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1H and 19F NMR studies on molecular motions and phase transitions in solid triethylammonium tetrafluoroborate
Journal of
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 345 (1995) 235-243
1H and 19F N M R studies on molecular motions and phase transitions in solid triethylammonium tetrafluoroborate Hiroshi Ono a, Riki Seki a, Ryuichi Ikeda a, Hiroyuki Ishida b'* ~Department of Chemistry, University of Tsukuba, Tsukuba 305, Japan bDepartment of Chemistrv, College of General Education, Okayama University, Okayama 700, Japan Received 7 July 1994
Abstract
Measurements by differential thermal analysis and differential scanning calorimetry and of the spin-lattice relaxation time (TI), the spin-spin relaxation time (T2), and the second moment (M2) of 1H and 19F N M R were carried out in the three solid phases of (CH3CH2)3NHBF 4. X-ray powder patterns were taken in the highest-temperature phase (Phase I) existing above 367 K and the room-temperature phase (Phase II) stable between 220 and 367 K. Phase I formed a NaC1type cubic structure with a = 11.65(3) A, Z = 4, V = 1581(13)A 3, and D x = 0.794gcm 3, and was expected to be an ionic plastic phase. In this phase, the self-diffusion of anions and the isotropic reorientation of cations were observed. Phase II formed a tetragonal structure with a = 12.47(1) and c=9.47(3)A, Z = 4 , V = 1473(6)A 3, and D x = 0.852gcm 3 From the present DSC and N M R results in this phase, the cations and/or anions were considered to be dynamically disordered states. The C3 reorientation of the cation about the N - H bond axis was detected and, in addition, the onset of nutation of the cations and local diffusion of the anions was suggested. In the low-temperature phase (Phase III) stable below 219 K, the C3 reorientations of the three methyl groups of cations and the isotropic reorientation of anions were observed. The motional parameters for these modes were evaluated.
1. Introduction
A l k y l a m m o n i u m tetrafluoroborates are k n o w n to have various solid-solid phase transitions [1-3]. O f these salts, we have recently revealed that in the highest temperature solid phase o f (CH3)2NNH3BF4 [4], ( C H 3 ) z N H 2 B F 4 [5], ( C H 3 ) 3 N H B F 4 [6], and ( C H 3 ) 3 N C H 2 C H z O H B F 4 [7], b o t h cations and anions undergo rapid selfdiffusion as well as isotropic reorientation. F r o m the t h e r m o d y n a m i c and molecular dynamics points ~" Dedicated to the memory of Professor Daiyu Nakamura. * Corresponding author. Elsevier Science B.V. SSDI 0 0 2 2 - 2 8 6 0 ( 9 4 ) 0 8 4 5 1 - 3
o f view, we have assigned these phases to the ionic plastic phase. Zabinska et al. [3] carried out differential scanning calorimetry (DSC) o f ( C H 3 C H 2 ) 3 N H B F 4 and have f o u n d two solid-solid phase transitions at 217 and 368 K. This thermal behavior is similar to that o f (CH3)3NHBF4 . Moreover, the melting e n t r o p y o f 17.4 J K I tool t evaluated f r o m their data is fairly low. We m a y expect f r o m these data that highly disordered states o f both cation and anions are realized in the highest temperature solid phase o f ( C H 3 C H 2 ) 3 N H B F 4. In the present investigation, we have carried out measurements o f the IH and 19F N M R spin-lattice
236
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
relaxation time (T1) and spin-spin relaxation time (T2), the second moment (M2) of IH and 19F N M R absorptions, differential thermal analysis (DTA), DSC, and powder X-ray diffractions, in order to clarify the dynamic behavior of the cations and anions in each solid phase and to reveal the presence of highly mobile ions in this salt.
(abbreviated to Tm and T2n, respectively, for IH, and Tw and T2F for 19F) were measured by use of a Bruker Pulse N M R spectrometer (model SXP100). TIH was determined at 34.1 and I I.8MHz, while Tw was determined at 32.1 and 14 MHz using the 180°-t-90 ° pulse sequence. Hahn's spin-echo method [9] was employed for the determination of TzH at 34.1 MHz and T2v at 32.1 MHz. Powder X-ray patterns were taken at about 300 and about 370 K by using a Philips X'Pert PW 3050/100 and a Rigaku R I N T 1000 diffractometer, respectively.
2. Experimental (CH3CH2)3NHBF 4 was prepared by neutralizing triethylamine with tetrafluoroboric acid. The obtained crystals were recrystallized three times from benzene. Found: C, 37.6; H, 8.54; N, 7.29%. Calculated for (CH3CH2)3NHBF4: C, 38.1; H, 8.47; N, 7.41%. Because of the strong hygroscopicity, the purified crystals were handled in a dry bag and dried under vacuum at 75°C for 24 h before the measurements o f N M R , DTA, and DSC. Phase transition temperatures and the corresponding enthalpy changes were redetermined by a home-made D T A apparatus [8] and a Daini Seikosha calorimeter (model SSC-560), respectively. M2 of I H and 19F N M R absorptions (abbreviated to M2H and M2F, respectively) were determined by use of a JEOL JNM-MW-40S spectrometer. T 1 and T2 of 1H and 19F N M R
3. Results D T A curves of (CH3CH2)3NHBF 4 recorded between 110 and 410 K are shown in Fig. 1. When the sample was heated, two large endothermic anomalies attributed to solid-solid phase transitions appeared at 219 and 367 K, and that of melting at 388 K. These temperatures agreed well with those reported by Zabinska et al. [3]. The revealed solid phases were designated in the order of decreasing temperatures as Phase I, II, and III. When the sample was cooled, however, three exothermic anomalies showing marked hystereses were observed. Enthalpy changes at the transitions EXO
195K
381K
( ENDO Ill
II
I
Fig. 1. DTA curves recorded in (CH3CH2)3NHBF4. The cooling and heating rate was approximately 1 K min I. I, I1, and III are the solid phases definedin the text.
H. Ono et al./Journalof Molecular Structure 345 (1995) 235 243 i
7 `¸ K
15
] 5 l o 3130 C
400
o
/
237
300
2f/()
10 ° I1
II[
,
I
E
~5 ~A,~A
t() °
10
© .,..~
*"
10-2
•
•
"
•
]
s,
~
• 10
2
10
4
~ Z~
~-
OL_
300
200
~0 400
2.h
10-4
(At~sH(III --~ II) and AtrsH(II
~
I))
and fusion
(&rus H ) determined by D S C were 7 . 5 ~ 0 . 1 kJ tool 1, 5 . 7 + 0 . 1 kJ mol 1, and 6.1zk0.1 kJ mol 1, respectively; then the associated entropy changes were evaluated to be 34 + 1 J K l m o l - i , 16 + 1 J K -1 mo1-1, and 16 + 1 J K i m o l - l , in the same order. Temperature dependences o f 11428 and M2F are shown in Fig. 2. Both M2~ and M2F have constant values o f 14.5 4- 0.5 G 2 and 2.6 • 0.3 G 2 (1 G = 1 x 10 4 T), respectively, in the range o f 130-190 K. With increasing temperature, both M2H and M2F decreased and reached almost constant values o f 1 . 3 ~ 0 . 2 G 2 and 1 . 1 + 0 . 2 G 2, respectively, and were maintained at these values up to the phase transition temperature (Ttr) f r o m Phase II to I (Ttr(II ~ I)). A t Ttr(II--~ I), a discontinuous change in M2H and M2F was observed. In Phase I, M2H decreased with increasing temperature and became 0.25 + 0.03 G 2. However, M2F in this phase was less than 0.05 G 2. The temperature dependences o f T1H, TIF , T2H, and TzF in Phases I and II are shown in Fig. 3. T m showed m a r k e d non-exponential recovery o f I H magnetization in the region 2 8 0 360 K in Phase II, while T~v became slightly nonexponential in the same temperature range. The non-exponential recovery curve o f TIH could be separated into two relaxation times, T1w and TIHt (TIH~ < TiHl ) according to the following
II 3
T/K Fig. 2. Temperature dependences of NMR second moment, M2, for IH (O) and IOF (&), respectively, observed in (CH3CH2)3NHBF4. The broken lines show the phase transition temperatures determined by DTA.
1
2.7 -
4 I(13T 1/ K-I
"
5
Fig. 3. Temperature dependences of spin lattice relaxation times for IH (Tin) and 19F (Tw) and spin spin relaxation times (T2H and T2v) observed in Phases I and II of (CH3CHz)3NHBF4; (o) Tm and TtH, (e) TIH~ at 34 MHz; ([2) Tm and TIH~;(11) Tlw at 11.8 MHz; (A) Tlv at 32 MHz; (o) Tiv at 14 MHz; (×) ~u at 34 MHz; (+) T2v at 32 MHz, where suffixes 1 and s mean the long and short components as given in text. The broken lines show the phase transition temperatures determined by DTA. Solid lines indicate the best fitted theoretical values• equation: [Mo - M~(t)]/2Mo = As exp ( - t / T m O + Al exp (--t/T1H,)
(1)
Here, M0 and M:(t) are z c o m p o n e n t s o f the 1H magnetization at thermal equilibrium and at time t after a 180 ° pulse, respectively, and As and A 1 are constants (As + Al = 1). Since it was difficult to obtain the two T1F values accurately from the slightly non-exponential recovery curve o f 19F magnetization, T~v was conventionally determined f r o m the initial linear portion o f l o g [ M 0 - Mz(t)]/2Mo versus t plots [10]. Both Tlv and TIH increased discontinuously at Ttr(II ~ I). TZH and T2v also increased discontinuously at this transition, in accordance with the results o f 342. In Phase I, TIH increased, whereas Tlv decreased, with increasing temperature. Fig. 4 shows temperature dependences o f TIH and Tw in Phase III. TIN at 34.1 and 11.8 M H z show a m i n i m u m o f 40 ms at a r o u n d 130 K and 15 ms at a r o u n d 110 K, respectively. T w at 32.1 M H z shows a m i n i m u m o f 18 ms at a r o u n d 160 K and a shoulder at a r o u n d 110 K. A discontinuous change in both TIH and TIF was observed at Ttr(III -+ II).
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
238
7"// K
200 10 ° ~-" -
150
100 I0 °
~ :2
< b...
10-1
10 1
&
i
o •
10 2
<'\ <> >>....
IO 2 III
•
.
t
6
_
L
_
A
_
8 10 103T 1 / K q
_
•
12
Fig. 4. Temperature dependences of spin lattice relaxation times for 1H (Tin) and 19F (TIF) observed in Phase Ill of (CH3CH2)3NHBF4: (©) TIH at 34 MHz; ([]) TtH at 11.8 MHz; (A) Tw at 32 MHz; (o) TIF at 14 MHz. The broken lines shows the phase transition temperatures determined by DTA. Solid lines indicate the best fitted theoretical values.
Table 2 Observed and calculated diffraction angles 20, relative intensities I, and their indexing hkl for X-ray powder patterns in Phase II of (CH3CH2)3NHBF4 at about 300 K (tetragonak a = 12.47(1), c = 9.43(3) A, and Z = 4) Observed
Calculated
20 (deg)
I (%)
20 (deg)
hkl
11.70 20.10 21.33 23.36 24.27 25.70 29.42 31.75 34.22 44.17
100 20 50 25 15 20 5 5 5 10
11.72 20.13 21.36 23.35 24.43 25.74 29.45 31.73 34.41 44.14
101 220 300 30l 311 320 312 203 402 610
4. Discussion
4,1. High-temperature phase (Phase I) P o w d e r X - r a y diffraction angles (20) o b t a i n e d at a b o u t 380 K in Phase I could be interpreted as facecentered cubic (f.c.c.) lattice with a = 11.65(3) A Z = 4, V = 1581(13) A 3, a n d D x = 0.794 g cm 3. The a d e q u a c y of the present analysis is shown in T a b l e 1. The angles (20) o b t a i n e d in Phase II at a b o u t 300 K are s h o w n in T a b l e 2. These angles correspond to a tetragonal lattice having constants of a = 12.47(1), c : 9 . 4 7 ( 3 ) A_, Z = 4 , V = 1473(6) A 3, a n d Dx = 0.852 g cm -3.
Table 1 Observed and calculated diffraction angles 20, relative intensities I, and their indexing hkl for X-ray powder pattern in Phase I of (CH3CH2)3NHBF4 at about 380 K (cubic, a = 11.65(3) A and Z 4) -
Observed
Calculated
20 (deg)
1 (%)
20 (deg)
hkl
13.19 15.19 21.64 25.40 26.52 30.64 33.52
5 60 100 70 5 40 10
13.16 15.21 21.57 25.36 26.50 30.70 33.53
Ill 200 220 311 222 400 331
The N a C l - t y p e f.c.c, structure of Phase I of ( C H 3 C H 2 ) 3 N H B F 4 d e t e r m i n e d in the present X - r a y diffraction study implies that b o t h cations a n d a n i o n s behave like spherical ions in the crystal. T h u s these ions are expected to have d y n a m i cally disordered o r i e n t a t i o n s in this phase. This is s u p p o r t e d by the observed low e n t r o p y of fusion (AfusS = 16 J K -1 mol 1), which is c o m p a r a b l e to those (AfusS <_ 20 J K 1 m o l - l ) observed in plastic phases o f m o l e c u l a r solids [11]. I f the cation is a s s u m e d to rotate isotropically a b o u t its center of gravity, its ionic radius is estimated to be 3.55 A o n the basis of the N a C l - t y p e structure determined, by using a n ionic radius of 2.28 A for a n isotropically r o t a t i n g B F 4 ion [12]. This radius o b t a i n e d is comp a r a b l e to 3.42 & evaluated as the longest distance between the H a t o m of the CH3 g r o u p of the cation a n d its center of gravity by using atomic parameters of the ( C H 3 C H z ) 3 N H + ion in the ordered phase of [ ( C H 3 C H J 3 N H ] E S n C I 6 crystal [13]. F o r the isotropic r e o r i e n t a t i o n s of both cation a n d a n i o n , M2H a n d M2F were evaluated to be 0.28 G 2 a n d 0.37 G 2, respectively, from the structure data o f this phase described above. M2H values of 0.25 + 0.03 G 2 observed a b o v e 375 K agree with the calculated one, while the observed MZF values,
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
<0.05 G 2, were much less than the calculated value. This indicates that the anion performs translational self-diffusion as well as isotropic reorientation. If the anionic self-diffusion is taken into account, calculated M2H and M2F values become 0.21 G 2 and ,~ 0 G 2, respectively, in good agreement with the observed M2H and MzF values. Since TIH and Tie in Phase I show exponential behavior and the slopes of log Tl~t and log T w versus T -~ plots are different signs, the relaxation processes effective in TIH and Tlv are different. From the discussion of 1142, the ionic motions mainly contributing TIH and TIF are considered to be the cationic isotropic reorientation and the anionic self-diffusion, respectively. An activation energy of 42 + 2 kJ tool -1 was obtained for the cationic reorientation from the slope of log TIH versus T - l plots. The slight frequency dependence observed in Tll-l at 34.1 and 11.8 MHz may be originated from IH-19F dipolar interactions between the cations and anions modulated by the anionic self-diffusion. Plots of log TIF and log T2F against T z show almost the same gradient but with different signs, indicating that T1F and Tzv are attributed to the same relaxation process, i.e. the anionic self-diffusion. From the gradient of the log Tie and log T2F vs. T 1 plots, we obtain the activation energies of anionic self-diffusion as 48 ± 2 and 52 zk 2 kJ mol -l, respectively. From the dynamic behavior of the cations and anions, and the small value of AfusS revealed in the present investigation, it is highly possible that Phase I with a NaCl-type cubic structure is an ionic plastic phase. (CH3)zNNH3BF 4 and (CH3)2NH2BF4 in the ionic plastic phase have been shown to form CsCl-type cubic structures [4,5]. Both cations and anions in these phases perform self-diffusion with activation energies of 41 kJ tool l and 32 kJ mo1-1 for BF4 in (CH3)zNNH3BF 4 and (CH3)2NHzBF4, respectively, and 42.5 kJ mol -I and 36 kJ mo1-1 for (CH3)zNNH~- and (CH3)zNH~-, respectively. Although the plastic phases of these salts are more dense than those of (CH3CH2)3NHBF4 (Dx((CH3)zNNH3BF4) = 1.421 g cm -3 [14] and D x ( ( C H 3 ) 2 N H z B F 4 ) = 1.44 g cm 3 [5]), the above results indicate that the constituent ions in the CsCl-type ionic plastic phases can migrate more
239
easily than those of the Nacl type. This difference can be explained by considering the simple diffusion mechanism of the monovacancy process. When an ion migrates to the nearest vacant site in the CsCl-type structure, it may directly move to the next site passing through an opening of a regular square surrounded by four counter ions. However, an ion in the NaCl-type structure cannot move directly to the nearest vacant site but has to pass an equilateral triangular opening surrounded by three counter ions. The effective area for passing through the opening is, therefore, much smaller than that in the CsCl-type phase. This results in only the small BF4 ions being able to diffuse, while the globular cations find it difficult to migrate in the NaCl-type plastic phase.
4.2. Room-temperature phase (Phase II) The considerably large transition entropy AtrsS(III ---+II) = 34 J K 1 mol-1 observed implies that the cations and/or anions acquire quite a large part of their motional freedom at Ttr(III --~ II). This phase is, therefore, considered as a dynamically disordered phase. This is supported by the fact that the Dx -- 0.852 g c m -3 in Phase II is comparable to that of 0.794 g cm -3 in Phase I revealed as the orientatinally disordered phase as discussed above. To interpret the M 2 values observed in Phase II, we calculated the MzH values for the following motional states of the cations: (1) the rigid lattice, (2) the C 3 reorientation of the three CH 3 groups about the respective C - C bond axes, (3) the reorientation of the whole CHsCH2 groups about the C - N bond axis together with the CH3 (73 reorientations, (4) the C~ reorientation of the cation about the N - H bond axis together with the CH3 C3 reorientation, (5) the C~ reorientation of the cation about the N - H bond axis together with the CH3 and CH3CH 2 reorientations. Note that the motional states (3) and (5) result in the disordered structures of the cations. MZF has been calculated for only the rigid lattice state of the anion. Since no crystal data are available, we have calculated M2 values arising from only intra-ionic magnetic dipolar interactions. In the
240
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
Table 3 Second moments M2H of ]H NMR absorptions calculated for (CH3CH2)3NHBF4 crystals Motional mode
M2H (02)
(1) Rigid lattice (2) CH 3 rotation (3) CH3CH2 rotation (4) Cationic C~ rotation + (2) (5) Cationic C~ rotation + (3)
24.9 (29.4)~ 13.7 5.4 3,4 0.64
a The value (M2F) of 19F in BF4 ions.
calculation, the C - H , N - H , and B - F distances were taken to be the usual values of 1.10 A, 1.02 A, and 1.43 /k, respectively, [15-17] and the bond angles of H - C - H , H-N-C, F-B-F were assumed to be tetrahedral. The parameters concerning the C and N atoms of the cation were used in accordance with the structure of the cation determined by X-ray diffraction [13]. The calculated values are given in Table 3. The almost constant M2H value of 1.3 G 2 observed above 280 K in Phase II is interpreted in terms of the model for the orientationally disordered cation which performs the C~ reorientation about the N - H bond axis together with the reorientations of the CH 3 and CH3CH 2 groups. The difference between the observed and calculated M2H values is attributable to the inter-ionic dipolar interactions. A decrease in M2H with increasing temperature from 220 K can, accordingly, be explained by the cation C~ reorientation. The decrease in M2F in the same temperature region is also explicable by this motion averaging the 19F-1H dipolar interactions between the rotating BF4 ions and the cations. This is because the isotropic reorientation of the anion is already excited in Phase III as described below and its correlation time (rv) is considered to be short enough to satisfy the motional narrowing limit, WF Tv << 1, where o~F is the 19F angular resonance frequency. The TIH minimum and the TIF hollow observed around 220 K, therefore, are attributable to the cation C~ reorientation. Since T1H and TIF are exponential and TtH is much shorter than TlF in this temperature range, by ignoring the contribution from I H - 1 9 F dipolar interactions we can
express T1H as
[18]
1/T1H -~ CHHg(COH, 7-H)
(2)
g(o~H, "rH) = "rn/(1 + w2T2) + 4"rn/(1 + 4w2T2) (3) where Tn and CHH stand for the correlation time of the cation C~ reorientation and the motional constant related to the MZH reduction due to this motion, respectively. WH is the 1H angular resonance frequency. Tw is determined mainly by modulation of the 1H-19F dipolar interactions due to the above cationic motion. Then Tw can be approximately expressed as [10, 18-20]
1/TIF = Cvlag(a~HV,Tn)
(4)
g(WHV,TH = TH/[1 + (WH -- WV)2~-2] + 37H/ 2 2 "4- 6rH/[1 + (0.)H + ~V)2T2 l (1 + O.,'HTH)
(5) where CFH is related to M2F contributed from the ] H - 1 9 F interactions which is averaged out by this reorientation. Eqs. (2)-(5) were fitted to the observed TlH and TlF values using the least squares method. In the calculations, we assumed an Arrhenius-type relationship between *H and the activation energy (Ea) of the motional process expressed as TH = T0exp (Ea/RT)
(6)
where T0 is the correlation time at the limit of infinite temperature. The unknown parameters (CHH, CHF, TO, and Ea) determined are given in Table 4, and the best-fit curves are shown in Fig. 3. In the temperature range 280-360 K, marked non-exponential behavior has been observed for TIH. However, TIF becomes slightly nonexponential. The fact that a TIF minimum at 14 MHz and a TIHS minimum at 11.8 MHz appeared almost at the same temperature and that the same was true for TIF at 32 MHz and T I w at 34 MHz indicates that the same motional process contributes TiF and TIHs. This motional process is attributed to an anionic motion for the following reasons. If a cationic motion is responsible for the relaxation, T w is determined by the
H. Ono et al./Journal o f Molecular Structure 345 (1995) 235-243
241
Table 4 Activation energies Ea, correlation times T0 at the limit of infinite temperature, and motional constants C evaluated for cationic and anionic motions in (CH3CH2)3NHBF 4 E a (kJ mo1-1)
7-0 (10 -13 s)
C (108 s -2)
Motional mode
Phase 1 42 4-2 48 5:3 (from Ti ) 52 4- 2 (from T2)
Cationic isotropic rotation Anionic self-diffusion
Phase H 184-2
2.7
45 4- 2
0.032
28±2
2.1
Phase III 6.5 + 1
80
Cationic C~ rotation
27 (CHH) 0.63 (Cv.) 11 (ChH)
Nutation of cationic C~ axis Anionic local diffusion
25 (CFF) 3.0 (CHF)
30 (CHH)
CH 3 rotation
1.5 (CHF) Cationic C~ rotation
22+5 12+ 1
4.9
19 (CFF) 6.4 (CFH) 30 (CFB) a
Anionic isotropic rotation
a Theoretical value.
l H - 1 9 F interactions averaged by this motion. Then the Tiv minimum is expected to become a similar value to the Tw hollow observed at around 220 K by considering that the Tin s minimum is comparable to the Tin minimum at around 220 K. However, the TIF minimum observed is much shorter than the T w hollow around 220 K. It is, therefore, considered that the relaxation process operative in the range 280-360 K is an anionic motion, and the non-exponential behavior of Tm is due to 1H-19F dipolar interactions modulated by the anionic motion. Above 360 K, distinct nonexponential behavior of T m is not observed, while TI H decreases with increasing temperature, indicating the onset of the other relaxation process caused by cationic motion. T I e above 285 K can be written in terms of the correlation time (rE) of the anionic motion [10,18-20]
1/Tw = CeFg(CoF,re) + Cheg(aJHF, rF)
(7)
where CvF and CUe are related to the M 2 F reduction through 19F-19F and 1 9 F - I H interactions, respectively. However, Tins and T1.~ may be
approximated by [10,18-20] t
2
t
1/TIH~ ----5Cnnrn + 5CHH/aJH rH + C.e{rF/[1
+
tr/-,/
;
2 /
e)2r2}}
1/Tlm~ = 5CHHrH + ~t~HH/WHrH
(8) (9)
where r~q is the correlation time of the cationic motion affecting TIH above 350 K. C~q. and CHF are the motional constants of this motion and the above anionic motion, respectively. By fitting Eqs. (6)-(9) to observed TIH and Tie values, we obtain an E a of 28 + 2 kJ mol I and 45 4- 2 kJ mo1-1 for the anionic and cationic motions, respectively. We expect that the T I e and T1HS minima are originated from inter-ionic 19F-19F dipolar interactions, because in Phase 1| intra-anion dipolar interactions are considered to be completely averaged out by the anionic isotropic reorientation whose onset is detected in Phase IV. It is, however, difficult to clarify the anionic motional mode from the observed M2 values because this motion is predicted to cause only a small reduction of 342 of about 0.2 G 2 which is roughly estimated
H. Ono et al./Journal 0s Molecular Structure 345 (1995) 235-243
242
from the TIF and TIHs minima, and this reduction is comparable to the experimental error of the present M2 measurements in this temperature range. In fact, no detectable M2 reduction assignable to this motion is observed. When the anions perform translational self-diffusion, inter-ionic dipolar interactions are averaged out and MzF becomes = 0 G* as seen in Phase I. If the anions perform local diffusion, i.e. the center of gravity of the anion is positionally disordered and the anion hops between these disordered sites, the inter-ionic interactions are partly averaged out and a small Ml reduction is expected. From the fact that the Ci and isotropic reorientations of the cations are observed at around 220 K in Phase II and above 370 K in Phase I, the cationic motion affecting TIH above 350 K in Phase II is the intermediate state of these two motions. As one of the probable motions, a nutation of the cation as a whole around the N-H bond axis is suggested. 4.3. Low-tempertaure phases (Phase III) By comparing the observed I%& values with the calculated ones shown in Table 3, almost the constant value of MZn observed between 150 and 180 K in Phase III can be interpreted in terms of the C3 reorientations of the three CH3 groups. The anions in this temperature range are considered to reorient isotropically, when the *H-19F dipolar interactions are taken into account between the anion and cation, whose contribution to MzF is roughly estimated to be 2-4 G’ from MzF values of 2.5-2.8 G2 reported for the isotropically reorienting BFT ion in NH4BF4 [17,21]. The TIH and TIF minima observed in Phase IV can be, accordingly, attributed to the CHs C3 reorientation and anion isotropic reorientation, respectively. T,, and TIH shoulders at around 110 and 160 K, respectively, are also attributable to these motions. TIH and TIF in this phase can be expressed as l/7-1,
=
CHHdWH,
l/T,,
=
CFFdWFI +
CFSdWFB>
7H) %)
+ + TF)
CHFduHF, CFHdWHF>
7~)
(10)
7F) (11)
g(uFBI (1
7F) +
~$7;)
=
TF/[l +
+
(WF
6~F/[l
+
(wF
d*d] +
+ uB)*$]
3’TF/
(12)
where TH and TF are the correlation times of the CH3 C3 reorientation and the anion isotropic reorientation, respectively. In Eq. (11) the intraanionic 19F- “B dipolar interactions are included [21]. wa is the angular resonance frequency of the “B nucleus. The motional constant, Cii (i,j = H, F, B), is the contribution to M2 of the i-th nucleas caused by its interactions with thej-th nuclei. For the intra-anionic dipolar interactions, Crr and Cra are expressed as [18,21] cFF
=
(9/10)4h2/rtF
(13)
CFB
=
(1/2)&h2/y&3
(14)
where TF and Yn are the gyromagnetic ratios of 19F and “B, respectively. The distances of F-F and B-F are donated by rFF, and rFa, respectively. Eqs. (10) and (11) were fitted to the observed T,H and TIF values using least squares method. In the calculations, we assumed the Arrhenius-type relationship given by Eq. (6) and the theoretical value of CFn was used. The unknown parameters (Ci,, ro, and E,) determined are shown in Table 3, and the best-fit curves are shown in Fig. 4. Above 190 K in Phase III, TIH decreases with increasing temperature, indicating the onset of a new cationic motion. Although it is difficult to determine the motional mode from the present data, if the cation is orientationally ordered in these phases, the only conceivable motion is CG reorientation of the cation about the N-H bond axis. Activation energy is evaluated to be roughly 22 % 5 kJ mall’ from the slope of TIH versus T-’ plots.
Acknowledgements The authors are grateful for the use of an X-ray diffractometer (Rigaku RINT 1000) equipped in the X-ray Laboratory of Okayama University. This work was partially supported by a Grant-in Aid for Scientific Research No. 06640658 from the Japanese Ministry of Education, Science and Culture.
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
References [1] G. Zabinska, P. Ferloni and M. Sanesi, J. Calorim., Anal. Therm. Thermodyn. Chim., 17 (1986) 250. [2] O. Yamamuro, M. Oguni, T. Matsuo and H. Suga, Thermochim. Acta, 99 (1986) 67. [3] G. Zabinska, P. Ferloni and M. Sanesi, Thermochim. Acta, 137 (1988) 39. [4] H. Ishida, K. Takagi and R. lkeda, Chem. Lett., (1992) 605. [5] H. Ishida, T. lwachido and R, Ikeda, Ber. Bunsenges. Phys. Chem., 96 (1992) 1468. [6] H. Ishida, N. Hayama and R. Ikeda, Chem. Lett., (1992) 1333. [7] H. Ishida, T. Asaji, Y. Furukawa and R. Ikeda, Chem. Lett., (1993) 1207. [8] Y. Kume, R. Ikeda and D. Nakamura, J. Magn. Reson., 33 (1979) 331. [9] E.L. Hahn, Phys. Rev., 80 (1950) 580. [10] J. Yamauchi and C.A. McDowell, J. Chem. Phys., 75 (1981) 577.
243
[11] J.N. Sherwood (Ed.), The Plastically Crystalline State, Wiley, New York, 1979. [12] A.F. Kapustinskii, Q. Rev., Chem. Soc., 20 (1956) 203. [13] O. Knop, T.S. Cameron, M.A. James and M. Falk, Can. J. Chem., 59 (1981) 2550. [14] M. Stammler and D. Orcutt, Adv. X-ray Anal., 5 (1961) 133. [15] E.R. Andrew and P.C. Canepa, J. Magn. Reson., 7 (1972) 429. [16] J. Tsau and D.F.R. Gilson, Can. J. Chem., 51 (1973) 1990. [17] D. Pendred and R.E. Richards, Trans. Faraday Soc., 51 (1955) 468. [18] A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, London, 1961. [19] D.E. O'Reilly, E.M. Peterson and T. Tsang, Phys. Rev., 160 (1967) 333. [20] S. Albert and H.S. Gutowsky, J. Chem. Phys., 59 (1973) 3585. [21] A.P. Caron, D.J. Huettner, J.L. Ragle, L. Sherk and T.R. Stengle, J. Chem. Phys., 47 (1967) 2577.
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 345 (1995) 235-243
1H and 19F N M R studies on molecular motions and phase transitions in solid triethylammonium tetrafluoroborate Hiroshi Ono a, Riki Seki a, Ryuichi Ikeda a, Hiroyuki Ishida b'* ~Department of Chemistry, University of Tsukuba, Tsukuba 305, Japan bDepartment of Chemistrv, College of General Education, Okayama University, Okayama 700, Japan Received 7 July 1994
Abstract
Measurements by differential thermal analysis and differential scanning calorimetry and of the spin-lattice relaxation time (TI), the spin-spin relaxation time (T2), and the second moment (M2) of 1H and 19F N M R were carried out in the three solid phases of (CH3CH2)3NHBF 4. X-ray powder patterns were taken in the highest-temperature phase (Phase I) existing above 367 K and the room-temperature phase (Phase II) stable between 220 and 367 K. Phase I formed a NaC1type cubic structure with a = 11.65(3) A, Z = 4, V = 1581(13)A 3, and D x = 0.794gcm 3, and was expected to be an ionic plastic phase. In this phase, the self-diffusion of anions and the isotropic reorientation of cations were observed. Phase II formed a tetragonal structure with a = 12.47(1) and c=9.47(3)A, Z = 4 , V = 1473(6)A 3, and D x = 0.852gcm 3 From the present DSC and N M R results in this phase, the cations and/or anions were considered to be dynamically disordered states. The C3 reorientation of the cation about the N - H bond axis was detected and, in addition, the onset of nutation of the cations and local diffusion of the anions was suggested. In the low-temperature phase (Phase III) stable below 219 K, the C3 reorientations of the three methyl groups of cations and the isotropic reorientation of anions were observed. The motional parameters for these modes were evaluated.
1. Introduction
A l k y l a m m o n i u m tetrafluoroborates are k n o w n to have various solid-solid phase transitions [1-3]. O f these salts, we have recently revealed that in the highest temperature solid phase o f (CH3)2NNH3BF4 [4], ( C H 3 ) z N H 2 B F 4 [5], ( C H 3 ) 3 N H B F 4 [6], and ( C H 3 ) 3 N C H 2 C H z O H B F 4 [7], b o t h cations and anions undergo rapid selfdiffusion as well as isotropic reorientation. F r o m the t h e r m o d y n a m i c and molecular dynamics points ~" Dedicated to the memory of Professor Daiyu Nakamura. * Corresponding author. Elsevier Science B.V. SSDI 0 0 2 2 - 2 8 6 0 ( 9 4 ) 0 8 4 5 1 - 3
o f view, we have assigned these phases to the ionic plastic phase. Zabinska et al. [3] carried out differential scanning calorimetry (DSC) o f ( C H 3 C H 2 ) 3 N H B F 4 and have f o u n d two solid-solid phase transitions at 217 and 368 K. This thermal behavior is similar to that o f (CH3)3NHBF4 . Moreover, the melting e n t r o p y o f 17.4 J K I tool t evaluated f r o m their data is fairly low. We m a y expect f r o m these data that highly disordered states o f both cation and anions are realized in the highest temperature solid phase o f ( C H 3 C H 2 ) 3 N H B F 4. In the present investigation, we have carried out measurements o f the IH and 19F N M R spin-lattice
236
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
relaxation time (T1) and spin-spin relaxation time (T2), the second moment (M2) of IH and 19F N M R absorptions, differential thermal analysis (DTA), DSC, and powder X-ray diffractions, in order to clarify the dynamic behavior of the cations and anions in each solid phase and to reveal the presence of highly mobile ions in this salt.
(abbreviated to Tm and T2n, respectively, for IH, and Tw and T2F for 19F) were measured by use of a Bruker Pulse N M R spectrometer (model SXP100). TIH was determined at 34.1 and I I.8MHz, while Tw was determined at 32.1 and 14 MHz using the 180°-t-90 ° pulse sequence. Hahn's spin-echo method [9] was employed for the determination of TzH at 34.1 MHz and T2v at 32.1 MHz. Powder X-ray patterns were taken at about 300 and about 370 K by using a Philips X'Pert PW 3050/100 and a Rigaku R I N T 1000 diffractometer, respectively.
2. Experimental (CH3CH2)3NHBF 4 was prepared by neutralizing triethylamine with tetrafluoroboric acid. The obtained crystals were recrystallized three times from benzene. Found: C, 37.6; H, 8.54; N, 7.29%. Calculated for (CH3CH2)3NHBF4: C, 38.1; H, 8.47; N, 7.41%. Because of the strong hygroscopicity, the purified crystals were handled in a dry bag and dried under vacuum at 75°C for 24 h before the measurements o f N M R , DTA, and DSC. Phase transition temperatures and the corresponding enthalpy changes were redetermined by a home-made D T A apparatus [8] and a Daini Seikosha calorimeter (model SSC-560), respectively. M2 of I H and 19F N M R absorptions (abbreviated to M2H and M2F, respectively) were determined by use of a JEOL JNM-MW-40S spectrometer. T 1 and T2 of 1H and 19F N M R
3. Results D T A curves of (CH3CH2)3NHBF 4 recorded between 110 and 410 K are shown in Fig. 1. When the sample was heated, two large endothermic anomalies attributed to solid-solid phase transitions appeared at 219 and 367 K, and that of melting at 388 K. These temperatures agreed well with those reported by Zabinska et al. [3]. The revealed solid phases were designated in the order of decreasing temperatures as Phase I, II, and III. When the sample was cooled, however, three exothermic anomalies showing marked hystereses were observed. Enthalpy changes at the transitions EXO
195K
381K
( ENDO Ill
II
I
Fig. 1. DTA curves recorded in (CH3CH2)3NHBF4. The cooling and heating rate was approximately 1 K min I. I, I1, and III are the solid phases definedin the text.
H. Ono et al./Journalof Molecular Structure 345 (1995) 235 243 i
7 `¸ K
15
] 5 l o 3130 C
400
o
/
237
300
2f/()
10 ° I1
II[
,
I
E
~5 ~A,~A
t() °
10
© .,..~
*"
10-2
•
•
"
•
]
s,
~
• 10
2
10
4
~ Z~
~-
OL_
300
200
~0 400
2.h
10-4
(At~sH(III --~ II) and AtrsH(II
~
I))
and fusion
(&rus H ) determined by D S C were 7 . 5 ~ 0 . 1 kJ tool 1, 5 . 7 + 0 . 1 kJ mol 1, and 6.1zk0.1 kJ mol 1, respectively; then the associated entropy changes were evaluated to be 34 + 1 J K l m o l - i , 16 + 1 J K -1 mo1-1, and 16 + 1 J K i m o l - l , in the same order. Temperature dependences o f 11428 and M2F are shown in Fig. 2. Both M2~ and M2F have constant values o f 14.5 4- 0.5 G 2 and 2.6 • 0.3 G 2 (1 G = 1 x 10 4 T), respectively, in the range o f 130-190 K. With increasing temperature, both M2H and M2F decreased and reached almost constant values o f 1 . 3 ~ 0 . 2 G 2 and 1 . 1 + 0 . 2 G 2, respectively, and were maintained at these values up to the phase transition temperature (Ttr) f r o m Phase II to I (Ttr(II ~ I)). A t Ttr(II--~ I), a discontinuous change in M2H and M2F was observed. In Phase I, M2H decreased with increasing temperature and became 0.25 + 0.03 G 2. However, M2F in this phase was less than 0.05 G 2. The temperature dependences o f T1H, TIF , T2H, and TzF in Phases I and II are shown in Fig. 3. T m showed m a r k e d non-exponential recovery o f I H magnetization in the region 2 8 0 360 K in Phase II, while T~v became slightly nonexponential in the same temperature range. The non-exponential recovery curve o f TIH could be separated into two relaxation times, T1w and TIHt (TIH~ < TiHl ) according to the following
II 3
T/K Fig. 2. Temperature dependences of NMR second moment, M2, for IH (O) and IOF (&), respectively, observed in (CH3CH2)3NHBF4. The broken lines show the phase transition temperatures determined by DTA.
1
2.7 -
4 I(13T 1/ K-I
"
5
Fig. 3. Temperature dependences of spin lattice relaxation times for IH (Tin) and 19F (Tw) and spin spin relaxation times (T2H and T2v) observed in Phases I and II of (CH3CHz)3NHBF4; (o) Tm and TtH, (e) TIH~ at 34 MHz; ([2) Tm and TIH~;(11) Tlw at 11.8 MHz; (A) Tlv at 32 MHz; (o) Tiv at 14 MHz; (×) ~u at 34 MHz; (+) T2v at 32 MHz, where suffixes 1 and s mean the long and short components as given in text. The broken lines show the phase transition temperatures determined by DTA. Solid lines indicate the best fitted theoretical values• equation: [Mo - M~(t)]/2Mo = As exp ( - t / T m O + Al exp (--t/T1H,)
(1)
Here, M0 and M:(t) are z c o m p o n e n t s o f the 1H magnetization at thermal equilibrium and at time t after a 180 ° pulse, respectively, and As and A 1 are constants (As + Al = 1). Since it was difficult to obtain the two T1F values accurately from the slightly non-exponential recovery curve o f 19F magnetization, T~v was conventionally determined f r o m the initial linear portion o f l o g [ M 0 - Mz(t)]/2Mo versus t plots [10]. Both Tlv and TIH increased discontinuously at Ttr(II ~ I). TZH and T2v also increased discontinuously at this transition, in accordance with the results o f 342. In Phase I, TIH increased, whereas Tlv decreased, with increasing temperature. Fig. 4 shows temperature dependences o f TIH and Tw in Phase III. TIN at 34.1 and 11.8 M H z show a m i n i m u m o f 40 ms at a r o u n d 130 K and 15 ms at a r o u n d 110 K, respectively. T w at 32.1 M H z shows a m i n i m u m o f 18 ms at a r o u n d 160 K and a shoulder at a r o u n d 110 K. A discontinuous change in both TIH and TIF was observed at Ttr(III -+ II).
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
238
7"// K
200 10 ° ~-" -
150
100 I0 °
~ :2
< b...
10-1
10 1
&
i
o •
10 2
<'\ <> >>....
IO 2 III
•
.
t
6
_
L
_
A
_
8 10 103T 1 / K q
_
•
12
Fig. 4. Temperature dependences of spin lattice relaxation times for 1H (Tin) and 19F (TIF) observed in Phase Ill of (CH3CH2)3NHBF4: (©) TIH at 34 MHz; ([]) TtH at 11.8 MHz; (A) Tw at 32 MHz; (o) TIF at 14 MHz. The broken lines shows the phase transition temperatures determined by DTA. Solid lines indicate the best fitted theoretical values.
Table 2 Observed and calculated diffraction angles 20, relative intensities I, and their indexing hkl for X-ray powder patterns in Phase II of (CH3CH2)3NHBF4 at about 300 K (tetragonak a = 12.47(1), c = 9.43(3) A, and Z = 4) Observed
Calculated
20 (deg)
I (%)
20 (deg)
hkl
11.70 20.10 21.33 23.36 24.27 25.70 29.42 31.75 34.22 44.17
100 20 50 25 15 20 5 5 5 10
11.72 20.13 21.36 23.35 24.43 25.74 29.45 31.73 34.41 44.14
101 220 300 30l 311 320 312 203 402 610
4. Discussion
4,1. High-temperature phase (Phase I) P o w d e r X - r a y diffraction angles (20) o b t a i n e d at a b o u t 380 K in Phase I could be interpreted as facecentered cubic (f.c.c.) lattice with a = 11.65(3) A Z = 4, V = 1581(13) A 3, a n d D x = 0.794 g cm 3. The a d e q u a c y of the present analysis is shown in T a b l e 1. The angles (20) o b t a i n e d in Phase II at a b o u t 300 K are s h o w n in T a b l e 2. These angles correspond to a tetragonal lattice having constants of a = 12.47(1), c : 9 . 4 7 ( 3 ) A_, Z = 4 , V = 1473(6) A 3, a n d Dx = 0.852 g cm -3.
Table 1 Observed and calculated diffraction angles 20, relative intensities I, and their indexing hkl for X-ray powder pattern in Phase I of (CH3CH2)3NHBF4 at about 380 K (cubic, a = 11.65(3) A and Z 4) -
Observed
Calculated
20 (deg)
1 (%)
20 (deg)
hkl
13.19 15.19 21.64 25.40 26.52 30.64 33.52
5 60 100 70 5 40 10
13.16 15.21 21.57 25.36 26.50 30.70 33.53
Ill 200 220 311 222 400 331
The N a C l - t y p e f.c.c, structure of Phase I of ( C H 3 C H 2 ) 3 N H B F 4 d e t e r m i n e d in the present X - r a y diffraction study implies that b o t h cations a n d a n i o n s behave like spherical ions in the crystal. T h u s these ions are expected to have d y n a m i cally disordered o r i e n t a t i o n s in this phase. This is s u p p o r t e d by the observed low e n t r o p y of fusion (AfusS = 16 J K -1 mol 1), which is c o m p a r a b l e to those (AfusS <_ 20 J K 1 m o l - l ) observed in plastic phases o f m o l e c u l a r solids [11]. I f the cation is a s s u m e d to rotate isotropically a b o u t its center of gravity, its ionic radius is estimated to be 3.55 A o n the basis of the N a C l - t y p e structure determined, by using a n ionic radius of 2.28 A for a n isotropically r o t a t i n g B F 4 ion [12]. This radius o b t a i n e d is comp a r a b l e to 3.42 & evaluated as the longest distance between the H a t o m of the CH3 g r o u p of the cation a n d its center of gravity by using atomic parameters of the ( C H 3 C H z ) 3 N H + ion in the ordered phase of [ ( C H 3 C H J 3 N H ] E S n C I 6 crystal [13]. F o r the isotropic r e o r i e n t a t i o n s of both cation a n d a n i o n , M2H a n d M2F were evaluated to be 0.28 G 2 a n d 0.37 G 2, respectively, from the structure data o f this phase described above. M2H values of 0.25 + 0.03 G 2 observed a b o v e 375 K agree with the calculated one, while the observed MZF values,
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
<0.05 G 2, were much less than the calculated value. This indicates that the anion performs translational self-diffusion as well as isotropic reorientation. If the anionic self-diffusion is taken into account, calculated M2H and M2F values become 0.21 G 2 and ,~ 0 G 2, respectively, in good agreement with the observed M2H and MzF values. Since TIH and Tie in Phase I show exponential behavior and the slopes of log Tl~t and log T w versus T -~ plots are different signs, the relaxation processes effective in TIH and Tlv are different. From the discussion of 1142, the ionic motions mainly contributing TIH and TIF are considered to be the cationic isotropic reorientation and the anionic self-diffusion, respectively. An activation energy of 42 + 2 kJ tool -1 was obtained for the cationic reorientation from the slope of log TIH versus T - l plots. The slight frequency dependence observed in Tll-l at 34.1 and 11.8 MHz may be originated from IH-19F dipolar interactions between the cations and anions modulated by the anionic self-diffusion. Plots of log TIF and log T2F against T z show almost the same gradient but with different signs, indicating that T1F and Tzv are attributed to the same relaxation process, i.e. the anionic self-diffusion. From the gradient of the log Tie and log T2F vs. T 1 plots, we obtain the activation energies of anionic self-diffusion as 48 ± 2 and 52 zk 2 kJ mol -l, respectively. From the dynamic behavior of the cations and anions, and the small value of AfusS revealed in the present investigation, it is highly possible that Phase I with a NaCl-type cubic structure is an ionic plastic phase. (CH3)zNNH3BF 4 and (CH3)2NH2BF4 in the ionic plastic phase have been shown to form CsCl-type cubic structures [4,5]. Both cations and anions in these phases perform self-diffusion with activation energies of 41 kJ tool l and 32 kJ mo1-1 for BF4 in (CH3)zNNH3BF 4 and (CH3)2NHzBF4, respectively, and 42.5 kJ mol -I and 36 kJ mo1-1 for (CH3)zNNH~- and (CH3)zNH~-, respectively. Although the plastic phases of these salts are more dense than those of (CH3CH2)3NHBF4 (Dx((CH3)zNNH3BF4) = 1.421 g cm -3 [14] and D x ( ( C H 3 ) 2 N H z B F 4 ) = 1.44 g cm 3 [5]), the above results indicate that the constituent ions in the CsCl-type ionic plastic phases can migrate more
239
easily than those of the Nacl type. This difference can be explained by considering the simple diffusion mechanism of the monovacancy process. When an ion migrates to the nearest vacant site in the CsCl-type structure, it may directly move to the next site passing through an opening of a regular square surrounded by four counter ions. However, an ion in the NaCl-type structure cannot move directly to the nearest vacant site but has to pass an equilateral triangular opening surrounded by three counter ions. The effective area for passing through the opening is, therefore, much smaller than that in the CsCl-type phase. This results in only the small BF4 ions being able to diffuse, while the globular cations find it difficult to migrate in the NaCl-type plastic phase.
4.2. Room-temperature phase (Phase II) The considerably large transition entropy AtrsS(III ---+II) = 34 J K 1 mol-1 observed implies that the cations and/or anions acquire quite a large part of their motional freedom at Ttr(III --~ II). This phase is, therefore, considered as a dynamically disordered phase. This is supported by the fact that the Dx -- 0.852 g c m -3 in Phase II is comparable to that of 0.794 g cm -3 in Phase I revealed as the orientatinally disordered phase as discussed above. To interpret the M 2 values observed in Phase II, we calculated the MzH values for the following motional states of the cations: (1) the rigid lattice, (2) the C 3 reorientation of the three CH 3 groups about the respective C - C bond axes, (3) the reorientation of the whole CHsCH2 groups about the C - N bond axis together with the CH3 (73 reorientations, (4) the C~ reorientation of the cation about the N - H bond axis together with the CH3 C3 reorientation, (5) the C~ reorientation of the cation about the N - H bond axis together with the CH3 and CH3CH 2 reorientations. Note that the motional states (3) and (5) result in the disordered structures of the cations. MZF has been calculated for only the rigid lattice state of the anion. Since no crystal data are available, we have calculated M2 values arising from only intra-ionic magnetic dipolar interactions. In the
240
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
Table 3 Second moments M2H of ]H NMR absorptions calculated for (CH3CH2)3NHBF4 crystals Motional mode
M2H (02)
(1) Rigid lattice (2) CH 3 rotation (3) CH3CH2 rotation (4) Cationic C~ rotation + (2) (5) Cationic C~ rotation + (3)
24.9 (29.4)~ 13.7 5.4 3,4 0.64
a The value (M2F) of 19F in BF4 ions.
calculation, the C - H , N - H , and B - F distances were taken to be the usual values of 1.10 A, 1.02 A, and 1.43 /k, respectively, [15-17] and the bond angles of H - C - H , H-N-C, F-B-F were assumed to be tetrahedral. The parameters concerning the C and N atoms of the cation were used in accordance with the structure of the cation determined by X-ray diffraction [13]. The calculated values are given in Table 3. The almost constant M2H value of 1.3 G 2 observed above 280 K in Phase II is interpreted in terms of the model for the orientationally disordered cation which performs the C~ reorientation about the N - H bond axis together with the reorientations of the CH 3 and CH3CH 2 groups. The difference between the observed and calculated M2H values is attributable to the inter-ionic dipolar interactions. A decrease in M2H with increasing temperature from 220 K can, accordingly, be explained by the cation C~ reorientation. The decrease in M2F in the same temperature region is also explicable by this motion averaging the 19F-1H dipolar interactions between the rotating BF4 ions and the cations. This is because the isotropic reorientation of the anion is already excited in Phase III as described below and its correlation time (rv) is considered to be short enough to satisfy the motional narrowing limit, WF Tv << 1, where o~F is the 19F angular resonance frequency. The TIH minimum and the TIF hollow observed around 220 K, therefore, are attributable to the cation C~ reorientation. Since T1H and TIF are exponential and TtH is much shorter than TlF in this temperature range, by ignoring the contribution from I H - 1 9 F dipolar interactions we can
express T1H as
[18]
1/T1H -~ CHHg(COH, 7-H)
(2)
g(o~H, "rH) = "rn/(1 + w2T2) + 4"rn/(1 + 4w2T2) (3) where Tn and CHH stand for the correlation time of the cation C~ reorientation and the motional constant related to the MZH reduction due to this motion, respectively. WH is the 1H angular resonance frequency. Tw is determined mainly by modulation of the 1H-19F dipolar interactions due to the above cationic motion. Then Tw can be approximately expressed as [10, 18-20]
1/TIF = Cvlag(a~HV,Tn)
(4)
g(WHV,TH = TH/[1 + (WH -- WV)2~-2] + 37H/ 2 2 "4- 6rH/[1 + (0.)H + ~V)2T2 l (1 + O.,'HTH)
(5) where CFH is related to M2F contributed from the ] H - 1 9 F interactions which is averaged out by this reorientation. Eqs. (2)-(5) were fitted to the observed TlH and TlF values using the least squares method. In the calculations, we assumed an Arrhenius-type relationship between *H and the activation energy (Ea) of the motional process expressed as TH = T0exp (Ea/RT)
(6)
where T0 is the correlation time at the limit of infinite temperature. The unknown parameters (CHH, CHF, TO, and Ea) determined are given in Table 4, and the best-fit curves are shown in Fig. 3. In the temperature range 280-360 K, marked non-exponential behavior has been observed for TIH. However, TIF becomes slightly nonexponential. The fact that a TIF minimum at 14 MHz and a TIHS minimum at 11.8 MHz appeared almost at the same temperature and that the same was true for TIF at 32 MHz and T I w at 34 MHz indicates that the same motional process contributes TiF and TIHs. This motional process is attributed to an anionic motion for the following reasons. If a cationic motion is responsible for the relaxation, T w is determined by the
H. Ono et al./Journal o f Molecular Structure 345 (1995) 235-243
241
Table 4 Activation energies Ea, correlation times T0 at the limit of infinite temperature, and motional constants C evaluated for cationic and anionic motions in (CH3CH2)3NHBF 4 E a (kJ mo1-1)
7-0 (10 -13 s)
C (108 s -2)
Motional mode
Phase 1 42 4-2 48 5:3 (from Ti ) 52 4- 2 (from T2)
Cationic isotropic rotation Anionic self-diffusion
Phase H 184-2
2.7
45 4- 2
0.032
28±2
2.1
Phase III 6.5 + 1
80
Cationic C~ rotation
27 (CHH) 0.63 (Cv.) 11 (ChH)
Nutation of cationic C~ axis Anionic local diffusion
25 (CFF) 3.0 (CHF)
30 (CHH)
CH 3 rotation
1.5 (CHF) Cationic C~ rotation
22+5 12+ 1
4.9
19 (CFF) 6.4 (CFH) 30 (CFB) a
Anionic isotropic rotation
a Theoretical value.
l H - 1 9 F interactions averaged by this motion. Then the Tiv minimum is expected to become a similar value to the Tw hollow observed at around 220 K by considering that the Tin s minimum is comparable to the Tin minimum at around 220 K. However, the TIF minimum observed is much shorter than the T w hollow around 220 K. It is, therefore, considered that the relaxation process operative in the range 280-360 K is an anionic motion, and the non-exponential behavior of Tm is due to 1H-19F dipolar interactions modulated by the anionic motion. Above 360 K, distinct nonexponential behavior of T m is not observed, while TI H decreases with increasing temperature, indicating the onset of the other relaxation process caused by cationic motion. T I e above 285 K can be written in terms of the correlation time (rE) of the anionic motion [10,18-20]
1/Tw = CeFg(CoF,re) + Cheg(aJHF, rF)
(7)
where CvF and CUe are related to the M 2 F reduction through 19F-19F and 1 9 F - I H interactions, respectively. However, Tins and T1.~ may be
approximated by [10,18-20] t
2
t
1/TIH~ ----5Cnnrn + 5CHH/aJH rH + C.e{rF/[1
+
tr/-,/
;
2 /
e)2r2}}
1/Tlm~ = 5CHHrH + ~t~HH/WHrH
(8) (9)
where r~q is the correlation time of the cationic motion affecting TIH above 350 K. C~q. and CHF are the motional constants of this motion and the above anionic motion, respectively. By fitting Eqs. (6)-(9) to observed TIH and Tie values, we obtain an E a of 28 + 2 kJ mol I and 45 4- 2 kJ mo1-1 for the anionic and cationic motions, respectively. We expect that the T I e and T1HS minima are originated from inter-ionic 19F-19F dipolar interactions, because in Phase 1| intra-anion dipolar interactions are considered to be completely averaged out by the anionic isotropic reorientation whose onset is detected in Phase IV. It is, however, difficult to clarify the anionic motional mode from the observed M2 values because this motion is predicted to cause only a small reduction of 342 of about 0.2 G 2 which is roughly estimated
H. Ono et al./Journal 0s Molecular Structure 345 (1995) 235-243
242
from the TIF and TIHs minima, and this reduction is comparable to the experimental error of the present M2 measurements in this temperature range. In fact, no detectable M2 reduction assignable to this motion is observed. When the anions perform translational self-diffusion, inter-ionic dipolar interactions are averaged out and MzF becomes = 0 G* as seen in Phase I. If the anions perform local diffusion, i.e. the center of gravity of the anion is positionally disordered and the anion hops between these disordered sites, the inter-ionic interactions are partly averaged out and a small Ml reduction is expected. From the fact that the Ci and isotropic reorientations of the cations are observed at around 220 K in Phase II and above 370 K in Phase I, the cationic motion affecting TIH above 350 K in Phase II is the intermediate state of these two motions. As one of the probable motions, a nutation of the cation as a whole around the N-H bond axis is suggested. 4.3. Low-tempertaure phases (Phase III) By comparing the observed I%& values with the calculated ones shown in Table 3, almost the constant value of MZn observed between 150 and 180 K in Phase III can be interpreted in terms of the C3 reorientations of the three CH3 groups. The anions in this temperature range are considered to reorient isotropically, when the *H-19F dipolar interactions are taken into account between the anion and cation, whose contribution to MzF is roughly estimated to be 2-4 G’ from MzF values of 2.5-2.8 G2 reported for the isotropically reorienting BFT ion in NH4BF4 [17,21]. The TIH and TIF minima observed in Phase IV can be, accordingly, attributed to the CHs C3 reorientation and anion isotropic reorientation, respectively. T,, and TIH shoulders at around 110 and 160 K, respectively, are also attributable to these motions. TIH and TIF in this phase can be expressed as l/7-1,
=
CHHdWH,
l/T,,
=
CFFdWFI +
CFSdWFB>
7H) %)
+ + TF)
CHFduHF, CFHdWHF>
7~)
(10)
7F) (11)
g(uFBI (1
7F) +
~$7;)
=
TF/[l +
+
(WF
6~F/[l
+
(wF
d*d] +
+ uB)*$]
3’TF/
(12)
where TH and TF are the correlation times of the CH3 C3 reorientation and the anion isotropic reorientation, respectively. In Eq. (11) the intraanionic 19F- “B dipolar interactions are included [21]. wa is the angular resonance frequency of the “B nucleus. The motional constant, Cii (i,j = H, F, B), is the contribution to M2 of the i-th nucleas caused by its interactions with thej-th nuclei. For the intra-anionic dipolar interactions, Crr and Cra are expressed as [18,21] cFF
=
(9/10)4h2/rtF
(13)
CFB
=
(1/2)&h2/y&3
(14)
where TF and Yn are the gyromagnetic ratios of 19F and “B, respectively. The distances of F-F and B-F are donated by rFF, and rFa, respectively. Eqs. (10) and (11) were fitted to the observed T,H and TIF values using least squares method. In the calculations, we assumed the Arrhenius-type relationship given by Eq. (6) and the theoretical value of CFn was used. The unknown parameters (Ci,, ro, and E,) determined are shown in Table 3, and the best-fit curves are shown in Fig. 4. Above 190 K in Phase III, TIH decreases with increasing temperature, indicating the onset of a new cationic motion. Although it is difficult to determine the motional mode from the present data, if the cation is orientationally ordered in these phases, the only conceivable motion is CG reorientation of the cation about the N-H bond axis. Activation energy is evaluated to be roughly 22 % 5 kJ mall’ from the slope of TIH versus T-’ plots.
Acknowledgements The authors are grateful for the use of an X-ray diffractometer (Rigaku RINT 1000) equipped in the X-ray Laboratory of Okayama University. This work was partially supported by a Grant-in Aid for Scientific Research No. 06640658 from the Japanese Ministry of Education, Science and Culture.
H. Ono et al./Journal of Molecular Structure 345 (1995) 235-243
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