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Chlorine nuclear quadrupole resonances and motion of pyridinium ions in pyridinium tetrachloroaurate(III)
221
Journal of Molecular Structure, 192 (1989) 221-227 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
CHLORINE NUCLEAR QUADRUPOLE RESONANCES MOTION OF PYRIDINIUM IONS IN PYRIDINIUM TETRACHLOROAURATE(II1)
AND
ATSUSHI ISHIKAWA, YUKARI ITO*, KEIZO HORIUCHI**, TETSUO ASAJI and DAIYU NAKAMURA Department of Chemistry, Faculty of Science, Nagoya University, Chikusa, Nagoya 464 (Japan) (Received 4 February 1988)
ABSTRACT The temperature dependences of %l NQR frequencies and of chlorine nuclear quadrupole relaxation times, T,, have been determined for pyridinium tetrachloroaurate(II1). The “%l NQR frequency of a single line appearing is 27.769 MHz at 293 K. With decreasing temperature, the NQR line is observed to become gradually broad and cannot be detected below ca. 230 K. 35C1T,, is observed to decrease with decreasing temperature from 800 ,asat 350 K to 170 ps at 273 K. This fast relaxation rate may be responsible for the disappearance of the NQR signal described above. T,, data are discussed by referring to the ‘H NMR T, data already determined. The dominant relaxation mechanism for T,, below ca. 350 K can be attributed to the fluctuation of the field gradient due to the motion of the pyridinium ions in the crystal. Above ca. 360 K, T,, decreases rapidly with increasing temperature suggesting the onset of a motion of [AuCl,] ions. The activation energy for the motion is estimated to be 67 kJ mol-‘. When the Larmor frequency of ‘H T, measurements is near to the NQR frequencies, anomalous temperature dependences of ‘H T, are observed, suggestingthe occurrence of dipolar-quadrupolar cross relaxation with chlorine nuclei.
INTRODUCTION
Since a pyridinium ion has an electric dipole moment, the molecular dynamics of pyridinium salts provide some interesting problems in relation to their electric properties. Very recently, we have extensively studied, by means of ‘H NMR experiments, the reorientational motion of pyridinium ions in pyridinium tetrachloroand tetrabromoaurate (III) about their pseudohexad axis C6’ which is perpendicular to the cationic plane and passes through the center of the cationic ring [ 11. In these salts, it has been shown that nonequivalence among the potential wells in the crystals must be taken into account to interpret properly the motion of pyridinium ions observed. *Present address: Government Industrial Research Institute, Nagoya, Kita, Nagoya 462, Japan. **Present address: Department of Chemistry, Division of General Education, University of the Ryukyus, Nishihara, Okinawa 903-01, Japan.
0022-2860/89/$03.50
0 1989 Elsevier Science Publishers B.V.
222
The orientational order-disorder of pyridinium ions in crystals gives rise to another important problem when the motion is frozen at lower temperatures. The 35C1 nuclear quadrupole resonance (NQR) signal of pyridinium tetrachloroaurate (III), (pyH) [ AuCl, 1, faded out below ca. 230 K [ 11. This fadeout phenomenon can be explained in terms of a static disorder of pyridinium ions in the crystal. On the other hand, the field gradient fluctuation will be produced at chlorine sites by the motion of pyridinium ions located near to the chlorines. This dynamic disorder of the cations may also be responsible for the fade-out phenomenon when the sample temperature decreases. To obtain information about the field gradient fluctuation at the chlorine site, the spinlattice relaxation times, T,o, of chlorine in pyridinium tetrachloroaurate (III) were observed as a function of temperature. EXPERIMENTAL
35C1 and 37C1 T,, and the resonance frequencies were determined for the same sample as used in previous work [ 11. The temperature dependence of T,, was determined by means of a home-made pulsed NQR spectrometer [2, 31. T,, values were measured by employing the 7r-r-n/2-z,-7r pulse sequence in which 7 was varied while 7, was set constant for about 150 ps. Almost exponential decay of the echo height after the pulse sequence was observed. The sample temperature was controlled and measured by use of a proportional temperature regulator together with a copper-constantan thermocouple. A modified Dean-type superregenerative spectrometer [4] was also employed for the measurements of the resonance frequencies. In the cw NQR measurements, a chromel-alumel thermocouple was used to determine the sample temperature. The observed temperature was estimated to be accurate within ? 1 K both in the cw and pulsed NQR measurements. For the ‘H NMR T, measurements, a conventional n-r-n/2 pulse sequence was used. The details of the measurements are the same as those reported elsewhere [ 11. RESULTS AND DISCUSSION
determined for dependence of 35C1 NQR frequencies in Fig. 1. The NQR signal could not be observed below ca. 230 K and above ca. 395 K. The temperature dependences of the 35C1and 37C1T,, are shown in Fig. 2, as well as those of the spin-lattice relaxation time T, of ‘H NMR at 10.5, 20.0 and 27.6 MHz. The ‘H T, data obtained at 10.5 MHz have already been reported [ 11.The 35C1 T,, showed a maximum value of 840 ps at 359 K. With decreasing and increasing temperature from 359 K, 35C1T,, decreased to 170 ,USat 273 K and 220 ps at 393 K, respectively. These fast relaxation rates may be responsible for the disappearance of the NQR signal described above. The isotope ratio Tla(37C1) /T,,(35C1) was determined The
(PYH)
temperature
[AuCLlis shown
223
27.41 250I
I 300
I T/K
400
350
Fig. 1. The temperature dependence of the Wl NQR frequencies determined for pyridinium tetrachloroaurate (III) by use of the cw (0 ) and pulsed (0 ) spectrometers. The resonance frequencies were not measured by the cw method at higher temperatures. 400 300
I 1 .: _ % _ f -%- +
200 I
T/K
100 I
(pyH)CAuCI~l +
“..
5
kK/T
10
Fig. 2. The temperature dependences of the 35C1 (0 ) and “7C1 ( 0 ) NQR spin-lattice relaxation time T,,, and the spin-lattice relaxation times Ti of ‘H NMR at the Larmor frequencies of 10.5 ( + ), 20.0 (A ) and 27.6 (A ) MHz observed for pyridinium tetrachloroaurate (III).
to be 1.6-t 0.1 and 1.020.1 in the temperature range below 350 K and above 370 K, respectively. The 35C1NQR frequencies and chlorine T,, values observed at various temperatures are listed in Table 1 along with the isotope ratios of T,,. In the ‘H T, measurements, anomalous temperature dependences of ‘H T, were observed below the temperature at which the T, minimum appeared, when the Larmor frequency of 20.0 or 27.6 MHz which is near to the 37C1or 35C1 NQR frequency, respectively, was employed. The anomaly is clearly recognized
224 TABLE 1 35C1NQR frequencies T,, (%l) determined
v, spin-lattice relaxation times T,,(35C1) and the isotope ratio TI,(37C1)/ at various temperatures for (pyH) [ AuCl,]
T W)
v (MHz)
232 255 279 341 359 380 389
27.93 27.866 27.808 27.629 27.572 27.496 27.470
t- 0.01 + 0.005 + 0.003 k 0.003 k 0.003 + 0.003 I!I0.003
T,Q(~~C~) (ms)
T~s(~‘C~)/T,,(~“C~)
0.22 0.69 0.84 0.46 0.27
1.6 1.6 1.3 1.0 1.0
when the above data are compared with those observed at the Larmor frequencies of 10.5, 16.0 and 45.5 MHz [ 11. This is probably due to the occurrence of dipolar-quadrupolar cross relaxation with chlorine nuclei. Chlorine nuclear quadrupole relaxation and the motion of pyridinium ions The temperature dependences of the chlorine T,, values below ca. 350 K cannot be explained on the basis of the libration model [5,6] or the Raman process [5,7,8] already discussed by several authors, because T,, values expected from either model should increase with decreasing temperature. However, the reverse temperature dependence was observed in this temperature range. These results are very similar to those reported by Sagisawa et al. [9] for the 35C1 NQR relaxation of a-NH,HgCl,, in which field-gradient fluctuation due to the motion of ammonium ions was shown to be responsible for the anomalous temperature dependence of the 35C1 T1o observed. In the present compound, it was shown by the ‘H NMR study [ 1]that pyridinium ions, having a large electric dipole moment, perform a fairly fast reorientational motion about the Cc’ axis in the crystal. Therefore, a similar mechanism is expected to operate. On the other hand, the possibility of a phase transition as the origin of the anomalous relaxation behavior can be excluded because no thermal anomaly was observed in the DTA measurements carried out in the temperature range 135-460 K [ 11. According to Woessner and Gutowsky [ 61, the T1o of chlorines due to fluctuations of the external field gradient is given, by assuming an axial field gradient at chlorine site, as
T1Q -1 where (q’/q) is a fluctuation
fraction
of the electric
field gradient,
z, is the
225
correlation time of the motion of the external atomic groups or ions (pyridinium ions in this case), and is the quadrupole resonance frequency in angular units. From the detailed analysis of ‘H NMR Ti, the correlation times of the motion of pyridinium ions could be estimated in the preceding paper [ 11. According to the above results, it was shown that the nonequivalence of the potential wells for the different orientations of the cation at the lattice site should be considered in order to understand the motion of pyridinium ions in the crystal. In conclusion this leads to the two independent correlation times rcl and z,~ for the reorientations about the Cc’ axis, which are written as mQ
7cl=
(2W, + IV,)-’
rcc2=(w2+2&)-1 Here, WI, IV, and IV, are transition probability rates assumed sented by a frequency factor K and the three different activation EB and EC, respectively, as
(2) (3) to be repreenergies EA,
W, =Kexp(
-EJRT)
(4)
W, =Kexp(
-E,/RT)
(5)
W, =Kexp(
-E,/RT)
(6)
Using the ‘H NMR T1 data obtained at the Larmor frequencies of 10.5, 16.0, and 45.5 MHz involving no effect from the cross relaxation with chlorines, three activation energies EA, EB and EC, and the inverse frequency factor K-’ were determined to be 21.8, 17.3 and 13.6 kJ mol-‘, and 7.0~ lo-‘* s, respectively [ 11. Putting these values into eqns. (2) and (3), the correlation times 7cland r& were estimatedas a fUnCtiOn OfteInperatUI'e. Since 7cscl is longer enough than r& below ca. 350 K, the spectral density J(W) which is defined by (7) is higher for zcl than rcz when the high temperature limit w2zc12<< 1 can be applied. The ‘H NMR T, observed below ca. 400 K is predominantly determined by the correlation time zcl above the temperature at which the ‘H T, shows a minimum [ 11. Using Larmor frequencies of 20.0 and 27.6 MHz which are close to the 37C1and 35C1NQR frequencies, respectively, the ‘H Tl minima were located around 195 K as shown in Fig. 2. Therefore, the spectral density at the quadrupole resonance frequencies is also expected to be effectively determined by the 7clin the temperature range between ca. 200 and 350 K. J(mQ)
226
1x10-”
I
I
I
I
I
3.6
2.8 kK/T
Fig. 3. The temperature dependence of the correlation times 7cl (0 ) estimated from the WI T,, data by assuming the fluctuation fraction of the electric field gradient, (q//q), as 0.075. The solid line shows 7cl determined from the detailed analysis of the ‘H NMR T, data of pyridinium tetrachloroaurate (III).
In the temperature range, in which T,o measurements were undertaken, the correlation time rc in eqn. (1) would be replaced by the zcl. Since c&r:, << 1 is held in this temperature range, the following equation is obtained.
The isotope ratio T,o ( 37C1)/T,, ( 35C1)of 1.6 2 0.1 determined below ca. 350 K agrees with the theoretically predicted value of 1.61 derived from eqn. (8). By use of eqn. (8), the quantities (q'/q)2Tc,were estimated from the measured T,, values as a function of temperature. In the calculation, oo/27r was substituted by the value of 28.5 MHz which is the 35C1NQR frequency of the fictitious rigid lattice of the present complex estimated from the temperature dependence of resonance frequencies [lo]. Assuming (q'/q)=0.075, the correlation times r,i obtained from the 35C1T1o data showed a good agreement with those determined by the ‘H NMR T, data [ 1 ] over the temperature range ca. 350-270 K. The results are shown in Fig. 3. The value estimated for the fluctuation fraction of the electric field-gradient lies in a reasonable range as compared with the reported value for cu-NH,HgCl, [91 or 2,2dichloropropane [ 61. Accordingly, the dominant relaxation mechanism responsible for the determination of Tls below ca. 350 K is attributable to the fluctuation of the field gradient due to the motion of the pyridinium ions located nearby. Reorientation of [AuClJ-
ions
The steep T,, decrease observed above ca. 360 K with increasing temperature may be ascribed to a reorientational motion of the [ AuCl,] - ions, since
227
the isotope ratio T,Q(37C1)/T,Q(35C1) of l.O+O.l observed above ca. 370 K agrees with the theory of relaxation based on the slow motional process [ ll131. Assuming a C, reorientation of the Ddh complex anions, T,, can be expressed as [ 141 Tla= (2/3)r=
(2/3)r,exp(E,/RT)
(9)
Here, the Arrhenius relationship between the correlation time 7 and the activation energy E, for the motion is assumed, and 7, is the correlation time at the limit of infinite temperature. The activation energy E, of 67.4 kJ mol-’ and the correlation time 7, of 3.7 x lo-l3 s were obtained by fitting the T,, data observed above ca. 370 K to eqn. (9 ). The value of E, thus derived agrees very well with the reported value of 67 kJ mol-’ for guanidinium tetrachloroaurate (III) [ 141. This indicates that the interionic hindrance barrier to the reorientation of the complex anion is almost the same for these two complex crystals regardless of the cations being different.
REFERENCES 1 2 3 4 5 6 I 8 9 10
Y. Ito, T. Asaji, R. Ikeda and D. Nakamura, Ber. Bunsenges. Phys. Chem., 92 (1988) 885. K. Horiuchi, R. Ikeda and D. Nakamura, Ber. Bunsenges. Phys. Chem., 91 (1987) 1351. A. Ishikawa, K. Horiuchi, R. Ikeda and D. Nakamura, J. Mol. Struct., 192 (1989) 237. D. Nakamura, Y. Kurita, K. Ito and M. Kubo, J. Am. Chem. Sot., 82 (1960) 5783. H. Chihara and N. Nakamura, Adv. Nucl. Quadrupole Reson., 4 (1980) 1. D.E. Woessner and H.S. Gutowsky, J. Chem. Phys., 39 (1963) 440. J. Van Kranendonk, Physica, 20 (1954) 781. J. Van Kranendonk and M.B. Walker, Can. J. Phys., 46 (1968) 2441. K. Sagisawa, H. Kiriyama and R. Kiriyama, Chem. Lett., (1975) 1285. T.P. Das and E.L. Hahn, Nuclear Quadrupole Resonance Spectroscopy, Solid State Physics, Suppl. 1, Academic Press, New York, 1958, pp. 41-49. 11 S. Alexander and A. Tzalmona, Phys. Rev., 138 (1965) A845. 12 K.R. Jeffrey and R.L. Armstrong, Phys. Rev., 174 (1968) 359. 13 M. Goldman, Spin Temperature and Nuclear Magnetic Resonance in Solids, Oxford University Press, London, 1970, pp. 67-74. 14 Y. Furukawa and D. Nakamura, Z. Naturforsch., Teil A, 41 (1986) 416.
Journal of Molecular Structure, 192 (1989) 221-227 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
CHLORINE NUCLEAR QUADRUPOLE RESONANCES MOTION OF PYRIDINIUM IONS IN PYRIDINIUM TETRACHLOROAURATE(II1)
AND
ATSUSHI ISHIKAWA, YUKARI ITO*, KEIZO HORIUCHI**, TETSUO ASAJI and DAIYU NAKAMURA Department of Chemistry, Faculty of Science, Nagoya University, Chikusa, Nagoya 464 (Japan) (Received 4 February 1988)
ABSTRACT The temperature dependences of %l NQR frequencies and of chlorine nuclear quadrupole relaxation times, T,, have been determined for pyridinium tetrachloroaurate(II1). The “%l NQR frequency of a single line appearing is 27.769 MHz at 293 K. With decreasing temperature, the NQR line is observed to become gradually broad and cannot be detected below ca. 230 K. 35C1T,, is observed to decrease with decreasing temperature from 800 ,asat 350 K to 170 ps at 273 K. This fast relaxation rate may be responsible for the disappearance of the NQR signal described above. T,, data are discussed by referring to the ‘H NMR T, data already determined. The dominant relaxation mechanism for T,, below ca. 350 K can be attributed to the fluctuation of the field gradient due to the motion of the pyridinium ions in the crystal. Above ca. 360 K, T,, decreases rapidly with increasing temperature suggesting the onset of a motion of [AuCl,] ions. The activation energy for the motion is estimated to be 67 kJ mol-‘. When the Larmor frequency of ‘H T, measurements is near to the NQR frequencies, anomalous temperature dependences of ‘H T, are observed, suggestingthe occurrence of dipolar-quadrupolar cross relaxation with chlorine nuclei.
INTRODUCTION
Since a pyridinium ion has an electric dipole moment, the molecular dynamics of pyridinium salts provide some interesting problems in relation to their electric properties. Very recently, we have extensively studied, by means of ‘H NMR experiments, the reorientational motion of pyridinium ions in pyridinium tetrachloroand tetrabromoaurate (III) about their pseudohexad axis C6’ which is perpendicular to the cationic plane and passes through the center of the cationic ring [ 11. In these salts, it has been shown that nonequivalence among the potential wells in the crystals must be taken into account to interpret properly the motion of pyridinium ions observed. *Present address: Government Industrial Research Institute, Nagoya, Kita, Nagoya 462, Japan. **Present address: Department of Chemistry, Division of General Education, University of the Ryukyus, Nishihara, Okinawa 903-01, Japan.
0022-2860/89/$03.50
0 1989 Elsevier Science Publishers B.V.
222
The orientational order-disorder of pyridinium ions in crystals gives rise to another important problem when the motion is frozen at lower temperatures. The 35C1 nuclear quadrupole resonance (NQR) signal of pyridinium tetrachloroaurate (III), (pyH) [ AuCl, 1, faded out below ca. 230 K [ 11. This fadeout phenomenon can be explained in terms of a static disorder of pyridinium ions in the crystal. On the other hand, the field gradient fluctuation will be produced at chlorine sites by the motion of pyridinium ions located near to the chlorines. This dynamic disorder of the cations may also be responsible for the fade-out phenomenon when the sample temperature decreases. To obtain information about the field gradient fluctuation at the chlorine site, the spinlattice relaxation times, T,o, of chlorine in pyridinium tetrachloroaurate (III) were observed as a function of temperature. EXPERIMENTAL
35C1 and 37C1 T,, and the resonance frequencies were determined for the same sample as used in previous work [ 11. The temperature dependence of T,, was determined by means of a home-made pulsed NQR spectrometer [2, 31. T,, values were measured by employing the 7r-r-n/2-z,-7r pulse sequence in which 7 was varied while 7, was set constant for about 150 ps. Almost exponential decay of the echo height after the pulse sequence was observed. The sample temperature was controlled and measured by use of a proportional temperature regulator together with a copper-constantan thermocouple. A modified Dean-type superregenerative spectrometer [4] was also employed for the measurements of the resonance frequencies. In the cw NQR measurements, a chromel-alumel thermocouple was used to determine the sample temperature. The observed temperature was estimated to be accurate within ? 1 K both in the cw and pulsed NQR measurements. For the ‘H NMR T, measurements, a conventional n-r-n/2 pulse sequence was used. The details of the measurements are the same as those reported elsewhere [ 11. RESULTS AND DISCUSSION
determined for dependence of 35C1 NQR frequencies in Fig. 1. The NQR signal could not be observed below ca. 230 K and above ca. 395 K. The temperature dependences of the 35C1and 37C1T,, are shown in Fig. 2, as well as those of the spin-lattice relaxation time T, of ‘H NMR at 10.5, 20.0 and 27.6 MHz. The ‘H T, data obtained at 10.5 MHz have already been reported [ 11.The 35C1 T,, showed a maximum value of 840 ps at 359 K. With decreasing and increasing temperature from 359 K, 35C1T,, decreased to 170 ,USat 273 K and 220 ps at 393 K, respectively. These fast relaxation rates may be responsible for the disappearance of the NQR signal described above. The isotope ratio Tla(37C1) /T,,(35C1) was determined The
(PYH)
temperature
[AuCLlis shown
223
27.41 250I
I 300
I T/K
400
350
Fig. 1. The temperature dependence of the Wl NQR frequencies determined for pyridinium tetrachloroaurate (III) by use of the cw (0 ) and pulsed (0 ) spectrometers. The resonance frequencies were not measured by the cw method at higher temperatures. 400 300
I 1 .: _ % _ f -%- +
200 I
T/K
100 I
(pyH)CAuCI~l +
“..
5
kK/T
10
Fig. 2. The temperature dependences of the 35C1 (0 ) and “7C1 ( 0 ) NQR spin-lattice relaxation time T,,, and the spin-lattice relaxation times Ti of ‘H NMR at the Larmor frequencies of 10.5 ( + ), 20.0 (A ) and 27.6 (A ) MHz observed for pyridinium tetrachloroaurate (III).
to be 1.6-t 0.1 and 1.020.1 in the temperature range below 350 K and above 370 K, respectively. The 35C1NQR frequencies and chlorine T,, values observed at various temperatures are listed in Table 1 along with the isotope ratios of T,,. In the ‘H T, measurements, anomalous temperature dependences of ‘H T, were observed below the temperature at which the T, minimum appeared, when the Larmor frequency of 20.0 or 27.6 MHz which is near to the 37C1or 35C1 NQR frequency, respectively, was employed. The anomaly is clearly recognized
224 TABLE 1 35C1NQR frequencies T,, (%l) determined
v, spin-lattice relaxation times T,,(35C1) and the isotope ratio TI,(37C1)/ at various temperatures for (pyH) [ AuCl,]
T W)
v (MHz)
232 255 279 341 359 380 389
27.93 27.866 27.808 27.629 27.572 27.496 27.470
t- 0.01 + 0.005 + 0.003 k 0.003 k 0.003 + 0.003 I!I0.003
T,Q(~~C~) (ms)
T~s(~‘C~)/T,,(~“C~)
0.22 0.69 0.84 0.46 0.27
1.6 1.6 1.3 1.0 1.0
when the above data are compared with those observed at the Larmor frequencies of 10.5, 16.0 and 45.5 MHz [ 11. This is probably due to the occurrence of dipolar-quadrupolar cross relaxation with chlorine nuclei. Chlorine nuclear quadrupole relaxation and the motion of pyridinium ions The temperature dependences of the chlorine T,, values below ca. 350 K cannot be explained on the basis of the libration model [5,6] or the Raman process [5,7,8] already discussed by several authors, because T,, values expected from either model should increase with decreasing temperature. However, the reverse temperature dependence was observed in this temperature range. These results are very similar to those reported by Sagisawa et al. [9] for the 35C1 NQR relaxation of a-NH,HgCl,, in which field-gradient fluctuation due to the motion of ammonium ions was shown to be responsible for the anomalous temperature dependence of the 35C1 T1o observed. In the present compound, it was shown by the ‘H NMR study [ 1]that pyridinium ions, having a large electric dipole moment, perform a fairly fast reorientational motion about the Cc’ axis in the crystal. Therefore, a similar mechanism is expected to operate. On the other hand, the possibility of a phase transition as the origin of the anomalous relaxation behavior can be excluded because no thermal anomaly was observed in the DTA measurements carried out in the temperature range 135-460 K [ 11. According to Woessner and Gutowsky [ 61, the T1o of chlorines due to fluctuations of the external field gradient is given, by assuming an axial field gradient at chlorine site, as
T1Q -1 where (q’/q) is a fluctuation
fraction
of the electric
field gradient,
z, is the
225
correlation time of the motion of the external atomic groups or ions (pyridinium ions in this case), and is the quadrupole resonance frequency in angular units. From the detailed analysis of ‘H NMR Ti, the correlation times of the motion of pyridinium ions could be estimated in the preceding paper [ 11. According to the above results, it was shown that the nonequivalence of the potential wells for the different orientations of the cation at the lattice site should be considered in order to understand the motion of pyridinium ions in the crystal. In conclusion this leads to the two independent correlation times rcl and z,~ for the reorientations about the Cc’ axis, which are written as mQ
7cl=
(2W, + IV,)-’
rcc2=(w2+2&)-1 Here, WI, IV, and IV, are transition probability rates assumed sented by a frequency factor K and the three different activation EB and EC, respectively, as
(2) (3) to be repreenergies EA,
W, =Kexp(
-EJRT)
(4)
W, =Kexp(
-E,/RT)
(5)
W, =Kexp(
-E,/RT)
(6)
Using the ‘H NMR T1 data obtained at the Larmor frequencies of 10.5, 16.0, and 45.5 MHz involving no effect from the cross relaxation with chlorines, three activation energies EA, EB and EC, and the inverse frequency factor K-’ were determined to be 21.8, 17.3 and 13.6 kJ mol-‘, and 7.0~ lo-‘* s, respectively [ 11. Putting these values into eqns. (2) and (3), the correlation times 7cland r& were estimatedas a fUnCtiOn OfteInperatUI'e. Since 7cscl is longer enough than r& below ca. 350 K, the spectral density J(W) which is defined by (7) is higher for zcl than rcz when the high temperature limit w2zc12<< 1 can be applied. The ‘H NMR T, observed below ca. 400 K is predominantly determined by the correlation time zcl above the temperature at which the ‘H T, shows a minimum [ 11. Using Larmor frequencies of 20.0 and 27.6 MHz which are close to the 37C1and 35C1NQR frequencies, respectively, the ‘H Tl minima were located around 195 K as shown in Fig. 2. Therefore, the spectral density at the quadrupole resonance frequencies is also expected to be effectively determined by the 7clin the temperature range between ca. 200 and 350 K. J(mQ)
226
1x10-”
I
I
I
I
I
3.6
2.8 kK/T
Fig. 3. The temperature dependence of the correlation times 7cl (0 ) estimated from the WI T,, data by assuming the fluctuation fraction of the electric field gradient, (q//q), as 0.075. The solid line shows 7cl determined from the detailed analysis of the ‘H NMR T, data of pyridinium tetrachloroaurate (III).
In the temperature range, in which T,o measurements were undertaken, the correlation time rc in eqn. (1) would be replaced by the zcl. Since c&r:, << 1 is held in this temperature range, the following equation is obtained.
The isotope ratio T,o ( 37C1)/T,, ( 35C1)of 1.6 2 0.1 determined below ca. 350 K agrees with the theoretically predicted value of 1.61 derived from eqn. (8). By use of eqn. (8), the quantities (q'/q)2Tc,were estimated from the measured T,, values as a function of temperature. In the calculation, oo/27r was substituted by the value of 28.5 MHz which is the 35C1NQR frequency of the fictitious rigid lattice of the present complex estimated from the temperature dependence of resonance frequencies [lo]. Assuming (q'/q)=0.075, the correlation times r,i obtained from the 35C1T1o data showed a good agreement with those determined by the ‘H NMR T, data [ 1 ] over the temperature range ca. 350-270 K. The results are shown in Fig. 3. The value estimated for the fluctuation fraction of the electric field-gradient lies in a reasonable range as compared with the reported value for cu-NH,HgCl, [91 or 2,2dichloropropane [ 61. Accordingly, the dominant relaxation mechanism responsible for the determination of Tls below ca. 350 K is attributable to the fluctuation of the field gradient due to the motion of the pyridinium ions located nearby. Reorientation of [AuClJ-
ions
The steep T,, decrease observed above ca. 360 K with increasing temperature may be ascribed to a reorientational motion of the [ AuCl,] - ions, since
227
the isotope ratio T,Q(37C1)/T,Q(35C1) of l.O+O.l observed above ca. 370 K agrees with the theory of relaxation based on the slow motional process [ ll131. Assuming a C, reorientation of the Ddh complex anions, T,, can be expressed as [ 141 Tla= (2/3)r=
(2/3)r,exp(E,/RT)
(9)
Here, the Arrhenius relationship between the correlation time 7 and the activation energy E, for the motion is assumed, and 7, is the correlation time at the limit of infinite temperature. The activation energy E, of 67.4 kJ mol-’ and the correlation time 7, of 3.7 x lo-l3 s were obtained by fitting the T,, data observed above ca. 370 K to eqn. (9 ). The value of E, thus derived agrees very well with the reported value of 67 kJ mol-’ for guanidinium tetrachloroaurate (III) [ 141. This indicates that the interionic hindrance barrier to the reorientation of the complex anion is almost the same for these two complex crystals regardless of the cations being different.
REFERENCES 1 2 3 4 5 6 I 8 9 10
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