURE
Potassium caproate
Lithium stearate
HI mG
HIIS gauss
z
Tl set
HI mG
KN gauss
Z
T, set
7.2 7.2 9.1 9.1 9.1
1.06 0.51 1.06 1.06 0.51
0.308 0.315 0.214 0.198 0.232
3.83 3.99 3.96 4.19 4.08
6.4 6.4 6.4 6.4 6.4 14.3
1.06 1.06 2.11 2.11 1.06 1.06
0.210 0.205 0.202 0.194 0.498” 0.342”
16.4 15.4 16.4 16.9 23.0” 18.9”
E From decay curves of the absorption signal q(max).
The results from two absorption signal u,(max) decay curves for LiC,, are also listed in Table 1. One of them was obtained with the same HI as the DSD curves, however, both the Tl and 2 values found are larger. The increase in 2 can be expected from BPP theory since it depends on g(d), but Tl should not. Also, the decrease in the absorption Z value on increasing HI from 6.4 to 14.3 mG does not agree with Eq. [ 11. On the other hand, the change in Z(0) with HI for KC6 (obtained by DSD) agrees quite well.
DISPERSION
SIGNAL
279
DECAY
DSD has also been used to measure T1 in LiCr, at 77 K, where it is too long to measure accurately by progressive saturation. The results from two decay curves are 95 and 96 set (H, = 4.5 mG, H,,, = 1.06 gauss, 2 = 0.0806 and 0.0817). In conclusion, the dispersion signal decay technique is particularly suitable for measuring long spin-lattice relaxation times in solids (at least with our simple apparatus) and, therefore, complements the progressive saturation method. Its other advantages are that H, does not have to be calibrated, the absorption spectrum is not needed, and it is faster to perform. With a faster recording device (such as an oscillograph or Computer of Average Transients) and an electronic rf gate, the technique should be useful for short T1 values as well. ACKNOWLEDGMENT The support and interest of Professor B. A. Dune11 in this work is greatly appreciated. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. Y.
W. R. JANZEN,
J. Magn. Resonance 10,263 (1973). N. BLOEMBERGEN, E. M. PURCELL, AND R. V. POUND, Phys. Rev. 73,679 (1948). M. GOLDMAN, J. Physique 25,843 (1964). B. N. PROVOTOROV,~. I?ksper. Teoret. Fiz. 41,1582 (1961); Soviet Physics JEPT14,1126 2. TRONTELJ, J. L. BJORKSTAM, AND R. JOHNSTON, J. Magn. Resonance 8,35 (1972). E. R. ANDREW, “Nuclear Magnetic Resonance,” p. 21, Cambridge University Press, S. LINDER, J. Chem. Phys. 26,900 (1957). G. W. SMITH, J. Chem. Phys. 36,308l (1962). G. W. SMITH, private communication.
(1962). London, 1955.