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A study of molecular motion in solid cyclopropane and cyclopropane clathrate deuterate by nuclear magnetic resonance absorption and relaxation methods
1 Jownal of Molecular Strmure, I6 (1973) l-10 @ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
A STUDY OF MOLECULAR _MOTION IN SOLID CYCLOPROPANE AND CYCLOPROPANE CLATHRATE DEUTERATE BY NUCLEAR MAGNETIC RESONANCE ABSORPTION AND RELAXATION METHODS
A. W. K. KHANZADA
Department
AND C. A. MCDOWELL
of Chemistry,
University of British Cohmrbia,
Vancouver 8, British Columbia (Canada)
(Received 30 October 1972)
ABSTRACT
Proton magnetic resonance absorption and spin-lattice relaxation measurements have been carried out for cyclopropane clathrate deuterate from 77 to 290 K together with spin-lattice relaxation measurements on solid cyclopropane from 90 to 146 K. The absorption measurement for the type I structure deuterate indicates the presence of an isotropic rotation of the cyclopropane molecule from about 230 K, while in the type II structure deuterate isotropic rotation of the enclathrated cyclopropane is present over all of the range of stability of the clathrate (-250 to 278 K). The spin-lattice relaxation measurements give an activation energy of 0.83 +0.03 kcal mole -’ for the barrier to reorientation (not assigned) of the cyclopropane molecules inside the clathrate deuterate cavities. In solid cyclopropane the barrier associated with the threefold axis rotation is found to be 4.8f0.2 kcal mole-‘.
INTRODUCTION
The clathrate hydrate and deuterate of cyclopropane has recently been studied by Hafemann and Miller ’ -’ . Their dissociation pressure versus temperature study shows that cyclopropane forms two types of clathrate hydrates: von Stackelberg’s 12 A type I structure cubic hydrate (C,H, - 73H,O), stable below 257.15 K and between 274.62 and 289.37 K; and von Stackelberg’s’ 17 A type II structure cubic hydrate (C3H6 - 17H,O), stable between 257.15 and 274.62 K. The corresponding
deuterate of von Stackelberg’s
type I structure is stable below
278.68 and 291.50 K, while the von Stackelberg’s type II structure deuterate is stable between 249.85 and 278.68 K. Majid et aL3 have also 250 K and between
2 studied van Stackelberg’s type I structure hydrate by dielectric relaxation, proton magnetic resonance, and dissociation pressure versus temperature me~urements.
The previous results reported by us4 on PMR studies of cyclopropane deuterate were in disagreement with the PMR resuIts of Majid et al.’ on cy~lopropa~~ hydrate, and which we found to arise because of the difficulty in the preparation (which will be outlined later) of the deuterate below 250 K. Because of the possibility of phase separation beIow 250 K, the previous data seemed mainly due to adsorbed cyclopropane on powdered D,O rather than the deuterate- The present report agrees very well with the PMR work on cycIopropane hydrate3. in addition to revised absorption measurements, relaxation data are also presented on the deuterate as well as on pure cycfopropane. Solid cyclopropane has already been studied by Hoch and Rushworth and their results can be taken to show the presence of a rigid structure with a second moment of -20 GZ existing over the
temperature range from 85 to 105 K. Above that temperature a molecular rotation around threefold axis (C,-rotation) occurs which causes the second moment to become - 11.5 G2 from I20 K up to the melting point. These authors, from their 5F1measurements, obtained an activation energy of 4.1 kcal mole-’ associated with the barrier ~ndering the C,-rotation. We have not attempted to revise the absorption measurements on solid cyciopropane, but have obtained T1 results by a more accurate pulse method which can be expected to give a better activation energy for comparison with simiiar data for the deuterate.
EXPERIMENTAL
We found the preparative method of Hafemann and Miller2 highly inconvenient for obtaining the pure deuterate because of two reasons: first, during the process of preparing finely powdered D,O, the deuterons of D,O are exchanged with protons by a sufficient amount (2-3 %) even in a moderately inert atmosphere. Secondly, to get deuterate of high purity, the exact amount of cyclopropane must be known, which is difficult using this technique. We observed after several unsuccessful attempts, that, the presence of excess of C3H6 does not favour the formation of the deuterate, but simply leaves some free cyclopropane, and some adsorbed on the powdered D,O surface even if the sample was left for fifteen days, _In some cases where the cyclopropane amount was fortunately less than the formula ratio, this method yielded the deuterate, but never better than about 80 % pure. In our earlier report, this method was followed using excess of C,H6. We
found that to get a satisfactory sample of the deuterate, C&H6 should either be in the exact amount, or sfightly less (0.2-0.4 %) than the formula ratio (C& D,O
- 7.67D20).
Cyclopropane (99.0 % pure) was obtained from Matheson Company, and (99.8 % d) from Stohier Isotope ChemicaIs. DZO was filled in about 4 cm
3 o.d. round-bottom glass tubes, and the exact amount of C3H6 was transferred after degassing the D,O. The tube was sealed, and the mixture was first shaken vigorously on a mechanical shaker at about 273 K for about 2-3 hours to prepare frozen D20 in slightly powdered form, and then shaken at dry ice temperature for 2-3 days. In some cases where excess D,O (-20 g) was used, the mixture took about a week to form a good specimen of the deuterate. The deuterate was extracted by breaking the tube inside a cold box held at 243 to 233 K by using a cold nitrogen gas flow. It was finely powdered and transferred to NMR tubes, which were sealed after degassing- The analysis of samples (three batches) was achieved by decomposing the deuterate, and measuring the amount of gas evolved. Such analysis give the purity for type I structure in the range C,Hs - (7.4-S. l)D,O. Two batches of samples were prepared for the type II structure deuterate separately in a similar way as before by shaking the mixture at 273 K. The analyses of these type II structure deuterate samples were in the range of C,H, - (18--19)D,O. The type II structure deuterate lost C3H6 when the sample was degassed. It was therefore sealed without removing the dissolved air and was studied only by continuous wave measurements at 16 MHz. To prepare the cyclopropane specimens the gas was directly transferred from a cylinder, and sealed in NMR tubes after removing the dissolved air by a freezepump-thaw method_ The absorption line measurements were performed at 16 MHz with a Varian VF-16 wide line spectrometer. Evidence of saturation was noticeable (particularly at high temperatures) in the absorption line measurements for the type I deuterate because of long Ti and T2’s. The minimum r.f. field (O-1-0.2 mG) was used at higher temperatures, while at other temperatures r.f. field of about 0.5 mG was used. The second moments were also obtained from a solid echo 9O-r-9O,0 pulse sequence on the solid specimen at 30 MHz, as suggested by Powles and Strange6 by fitting the solid echo G(t) to an expression of the type G(t) = l-
;A&+
;A+. .
. .
where t is time in s and @, is the nth moment. Relaxation measurements were performed at 30 MHz using a Bruker pulse spectrometer. Because of the narrow line, a Varian 12-inch magnet with a superstabilizer was used. T1 values of less than 3 seconds were measured by a 180”-r-90” pulse sequence with an HI correction as suggested by van Putte’ and Kumar and Johnson’. T1 values of larger than 3 s and less than 10 s were measured both from 90-r-90, and n 90-r-90 (saturation) sequences ’ - 1’ _ Tl values of larger than 10 s were measured by IZ 90-r-90 (saturation) sequence only. The signal height after 180-r-90, 90-r-90, and saturation sequence was measured both from photographs obtained from Tektronix 549 Storage Oscilloscope equipped with type 1Al dual-trace plug-in unit; &id by using a Bruker Pulsed Gated Integrator B-KR 300 Z15, the output of which
4
was connected to a digital voltmeter. We found the saturation sequence less time consuming and better than the 90--90 pulse sequence, especially for averaging slightly noisy free induction decay curves (for the deuterate) even for the range of 2-10 s. The relaxation function R(t) [R(t) = {M,,--M,(t)}/(2M,) for 180-r-90 pulse sequence, and R(t) = (M,-, - MZ(t)}/MO for 90”-r-90” or saturation sequence, where AI,-,is equilibrium magnetization; i.e., magnetization after a 90” pulse, and M=(f) is the magnetization after the sequence] was exponential in all cases.
EXPERIMENTAL
RESULTS
(a) Absorption measurements The rest&s of second moment calculations are summarized in Table 1. The experimental second moments for cyclopropane deuterate (Fig. 1) vary very slowly from 1.9 +0.2 G2 at 77 K to a plateau value of O-6+0.1 GZ around 230 K. The latter value is consistent within experimental uncertainty, with isotropic rotation of the cyclopropane moIecule inside the 14-hedra of type I structure. The type II deuterate shows a second moment of 0.25f0.05 G* in its stability range of 251 to 278 K, which is also consistent with the isotropic rotation of the cyclopropane molecule inside the 16-hedra of type II structure. TABLE
1
THJZORETICALSECOND
Type of motion
Rigid CB-rotation
MOMENTS
FORCYCLOPROPANE
CLATHRATEDEUTERATFS
Type II
Type 1 Intra
Inter”
Total
Intra
Inter”
12.85 9.99
N0.90 No.4
-13.8 -10.4
12.85 9.99
N0.3b
-13.2
4.2
-10.2
o_ 15-0.20b
0.1 s-o.20
0.0
Isotropic
(Gau&)
0.35-0.4b
0.35-0.4
0.0
Total
a Includes an approximate deuteron contribution. D Ref. 11, including deuteron contribution.
i loo I
Fig.
200
300
Temperature PK)
1. Plot of the second moment against temperature for cyclopropane deuterate. 0 Cw measurements at 16 MHz. Y Pulse method using a solid echo (90°-~-90090~) pulse sequence. A Type II deuterate studied separately by cw measurements at 16 MHz.
5
(5) Relaxation measurements The temperature dependence of TI for solid cyclopropane is shown in Fig. 2. That figure shows a range of values of TX equal to 89 1 f 34 s at 90 K and reaching
.,i 90
a0
loo
Fig. 2. Temperature 30 MHz.
110
dependence
I50
of spin-lattice
relaxation
time,
T1 for solid
cyclopropane
62_t2 ms near the melting point (145 K). If the motional process is governed a unique correlation time TV, TI is related to rc by the BPP equation,
l
-= Tl
c
1
(
=c
1+o,2.r,
+
4L I+ 40(&2
1
=
2_-r(I+l) y4h2 5
r6
where r is interproton
= --3
10
distance
y+i2
are
(3)
r6 and I is the nuclear
by
(2)
1
where C, is constant, which for a CH, group (assuming that CH2 protons the dominating relaxation mechanism) is given by the expression12 c
at
spin. Equation
(2) gives a
6 . .
mrmmum at wo7= = 0.6I6, The theoretical value of TX minimum using eqns. (2) 106 rad s-r is 30 ms. It thus appears that cyclopropane and (3) at w. = 2zx30x melts before a minimum in I; is achieved. The value of 62 ms from 143 to 145 K and becoming slightly higher at the melting point seems to be due to some premelting of the cyclopropane. The activation energy associated with a C,-rotation is obtained from the pjot of In Z”Xversus (l/Z”) from Fig. 3. On the Iow temperature side of minimum oorc >> 1. Equation (2) therefore reduces to
-=I
2Cl
Tl
0022;,
orT,
fG2~O=P
(& )
= -
~j
2c1
Figure 3 shows that where z, obeys the Arrhenius equation z, = r. exp(IZJRT). this reorientation process follows the Arrhenius equation, and a plot of In T, versus (l/T) is a good straight line (Fig. 3) according to eqn. (4). The activation energy & obtained from the slope of this straight line is 4.8kO.2 kcal mole-’ which is in agreement with a value of 4.1 kcal mole- ’ obtained by Hoch and Rushworths.
II
lo
9
8
7 -&h
Fig. 3, Plot of In TX versus ZooofT (EC-‘) for solid cyclopropane.
7
- 20
20
-
%
-
9 6 5 4
-
3
-
2
Temperature(%) I
80
I I loo
I * 120
I * 140
9. 160
I I I I 160 200
* 1 I I * II. 220 240 260 280
1 300
I
Fig. 4. Plot of the spin-lattice relaxation time, TX against temperature for cyclopropane deuterate at 30 MHz.
The cyclopropane deuterate shows a similar behaviour for TI versus temperature curves as we observed for other deuterates’ 3- 15. The temperature dependence of Tr is plotted in Fig. 4. Unfortunately, the Tr data cannot be analysed in terms of BPP theory because a minimum in the TI curve was not achieved. The TI versus temperature curve follows the Arrhenius law from 77 to 125 K. The activation energy is therefore derived from the slope of the linear portion (77 to 125 K) of In Tr versus I/T curves as shown in Fig. 5. [On the high temperature side of the minimum oorc << I, eqn. (2) then reduces to (l/T,) = 5C,r= = 5C,r, exp(EJRT).] A value of 0.83 f0.03 kcal mole- ’ is obtained from
a
12
II
IO
9
8
7
6
5
4
3-
Fig. 5. Plot of In TX against reciprocal of the absolute temperature for cyclopropane deuterate.
8
this slope, but this value is not assigned to any mode of rotation. It is not associated with isotropic rotation, because the second moment in this temperature range is much higher than the isotropic value. On the other hand we have no low temperature data on either the second moment or T1 (lower than 77 K) from which the mode of rotation may be decided. The constant value of Tr = 28+2 s from about 200 K and upwards seems to be due to isotropic rotation of the cyclopropane molecules inside the deuterate cages. We could not obtain T1 data on separately prepared type II deuterate specimens,
as this deuterate loses C,H,
on removing
the dissolved air. The results for the region of 250 to 278 K are thought to be for
the type II clathrate, on the assumption that type I is converted completely to type II in this range, although this assumption is not necessarily true unless the excess gas is pumped out i6. The Tr measurements in this temperature range (250 to 278 K) did indicate some free cyclopropane, an indication that some of type I is converted to the type 11 deuterate.
DISCUSSION
The second moment for the type I deuterate approaches a pIateau value of 0.6kO.l G2 around 230 K which we assigned as being due to isotropic rotation of the cyclopropane molecule. This value is slightly higher than the calculated vaIue of 0.35-0.4 GZ for isotropic rotation. The r-f. field used at these temperatures was definitely low in order to avoid saturation. These absorption results are further supplemented by solid echo measurements which give nearly the same value for the second moment. Possibly this higher value may arise from either the presence of free cycIopropane or some exchange of the deuterons of D,O with protons from moist air. As a precaution samples which showed a trace of free gas were further evacuated before taking measurements_ The second possibility of exchange was, however, present but at the most to the extent of 2 % (as seen from the analysis of decomposed studied samples). This latter could increase the second moment to about 0.06 G2, which makes the theoretical value in the range of 0.41-0.46 G2. The experimental value is still higher and this could well be due to experimental uncertainties in the measurements. We can, however, compare these results with the available results on a similar deuterate; i.e., ethylene oxide deuterate. Garg et al.” obtained second moment values of 1.8 G2 at 77 K, 0.5-6 G2 between 130 and 200 K, and 0.3kO.05 G2 as the plateau value between 230 and 270 K. Our unpublished results’ 5, and the work of Afanas’ev and Kvlidize” show similar results: I-9-2 G2 at 77 K, and a plateau value of 0.4 G2 in the temperature range from -230 to 270 K). The theoretical value of the second moment for isotropic rotation in ethylene oxide deuterate given by Garg et al.” is 0.24 G2. Clearly this small difference is due to experimental uncertainty_ There is no reason to consider saturation, however, in this case because ethylene oxide shows a maximum value of
9 TX around 15 s at 60 MHzlS, while cyclopropane shows a maximum value of 28 s at 30 MHz. The results cannot be improved even by the use of higher frequencies because of the long T2 value and probably also a long TI value. The activation energy of 0.83 kcal mole-’ for the cyclopropane deuterate is comparable to an activation energy of 0.98+0.02 kcal mole-’ for the ethylene oxide deuterate15. The plateau value of 28 + 2 s from - 200 K and onwards could be due to isotropic rotation of the cyclopropane molecule with a correiation time of the order 10-r’ s as was observed by Davies and Williams for ethylene oxidelg_ No attempt was made to derive correlation times from the BPP equation for solid cyclopropane as the true value of experimental minimum is not reached in the experiments carried out at 30 MHz. We neglected the contribution from other CH, groups in the TI minimum calculation because of the lack of complete crystal structural data on solid cyclopropane as only the unit cell dimensions are known2’_ The present activation energy of 4.8 kcal mole-’ for the C,-rotation is, however, probably more accurate than the value of 4.1 kcal mole-’ obtained by Hoch and Rushworth because the present method gives better values for TI. Their value of 0.12 s at the melting point estimated from experimental results obtained using a progressive saturation technique at 22.14 MHz* seems to be doubtful. In the light of our results at 30 MHz (T, value of 6222 ms at the melting point) using the most accurate 180-7-90 pulse technique with a HI correction, shows that the Hoch and Rushworth value may be too high*.
ACKNOWLEDGEMENT
We wish to thank the National Research Council of Canada for generous grants in support of this work. We are also indebted to Dr. P. Raghunathan for many interesting and helpful discussions.
REFERENCES 1 D. R. HAFEMANN AND S. L. MILLER, J. Phys. C/tent., 73 (1969) 1392. 2 D. R. HAFEMANN AND S. L. MILLER, J. Phys. Chem., 73 (1969) 1398_ 3 Y. A. MAJID, S. K. GARG AND D. W. DAVIDSON, Cm. J. Clxem., 47 (1969) 4697. 4 A. W. K. KHANZADA AND C. A. MCDOWELL, J. Mol. Strttcfttre, 7 (1971) 241. 5 M. J. R. HOCH AND F. A. RUSHWORTH, in B. PESCE(editor), Nuclear Magnetic Resonunce itr C’lrentistry, Academic Press, New York, 1965, p_ 243. 6 J. G. POWLES AND J. H. STRANGE, Proc. Phys. Sot. Londorr, 82 (1963) 6. 7 K. VON Pu-rr~, J. Mugn. Res., 2 (1970) 216. 8 ANIL KUMAR AND C. S. JOHNSONJR., J. Magn. Res., 7 (1972) 55. 9 Pulsed NMR Spectrometers, Bruker Scientific Inc., Elmsford, New York, undated, pp. 3-L
* There is no mention of the w0 value or the method of measurement in ref. 5, so we quote the frequency 22.14 MHz and the technique of measurement from their earlier work”.
10 10 T. C.
FARRAR AND E. D. BECKER,Palsed
and Foarier
Transform
NMR,
Academic Press,
New York, 1971, p. 22.
SMITH, J. Chem. Phys., 42 (1965) 4229. 12 A. ABRAGAM, The Principles of N&ear Magnetism, Oxford University Press, Oxford, 1961, p. 300. 13 P. S. ALLEN, A. W. K. KHANZADA AND C. A. MCDOWELL, 3. Mol. Srractare, 14 (1972) 9.
11 G. W.
14 M. B. DUNN AND C. A. MCDOWELL, Cilem.Phys. Lett., 15 (1973) 508. IS A. W. K. KHANZADA, C. A. MCDOWELL AND P. RAGHUNATHAN,to be published. 16 D. W. DAVIDSON, personal communication. 17 S. K_ GARG, B. MORRIS AND D. W. DAVIDSON, J. Chem. Sot.,
18 B. L. AFANAS'EV 183 (1968)
AND V. I. KVLIVIDE,Dokl.
816 (English
Akad. Nauk SSSR,
Faraday II, 68 (1972) 481. 183 (1968) 360 (Russian),
translation).
19 M. DAVIES AND K. WILLIAMS, Trans. Faraday Sac., 64 (1968) 529. 20 J. B. BATES, D. E. SANDS AND W. H. SMITH. J_ Chem Phys., 51 (1969) 105. 21 M. J. R. HOCH AND F. A. RUSHWORTH, Proc. Phys. Sot. London, 83 (1964)
949.
A STUDY OF MOLECULAR _MOTION IN SOLID CYCLOPROPANE AND CYCLOPROPANE CLATHRATE DEUTERATE BY NUCLEAR MAGNETIC RESONANCE ABSORPTION AND RELAXATION METHODS
A. W. K. KHANZADA
Department
AND C. A. MCDOWELL
of Chemistry,
University of British Cohmrbia,
Vancouver 8, British Columbia (Canada)
(Received 30 October 1972)
ABSTRACT
Proton magnetic resonance absorption and spin-lattice relaxation measurements have been carried out for cyclopropane clathrate deuterate from 77 to 290 K together with spin-lattice relaxation measurements on solid cyclopropane from 90 to 146 K. The absorption measurement for the type I structure deuterate indicates the presence of an isotropic rotation of the cyclopropane molecule from about 230 K, while in the type II structure deuterate isotropic rotation of the enclathrated cyclopropane is present over all of the range of stability of the clathrate (-250 to 278 K). The spin-lattice relaxation measurements give an activation energy of 0.83 +0.03 kcal mole -’ for the barrier to reorientation (not assigned) of the cyclopropane molecules inside the clathrate deuterate cavities. In solid cyclopropane the barrier associated with the threefold axis rotation is found to be 4.8f0.2 kcal mole-‘.
INTRODUCTION
The clathrate hydrate and deuterate of cyclopropane has recently been studied by Hafemann and Miller ’ -’ . Their dissociation pressure versus temperature study shows that cyclopropane forms two types of clathrate hydrates: von Stackelberg’s 12 A type I structure cubic hydrate (C,H, - 73H,O), stable below 257.15 K and between 274.62 and 289.37 K; and von Stackelberg’s’ 17 A type II structure cubic hydrate (C3H6 - 17H,O), stable between 257.15 and 274.62 K. The corresponding
deuterate of von Stackelberg’s
type I structure is stable below
278.68 and 291.50 K, while the von Stackelberg’s type II structure deuterate is stable between 249.85 and 278.68 K. Majid et aL3 have also 250 K and between
2 studied van Stackelberg’s type I structure hydrate by dielectric relaxation, proton magnetic resonance, and dissociation pressure versus temperature me~urements.
The previous results reported by us4 on PMR studies of cyclopropane deuterate were in disagreement with the PMR resuIts of Majid et al.’ on cy~lopropa~~ hydrate, and which we found to arise because of the difficulty in the preparation (which will be outlined later) of the deuterate below 250 K. Because of the possibility of phase separation beIow 250 K, the previous data seemed mainly due to adsorbed cyclopropane on powdered D,O rather than the deuterate- The present report agrees very well with the PMR work on cycIopropane hydrate3. in addition to revised absorption measurements, relaxation data are also presented on the deuterate as well as on pure cycfopropane. Solid cyclopropane has already been studied by Hoch and Rushworth and their results can be taken to show the presence of a rigid structure with a second moment of -20 GZ existing over the
temperature range from 85 to 105 K. Above that temperature a molecular rotation around threefold axis (C,-rotation) occurs which causes the second moment to become - 11.5 G2 from I20 K up to the melting point. These authors, from their 5F1measurements, obtained an activation energy of 4.1 kcal mole-’ associated with the barrier ~ndering the C,-rotation. We have not attempted to revise the absorption measurements on solid cyciopropane, but have obtained T1 results by a more accurate pulse method which can be expected to give a better activation energy for comparison with simiiar data for the deuterate.
EXPERIMENTAL
We found the preparative method of Hafemann and Miller2 highly inconvenient for obtaining the pure deuterate because of two reasons: first, during the process of preparing finely powdered D,O, the deuterons of D,O are exchanged with protons by a sufficient amount (2-3 %) even in a moderately inert atmosphere. Secondly, to get deuterate of high purity, the exact amount of cyclopropane must be known, which is difficult using this technique. We observed after several unsuccessful attempts, that, the presence of excess of C3H6 does not favour the formation of the deuterate, but simply leaves some free cyclopropane, and some adsorbed on the powdered D,O surface even if the sample was left for fifteen days, _In some cases where the cyclopropane amount was fortunately less than the formula ratio, this method yielded the deuterate, but never better than about 80 % pure. In our earlier report, this method was followed using excess of C,H6. We
found that to get a satisfactory sample of the deuterate, C&H6 should either be in the exact amount, or sfightly less (0.2-0.4 %) than the formula ratio (C& D,O
- 7.67D20).
Cyclopropane (99.0 % pure) was obtained from Matheson Company, and (99.8 % d) from Stohier Isotope ChemicaIs. DZO was filled in about 4 cm
3 o.d. round-bottom glass tubes, and the exact amount of C3H6 was transferred after degassing the D,O. The tube was sealed, and the mixture was first shaken vigorously on a mechanical shaker at about 273 K for about 2-3 hours to prepare frozen D20 in slightly powdered form, and then shaken at dry ice temperature for 2-3 days. In some cases where excess D,O (-20 g) was used, the mixture took about a week to form a good specimen of the deuterate. The deuterate was extracted by breaking the tube inside a cold box held at 243 to 233 K by using a cold nitrogen gas flow. It was finely powdered and transferred to NMR tubes, which were sealed after degassing- The analysis of samples (three batches) was achieved by decomposing the deuterate, and measuring the amount of gas evolved. Such analysis give the purity for type I structure in the range C,Hs - (7.4-S. l)D,O. Two batches of samples were prepared for the type II structure deuterate separately in a similar way as before by shaking the mixture at 273 K. The analyses of these type II structure deuterate samples were in the range of C,H, - (18--19)D,O. The type II structure deuterate lost C3H6 when the sample was degassed. It was therefore sealed without removing the dissolved air and was studied only by continuous wave measurements at 16 MHz. To prepare the cyclopropane specimens the gas was directly transferred from a cylinder, and sealed in NMR tubes after removing the dissolved air by a freezepump-thaw method_ The absorption line measurements were performed at 16 MHz with a Varian VF-16 wide line spectrometer. Evidence of saturation was noticeable (particularly at high temperatures) in the absorption line measurements for the type I deuterate because of long Ti and T2’s. The minimum r.f. field (O-1-0.2 mG) was used at higher temperatures, while at other temperatures r.f. field of about 0.5 mG was used. The second moments were also obtained from a solid echo 9O-r-9O,0 pulse sequence on the solid specimen at 30 MHz, as suggested by Powles and Strange6 by fitting the solid echo G(t) to an expression of the type G(t) = l-
;A&+
;A+. .
. .
where t is time in s and @, is the nth moment. Relaxation measurements were performed at 30 MHz using a Bruker pulse spectrometer. Because of the narrow line, a Varian 12-inch magnet with a superstabilizer was used. T1 values of less than 3 seconds were measured by a 180”-r-90” pulse sequence with an HI correction as suggested by van Putte’ and Kumar and Johnson’. T1 values of larger than 3 s and less than 10 s were measured both from 90-r-90, and n 90-r-90 (saturation) sequences ’ - 1’ _ Tl values of larger than 10 s were measured by IZ 90-r-90 (saturation) sequence only. The signal height after 180-r-90, 90-r-90, and saturation sequence was measured both from photographs obtained from Tektronix 549 Storage Oscilloscope equipped with type 1Al dual-trace plug-in unit; &id by using a Bruker Pulsed Gated Integrator B-KR 300 Z15, the output of which
4
was connected to a digital voltmeter. We found the saturation sequence less time consuming and better than the 90--90 pulse sequence, especially for averaging slightly noisy free induction decay curves (for the deuterate) even for the range of 2-10 s. The relaxation function R(t) [R(t) = {M,,--M,(t)}/(2M,) for 180-r-90 pulse sequence, and R(t) = (M,-, - MZ(t)}/MO for 90”-r-90” or saturation sequence, where AI,-,is equilibrium magnetization; i.e., magnetization after a 90” pulse, and M=(f) is the magnetization after the sequence] was exponential in all cases.
EXPERIMENTAL
RESULTS
(a) Absorption measurements The rest&s of second moment calculations are summarized in Table 1. The experimental second moments for cyclopropane deuterate (Fig. 1) vary very slowly from 1.9 +0.2 G2 at 77 K to a plateau value of O-6+0.1 GZ around 230 K. The latter value is consistent within experimental uncertainty, with isotropic rotation of the cyclopropane moIecule inside the 14-hedra of type I structure. The type II deuterate shows a second moment of 0.25f0.05 G* in its stability range of 251 to 278 K, which is also consistent with the isotropic rotation of the cyclopropane molecule inside the 16-hedra of type II structure. TABLE
1
THJZORETICALSECOND
Type of motion
Rigid CB-rotation
MOMENTS
FORCYCLOPROPANE
CLATHRATEDEUTERATFS
Type II
Type 1 Intra
Inter”
Total
Intra
Inter”
12.85 9.99
N0.90 No.4
-13.8 -10.4
12.85 9.99
N0.3b
-13.2
4.2
-10.2
o_ 15-0.20b
0.1 s-o.20
0.0
Isotropic
(Gau&)
0.35-0.4b
0.35-0.4
0.0
Total
a Includes an approximate deuteron contribution. D Ref. 11, including deuteron contribution.
i loo I
Fig.
200
300
Temperature PK)
1. Plot of the second moment against temperature for cyclopropane deuterate. 0 Cw measurements at 16 MHz. Y Pulse method using a solid echo (90°-~-90090~) pulse sequence. A Type II deuterate studied separately by cw measurements at 16 MHz.
5
(5) Relaxation measurements The temperature dependence of TI for solid cyclopropane is shown in Fig. 2. That figure shows a range of values of TX equal to 89 1 f 34 s at 90 K and reaching
.,i 90
a0
loo
Fig. 2. Temperature 30 MHz.
110
dependence
I50
of spin-lattice
relaxation
time,
T1 for solid
cyclopropane
62_t2 ms near the melting point (145 K). If the motional process is governed a unique correlation time TV, TI is related to rc by the BPP equation,
l
-= Tl
c
1
(
=c
1+o,2.r,
+
4L I+ 40(&2
1
=
2_-r(I+l) y4h2 5
r6
where r is interproton
= --3
10
distance
y+i2
are
(3)
r6 and I is the nuclear
by
(2)
1
where C, is constant, which for a CH, group (assuming that CH2 protons the dominating relaxation mechanism) is given by the expression12 c
at
spin. Equation
(2) gives a
6 . .
mrmmum at wo7= = 0.6I6, The theoretical value of TX minimum using eqns. (2) 106 rad s-r is 30 ms. It thus appears that cyclopropane and (3) at w. = 2zx30x melts before a minimum in I; is achieved. The value of 62 ms from 143 to 145 K and becoming slightly higher at the melting point seems to be due to some premelting of the cyclopropane. The activation energy associated with a C,-rotation is obtained from the pjot of In Z”Xversus (l/Z”) from Fig. 3. On the Iow temperature side of minimum oorc >> 1. Equation (2) therefore reduces to
-=I
2Cl
Tl
0022;,
orT,
fG2~O=P
(& )
= -
~j
2c1
Figure 3 shows that where z, obeys the Arrhenius equation z, = r. exp(IZJRT). this reorientation process follows the Arrhenius equation, and a plot of In T, versus (l/T) is a good straight line (Fig. 3) according to eqn. (4). The activation energy & obtained from the slope of this straight line is 4.8kO.2 kcal mole-’ which is in agreement with a value of 4.1 kcal mole- ’ obtained by Hoch and Rushworths.
II
lo
9
8
7 -&h
Fig. 3, Plot of In TX versus ZooofT (EC-‘) for solid cyclopropane.
7
- 20
20
-
%
-
9 6 5 4
-
3
-
2
Temperature(%) I
80
I I loo
I * 120
I * 140
9. 160
I I I I 160 200
* 1 I I * II. 220 240 260 280
1 300
I
Fig. 4. Plot of the spin-lattice relaxation time, TX against temperature for cyclopropane deuterate at 30 MHz.
The cyclopropane deuterate shows a similar behaviour for TI versus temperature curves as we observed for other deuterates’ 3- 15. The temperature dependence of Tr is plotted in Fig. 4. Unfortunately, the Tr data cannot be analysed in terms of BPP theory because a minimum in the TI curve was not achieved. The TI versus temperature curve follows the Arrhenius law from 77 to 125 K. The activation energy is therefore derived from the slope of the linear portion (77 to 125 K) of In Tr versus I/T curves as shown in Fig. 5. [On the high temperature side of the minimum oorc << I, eqn. (2) then reduces to (l/T,) = 5C,r= = 5C,r, exp(EJRT).] A value of 0.83 f0.03 kcal mole- ’ is obtained from
a
12
II
IO
9
8
7
6
5
4
3-
Fig. 5. Plot of In TX against reciprocal of the absolute temperature for cyclopropane deuterate.
8
this slope, but this value is not assigned to any mode of rotation. It is not associated with isotropic rotation, because the second moment in this temperature range is much higher than the isotropic value. On the other hand we have no low temperature data on either the second moment or T1 (lower than 77 K) from which the mode of rotation may be decided. The constant value of Tr = 28+2 s from about 200 K and upwards seems to be due to isotropic rotation of the cyclopropane molecules inside the deuterate cages. We could not obtain T1 data on separately prepared type II deuterate specimens,
as this deuterate loses C,H,
on removing
the dissolved air. The results for the region of 250 to 278 K are thought to be for
the type II clathrate, on the assumption that type I is converted completely to type II in this range, although this assumption is not necessarily true unless the excess gas is pumped out i6. The Tr measurements in this temperature range (250 to 278 K) did indicate some free cyclopropane, an indication that some of type I is converted to the type 11 deuterate.
DISCUSSION
The second moment for the type I deuterate approaches a pIateau value of 0.6kO.l G2 around 230 K which we assigned as being due to isotropic rotation of the cyclopropane molecule. This value is slightly higher than the calculated vaIue of 0.35-0.4 GZ for isotropic rotation. The r-f. field used at these temperatures was definitely low in order to avoid saturation. These absorption results are further supplemented by solid echo measurements which give nearly the same value for the second moment. Possibly this higher value may arise from either the presence of free cycIopropane or some exchange of the deuterons of D,O with protons from moist air. As a precaution samples which showed a trace of free gas were further evacuated before taking measurements_ The second possibility of exchange was, however, present but at the most to the extent of 2 % (as seen from the analysis of decomposed studied samples). This latter could increase the second moment to about 0.06 G2, which makes the theoretical value in the range of 0.41-0.46 G2. The experimental value is still higher and this could well be due to experimental uncertainties in the measurements. We can, however, compare these results with the available results on a similar deuterate; i.e., ethylene oxide deuterate. Garg et al.” obtained second moment values of 1.8 G2 at 77 K, 0.5-6 G2 between 130 and 200 K, and 0.3kO.05 G2 as the plateau value between 230 and 270 K. Our unpublished results’ 5, and the work of Afanas’ev and Kvlidize” show similar results: I-9-2 G2 at 77 K, and a plateau value of 0.4 G2 in the temperature range from -230 to 270 K). The theoretical value of the second moment for isotropic rotation in ethylene oxide deuterate given by Garg et al.” is 0.24 G2. Clearly this small difference is due to experimental uncertainty_ There is no reason to consider saturation, however, in this case because ethylene oxide shows a maximum value of
9 TX around 15 s at 60 MHzlS, while cyclopropane shows a maximum value of 28 s at 30 MHz. The results cannot be improved even by the use of higher frequencies because of the long T2 value and probably also a long TI value. The activation energy of 0.83 kcal mole-’ for the cyclopropane deuterate is comparable to an activation energy of 0.98+0.02 kcal mole-’ for the ethylene oxide deuterate15. The plateau value of 28 + 2 s from - 200 K and onwards could be due to isotropic rotation of the cyclopropane molecule with a correiation time of the order 10-r’ s as was observed by Davies and Williams for ethylene oxidelg_ No attempt was made to derive correlation times from the BPP equation for solid cyclopropane as the true value of experimental minimum is not reached in the experiments carried out at 30 MHz. We neglected the contribution from other CH, groups in the TI minimum calculation because of the lack of complete crystal structural data on solid cyclopropane as only the unit cell dimensions are known2’_ The present activation energy of 4.8 kcal mole-’ for the C,-rotation is, however, probably more accurate than the value of 4.1 kcal mole-’ obtained by Hoch and Rushworth because the present method gives better values for TI. Their value of 0.12 s at the melting point estimated from experimental results obtained using a progressive saturation technique at 22.14 MHz* seems to be doubtful. In the light of our results at 30 MHz (T, value of 6222 ms at the melting point) using the most accurate 180-7-90 pulse technique with a HI correction, shows that the Hoch and Rushworth value may be too high*.
ACKNOWLEDGEMENT
We wish to thank the National Research Council of Canada for generous grants in support of this work. We are also indebted to Dr. P. Raghunathan for many interesting and helpful discussions.
REFERENCES 1 D. R. HAFEMANN AND S. L. MILLER, J. Phys. C/tent., 73 (1969) 1392. 2 D. R. HAFEMANN AND S. L. MILLER, J. Phys. Chem., 73 (1969) 1398_ 3 Y. A. MAJID, S. K. GARG AND D. W. DAVIDSON, Cm. J. Clxem., 47 (1969) 4697. 4 A. W. K. KHANZADA AND C. A. MCDOWELL, J. Mol. Strttcfttre, 7 (1971) 241. 5 M. J. R. HOCH AND F. A. RUSHWORTH, in B. PESCE(editor), Nuclear Magnetic Resonunce itr C’lrentistry, Academic Press, New York, 1965, p_ 243. 6 J. G. POWLES AND J. H. STRANGE, Proc. Phys. Sot. Londorr, 82 (1963) 6. 7 K. VON Pu-rr~, J. Mugn. Res., 2 (1970) 216. 8 ANIL KUMAR AND C. S. JOHNSONJR., J. Magn. Res., 7 (1972) 55. 9 Pulsed NMR Spectrometers, Bruker Scientific Inc., Elmsford, New York, undated, pp. 3-L
* There is no mention of the w0 value or the method of measurement in ref. 5, so we quote the frequency 22.14 MHz and the technique of measurement from their earlier work”.
10 10 T. C.
FARRAR AND E. D. BECKER,Palsed
and Foarier
Transform
NMR,
Academic Press,
New York, 1971, p. 22.
SMITH, J. Chem. Phys., 42 (1965) 4229. 12 A. ABRAGAM, The Principles of N&ear Magnetism, Oxford University Press, Oxford, 1961, p. 300. 13 P. S. ALLEN, A. W. K. KHANZADA AND C. A. MCDOWELL, 3. Mol. Srractare, 14 (1972) 9.
11 G. W.
14 M. B. DUNN AND C. A. MCDOWELL, Cilem.Phys. Lett., 15 (1973) 508. IS A. W. K. KHANZADA, C. A. MCDOWELL AND P. RAGHUNATHAN,to be published. 16 D. W. DAVIDSON, personal communication. 17 S. K_ GARG, B. MORRIS AND D. W. DAVIDSON, J. Chem. Sot.,
18 B. L. AFANAS'EV 183 (1968)
AND V. I. KVLIVIDE,Dokl.
816 (English
Akad. Nauk SSSR,
Faraday II, 68 (1972) 481. 183 (1968) 360 (Russian),
translation).
19 M. DAVIES AND K. WILLIAMS, Trans. Faraday Sac., 64 (1968) 529. 20 J. B. BATES, D. E. SANDS AND W. H. SMITH. J_ Chem Phys., 51 (1969) 105. 21 M. J. R. HOCH AND F. A. RUSHWORTH, Proc. Phys. Sot. London, 83 (1964)
949.