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Pyrrolidine conformation: A low-temperature dielectric relaxation study
Chemical Physics 121 (1988) 131-136 North-Holland, Amsterdam
131
PYRROLIDINE CONFORMATION: A LOW-TEMPERATURE DIELECTRIC
RELAXATION
STUDY
John GILCHRIST Cenrre de Recherches sur les Trk Basses TempPratures, CNRS, 25 Avenue des Martyrs, BP 166 X, 38042 Grenoble CPdex, France
Jean-Claude
DUPLAN
Laboratoire de Spectroscopic
Hertzienne,
Universite Claude Bernard Lyon I, 69622 Villeurbanne CPdex, France
and Yves INFARNET Laboratoire de Chimie Organique, Universite Claude Bernard Lyon I, 69622 Villeurbanne CPdex, France Received
5 October
1987
The 4.2 K dielectric relaxation rates of pyrrolidine, several of its derivatives and other secondary amines absorbed in polyethylene and polypropylene are compared and it is concluded that pyrrolidine prefers the C, (“envelope”) conformation in which the CNC bond angle is smallest and the nitrogen inversion barrier highest. 3-methyl-3-propylpyrrolidine also prefers this conformation, though less markedly. Incorporation into a bicyclic structure can cause the pyrrolidine ring to be distorted beyond the range of forms observed in the monocyclic species.
1. Introduction In his review of nitrogen inversion Lehn [l] drew attention to the use of amine groups as probes for understanding structural effects in molecules, since inversion barriers are strongly dependent on molecular structure, and in particular on CNC bond angles, when strained. When dissolved in non-crystallising hydrocarbon solvents or absorbed in hydrocarbon polymers many secondary amines exhibit dielectric relaxations which can be observed at liquid-helium temperature and used to estimate the inversion barriers [2,3]. The method is particularly valuable in the case of molecules with two or more rate processes, for example the nitrogen inversion and the ring-pucker inversion in piperidine. When thermal activation is negligible the only active process is the one which has an appreciable tunneling rate - i.e. the one which involves movement of hydrogen atoms, 0301-0104/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
not carbons - irrespective of whether this has the lowest potential barrier or not. We have applied the method to pyrrolidine, where the processes are nitrogen inversion and pseudorotation. For comparison with pyrrolidine (compound 1) we have studied two monocyclic alkyl derivatives (2 and 3) and three bicyclic compounds containing the pyrrolidine ring (4-6). (See structures in scheme 1.) The monocyclic alkyl derivatives are likely to have modified pseudorotational potentials while complete inhibition of pseudorotation is likely in the bicyclic compounds. Results for compounds la, 2 and 4 have already been reported [2,3]. At the time it was thought that pyrrolidine would have a very low pseudorotation barrier [4-61 with a possible preference for the C, (“twist”) conformation [7], but our studies indicated a strong preference for the conformation characterised by slow nitrogen inversion which, as explained below, would be the C, (“envelope”) B.V.
J. Gilchrist et al. / Low-temperature
132
R
H
cl l.a)
R = H
l.b)
R = D
30(?-
H
q ‘o(
-0
18X
6 brad&l
N
I
. m
200
3.
2.
dielectric relaxation of pyrrolidine
1 I I
I
.
n
38
.
’
NH oz 4.
5.
(cis)
6.
Scheme 1.
conformation. Recent microwave [8], ab initio and electron diffraction studies [9] have shown that the C, conformer is, in fact, distinctly the more stable in gaseous pyrrolidine. After reporting relevant new experimental results (section 2) we discuss what more can be deduced about the pseudorotational potentials of compounds 1, 2 and 3 from the dielectric relaxation curves (section 3).
2. New experimental results Compound 3 was prepared using the method described by Lunt [lo]. Compound 5 was synthesised by reduction of nortropinone (Wolff-Kishner reaction modified by Huang-Minlon). Compound 6 was prepared by LiAlH, reduction of cis-hexahydrophthalimide which was obtained from cishexahydrophthalic anhydride [ll]. As before [2,3] 130 pm thick films of polyethylene (poly-C,D,) or polypropylene (poly-C,H,) were immersed in the compound or its cyclohexane solution, mounted between indium electrodes and studied, usually at 4.2 K, with a transformer capacitance bridge (10 Hz-10 kHz) and by calorimetric measurement of dielectric loss (1 kHz-10 MHz). Results for compounds lb and 5 are shown in figs. 1 and 2. Figure 1 requires two comments. Firstly we find as before that when the amine has been mixed with water and (incompletely) dried with
lo
Km
lk fDtr)
X)k
Fig. 1. (+ ) dielectric loss angle of poly-C,D, containing pyrrolidine previously mixed with an equal volume of D,O and dried with anhydrous Na,CO,, at 4.2 K; (x) idem but with H,O instead of D,O; (0) curve constituted by subtracting 20% of the curve ( X) from the curve ( + ), to represent the contribution of compound lb supposing the sample treated with D,O to have been incompletely deuterated. (0) Analogous data for poly-CsH, films containing the same pyrrohdine samples.
Na,CO, the relaxation strength is reduced. Secondly, the deuteration shift cannot be evaluated because compound lb has its loss peak well below our spectral range. The shift must be of several decades and demonstrates that the relaxation is due to nitrogen inversion, not pseudorotation. Fig. 2 requires one comment. As usual [3] the relaxation is about twice as fast in poly-C,H, as in poly-C,D,. This can be explained by the macroscopic properties of the polymers without reference to their molecular structure. Poly-C,H, has lower elastic moduli and sound velocities than poly-C,D,, so has a higher density of phonon states. The dominant relaxation mechanism is phonon-assisted tunnelling [12] and the rate is proportional to the phonon density of states. Compounds 3 and 6 each exhibited a single loss peak at 4.2 K. In poly-C,D,, compound 3 (2,2,5,5-tetramethylpyrrolidine) caused a 1.6 mrad peak at 130 kHz and in poly-C,H,, 3.0 mrads at 240 kHz. These loss curves were 2.7 decades broad at half-peak height. For compound 6 (cis-perhydroisoindole) the data were respectively 830 prad
133
J. Gilchrist et al. / Low-temperature dielectric relaxation of pyrrolidine
l
l%
400-
.
l \
\
-O\ O\ 200-
0
Fig. 2. (0) Dielectric loss angle of poly-C,D, containing compound 5 (nortropane) at 4.2 K; (0) poly-CsH, idem. At 5.35 K the poly-C,D, sample had a loss peak of 270 prad at 13.5 Hz and at 7.0 K a loss peak of 277 prad at 26 Hz; by extrapolation, 8 Hz at 4.2 K.
at 1.0 MHz (2.2 decades broad at half-peak height) and 1630 prad at 1.5 MHz.
3. Discussion In the previous study of secondary amines [3] approximate empirical relations were derived which relate relaxation rate to nitrogen inversion barrier, Flnv: A2=15THzxf,,
(I)
V,,, = 1820 - 180 In A.
(2)
Here f, is the relaxation frequency in a poly-C,D, matrix at 4.2 K and A is the tunnel splitting. In the second expression A is to be expressed in GHz and Vi, in cm -l. Together these merely express the fact that f,,, varies nearly exponentially with V,,, over the spectral range investigated. The use of expressions (1) and (2) is exemplified in table 1. It is well known that Vi, depends markedly on the CNC bond angle (&NC = 0) and is much higher in aziridines and azetidines (small 0) than in the unstrained dialkylamines or piperidine [l].
When strain xylamine or lowered [2,3]. lar molecules 8 varies with 8=
opens the angle, as in dicyclohe2,2,6,6_tetramethylpiperidine Vi,, is In the case of pyrrolidine and simide Leeuw et al. [13] have shown that the pseudorotation angle, 9, as:
e, - a cam 2+.
(3)
Here we have adopted Pfafferott’s [9] definition of
Table 1 Relaxation frequencies (at 4.2 K, in poly-C,D,) of three endocyclic secondary amines, with approximate tunnel splittings from eq. (l), nitrogen inversion barriers from eq. (2) and CNC bond angles known or estimated independently. Note that tunneling is between inequivalent axial and equatorial conformations which are made nearly energetically equivalent by intermolecular interactions. A is not a parameter which could be determined by gas-phase spectroscopy and should not be confused with the tunneling splitting of ref. [8] which involves both nitrogen inversion and st pseudorotation
piperidine la (pyrrolidine) 5 (nortropane)
f,n WI
A W-W
5, (cm-‘)
e (de@
20k [2] 560 [2] 8
550 92 11
1930 2250 2630
109.8 [9] 105.2 [9] 101-103
134
J. Gilchrist et al. / Low-temperature
pseudorotation angle in which cp= 0 or n means the C, conformation and I#J= f $r means C,. De Leeuw et al. had P = $I f $r. u is positive and varies from one compound to another as the square of the pseudorotational puckering amplitude. Thus pyrrolidine, like tetrahydrofuran should have a = 2.1° [9] and putting 8, = 107.3” would give Pfafferott’s value of 105.2” for 6 of C, pyrrolidine, and 109.4” for C,. It is likely that a linear relation between V,,, and 0 would be a good approximation over this limited range, so we can assume f, varies exponentially with 8. Writing the pseudorotational potential in the form: V($)
= i&(1 + iV,(l
- cos $) + i&(1-
cos 2$)
- cos 3+) + $Vd(l - cos 4$), (4)
the set of coefficients Vi = 0.97 kcal/mol, I’, = 1.12 kcal/mol, V, = V, = 0 gives a good approximation to V(+) as calculated by Pfafferott [9] when nitrogen polarisation functions were included. As the matrix is cooled the pyrrolidine (or compound 2 or 3) is assumed to maintain a Boltzmann distribution of cp values until some temperature Tf where pseudorotation becomes inhibited by intermolecular interactions. We imagine the molecules to be trapped in cages which become more rigid as the matrix is cooled. At 4.2 K, + will have the Boltzmann distribution corresponding to the fictive temperature T,. Then we find
a(f) = h~2Texp[ - W#WkT/] X{[fi’f
exp(b cos2+)]”
+[foelf exp(b COS~+)]-~}-~
d+.
(5)
In this expression S,, fo, b and m are adjustable parameters to fit the experimental dielectric loss curves. If we had assumed that a uniquely defined V,,, corresponds to each $I value we should have put m = 1 so the integrand would express the Debye function for the loss observed at frequency f due to a relaxation of frequency f. exp( - b x cos 2+). However, open-chain secondary amines all have loss curves broader than Debye curves [2]
dielectric relaxation ofpyrrolidine
due to a modulation of Vi,, by intermolecular interactions and we have allowed that the same would be true of pyrrolidine even though $I and 8 were fixed, using an empirical Jonscher [14] function in which 0 < m -c 1. b incorporates the constant a of eq. (3), the coefficient of In A in eq. (2) and the coefficient relating V,,, to 8. In the case of a freely pseudorotating molecule, whose conformation is determined solely by random intermolecular interactions, V(+)/kT, = 0. Then S(ln f) is a symmetric two-peaked function provided bm > 2. The peaks correspond to the concentrations of cos 2$ values near f 1. Unequal peaks result when V,/kT,# 0. However the two peaks in the loss curve of compound 2 are too well resolved to fit the expression unless a V, term is also introduced which has the effect of favoring extreme cos ~I#I values. This is illustrated in fig. 3. Parameters needed to fit the curve of compound 2 in poly-C,H, published earlier [3] are m = 0.50, b = 3.6, V,/kTf= 0.46, V,/kT/= 4.8, f. = 42 kHz. An appreciable V,/kTf value is also needed to best fit the pyrrolidine data. In particular the published [3] curve of pyrrolidine in poly-C,H, which had a peak near 1 kHz and a shoulder near 500 kHz is best fitted with m = 0.55, b = 4.15, V1/kTf = 2.6, VJkT, = 1.6, f. = 34 kHz. To summarise, the pyrrolidine and compound 2 data are both best fitted with m = 0.5, b = 4, fa = 40 kHz (in poly-C,H,), 25 kHz (in poly-C,D,). b= 4 implies the relation:
fm/fo= ev[l.%~ - &>I.
(6)
V, is positive for both compounds, indicating that the C, conformation is more stable in each case. However we have not taken the V, value into account here and should have done so by recognising that the intrinsic energy difference between the equatorial and axial forms will weaken the dielectric absorption due to C,, or nearly C, molecules since only those for which intermolecular interactions cancel out V, (to within 2kT) will participate in the relaxation. This was discussed earlier [2] with reference to piperidine, where it was noted that pyrrolidine produces a stronger relaxation than piperidine though not as strong as the open-chain secondary amines of similar molec-
J. Gilchrist et al. / Low-iemperaiure
0
no
Fig. 3. Dielectric loss angle of poly-C,D, parameters m = 0.56, b = 3.7, Vz/kT/
I
I
lk
lok
I
lOOk
I
1M
I
f&42)
10M
containing compound 2 (3-methyl-3-propyl pyrrolidine) at 4.2 K, fitted with eq. (5) and = 3.6, f. = 25 kHz. The dashed line is an attempted fit with V.,/kT/ = 0, where m = 0.8, b = 5.0, V,/kT, = 0.32, f. = 25 kHz.
= 0.32, Vd/kT,
weight. These species were assumed to have similar solubilities in poly-C,D, or poly-C,H, so it is to be deduced that pyrrolidine (in C, form) has lower intrinsic equatorial-axial energy difference than piperidine, in contradiction to current estimates for the gas phase. C2 pyrrolidine, however, would be analogous to diethylamine etc. which invert between intrinsically equivalent conformers, so that the dielectric absorption of a matrix containing equal concentrations of C, and C, pyrrolidine would owe more to the latter than to the former - i.e. more to the fast-relaxing species than to the slower. This means we have underestimated VJkTf for compounds 1 and 2 since the C, conformer must be even more numerically dominant than the loss curves at first sight suggest. Similarly the C, form of compound 3 may not have been so completely absent as suggested by the loss curves. However the need for a rather large V,/kTf value is not diminished. Assuming V, = 1.12 kcal/mole and VJkTf = 2.6-4.2 we would deduce Tf= 130-220 K for pyrrolidine in poly-C,H,, which is the order of the glass transition temperature for the amorphous parts of the polymer matrix. However we know that pyrrolidine, like tetrahydrofuran, can reorientate down to 30 K in poly-C,H, (down to below 50 K at 1 kHz [15]) and so long as the molecules can orientate, the matrix would not be expected to inhibit pseudorotation. A more likely value for Tf is = 30 K, which also allows V, to be reasonably small.
ular
135
dielectric relaxation of pyrrolidine
VJkT, may be as high as 5 or 6 but not as high as 19, the value obtained by taking the gas phase V, value. The loss peak of compound 3 occurred within the spectral range where pyrrolidine is capable of exhibiting a loss peak if forced to adopt different pseudorotation angles. A more specific effect of the geminal methyl pairs, for example a modified pucker amplitude a is therefore possible but is not demonstrated. So far we have discussed the data- of compounds l-3 without direct comparison with other amine species. As soon as this comparison is attempted we find a difficulty in that f, values range upwards as well as downwards from f, of the unstrained species: the dialkylamines and piperidine. These have f, = 20 kHz at 4.2 K in poly-C,D, [2] and for the latter 8 = 109.8“ [9]. This might be taken to suggest that 8 of pyrrolidine would range as high as 112” in the C, conformation, which seems unlikely. More probably 109.4” is correct but Vi,, is not uniquely determined as a function of 6 and depends separately on electronic factors not reflected in the value of 8. In C, pyrrolidine the strained CCC angles would be relevant. The data of the bicyclic compounds 4-6 must also be interpreted subject to this cautionary remark. For each of compounds 4-6 we found a single loss peak. Compounds 4 and 5 have the same bicyclic structure with the aza group placed differ-
136
J. Gilchrist et al. / Low-temperature
ently. If the effect of the three-carbon bridge were simply to force the five-membered ring to adopt a partjcular cp value, this value would be = $n for compound 4, 0 for 5. Certainly compound 4 has the expected f,,, value, and 5 relaxes more slowly, but it also relaxes far more slowly than compounds l-3, so the five-membered ring is apparently distorted into a form unobtainable in a monocyclic molecule. In fact 8 can be estimated from the following data: the bridge-head carbons of the analogous hydrocarbon are 2.361 A apart [16]; theoaverage CC bond length in cyclopentane is 1.546 A (quoted in ref. [9]); if C,Cs and C,C, of bicyclo[3,2,l]octane are assumed to be the same, the angle C,C,C, is 99.6 O; in rings (e.g., azetidine, piperidine) the CNC angle is generally a little wider than the analogous CCC angle, so in the present case perhaps 101-103” (table 1). Eq. (6) would suggest 103.1“. In the case of compound 6, the pyrrolidine ring would be expected to be nearer C, than C, and the relaxation to be fast. In fact it is slightly faster than any of compounds l-3. Eq. (6) would suggest 8 = 109.2”.
4. Conclusions The recent findings about the pseudorotational potential of pyrrolidine [8,9] have enabled us to understand why this molecule has a fairly well-defined relaxation rate that involves nitrogen inversion without pseudorotation and which is much slower than in piperidine. We can also understand why derivatives like compound 2 tend to have more dielectric loss at higher frequencies, even having a second loss peak. We have not been able to understand the details of the loss curves unless by supposing that the nitrogen inversion barrier is
dielectric relaxation of pyrrolidine
not determined uniquely by CNC bond angle and also that in the matrix, the molecules have a strong preference for C, or C, over intermediate configurations.
Acknowledgement Compounds 3, 5 and 6 were synthesized by T. Reix, C. Roux, C. Aurenge and R. Pomes. Nortropinone hydrochloride, the starting point for compound 5 was kindly supplied by A. Lindenmann and H. Friedli, Sandoz AG, Basle.
References 111J.M. Lehn, Forts&. Chem. Forsch. 15 (1970) 311. PI J. Gilchrist, Chem. Phys. 65 (1982) 1. I31 J. Gilchrist and H. Godfrin, Chem. Phys. 79 (1983) 307. G.C. Sinke, R.A. McDonald, W.R. [41 D.L. Hildenbrand, Kramer and D.R. Stull, J. Chem. Phys. 31 (1959) 650. 151 J.C. Evans and J.C. Wahr, J. Chem. Phys. 31 (1959) 655. 161J.P. McCullough, D.R. Douslin, W.N. Hubbard, S.S. Todd, J.F. Messerly, LA. Hossenlopp, F.R. Frow, J.P. Dawson and G. Waddington, J. Am. Chem. Sot. 81 (1959) 5884. [71 K.S. Pitzer and W.E. Donath, J. Am. Chem. Sot. 81 (1959) 3213. H. Oberhammer, G. Pfafferott, R.R. PI W. Caminati, Filgueira and C.H. Gomez, J. Mol. Spectry. 106 (1984) 217. H. Oberhammer, J.E. Boggs and W. 191 G. Pfafferott, Caminati, J. Am. Chem. Sot. 107 (1985) 2305. Symposium on 1101 E. Lunt, Proceedings of the International Nitro-compounds . Warsaw, 1963 (Warsaw, 1965) p. 291. P11 A. Dunet, R. Ratouis, D. Cadiot and A. Willemart, Bull. Sot. Chim. France (1956) 906. [12] W.A. Phillips, Proc. Roy. Sot. A 319 (1970) 565. [13] F.A.A.M. de Leeuw, P.N. van Kampen, C. Altona, E. Diez and A.L. Esteban, J. Mol. Struct. 125 (1984) 67. [14] A.K. Jonscher, CoUoid Polym. Sci 253 (1975) 231. [IS] J. Gilchrist, Chem. Phys. 70 (1982) 353. [16] V.S. Mastryukov, J. Mol. Struct. 96 (1983) 361.
131
PYRROLIDINE CONFORMATION: A LOW-TEMPERATURE DIELECTRIC
RELAXATION
STUDY
John GILCHRIST Cenrre de Recherches sur les Trk Basses TempPratures, CNRS, 25 Avenue des Martyrs, BP 166 X, 38042 Grenoble CPdex, France
Jean-Claude
DUPLAN
Laboratoire de Spectroscopic
Hertzienne,
Universite Claude Bernard Lyon I, 69622 Villeurbanne CPdex, France
and Yves INFARNET Laboratoire de Chimie Organique, Universite Claude Bernard Lyon I, 69622 Villeurbanne CPdex, France Received
5 October
1987
The 4.2 K dielectric relaxation rates of pyrrolidine, several of its derivatives and other secondary amines absorbed in polyethylene and polypropylene are compared and it is concluded that pyrrolidine prefers the C, (“envelope”) conformation in which the CNC bond angle is smallest and the nitrogen inversion barrier highest. 3-methyl-3-propylpyrrolidine also prefers this conformation, though less markedly. Incorporation into a bicyclic structure can cause the pyrrolidine ring to be distorted beyond the range of forms observed in the monocyclic species.
1. Introduction In his review of nitrogen inversion Lehn [l] drew attention to the use of amine groups as probes for understanding structural effects in molecules, since inversion barriers are strongly dependent on molecular structure, and in particular on CNC bond angles, when strained. When dissolved in non-crystallising hydrocarbon solvents or absorbed in hydrocarbon polymers many secondary amines exhibit dielectric relaxations which can be observed at liquid-helium temperature and used to estimate the inversion barriers [2,3]. The method is particularly valuable in the case of molecules with two or more rate processes, for example the nitrogen inversion and the ring-pucker inversion in piperidine. When thermal activation is negligible the only active process is the one which has an appreciable tunneling rate - i.e. the one which involves movement of hydrogen atoms, 0301-0104/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
not carbons - irrespective of whether this has the lowest potential barrier or not. We have applied the method to pyrrolidine, where the processes are nitrogen inversion and pseudorotation. For comparison with pyrrolidine (compound 1) we have studied two monocyclic alkyl derivatives (2 and 3) and three bicyclic compounds containing the pyrrolidine ring (4-6). (See structures in scheme 1.) The monocyclic alkyl derivatives are likely to have modified pseudorotational potentials while complete inhibition of pseudorotation is likely in the bicyclic compounds. Results for compounds la, 2 and 4 have already been reported [2,3]. At the time it was thought that pyrrolidine would have a very low pseudorotation barrier [4-61 with a possible preference for the C, (“twist”) conformation [7], but our studies indicated a strong preference for the conformation characterised by slow nitrogen inversion which, as explained below, would be the C, (“envelope”) B.V.
J. Gilchrist et al. / Low-temperature
132
R
H
cl l.a)
R = H
l.b)
R = D
30(?-
H
q ‘o(
-0
18X
6 brad&l
N
I
. m
200
3.
2.
dielectric relaxation of pyrrolidine
1 I I
I
.
n
38
.
’
NH oz 4.
5.
(cis)
6.
Scheme 1.
conformation. Recent microwave [8], ab initio and electron diffraction studies [9] have shown that the C, conformer is, in fact, distinctly the more stable in gaseous pyrrolidine. After reporting relevant new experimental results (section 2) we discuss what more can be deduced about the pseudorotational potentials of compounds 1, 2 and 3 from the dielectric relaxation curves (section 3).
2. New experimental results Compound 3 was prepared using the method described by Lunt [lo]. Compound 5 was synthesised by reduction of nortropinone (Wolff-Kishner reaction modified by Huang-Minlon). Compound 6 was prepared by LiAlH, reduction of cis-hexahydrophthalimide which was obtained from cishexahydrophthalic anhydride [ll]. As before [2,3] 130 pm thick films of polyethylene (poly-C,D,) or polypropylene (poly-C,H,) were immersed in the compound or its cyclohexane solution, mounted between indium electrodes and studied, usually at 4.2 K, with a transformer capacitance bridge (10 Hz-10 kHz) and by calorimetric measurement of dielectric loss (1 kHz-10 MHz). Results for compounds lb and 5 are shown in figs. 1 and 2. Figure 1 requires two comments. Firstly we find as before that when the amine has been mixed with water and (incompletely) dried with
lo
Km
lk fDtr)
X)k
Fig. 1. (+ ) dielectric loss angle of poly-C,D, containing pyrrolidine previously mixed with an equal volume of D,O and dried with anhydrous Na,CO,, at 4.2 K; (x) idem but with H,O instead of D,O; (0) curve constituted by subtracting 20% of the curve ( X) from the curve ( + ), to represent the contribution of compound lb supposing the sample treated with D,O to have been incompletely deuterated. (0) Analogous data for poly-CsH, films containing the same pyrrohdine samples.
Na,CO, the relaxation strength is reduced. Secondly, the deuteration shift cannot be evaluated because compound lb has its loss peak well below our spectral range. The shift must be of several decades and demonstrates that the relaxation is due to nitrogen inversion, not pseudorotation. Fig. 2 requires one comment. As usual [3] the relaxation is about twice as fast in poly-C,H, as in poly-C,D,. This can be explained by the macroscopic properties of the polymers without reference to their molecular structure. Poly-C,H, has lower elastic moduli and sound velocities than poly-C,D,, so has a higher density of phonon states. The dominant relaxation mechanism is phonon-assisted tunnelling [12] and the rate is proportional to the phonon density of states. Compounds 3 and 6 each exhibited a single loss peak at 4.2 K. In poly-C,D,, compound 3 (2,2,5,5-tetramethylpyrrolidine) caused a 1.6 mrad peak at 130 kHz and in poly-C,H,, 3.0 mrads at 240 kHz. These loss curves were 2.7 decades broad at half-peak height. For compound 6 (cis-perhydroisoindole) the data were respectively 830 prad
133
J. Gilchrist et al. / Low-temperature dielectric relaxation of pyrrolidine
l
l%
400-
.
l \
\
-O\ O\ 200-
0
Fig. 2. (0) Dielectric loss angle of poly-C,D, containing compound 5 (nortropane) at 4.2 K; (0) poly-CsH, idem. At 5.35 K the poly-C,D, sample had a loss peak of 270 prad at 13.5 Hz and at 7.0 K a loss peak of 277 prad at 26 Hz; by extrapolation, 8 Hz at 4.2 K.
at 1.0 MHz (2.2 decades broad at half-peak height) and 1630 prad at 1.5 MHz.
3. Discussion In the previous study of secondary amines [3] approximate empirical relations were derived which relate relaxation rate to nitrogen inversion barrier, Flnv: A2=15THzxf,,
(I)
V,,, = 1820 - 180 In A.
(2)
Here f, is the relaxation frequency in a poly-C,D, matrix at 4.2 K and A is the tunnel splitting. In the second expression A is to be expressed in GHz and Vi, in cm -l. Together these merely express the fact that f,,, varies nearly exponentially with V,,, over the spectral range investigated. The use of expressions (1) and (2) is exemplified in table 1. It is well known that Vi, depends markedly on the CNC bond angle (&NC = 0) and is much higher in aziridines and azetidines (small 0) than in the unstrained dialkylamines or piperidine [l].
When strain xylamine or lowered [2,3]. lar molecules 8 varies with 8=
opens the angle, as in dicyclohe2,2,6,6_tetramethylpiperidine Vi,, is In the case of pyrrolidine and simide Leeuw et al. [13] have shown that the pseudorotation angle, 9, as:
e, - a cam 2+.
(3)
Here we have adopted Pfafferott’s [9] definition of
Table 1 Relaxation frequencies (at 4.2 K, in poly-C,D,) of three endocyclic secondary amines, with approximate tunnel splittings from eq. (l), nitrogen inversion barriers from eq. (2) and CNC bond angles known or estimated independently. Note that tunneling is between inequivalent axial and equatorial conformations which are made nearly energetically equivalent by intermolecular interactions. A is not a parameter which could be determined by gas-phase spectroscopy and should not be confused with the tunneling splitting of ref. [8] which involves both nitrogen inversion and st pseudorotation
piperidine la (pyrrolidine) 5 (nortropane)
f,n WI
A W-W
5, (cm-‘)
e (de@
20k [2] 560 [2] 8
550 92 11
1930 2250 2630
109.8 [9] 105.2 [9] 101-103
134
J. Gilchrist et al. / Low-temperature
pseudorotation angle in which cp= 0 or n means the C, conformation and I#J= f $r means C,. De Leeuw et al. had P = $I f $r. u is positive and varies from one compound to another as the square of the pseudorotational puckering amplitude. Thus pyrrolidine, like tetrahydrofuran should have a = 2.1° [9] and putting 8, = 107.3” would give Pfafferott’s value of 105.2” for 6 of C, pyrrolidine, and 109.4” for C,. It is likely that a linear relation between V,,, and 0 would be a good approximation over this limited range, so we can assume f, varies exponentially with 8. Writing the pseudorotational potential in the form: V($)
= i&(1 + iV,(l
- cos $) + i&(1-
cos 2$)
- cos 3+) + $Vd(l - cos 4$), (4)
the set of coefficients Vi = 0.97 kcal/mol, I’, = 1.12 kcal/mol, V, = V, = 0 gives a good approximation to V(+) as calculated by Pfafferott [9] when nitrogen polarisation functions were included. As the matrix is cooled the pyrrolidine (or compound 2 or 3) is assumed to maintain a Boltzmann distribution of cp values until some temperature Tf where pseudorotation becomes inhibited by intermolecular interactions. We imagine the molecules to be trapped in cages which become more rigid as the matrix is cooled. At 4.2 K, + will have the Boltzmann distribution corresponding to the fictive temperature T,. Then we find
a(f) = h~2Texp[ - W#WkT/] X{[fi’f
exp(b cos2+)]”
+[foelf exp(b COS~+)]-~}-~
d+.
(5)
In this expression S,, fo, b and m are adjustable parameters to fit the experimental dielectric loss curves. If we had assumed that a uniquely defined V,,, corresponds to each $I value we should have put m = 1 so the integrand would express the Debye function for the loss observed at frequency f due to a relaxation of frequency f. exp( - b x cos 2+). However, open-chain secondary amines all have loss curves broader than Debye curves [2]
dielectric relaxation ofpyrrolidine
due to a modulation of Vi,, by intermolecular interactions and we have allowed that the same would be true of pyrrolidine even though $I and 8 were fixed, using an empirical Jonscher [14] function in which 0 < m -c 1. b incorporates the constant a of eq. (3), the coefficient of In A in eq. (2) and the coefficient relating V,,, to 8. In the case of a freely pseudorotating molecule, whose conformation is determined solely by random intermolecular interactions, V(+)/kT, = 0. Then S(ln f) is a symmetric two-peaked function provided bm > 2. The peaks correspond to the concentrations of cos 2$ values near f 1. Unequal peaks result when V,/kT,# 0. However the two peaks in the loss curve of compound 2 are too well resolved to fit the expression unless a V, term is also introduced which has the effect of favoring extreme cos ~I#I values. This is illustrated in fig. 3. Parameters needed to fit the curve of compound 2 in poly-C,H, published earlier [3] are m = 0.50, b = 3.6, V,/kTf= 0.46, V,/kT/= 4.8, f. = 42 kHz. An appreciable V,/kTf value is also needed to best fit the pyrrolidine data. In particular the published [3] curve of pyrrolidine in poly-C,H, which had a peak near 1 kHz and a shoulder near 500 kHz is best fitted with m = 0.55, b = 4.15, V1/kTf = 2.6, VJkT, = 1.6, f. = 34 kHz. To summarise, the pyrrolidine and compound 2 data are both best fitted with m = 0.5, b = 4, fa = 40 kHz (in poly-C,H,), 25 kHz (in poly-C,D,). b= 4 implies the relation:
fm/fo= ev[l.%~ - &>I.
(6)
V, is positive for both compounds, indicating that the C, conformation is more stable in each case. However we have not taken the V, value into account here and should have done so by recognising that the intrinsic energy difference between the equatorial and axial forms will weaken the dielectric absorption due to C,, or nearly C, molecules since only those for which intermolecular interactions cancel out V, (to within 2kT) will participate in the relaxation. This was discussed earlier [2] with reference to piperidine, where it was noted that pyrrolidine produces a stronger relaxation than piperidine though not as strong as the open-chain secondary amines of similar molec-
J. Gilchrist et al. / Low-iemperaiure
0
no
Fig. 3. Dielectric loss angle of poly-C,D, parameters m = 0.56, b = 3.7, Vz/kT/
I
I
lk
lok
I
lOOk
I
1M
I
f&42)
10M
containing compound 2 (3-methyl-3-propyl pyrrolidine) at 4.2 K, fitted with eq. (5) and = 3.6, f. = 25 kHz. The dashed line is an attempted fit with V.,/kT/ = 0, where m = 0.8, b = 5.0, V,/kT, = 0.32, f. = 25 kHz.
= 0.32, Vd/kT,
weight. These species were assumed to have similar solubilities in poly-C,D, or poly-C,H, so it is to be deduced that pyrrolidine (in C, form) has lower intrinsic equatorial-axial energy difference than piperidine, in contradiction to current estimates for the gas phase. C2 pyrrolidine, however, would be analogous to diethylamine etc. which invert between intrinsically equivalent conformers, so that the dielectric absorption of a matrix containing equal concentrations of C, and C, pyrrolidine would owe more to the latter than to the former - i.e. more to the fast-relaxing species than to the slower. This means we have underestimated VJkTf for compounds 1 and 2 since the C, conformer must be even more numerically dominant than the loss curves at first sight suggest. Similarly the C, form of compound 3 may not have been so completely absent as suggested by the loss curves. However the need for a rather large V,/kTf value is not diminished. Assuming V, = 1.12 kcal/mole and VJkTf = 2.6-4.2 we would deduce Tf= 130-220 K for pyrrolidine in poly-C,H,, which is the order of the glass transition temperature for the amorphous parts of the polymer matrix. However we know that pyrrolidine, like tetrahydrofuran, can reorientate down to 30 K in poly-C,H, (down to below 50 K at 1 kHz [15]) and so long as the molecules can orientate, the matrix would not be expected to inhibit pseudorotation. A more likely value for Tf is = 30 K, which also allows V, to be reasonably small.
ular
135
dielectric relaxation of pyrrolidine
VJkT, may be as high as 5 or 6 but not as high as 19, the value obtained by taking the gas phase V, value. The loss peak of compound 3 occurred within the spectral range where pyrrolidine is capable of exhibiting a loss peak if forced to adopt different pseudorotation angles. A more specific effect of the geminal methyl pairs, for example a modified pucker amplitude a is therefore possible but is not demonstrated. So far we have discussed the data- of compounds l-3 without direct comparison with other amine species. As soon as this comparison is attempted we find a difficulty in that f, values range upwards as well as downwards from f, of the unstrained species: the dialkylamines and piperidine. These have f, = 20 kHz at 4.2 K in poly-C,D, [2] and for the latter 8 = 109.8“ [9]. This might be taken to suggest that 8 of pyrrolidine would range as high as 112” in the C, conformation, which seems unlikely. More probably 109.4” is correct but Vi,, is not uniquely determined as a function of 6 and depends separately on electronic factors not reflected in the value of 8. In C, pyrrolidine the strained CCC angles would be relevant. The data of the bicyclic compounds 4-6 must also be interpreted subject to this cautionary remark. For each of compounds 4-6 we found a single loss peak. Compounds 4 and 5 have the same bicyclic structure with the aza group placed differ-
136
J. Gilchrist et al. / Low-temperature
ently. If the effect of the three-carbon bridge were simply to force the five-membered ring to adopt a partjcular cp value, this value would be = $n for compound 4, 0 for 5. Certainly compound 4 has the expected f,,, value, and 5 relaxes more slowly, but it also relaxes far more slowly than compounds l-3, so the five-membered ring is apparently distorted into a form unobtainable in a monocyclic molecule. In fact 8 can be estimated from the following data: the bridge-head carbons of the analogous hydrocarbon are 2.361 A apart [16]; theoaverage CC bond length in cyclopentane is 1.546 A (quoted in ref. [9]); if C,Cs and C,C, of bicyclo[3,2,l]octane are assumed to be the same, the angle C,C,C, is 99.6 O; in rings (e.g., azetidine, piperidine) the CNC angle is generally a little wider than the analogous CCC angle, so in the present case perhaps 101-103” (table 1). Eq. (6) would suggest 103.1“. In the case of compound 6, the pyrrolidine ring would be expected to be nearer C, than C, and the relaxation to be fast. In fact it is slightly faster than any of compounds l-3. Eq. (6) would suggest 8 = 109.2”.
4. Conclusions The recent findings about the pseudorotational potential of pyrrolidine [8,9] have enabled us to understand why this molecule has a fairly well-defined relaxation rate that involves nitrogen inversion without pseudorotation and which is much slower than in piperidine. We can also understand why derivatives like compound 2 tend to have more dielectric loss at higher frequencies, even having a second loss peak. We have not been able to understand the details of the loss curves unless by supposing that the nitrogen inversion barrier is
dielectric relaxation of pyrrolidine
not determined uniquely by CNC bond angle and also that in the matrix, the molecules have a strong preference for C, or C, over intermediate configurations.
Acknowledgement Compounds 3, 5 and 6 were synthesized by T. Reix, C. Roux, C. Aurenge and R. Pomes. Nortropinone hydrochloride, the starting point for compound 5 was kindly supplied by A. Lindenmann and H. Friedli, Sandoz AG, Basle.
References 111J.M. Lehn, Forts&. Chem. Forsch. 15 (1970) 311. PI J. Gilchrist, Chem. Phys. 65 (1982) 1. I31 J. Gilchrist and H. Godfrin, Chem. Phys. 79 (1983) 307. G.C. Sinke, R.A. McDonald, W.R. [41 D.L. Hildenbrand, Kramer and D.R. Stull, J. Chem. Phys. 31 (1959) 650. 151 J.C. Evans and J.C. Wahr, J. Chem. Phys. 31 (1959) 655. 161J.P. McCullough, D.R. Douslin, W.N. Hubbard, S.S. Todd, J.F. Messerly, LA. Hossenlopp, F.R. Frow, J.P. Dawson and G. Waddington, J. Am. Chem. Sot. 81 (1959) 5884. [71 K.S. Pitzer and W.E. Donath, J. Am. Chem. Sot. 81 (1959) 3213. H. Oberhammer, G. Pfafferott, R.R. PI W. Caminati, Filgueira and C.H. Gomez, J. Mol. Spectry. 106 (1984) 217. H. Oberhammer, J.E. Boggs and W. 191 G. Pfafferott, Caminati, J. Am. Chem. Sot. 107 (1985) 2305. Symposium on 1101 E. Lunt, Proceedings of the International Nitro-compounds . Warsaw, 1963 (Warsaw, 1965) p. 291. P11 A. Dunet, R. Ratouis, D. Cadiot and A. Willemart, Bull. Sot. Chim. France (1956) 906. [12] W.A. Phillips, Proc. Roy. Sot. A 319 (1970) 565. [13] F.A.A.M. de Leeuw, P.N. van Kampen, C. Altona, E. Diez and A.L. Esteban, J. Mol. Struct. 125 (1984) 67. [14] A.K. Jonscher, CoUoid Polym. Sci 253 (1975) 231. [IS] J. Gilchrist, Chem. Phys. 70 (1982) 353. [16] V.S. Mastryukov, J. Mol. Struct. 96 (1983) 361.