- Email: [email protected]
An NMR investigation of the dynamics of a methyl group with tunneling frequency 3.4 MHz
ELSEVIER
Physica B 202 (1994) 311-314
An NMR investigation of the dynamics of a methyl group with tunneling frequency 3.4 MHz M. Van Cleemput, 1 A.J. Horsewill,* L. Van Gerven Laboratorium voor Vaste Stof-Fysika en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
Abstract The ground state tunneling frequency (vt = 3.39 MHz) of the methyl groups in 2,5-dimethyl-l,3,4-thiadiazole has been measured using low field NMR-spectroscopy. Using a variety of rapid field cycling NMR techniques the temperature dependence of vt and the correlation time for incoherent reorientation zc have also been measured. These have enabled the dynamics of the methyl groups to be studied from the quantum regime into the classical regime. These dynamics can be well described with a purely threefold barrier of V/kB = 1175 K.
1. Introduction N M R and INS are complementary techniques for the study of methyl group dynamics. Tunneling frequencies can be determined using INS and level crossing N M R (130GHz 1> vt i> 10MHz) or low field N M R spectroscopy (1 MHz >~ vt/> 20 kHz). The region between approximately 1 and 10 MHz is not easily accessible by these experimental techniques. Our measurements on 2,5-dimethyl-l,3,4thiadiazole (vt = 3.39 MHz) illustrate that low field N M R spectroscopy can be extended to significantly higher tunneling frequencies. To achieve this, the enhancement of the normally forbidden transitions near the level crossings Vo = vt/2 or Vo = vt was utilized. The smooth temperature evolution in the methyl group dynamics, from coherent tunneling at low
*Corresponding author; permanent address: Department of Physics, University of Nottingham, Nottingham NG7 2RD, UK. 1Present address: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX3 0JZ, UK.
temperatures to incoherent thermal activation at higher temperatures, was clearly observed for this strongly hindered methyl rotor. This information was obtained using various N M R techniques, most of which employ fast field cycling. The results can be interpreted in relation to the potential barrier experienced by the methyl group, which in its turn can be deduced from the ground state tunneling frequency.
2. Measurement of the tunneling frequency of 2,5-dimethyl-l,3,4-thiadiazole The temperature dependence of the spin-lattice relaxation time T1 of 2,5-dimethyl-l,3,4-thiadiazole (C4H6N2S) is shown in Fig. 1. According to the methyl thermometer model [1] the minimum at 8 9 K indicates that this methyl compound has a tunneling frequency of the order of 5 MHz. Low field N M R spectroscopy was used to determine vt more accurately. This method uses fast field cycling (50 T/s) in order to combine the preparation of the initial nuclear magnetic state and the
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD! 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 2 0 9 - E
M. Van Cleemput et al./ Physica B 202 (1994) 311-314
312
100
:i
i
i
i
i
,
,
,
i
I
,
i
=
,
I
,
,
I
i
1
I
,
,
,:
14.4 mT
O O o
10
o
o
%
o o
¢-
o 3.3
o
o
3.4
3.5
0.1
0.01
I
I
I
l
I
l
5 Inverse
I
I
l
i
i
10 temperature
i
i
l
15
I
i
I
I
l
20
I
[
i
25
( 10"3K"1)
1.5
1.7
1.8
1.9
c
82.2 mT
Fig. 1. The temperature dependence of the proton spin-lattice relaxation time T1 2,5-dimethyl-l,3,4-thiadiazole measured at Vo = 21 MHz.
measurement of the final magnetisation at high field with the resonant absorption of radio frequency energy at low field [-2]. This is realized using the following sequence. After destroying the proton nuclear magnetisation with a comb of 90 ° pulses at a magnetic field of 0.53 T, resonant with the spectrometer frequency of 22AMHz, the field is switched to a higher value ( ~ 1 T) where the nuclear spin system is allowed to relax during a fixed period, giving rise to a certain magnetisation. The field is then switched to a low value (of the order of 10 mT) where RF irradiation is applied. Afterwards the field is switched back to 0.53 T where the final magnetisation is measured. This sequence is repeated with systematic increments of the irradiation frequency. If the applied irradiation is resonant, the initial magnetisation will be destroyed, resulting in a dip in the magnetisation versus irradiation frequency curve. At low field the energy difference between the Zeeman levels is very small so these levels are efficiently mixed by the dipolar interaction. This leads to less stringent selection rules than at higher
1.6
3.3
3.4
3.5
3.6
3.7
Irradiation frequency (MHz)
Fig. 2. N M R spectra of 2,5-dimethyl-l,3,4-thiadiazole at 30 K and in a field of (a) 14.4mT, (b) 35.8mT, close to the level crossing at v0 = ½vt and (c) 82.2 mT, close to the level crossing at Vo = yr. The transitions are labelled as follows: A for Am = I transition, a for its low frequency tunneling sideband, b - for the low frequency sideband of the Am = 2 transition and C for Am = 0.
fields so that the multiple quantum lines at 2Vo, and sometimes also at 3Vo, appear in the low field spectrum. For the same reason several tunneling lines can turn up if the tunneling frequency is small as well. They correspond to a change in symmetry from A to E or vice versa and can be found at the frequencies Vo + vt, 2Vo +__vt and vt. These tunneling lines enables us to determine the tunneling frequency vt [-2, 3]. It is clear that the probability of the tunneling transitions decreases for increasing tunneling
M. Van Cleemput et al./ Physica B 202 (1994) 311-314
frequencies. There are nevertheless other fields where some E levels lie in the vicinity of A levels and where the tunneling tansitions consequently have enhanced probability, namely near the level crossings Vo = vt and Vo = ½vt. This implies that even for large vt tunneling lines can be observed in spectra if they are measured at irradiation fields close to a level crossing field. More specifically the I v 0 - vtr line will appear with increased intensity near v0 vt/2 and the 12Vo - vii and the vt lines near Vo = vt. This is a very useful feature to determine a relatively high tunneling frequency (vt >> 1 MHz) accurately, but in order to find the right fields vt has to be known reasonably well already. 2,5-dimethyl-l,3,4-thiadiazole was investigated using a combination of low field and "level crossing field" spectroscopy. In a spectrum measured at 30 K and in a low field of 14.4 m T (Fig. 2(a)), a line appeared at a frequency of 3.35 MHz. Its position was independent of magnetic field and it was identified as a Am = 0 transition. The position of this line reveals the tunneling frequency vt = 3.35MHz. This was then verified at 35.8 MT, near the level crossings Vo = vt/2, (Fig. 2(b)) and at 82.2 mT, near Vo = vt (Fig. 2(c)). In our spectra we observed that the appropriate tunneling lines become more intense as the irradiation field approaches a level crossing.
3.43.2 "r"
3.0 2.8 2.6
=
3. Measurement of the temperature dependence of the dynamics The idea of extending the "low" field spectroscopy to "level crossing field" spectroscopy was exploited to measure vt as a function of temperature. The results are shown in Fig. 3. This temperature dependence explains why the tunneling frequencies obtained from the three spectra shown in Fig. 2, recorded at slightly varying temperatures, differ and do not exactly correspond with the ground state value. The temperature dependence of the correlation time of the incoherent methyl reorientation was also studied. At low temperatures z¢ was derived from the spin conversion time, which is in fact the characteristic relaxation time of the A and E energy levels to thermal equilibrium with the lattice. More
313
,
,
,
,
,
,
30
,
,
,
,
,
40
,
50
Temperature (K)
Fig. 3. The temperature dependence of the tunneling frequency vt(T). The solid line is the fit to the Allen model.
I
I
I
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
10 -1
10 -3
/
10 -s
I 0 -7
10-11
I 0
S
e
I
I
10
I
I
J
0
I
I
I
20
I
I
I
t
I
I
30
I
J
J
40
Inversetemperature (1 031<-I )
Fig. 4. The temperature dependence of the correlation time zc for incoherent reorientation, ([~) measured by spin-conversion and (©) measured by T1. The slopes of the solid lines represent the activation energies in the limits of low and high temperature.
details about the spin conversion measurements and the way to deduce Tc can be found in Ref. [4]. The zc values we obtained in this way are shown by the squares in Fig. 4. At higher temperatures ~ was derived from the spin-lattice relaxation times (Fig. 1) and these values are given by the circles in Fig. 4.
314
M. Van Cleemput et al./ Physica B 202 (1994) 311~14
Table 1 V/ke (K) 3-fold barrier 1175 (theory) vt(T) -(experiment) zc(T) -(experiment)
v° vlt Eol/ks ( V - Eo)/kB (MHz) (MHz) (K) (K) 3.40
189
265
3.39
191
285
--
--
286
1037
5. Conclusions 1013
4. Discussion The vt(T ) dependence corresponds very well with the model of Allen [5], in which the effective tunneling frequency is expressed as vt(T) =
energy of 1 0 1 3 K corresponds well with V - E o which, being the height of the barrier from the g r o u n d state, is the value expected on purely classical grounds.
v° + vt1 exp( - Eol/kBT) 1 + exp( -- Eol/kBT)
vt° and vt~ are the tunnel splittings in the g r o u n d and first librational states and Eol is the energy difference between the lowest two librational levels. The solid line in Fig. 3 represents the fit of this model and was obtained with v° = 3 . 3 9 M H z , vt~ = 191 M H z and Eol/ke = 285 K. The low temperature slope of the z¢(T-1) curve leads to consistent results, namely EA/kB = 286 K. F o r high temperatures an activation energy EA/kB = 1013 K is found. In the intermediate temperature region EA/kB ,~ 810 K. In Table 1 we compare these values with the energy levels and transition frequencies of a methyl g r o u p assuming a purely threefold potential barrier V/kB = 1175 K. Very g o o d agreement is found for v°, vt1 and Eol. Furthermore, we see that at low temperature the incoherent dynamics measured by z¢ are dominated by the g r o u n d and first excited librational states only. As the temperature increases so higher excited librational states begin to contribute to the d y n a m ics and the activation energy of the z¢ curve increases. In the high temperature limit the activation
Using low field N M R spectroscopy the tunneling frequency of methyl groups in 2,5-dimethyl-l,3,4thiadiazole has been measured ( v ° = 3 . 3 9 _ + 0.01 MHz). It was shown that this experimental technique is still very powerful for the determination of tunneling frequencies vt >> 1 M H z , provided that an approximate value is k n o w n so that spectra near the level crossing fields can be obtained. We also measured the temperature dependence of vt and of the correlation time of the incoherent reorientation zc. O u r results can be explained consistently assuming a purely threefold hindering barrier of 1175K.
Acknowledgements This work is supported by the Belgian 'Interuniversitair Instituut v o o r Kernwetenschappen'. M V C also received financial support from this Institute. A J H wishes to thank the Katholieke Universiteit, Leuven for the invitation to visit the host laboratory on study leave. This work was carried out during this period.
References [1] S. Clough, A. Heidemann, A.J. Horsewill, J.D. Lewis and M.N. Paley, J. Phys. C 15 (1982) 2495. [2] S. Clough, A.J. Horsewill, P.J. McDonald and F.O. Zelaya, Phys. Rev. Lett. 55 (1985) 1794. [3] A.J. Horsewill and A. Aibout, J. Phys. C 1 (1989) 10533. I-4] G, Vandemaele, A. Buekenhoudt and L. Van Gerven, J. Magn. Res. 89 (1990) 522; A. Buekenhoudt and L. Van Gerven, Phys. Rev. B 46 (1992) 5377. 1-5] P.S. Allen, J. Phys. C 7 (1974) L22.
Physica B 202 (1994) 311-314
An NMR investigation of the dynamics of a methyl group with tunneling frequency 3.4 MHz M. Van Cleemput, 1 A.J. Horsewill,* L. Van Gerven Laboratorium voor Vaste Stof-Fysika en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
Abstract The ground state tunneling frequency (vt = 3.39 MHz) of the methyl groups in 2,5-dimethyl-l,3,4-thiadiazole has been measured using low field NMR-spectroscopy. Using a variety of rapid field cycling NMR techniques the temperature dependence of vt and the correlation time for incoherent reorientation zc have also been measured. These have enabled the dynamics of the methyl groups to be studied from the quantum regime into the classical regime. These dynamics can be well described with a purely threefold barrier of V/kB = 1175 K.
1. Introduction N M R and INS are complementary techniques for the study of methyl group dynamics. Tunneling frequencies can be determined using INS and level crossing N M R (130GHz 1> vt i> 10MHz) or low field N M R spectroscopy (1 MHz >~ vt/> 20 kHz). The region between approximately 1 and 10 MHz is not easily accessible by these experimental techniques. Our measurements on 2,5-dimethyl-l,3,4thiadiazole (vt = 3.39 MHz) illustrate that low field N M R spectroscopy can be extended to significantly higher tunneling frequencies. To achieve this, the enhancement of the normally forbidden transitions near the level crossings Vo = vt/2 or Vo = vt was utilized. The smooth temperature evolution in the methyl group dynamics, from coherent tunneling at low
*Corresponding author; permanent address: Department of Physics, University of Nottingham, Nottingham NG7 2RD, UK. 1Present address: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX3 0JZ, UK.
temperatures to incoherent thermal activation at higher temperatures, was clearly observed for this strongly hindered methyl rotor. This information was obtained using various N M R techniques, most of which employ fast field cycling. The results can be interpreted in relation to the potential barrier experienced by the methyl group, which in its turn can be deduced from the ground state tunneling frequency.
2. Measurement of the tunneling frequency of 2,5-dimethyl-l,3,4-thiadiazole The temperature dependence of the spin-lattice relaxation time T1 of 2,5-dimethyl-l,3,4-thiadiazole (C4H6N2S) is shown in Fig. 1. According to the methyl thermometer model [1] the minimum at 8 9 K indicates that this methyl compound has a tunneling frequency of the order of 5 MHz. Low field N M R spectroscopy was used to determine vt more accurately. This method uses fast field cycling (50 T/s) in order to combine the preparation of the initial nuclear magnetic state and the
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD! 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 2 0 9 - E
M. Van Cleemput et al./ Physica B 202 (1994) 311-314
312
100
:i
i
i
i
i
,
,
,
i
I
,
i
=
,
I
,
,
I
i
1
I
,
,
,:
14.4 mT
O O o
10
o
o
%
o o
¢-
o 3.3
o
o
3.4
3.5
0.1
0.01
I
I
I
l
I
l
5 Inverse
I
I
l
i
i
10 temperature
i
i
l
15
I
i
I
I
l
20
I
[
i
25
( 10"3K"1)
1.5
1.7
1.8
1.9
c
82.2 mT
Fig. 1. The temperature dependence of the proton spin-lattice relaxation time T1 2,5-dimethyl-l,3,4-thiadiazole measured at Vo = 21 MHz.
measurement of the final magnetisation at high field with the resonant absorption of radio frequency energy at low field [-2]. This is realized using the following sequence. After destroying the proton nuclear magnetisation with a comb of 90 ° pulses at a magnetic field of 0.53 T, resonant with the spectrometer frequency of 22AMHz, the field is switched to a higher value ( ~ 1 T) where the nuclear spin system is allowed to relax during a fixed period, giving rise to a certain magnetisation. The field is then switched to a low value (of the order of 10 mT) where RF irradiation is applied. Afterwards the field is switched back to 0.53 T where the final magnetisation is measured. This sequence is repeated with systematic increments of the irradiation frequency. If the applied irradiation is resonant, the initial magnetisation will be destroyed, resulting in a dip in the magnetisation versus irradiation frequency curve. At low field the energy difference between the Zeeman levels is very small so these levels are efficiently mixed by the dipolar interaction. This leads to less stringent selection rules than at higher
1.6
3.3
3.4
3.5
3.6
3.7
Irradiation frequency (MHz)
Fig. 2. N M R spectra of 2,5-dimethyl-l,3,4-thiadiazole at 30 K and in a field of (a) 14.4mT, (b) 35.8mT, close to the level crossing at v0 = ½vt and (c) 82.2 mT, close to the level crossing at Vo = yr. The transitions are labelled as follows: A for Am = I transition, a for its low frequency tunneling sideband, b - for the low frequency sideband of the Am = 2 transition and C for Am = 0.
fields so that the multiple quantum lines at 2Vo, and sometimes also at 3Vo, appear in the low field spectrum. For the same reason several tunneling lines can turn up if the tunneling frequency is small as well. They correspond to a change in symmetry from A to E or vice versa and can be found at the frequencies Vo + vt, 2Vo +__vt and vt. These tunneling lines enables us to determine the tunneling frequency vt [-2, 3]. It is clear that the probability of the tunneling transitions decreases for increasing tunneling
M. Van Cleemput et al./ Physica B 202 (1994) 311-314
frequencies. There are nevertheless other fields where some E levels lie in the vicinity of A levels and where the tunneling tansitions consequently have enhanced probability, namely near the level crossings Vo = vt and Vo = ½vt. This implies that even for large vt tunneling lines can be observed in spectra if they are measured at irradiation fields close to a level crossing field. More specifically the I v 0 - vtr line will appear with increased intensity near v0 vt/2 and the 12Vo - vii and the vt lines near Vo = vt. This is a very useful feature to determine a relatively high tunneling frequency (vt >> 1 MHz) accurately, but in order to find the right fields vt has to be known reasonably well already. 2,5-dimethyl-l,3,4-thiadiazole was investigated using a combination of low field and "level crossing field" spectroscopy. In a spectrum measured at 30 K and in a low field of 14.4 m T (Fig. 2(a)), a line appeared at a frequency of 3.35 MHz. Its position was independent of magnetic field and it was identified as a Am = 0 transition. The position of this line reveals the tunneling frequency vt = 3.35MHz. This was then verified at 35.8 MT, near the level crossings Vo = vt/2, (Fig. 2(b)) and at 82.2 mT, near Vo = vt (Fig. 2(c)). In our spectra we observed that the appropriate tunneling lines become more intense as the irradiation field approaches a level crossing.
3.43.2 "r"
3.0 2.8 2.6
=
3. Measurement of the temperature dependence of the dynamics The idea of extending the "low" field spectroscopy to "level crossing field" spectroscopy was exploited to measure vt as a function of temperature. The results are shown in Fig. 3. This temperature dependence explains why the tunneling frequencies obtained from the three spectra shown in Fig. 2, recorded at slightly varying temperatures, differ and do not exactly correspond with the ground state value. The temperature dependence of the correlation time of the incoherent methyl reorientation was also studied. At low temperatures z¢ was derived from the spin conversion time, which is in fact the characteristic relaxation time of the A and E energy levels to thermal equilibrium with the lattice. More
313
,
,
,
,
,
,
30
,
,
,
,
,
40
,
50
Temperature (K)
Fig. 3. The temperature dependence of the tunneling frequency vt(T). The solid line is the fit to the Allen model.
I
I
I
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
10 -1
10 -3
/
10 -s
I 0 -7
10-11
I 0
S
e
I
I
10
I
I
J
0
I
I
I
20
I
I
I
t
I
I
30
I
J
J
40
Inversetemperature (1 031<-I )
Fig. 4. The temperature dependence of the correlation time zc for incoherent reorientation, ([~) measured by spin-conversion and (©) measured by T1. The slopes of the solid lines represent the activation energies in the limits of low and high temperature.
details about the spin conversion measurements and the way to deduce Tc can be found in Ref. [4]. The zc values we obtained in this way are shown by the squares in Fig. 4. At higher temperatures ~ was derived from the spin-lattice relaxation times (Fig. 1) and these values are given by the circles in Fig. 4.
314
M. Van Cleemput et al./ Physica B 202 (1994) 311~14
Table 1 V/ke (K) 3-fold barrier 1175 (theory) vt(T) -(experiment) zc(T) -(experiment)
v° vlt Eol/ks ( V - Eo)/kB (MHz) (MHz) (K) (K) 3.40
189
265
3.39
191
285
--
--
286
1037
5. Conclusions 1013
4. Discussion The vt(T ) dependence corresponds very well with the model of Allen [5], in which the effective tunneling frequency is expressed as vt(T) =
energy of 1 0 1 3 K corresponds well with V - E o which, being the height of the barrier from the g r o u n d state, is the value expected on purely classical grounds.
v° + vt1 exp( - Eol/kBT) 1 + exp( -- Eol/kBT)
vt° and vt~ are the tunnel splittings in the g r o u n d and first librational states and Eol is the energy difference between the lowest two librational levels. The solid line in Fig. 3 represents the fit of this model and was obtained with v° = 3 . 3 9 M H z , vt~ = 191 M H z and Eol/ke = 285 K. The low temperature slope of the z¢(T-1) curve leads to consistent results, namely EA/kB = 286 K. F o r high temperatures an activation energy EA/kB = 1013 K is found. In the intermediate temperature region EA/kB ,~ 810 K. In Table 1 we compare these values with the energy levels and transition frequencies of a methyl g r o u p assuming a purely threefold potential barrier V/kB = 1175 K. Very g o o d agreement is found for v°, vt1 and Eol. Furthermore, we see that at low temperature the incoherent dynamics measured by z¢ are dominated by the g r o u n d and first excited librational states only. As the temperature increases so higher excited librational states begin to contribute to the d y n a m ics and the activation energy of the z¢ curve increases. In the high temperature limit the activation
Using low field N M R spectroscopy the tunneling frequency of methyl groups in 2,5-dimethyl-l,3,4thiadiazole has been measured ( v ° = 3 . 3 9 _ + 0.01 MHz). It was shown that this experimental technique is still very powerful for the determination of tunneling frequencies vt >> 1 M H z , provided that an approximate value is k n o w n so that spectra near the level crossing fields can be obtained. We also measured the temperature dependence of vt and of the correlation time of the incoherent reorientation zc. O u r results can be explained consistently assuming a purely threefold hindering barrier of 1175K.
Acknowledgements This work is supported by the Belgian 'Interuniversitair Instituut v o o r Kernwetenschappen'. M V C also received financial support from this Institute. A J H wishes to thank the Katholieke Universiteit, Leuven for the invitation to visit the host laboratory on study leave. This work was carried out during this period.
References [1] S. Clough, A. Heidemann, A.J. Horsewill, J.D. Lewis and M.N. Paley, J. Phys. C 15 (1982) 2495. [2] S. Clough, A.J. Horsewill, P.J. McDonald and F.O. Zelaya, Phys. Rev. Lett. 55 (1985) 1794. [3] A.J. Horsewill and A. Aibout, J. Phys. C 1 (1989) 10533. I-4] G, Vandemaele, A. Buekenhoudt and L. Van Gerven, J. Magn. Res. 89 (1990) 522; A. Buekenhoudt and L. Van Gerven, Phys. Rev. B 46 (1992) 5377. 1-5] P.S. Allen, J. Phys. C 7 (1974) L22.