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Molecular structure of the rotational isomers in short chain n-perfluoroalkanes
Journal of Molecuhr Structure, 118 (1984) 245-255 Eisevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
MOLECULAR, STRUCTURE OF THE ROTATIONAL SHORT CHAIN n-PERFLUOROALKANES
M. CAMPOS-VALLElTE*
ISOMERS
IN
and M. REY-LAFON
Laborafoire de Spectroscopic Infmrouge, L.A. 124. Universitt? de Bordeaux I. 35I. cows de la Lib&ration, 33405 Talence Cddex (France) (Received 1 February 1984, in final form 3 April 1984)
ABSTRACT The structure of the isomers present in the different physical states of n-C,F,,,, is discussed, using previously published experimental data from and n-C,F,, n-C,F,, IR and Raman spectroscopy and an approximate force field. It is proposed that the gauche form of n-C,F,,, observed only in the gas and the liquid, is characterized by an internai rotational angle of about 120”. At least three non-trans forms exist in the gaseous and the liquid states of the C, compound, but they disappear in the crystal In contrast, the two solid phases of nC,F,, which are stable at high temperatures are disordered and contain one or two gauche isomers; only the lowest temperature one possesses the ahtmns form alone. INTRODUCTION
In a previous paper [l], we have shown the existence of conformational equilibria in the gaseous and the liquid states of n-perfluorobutane, nperfluorohexane and n-perfluorooctane and in some solid phases of the latter, using IR and Raman spectroscopy. We were able to demonstrate that the isomer which is present in the low-temperature solid phase is an all-trans one; it is slightly distorted from planarity for the C6 and Cs compounds. In addition, n-C4Flo was found to possess only two forms. However, we were unable to propose a structure for the isomers; we could only suggest that the internal rotational angle characteristic of the non-trans form of n-&Fro (the “‘gauche” form) is about 120”, on the basis of the magnitude of some frequency shifts for the same vibration of the two isomers and the value of the enthalpy difference between the two structures in the gaseous state In the present work, we propose an interpretation of the vibrational spectra of the all-Pans forms, using normal coordinate calculation, and we discuss the geometry of the other conformers present in the different phases of the three molecules.
*Present address: Facultad de Ciencias Basicas y Fannaceuticas, Casiiia 653, Santiago, Chile. 0022-2860/84/$03.00
o 1984 Elsevier Science Publishers B.V.
Universitad de Chile,
246 NORMAL
COORDINATE
TREATMENT
OF THE ALCTRANS
FORMS
Normal-mode calculations have been carried out for short fluorinated molecules 12-41 and for the polymer PTFE [see, e.g., 5, S] but none has been published for the n-perfluoroalkane series. Therefore we have tried to obtain approximate force constants which account for the experimental results relative to the all-trans isomers of the three molecules nC,FIO, n-C6F14 and nC8FIs [l]. Structure
and coordinates
As the structure of these compounds is not known, we have taken the following bond lengths from electron diffraction measurements on CzF6 [7]: C-F = 1.326 A, C-C = 1.545 A; all angles are assumed to be tetrahedral and the symmetry group is C?h. Local symmetry coordinates, allowing a direct comparison with experimental results, are used: they are symmetry coordinates of the CFB groups and linear combinations of internal coordinates identical to those used by Rabolt and Fanconi [5] for the CF2 groups. Torsional coordinates are defined as the sum of all the dihedral angles involved. Force field The calculation is carried out using the method of Wilson et al. [S] and a valence force field. As the number of experimental frequencies was not sufficient to build up a force field, we took the force constants from the literature for the CFB groups [2-41 and from the force field proposed for PTFE by Rabolt and Fanconi [5] for the CF2 groups and the carbon skeleton. The initial force field is written using the same approximation as the kinetic energy, i.e. interactions between vibrations not involving a common atom are assumed to be zero. We added some interaction constants which exist in the force field of the n-alkanes [9] and two others involving CFB stretching or bending vibrations: in fact the frequencies of these modes are lower than the corresponding wave numbers of the CH3 group, which allows different couplings. Some initial force constants were modified in order to obtain the experimental wave numbers and potential energy distribution (PED) of characteristic bands whose assignment is obvious in the three molecules [l] : FIv(CC)CF~AZF,I,
FhW’dI,
F(dW
FMCJMl,
CF1-CFal, fE~s(-',), UCF,)l, ~C&WWl -
f[4CF2)9
4-'2)Iw
The interaction constants f[v(CC), s(CF,)],, f[u,(CF,), 6 (CCC)] and f[r,! (CF3), 6 (CCC)] were set to zero because they had no effect on the frequencies or the potential energy distribution. By assuming F[6 (CCC)] = 1.76, as proposed for PTFE [5], the frequency calculated for S(CCC) (A,) of the three molecules is far lower than the experimental wave number: to obtain good agreement, it was necessary to
247 increase F[6 (CCC)]
to 1.98 and to introduce f[ui(CF,), 6 (CCC)], which allows the contribution of 6 (CCC) to the mode near 1385 cm-’ to be reduced. The band corresponding to the torsion around the central C-C bond of n-C4Flo is not observed. The wave number calculated with the force constant F[T(CC)], determined by Rabolt and Fanconi for P’I’FE [5], leads to a potential barrier of 2.09 kcal mol-‘. Bates and Stockmayer have calculated the conformational energies of the isolated n-C4FIo molecule with the help of a semiempirical potential; they considered the potential barrier to the internal rotation about the C--C bond, EO, as a parameter and then calculated the energy difference A.E between a slightly distorted planar conformation and a form with an internal rotational angle of 120” + 15” IlO, 111. When the value of AE is close to the value we measured previously in the gaseous state, 1210 + 120 cal mol-’ [ 11, E. falls between 1.5 and 2.8 kcal mol-I. Although I& is a parameter which does not take into account interactions between nonbonded atoms, its value can be compared to the above-calculated barrier and is consistent with a geometry of the gauche form having an internal rotation angle of about 120”. The approximate force field obtained is given in Table 1; the mean difTABLE
1
Force comtants Coordinate(s) involved
u,WF,) v;(CF,) u,(CF,) 6 ,(CF,) 6;(CF,l 6 ,WF,) rl, (CF,) QWF,) dCF,l
V(CC) l--2b Y(CC) 2-3 6 (CCC) s(CC) u,(CF,) u,(CF,) 6 (CF,) w (CF,) r(CF,) WF,) r(CF,), ua(CF,) [r(CF,), ua(CFz)I, iForce
Force con&ax@ 7.27 4.86 4.61 2.0 1.94 2.34 0.97 1.46 0.043 4.6 4.53 1.98 0.05 6.38 6.18 1.49 1.08 1.48 1.41 1.36 -0.1
Coordinate(s) involved
[r(CF,). r(CF,)I, r(CF,), HCF,) r(CF,), s,(CF,) r&F,), rl(CF,) 4C’3,-r u&F,) 4CC),,, 6,(‘=,) 4CC)z,, w (CF,) .(CC).. >6 (CF,) dCQ--l, uSWF,) c4ca WC)l, V(CC), 6 (CCC) [4CC), 6 (CCC)l, Im (CFz), 6 WCC)l, [w(CF,), 6WF,)l, Iw(CF,), wWF,)I, 6SF,), u&F,) 6 (CF,), 6 (CCC) v&F,), 6,WF,) QCF,), 6 (CCC) ua(CF,), 6,WF,) QGF,), WF,)
constant units: stretch, mdyn A 1 ;stretch-bend, Ps7
Force constanta -0.13 -0.09 0.17 0.37 0.9 -0.66 -0.38 -0.03 1.31 0.17 0.15 0.15 0.2 -0.1 -0.03 0.25 0.13 0.60 -0.76 -0.63 -0.38
mdyn rad* ; bend, mdyn A rad*.
248
ference between calculated and experimental frequencies is 8 cm-’ for n-C4Flo and about 13 cm-l for n-C6F14 and n-CsF1s. We did not try to improve the agreement by means of a refinement method because of the small amount of experimenM data compared to the number of force constants. Assignments Tables of the calculated frequencies and potential energy distributions are available on request [12]. Numerous normal modes involve several coordinates; the stretching vibrations v(CC) in particular are strongly coupled. The bands located between 1100 and 1400 cm-’ arise from the same motions in the three molecules: CFB stretching and bending, v(CC) and 6 (CCC) vibrations. The calculation indicates an increasing contribution of the last two motions with the lengthening of the chain in this hequency range, especially for the mode near 1385 cm-’ which no longer involves the CFB motions in C6 and CB molecules; the 1325 cm-’ frequency of these two compounds is due mainly to v’(CFB) and 6:(CF3). These observations can be compared with the values found in the literature: in C3F8 no contribution from 6 (CCC) is found in the modes calculated at frequencies higher than 1300 cm-’ [4]; in contrast, a high percentage of this movement has been calculated in the potential energy distribution of the modes at about 1380 and 1345 cm-’ for PTFE 1131. Only one B, vibration of n-perfluorohexane is calculated near 610 cm-‘, but two lines with close intensities are observed at 604 and 612 cm-’ (Fig. 1); they can arise from a Fermi resonance between the fundamental and the B, level [295(A,) + 313(B,) cm-‘] ; modification of the relative intensities of the two bands at the p-haze change agrees with the proposed assignment, since the 313 cm-l band intensity also varies. The bandwidth in the liquid spectrum can be due to the transitions of the other isomers. In the Raman spectrum of PTFE [14], two bands located near 600 cm-’ have been assigned to the same mode of two different conformations: the lower frequency band is associated with the regular helicoidal structure, the higher hequency one to planar defects; raising the temperature increases the relative intensity of the defect band. In the case of n-C6Fls, the evolution of the relative intensity of these bands is not concordant with this hypothesis; moreover, similar khaviour is not observed in the spectra of n-CsF1s. Finally, the frequency calculated for this mode is not modified by introducing one or two internal rotations of 15 to 120” around C-C bonds. Below 600 cm-l, fundamental transitions account for the most important bands. It should be noted that the addition of a CF2 group increases the wave number of the highest frequency mode involving r(CF*). Only one fundamental of A, symmetry and one of A, symmetry can be assigned to the bands of nCsFls at 358 and 348 cm -’ ; the intensity of the A, mode in the Raman spectrum can be explained by coupling, since these two vibrations are of A symmetry for a distorted molecule [l] .
249
630
600 crrrl
Fig. 1. Temperature 650
dependence
of
the
Raman
spectrum
of
n-C!,F,,
between
580
and
cm-‘.
Lengthening the chain modifies the frequencies near 290 and 200 cm-’ only little; for n-C4Fro, the first frequency has been assigned to a B, mode [l] ; corresponding PEDs are nearly the same for all three molecules. The potential barrier to rotation of the CF3 group in n-C4Flo estimated from the Raman B, frequency, 34 cm-‘, and the calculated A, wave number, 29 cm-‘, is 1376 cal mol-‘; this value is intermediate between 920 cal mol-’ found by Durig and Church for CF3COCH3 [15] and about 3500 cal mol-’ estimated by Pace and co-workers for CBFB [16-18 J SPECTRUM
OF THE
GAUCHE
ISOMERS
Our main purrose is to determine the structure of the non-frans isomers; we put forward the hypothesis that the frequency differences between the two forms are due essentially to the kinetic energy, as was assumed for ‘Lhe polymer [19], and applied the above approximate force field to different molecular conformations. n-Perfluorobu
tune
We have demonstrated that only two rotational isomers exist in either gaseous or liquid n-C4Flo [l]. The three geometries tested differed in the value of the dihedral angle C1C2C3, C2CSC4; this was set to be 15”, 105”,
250
120”, 135” and 165”. The results show that the frequencies are slightly modified by a rotation of 15”. The existence of an angle of 120” (+15’) is necessary to calculate the most characteristic experimental wave numbers of the gauche form, in particular those at 1354, 1064 and 958 cm-‘*. The frequencies of the stretching vibrations and those of the rL(CFJ) and r(CF,) modes are the most sensitive to molecular geometry. All the additional bands in the spectra of gaseous and liquid states are accounted for, except a few weak ones which probably arise from two energy levels. The largest disagreement between experimental and calculated frequencies is 11.6 cm-‘. Numerous couplings are also found for that isomer. Therefore, we assume that the less stable form of n-C4Flo has a gauche structure with an internal rotational angle of about 120°, in agreement with the minimum energy structure calculated by Bates and Stockmayer [lo, 111. n-Perfluorohexane
and n-perfluomoctane
The experimental study has shown that the rotation angle about a C-C bond is the same for all three n-perfluoroalkanes [l] ; thus, we assume that the possible structures for the gauche isomers of n-C6F14 and n-CsFls are combinations of the two bond configurations of nC4Flo. In order to determine the most probable geometries of the isomers, we have carried out a calculation of the statistical distribution probability for the isolated molecules 1201. The free energy difference between the trans (2’) and gauche (G) configurations of a bond was calculated for the two isomers of n-C4Fio in the gaseous state from the measured enthalpy difference, AHg [l] , and calculated entropies_ At 298 K, AG, is equal to -729 cal mol-l. This value was assigned to each gmtche rotation and the results are given in Table 2. n-Perfluomhexane Five gauche isomers are present in quantities above 4% at room temperature. The representations of their molecular vibrations are r
TTG
r
TGT
r
GTG’
=I? = --
TGG
r GTG
=54A =
28A + 26B
27~!, + 27A,
Only some frequency domains in the gas and the liquid spectra allow a qualitative discussion on the presence of one or severalgauche conformers. Whatever the isomer is, only one fundamental is expected and calculated between 1120 and 1000 cm-‘; only one is observed for the all-trans form (7’2’7’) at 1104 cm-l (B,); three other bands are seen in this frequency range *A table of calculated frequencies 120’ is available on request [ 121.
and PEDs of the isomer with a dihedral angle of
251 TABLE 2 Distribution of rotational
Compound
n-W,,
n-C,F,,
isomersin the gaseousstateat 298 X Isomer
Multiplicity
Percentage 29.6 32.9
TGT TGG GTG GTG’ TGG’ GGG GG’G GGG’
1 4 2 4 2 2 4 2 2 4
TTTTG TTTGT TTGTr GlTTG GTTTG’ TGTGT TGTG’T TTTGG TTGTG TTGGT TTG’ TG TG!Ki’G TGT!iW
1 4 4 2 2 2 2 2 4 4 4 4 4 4
TTG
aGG’ (G c G T) energy is taken to be 4-5
kcal
16.4 8.2 4.1 4.1 -0a 1.2 -0 -0 8.2 12.6 12.6 6.3 2.45 2.45 2.45 2.3 4.9 4.9 4.9 4.9 4.9 4.9
mol-’ [ 211.
in the IR spectrum of the amorphous state (Table 3). The one at 1073 cm-‘, which is observed in both the IR and the Raman spectra (very very weak) cannot come from a centrosymmetic structure, such as GTG’; because it is polarized in the Raman spectrum 1223, it is assigned to the TTG form, which is more abundant than TGG or GTG, since it would be of B symmetry for TGT (Table 3). The weak bands at 1054 and 1045 cm-‘, observed in the IR spectrum of the amorphous state, belong to a complex group of bands; they can come from the same mode of two other conformers. The relative intensity of these three absorptions agree with the proposed assignment. In the spectral domain 1000-910 cm-’ only one band (A,) exists for !ZY’T (977 cm”), and only one is calculated for each other isomer; it belongs to A symmetry for the TTG, TGT, TGG and GTG forms and to A, symmetry for GTG’. Two IR and Raman-active bands can be assigned to this mode: the higher frequency one at 992 cm-’ to TTG and the lower frequency one at 928 cm-’ to TGT, from the proximity of experimental and calculated frequencies and band intensities (Table 3). A very weak polarized Raman line at 961 cm-‘, which has no equivalent in the IR
252 TABLE
3
Proposed assignments for some bands of n-C,F,,
“& Ill (cm-l) lO”3
IR--R(P)
739 IR 730 IR-R 713 IR
isomers
Calculated frequencies (cm-) TTG
1054 IR 1045 IR 992 IR-R(P) 979 IR 928 961 R(P) IR-R(P) 863 IR 856 IR 818 IR-R 756 790 IR R
gauche
TGT
TGG
GTG
GTG’
1094 (B)
1076
1058(B) 967 (A)
1058 (Au)
1072 970 953 933
855
846 (B)
845 (A,)
769 (A)
770
770 (A)
770 (A,)
730 (B)
739 666
739 (B) 660 (A)
842 (B) 818 769 714 671
968 (A,)
(A)
738 (Au)
aIR frequencies (except those underlined, which refer to the Raman spectrum) of the amorphous state.
spectrum, comes perhaps from the same GTG’ mode calculated at 968 cm-‘. The rather intense IR band at 979 cm-‘, the calculated frequency of which is the same as for TTT, is probably due to TGG. One fundamental vibration is calculated for each isomer in the frequency raigt: 900-780 cm-‘; in addition to the absorptions assigned to the TTT isomer, a B, fundamental at 796 cm-’ and several combination bands, e.g. that at 830 cm-‘, two fairly intense bands at 818 and 856 cm-’ and a weak one at 863 cm-’ are observed in the IR spectrum; the one only 818 cm-l is seen in the Raman spectrum with a very weak intensity. The relative intensity variation of the bands at 818 and 856 cm-’ and of a band of the all-trans isomer as a function of temperature in the gaseous state is consistent with the presence of only one gaudhe bond in the molecule; comparison with calculated frequencies leads to an assignment of 818 cm-’ to TTG and 856 cm-’ to TGT. The other maximum may arise from the same mode, calculated at 845 cm-’ for GTG’ (A,) or 855 cm-l for TGG (A) (Table 3). Two vibrations of A, symmetry, 757 and 715 cm-‘, and one of B, symmetry, 719 cm-l, of the TTT form are located between 790 and 700 cm-‘; three fundamentals are expected in this frequency range for each isomer. Four bands or shoulders which could be due to gauche forms are observed in the IR spectrum, two only in the Raman spectrum. The highest frequency mode, of A, symmelzy for the all-trans form, is calculated at the same frequency for all the conformers; since it is at 757 cm-’ for TTT, the IR frequency of 756 cm-l is assigned to the same mode for all the conformers
except GTG’; indeed, the corresponding vibration of this latter form is not IR active and may give rise to the weak Reman line at 790 cm-‘. The weak absorption at 739 cm-’ which has no equivalent in the Reman spectrum can be assigned to an A, mode of the GTG’ form. This analysis confirms that at least three forms other than TTT exist in liquid and in gaseous n-CsF14; only the TTT isomer is present in both solids
111. n-Petiluorooctane
Based on a consideration of the calculated percentage of the isomers, only the gauche forms TTTTG, TTTGT and TTGTT are expected to show bands of a noticeable intensity in the spectrum of the gas (Table 2). As there is no evidence for the occurrence of new bands on going from the gas to the liquid, and as out force field is roughly approximate for the gauche isomers, we did not look for other forms in the condensed stems; for instance, we did not search for the presence of kinks (GT,,, 1 G’) as in molten alkanes. However, this possibility cannot be excluded. The vibrational representations of the above gauche isomers are r
T!MTG
r TTGT_T
=r =
T’ITGT
37A
=
72A
+ 35B
All the vibrations are IR and Reman active; the A ones are polarized in the Raman spectrum. We shall denote by (i), (ii) and (iii) those isomers present in the liquid which disappear when the temperature is decreased and tend towards the solids I, II and III, respectively. We discuss here only a few spectral domains, in which a small n-umber of fundarnent.al vibrations are expected for each isomer. In the 1110-950 cm-’ spectral range, two fundamental vibrations of the all-tralzs form, one of symmetry B, at 1006 cm-‘, the other of symmetry A, at 1103 cm-‘, are found; two modes are calculated for each isomer TTTTG, TTTGT and TTGTT, at 998 and 1076 cm-‘, 984 and 1089 cm-’ and 1019 and 1058 cm-‘, respectively, corresponding to the motions v(CC) and v,(CF,) coupled with w(CF,) for all three molecules. A polarized Reman line at 1077 cm-’ disappears at the liquid-solid I transition and belongs to the (i) isomer. The absorptions at 1078 and 1100 cm-’ vanish at the solid Isolid II and solid II-solid III transitions, respectively; they arise from the (ii) and (iii) forms. Between 950 and 830 cm-‘, only one A, band at 864 cm-’ exists in the spectrum of the all-tins isomer and only one vibration, IR - and Ramanactive, is expected for each conformer; the PED is the same for all the isomers. In addition to some very weak absorptions, two similarly intense bands at 882 and 833 cm-’ and a shoulder at 890 cm-’ are observed in the spectrum of the liquid or amorphous state; three poIerized Raman lines at 895 (weak), 883 and 834 cm-’ (very weak) correspond to them (Table 4);
254
TABLE 4 Proposed assignments for some bands of gauche range 900-600 cm*
““Lp Cl1
isomers of n-C,F,,
Calculated frequencies (cm*)
Assignment
(cm-‘) 895 883 834 780 753 748 745 741 730 722 712 706
TllTGT
IR-R(P) IR-R(P) IR-R(P) IR-R(P) R(P) (iii) IR (ii) R(P) (i) IR (i) IR (i) IR (i) R(P) (i) IR (ii)
(ii) (iii) (i) (ii)
aRaman frequencies (except liquid state.
within the frequency
884 884
877 877
784 764 764
788 763 763
lTGTT
854 (A)
762 795 701 674 672 674
(A) (8) (B) (B) (A)
673
those underlined, which refer to the IR spectrum) of the
band at 834 cm-’ vanishes at the liqui&solid transition in the two spectra and corresponds to the (i) isomer; the Raman line at 895 cm-’ no longer exists in the solid II spectrum and is due to the (ii) isomer; the intensity of the band at 883 cm-l decreases at every transition and becomes zero at the lowest temperature one, which leads us to attribute it to the (iii) form. These results can be compared with those of normal-mode calculations for the mode expected in this frequency interval: the frequencies obtained for TTTTG and TTTGT are close, 884 and 877 cm-‘, that for TTGTT being lower at 854 cm- I. This frequency difference exists in the experimental assignments and could suggest that the (i) form is TTGTT; polarization of the line at 834 cm-’ agrees with this interpretation. Four vibrations of the all-trans isomer, two of A, symmetry (749 and 725 cm-‘) and two of B, symmetry (769 and 708 cm-‘) are located betr ween 800 and 700 cm-‘. Many maxima exist in the IR and Raman spectra of the liquid and amorphous states in this frequency range. The polarized Raman line at 745 cm-l, the one at 712 cm-’ and three IR bands at 722, 730 and 741 cm-’ vanish on solidification and are assigned to the (i) isomer The line at 780 cm-’ disappears at the solid I-solid II transition and belongs to the (ii) form. Another polarized Raman line at 753 cm-’ is very ternperature dependent; its intensity decreases on passing to the solid state and becomes zero in the solid III spectrum and it can be assigned to the (iii) form. A weak absorption at 748 cm-’ and the band at 706 cm-l seem to disappear at the solid I-solid II tiansition.
the
The disappearance
of two polarized
Raman
lines at 140
and 165 cm-’
at
255
the liquid--solid transition agrees with the hypothesis that the (i) form has TTGTT structure, since two A vibrations having S(CCC) character (LAM modes) are calculated at 144 and 174 cm-’ only for this molecule. Moreover, the TTGTT geometry is the only one which allows one to calculate a normal mode at 104 cm-‘, thus accounting for the weak line at 103 cm-’ in the spectrum of the liquid at -23°C. Thus the spectra of the different physical states can be analysed using the hypothesis of the presence of the four statistically most abundant isomers in the gaseous and the liquid states. It is shown that one of these forms disappears at each transition; it is suggested that the isomer present in the liquid and which does not exist in the solid phases has the TTGTT structure; some of its bands can be assigned. The existence of a conformational disorder in the two solid phases which are stable above 190 and 200 K agrees with the high value of the transition entropy [ 231. ACKNOWLEDGEMENT
The authors discussions.
are grateful
to
Dr
C.
Garrigou-Lagrange for
helpful
REFERENCES 1 M. Campos-Vallette and M. Rey-Lafon, J. MoL Struct., 101 (1983) 23. 2 R. Grigorovici, A. Butucelea, V. E. Sahini and M. K. Dearmond, Rev. Roum. Chim., 21(1976) 965. 3 (a) G. A. Crowder, J. Fluorine Chea, 10 (1977) 241. (b) G. A Crowder and H. K. Mao, J. Mol. Struct., 18 (1973) 33. 4 H. Burger and G. Pawelke, Spectrochim. Acta, Part A, 35 (1979) 525. 5 J. F. Rabolt and B. Fanconi, Macromolecules, 11 (1978) 740. 6 L. Piseri, B. M. Powell and G. Dolling, J. Chem. Phys., 58 (1973) 158. 7 K. L. Gallaher, A Yokozeki and S. H. Bauer, J. Phys Chem., 78 (1974) 2389. 8 E. B. Wilson, Jr., J. C. Decius and P. Cross, Molecular Vibrations, McGraw-Hill (1955). 9 R. G. Snyder, J. Chem. Phys., 47 (1967) 1316. 10 T. W. Bates and W. H. Stockmayer, Am. Chem. Sot., Div. Polym. Chem., 7 (1966) 1137. 11 (a) T. W. Bates, Trans Faraday Sot., 63 (1967) 1825. (b)T. W. Bates and W. H. Stockmayer, J. Chem. Phys., 45 (1966) 2321. 12 Sup. Pub. No. 26268, (3 pages) available from the British Library Lending Division. 13 M. J. Hannon, F. J. Boerio and J. L. Koening, J. Chem. Phys., 50 (1969) 2829. 14 H. Tanaka and T. Takemura, Polym. J., 12 (1980) 355. 15 J. R. Durig and J. S. Church, Spectrochim Acta, Part A, 36 (1980) 957. 16 E. L. Pace, A. C. Plaush and H. V. Samuelson, Spectrochim. Acta, 22 (1966) 993. 17 E. L. Pace and A. C. Plaush, J. Chem. Phys, 47 (1967) 38. 18 J. H. Smith and E. L. Pace, J. Phys Chem., 73 (1969) 2368. 19 G. Zerbi and M. Sacchi, Macromolecules, 6 (1973) 692. 20 P. J. Flory and R. L. Jemigan, J. Chem. Phys, 42 (1965) 3509. 21 A E. Tonelli, Polymer, 17 (1976) 695. 22 P. Piaggio, P. G. Francese, G. Masetti and G. Dellepiane, J. Mol. Struct., 26 (1975) 421. 23M. Campos-Vallette, M. Rey-Lafon and R. Lagnier, Chem. Phys. Lett.. 69 (1982) 189.
MOLECULAR, STRUCTURE OF THE ROTATIONAL SHORT CHAIN n-PERFLUOROALKANES
M. CAMPOS-VALLElTE*
ISOMERS
IN
and M. REY-LAFON
Laborafoire de Spectroscopic Infmrouge, L.A. 124. Universitt? de Bordeaux I. 35I. cows de la Lib&ration, 33405 Talence Cddex (France) (Received 1 February 1984, in final form 3 April 1984)
ABSTRACT The structure of the isomers present in the different physical states of n-C,F,,,, is discussed, using previously published experimental data from and n-C,F,, n-C,F,, IR and Raman spectroscopy and an approximate force field. It is proposed that the gauche form of n-C,F,,, observed only in the gas and the liquid, is characterized by an internai rotational angle of about 120”. At least three non-trans forms exist in the gaseous and the liquid states of the C, compound, but they disappear in the crystal In contrast, the two solid phases of nC,F,, which are stable at high temperatures are disordered and contain one or two gauche isomers; only the lowest temperature one possesses the ahtmns form alone. INTRODUCTION
In a previous paper [l], we have shown the existence of conformational equilibria in the gaseous and the liquid states of n-perfluorobutane, nperfluorohexane and n-perfluorooctane and in some solid phases of the latter, using IR and Raman spectroscopy. We were able to demonstrate that the isomer which is present in the low-temperature solid phase is an all-trans one; it is slightly distorted from planarity for the C6 and Cs compounds. In addition, n-C4Flo was found to possess only two forms. However, we were unable to propose a structure for the isomers; we could only suggest that the internal rotational angle characteristic of the non-trans form of n-&Fro (the “‘gauche” form) is about 120”, on the basis of the magnitude of some frequency shifts for the same vibration of the two isomers and the value of the enthalpy difference between the two structures in the gaseous state In the present work, we propose an interpretation of the vibrational spectra of the all-Pans forms, using normal coordinate calculation, and we discuss the geometry of the other conformers present in the different phases of the three molecules.
*Present address: Facultad de Ciencias Basicas y Fannaceuticas, Casiiia 653, Santiago, Chile. 0022-2860/84/$03.00
o 1984 Elsevier Science Publishers B.V.
Universitad de Chile,
246 NORMAL
COORDINATE
TREATMENT
OF THE ALCTRANS
FORMS
Normal-mode calculations have been carried out for short fluorinated molecules 12-41 and for the polymer PTFE [see, e.g., 5, S] but none has been published for the n-perfluoroalkane series. Therefore we have tried to obtain approximate force constants which account for the experimental results relative to the all-trans isomers of the three molecules nC,FIO, n-C6F14 and nC8FIs [l]. Structure
and coordinates
As the structure of these compounds is not known, we have taken the following bond lengths from electron diffraction measurements on CzF6 [7]: C-F = 1.326 A, C-C = 1.545 A; all angles are assumed to be tetrahedral and the symmetry group is C?h. Local symmetry coordinates, allowing a direct comparison with experimental results, are used: they are symmetry coordinates of the CFB groups and linear combinations of internal coordinates identical to those used by Rabolt and Fanconi [5] for the CF2 groups. Torsional coordinates are defined as the sum of all the dihedral angles involved. Force field The calculation is carried out using the method of Wilson et al. [S] and a valence force field. As the number of experimental frequencies was not sufficient to build up a force field, we took the force constants from the literature for the CFB groups [2-41 and from the force field proposed for PTFE by Rabolt and Fanconi [5] for the CF2 groups and the carbon skeleton. The initial force field is written using the same approximation as the kinetic energy, i.e. interactions between vibrations not involving a common atom are assumed to be zero. We added some interaction constants which exist in the force field of the n-alkanes [9] and two others involving CFB stretching or bending vibrations: in fact the frequencies of these modes are lower than the corresponding wave numbers of the CH3 group, which allows different couplings. Some initial force constants were modified in order to obtain the experimental wave numbers and potential energy distribution (PED) of characteristic bands whose assignment is obvious in the three molecules [l] : FIv(CC)CF~AZF,I,
FhW’dI,
F(dW
FMCJMl,
CF1-CFal, fE~s(-',), UCF,)l, ~C&WWl -
f[4CF2)9
4-'2)Iw
The interaction constants f[v(CC), s(CF,)],, f[u,(CF,), 6 (CCC)] and f[r,! (CF3), 6 (CCC)] were set to zero because they had no effect on the frequencies or the potential energy distribution. By assuming F[6 (CCC)] = 1.76, as proposed for PTFE [5], the frequency calculated for S(CCC) (A,) of the three molecules is far lower than the experimental wave number: to obtain good agreement, it was necessary to
247 increase F[6 (CCC)]
to 1.98 and to introduce f[ui(CF,), 6 (CCC)], which allows the contribution of 6 (CCC) to the mode near 1385 cm-’ to be reduced. The band corresponding to the torsion around the central C-C bond of n-C4Flo is not observed. The wave number calculated with the force constant F[T(CC)], determined by Rabolt and Fanconi for P’I’FE [5], leads to a potential barrier of 2.09 kcal mol-‘. Bates and Stockmayer have calculated the conformational energies of the isolated n-C4FIo molecule with the help of a semiempirical potential; they considered the potential barrier to the internal rotation about the C--C bond, EO, as a parameter and then calculated the energy difference A.E between a slightly distorted planar conformation and a form with an internal rotational angle of 120” + 15” IlO, 111. When the value of AE is close to the value we measured previously in the gaseous state, 1210 + 120 cal mol-’ [ 11, E. falls between 1.5 and 2.8 kcal mol-I. Although I& is a parameter which does not take into account interactions between nonbonded atoms, its value can be compared to the above-calculated barrier and is consistent with a geometry of the gauche form having an internal rotation angle of about 120”. The approximate force field obtained is given in Table 1; the mean difTABLE
1
Force comtants Coordinate(s) involved
u,WF,) v;(CF,) u,(CF,) 6 ,(CF,) 6;(CF,l 6 ,WF,) rl, (CF,) QWF,) dCF,l
V(CC) l--2b Y(CC) 2-3 6 (CCC) s(CC) u,(CF,) u,(CF,) 6 (CF,) w (CF,) r(CF,) WF,) r(CF,), ua(CF,) [r(CF,), ua(CFz)I, iForce
Force con&ax@ 7.27 4.86 4.61 2.0 1.94 2.34 0.97 1.46 0.043 4.6 4.53 1.98 0.05 6.38 6.18 1.49 1.08 1.48 1.41 1.36 -0.1
Coordinate(s) involved
[r(CF,). r(CF,)I, r(CF,), HCF,) r(CF,), s,(CF,) r&F,), rl(CF,) 4C’3,-r u&F,) 4CC),,, 6,(‘=,) 4CC)z,, w (CF,) .(CC).. >6 (CF,) dCQ--l, uSWF,) c4ca WC)l, V(CC), 6 (CCC) [4CC), 6 (CCC)l, Im (CFz), 6 WCC)l, [w(CF,), 6WF,)l, Iw(CF,), wWF,)I, 6SF,), u&F,) 6 (CF,), 6 (CCC) v&F,), 6,WF,) QCF,), 6 (CCC) ua(CF,), 6,WF,) QGF,), WF,)
constant units: stretch, mdyn A 1 ;stretch-bend, Ps7
Force constanta -0.13 -0.09 0.17 0.37 0.9 -0.66 -0.38 -0.03 1.31 0.17 0.15 0.15 0.2 -0.1 -0.03 0.25 0.13 0.60 -0.76 -0.63 -0.38
mdyn rad* ; bend, mdyn A rad*.
248
ference between calculated and experimental frequencies is 8 cm-’ for n-C4Flo and about 13 cm-l for n-C6F14 and n-CsF1s. We did not try to improve the agreement by means of a refinement method because of the small amount of experimenM data compared to the number of force constants. Assignments Tables of the calculated frequencies and potential energy distributions are available on request [12]. Numerous normal modes involve several coordinates; the stretching vibrations v(CC) in particular are strongly coupled. The bands located between 1100 and 1400 cm-’ arise from the same motions in the three molecules: CFB stretching and bending, v(CC) and 6 (CCC) vibrations. The calculation indicates an increasing contribution of the last two motions with the lengthening of the chain in this hequency range, especially for the mode near 1385 cm-’ which no longer involves the CFB motions in C6 and CB molecules; the 1325 cm-’ frequency of these two compounds is due mainly to v’(CFB) and 6:(CF3). These observations can be compared with the values found in the literature: in C3F8 no contribution from 6 (CCC) is found in the modes calculated at frequencies higher than 1300 cm-’ [4]; in contrast, a high percentage of this movement has been calculated in the potential energy distribution of the modes at about 1380 and 1345 cm-’ for PTFE 1131. Only one B, vibration of n-perfluorohexane is calculated near 610 cm-‘, but two lines with close intensities are observed at 604 and 612 cm-’ (Fig. 1); they can arise from a Fermi resonance between the fundamental and the B, level [295(A,) + 313(B,) cm-‘] ; modification of the relative intensities of the two bands at the p-haze change agrees with the proposed assignment, since the 313 cm-l band intensity also varies. The bandwidth in the liquid spectrum can be due to the transitions of the other isomers. In the Raman spectrum of PTFE [14], two bands located near 600 cm-’ have been assigned to the same mode of two different conformations: the lower frequency band is associated with the regular helicoidal structure, the higher hequency one to planar defects; raising the temperature increases the relative intensity of the defect band. In the case of n-C6Fls, the evolution of the relative intensity of these bands is not concordant with this hypothesis; moreover, similar khaviour is not observed in the spectra of n-CsF1s. Finally, the frequency calculated for this mode is not modified by introducing one or two internal rotations of 15 to 120” around C-C bonds. Below 600 cm-l, fundamental transitions account for the most important bands. It should be noted that the addition of a CF2 group increases the wave number of the highest frequency mode involving r(CF*). Only one fundamental of A, symmetry and one of A, symmetry can be assigned to the bands of nCsFls at 358 and 348 cm -’ ; the intensity of the A, mode in the Raman spectrum can be explained by coupling, since these two vibrations are of A symmetry for a distorted molecule [l] .
249
630
600 crrrl
Fig. 1. Temperature 650
dependence
of
the
Raman
spectrum
of
n-C!,F,,
between
580
and
cm-‘.
Lengthening the chain modifies the frequencies near 290 and 200 cm-’ only little; for n-C4Fro, the first frequency has been assigned to a B, mode [l] ; corresponding PEDs are nearly the same for all three molecules. The potential barrier to rotation of the CF3 group in n-C4Flo estimated from the Raman B, frequency, 34 cm-‘, and the calculated A, wave number, 29 cm-‘, is 1376 cal mol-‘; this value is intermediate between 920 cal mol-’ found by Durig and Church for CF3COCH3 [15] and about 3500 cal mol-’ estimated by Pace and co-workers for CBFB [16-18 J SPECTRUM
OF THE
GAUCHE
ISOMERS
Our main purrose is to determine the structure of the non-frans isomers; we put forward the hypothesis that the frequency differences between the two forms are due essentially to the kinetic energy, as was assumed for ‘Lhe polymer [19], and applied the above approximate force field to different molecular conformations. n-Perfluorobu
tune
We have demonstrated that only two rotational isomers exist in either gaseous or liquid n-C4Flo [l]. The three geometries tested differed in the value of the dihedral angle C1C2C3, C2CSC4; this was set to be 15”, 105”,
250
120”, 135” and 165”. The results show that the frequencies are slightly modified by a rotation of 15”. The existence of an angle of 120” (+15’) is necessary to calculate the most characteristic experimental wave numbers of the gauche form, in particular those at 1354, 1064 and 958 cm-‘*. The frequencies of the stretching vibrations and those of the rL(CFJ) and r(CF,) modes are the most sensitive to molecular geometry. All the additional bands in the spectra of gaseous and liquid states are accounted for, except a few weak ones which probably arise from two energy levels. The largest disagreement between experimental and calculated frequencies is 11.6 cm-‘. Numerous couplings are also found for that isomer. Therefore, we assume that the less stable form of n-C4Flo has a gauche structure with an internal rotational angle of about 120°, in agreement with the minimum energy structure calculated by Bates and Stockmayer [lo, 111. n-Perfluorohexane
and n-perfluomoctane
The experimental study has shown that the rotation angle about a C-C bond is the same for all three n-perfluoroalkanes [l] ; thus, we assume that the possible structures for the gauche isomers of n-C6F14 and n-CsFls are combinations of the two bond configurations of nC4Flo. In order to determine the most probable geometries of the isomers, we have carried out a calculation of the statistical distribution probability for the isolated molecules 1201. The free energy difference between the trans (2’) and gauche (G) configurations of a bond was calculated for the two isomers of n-C4Fio in the gaseous state from the measured enthalpy difference, AHg [l] , and calculated entropies_ At 298 K, AG, is equal to -729 cal mol-l. This value was assigned to each gmtche rotation and the results are given in Table 2. n-Perfluomhexane Five gauche isomers are present in quantities above 4% at room temperature. The representations of their molecular vibrations are r
TTG
r
TGT
r
GTG’
=I? = --
TGG
r GTG
=54A =
28A + 26B
27~!, + 27A,
Only some frequency domains in the gas and the liquid spectra allow a qualitative discussion on the presence of one or severalgauche conformers. Whatever the isomer is, only one fundamental is expected and calculated between 1120 and 1000 cm-‘; only one is observed for the all-trans form (7’2’7’) at 1104 cm-l (B,); three other bands are seen in this frequency range *A table of calculated frequencies 120’ is available on request [ 121.
and PEDs of the isomer with a dihedral angle of
251 TABLE 2 Distribution of rotational
Compound
n-W,,
n-C,F,,
isomersin the gaseousstateat 298 X Isomer
Multiplicity
Percentage 29.6 32.9
TGT TGG GTG GTG’ TGG’ GGG GG’G GGG’
1 4 2 4 2 2 4 2 2 4
TTTTG TTTGT TTGTr GlTTG GTTTG’ TGTGT TGTG’T TTTGG TTGTG TTGGT TTG’ TG TG!Ki’G TGT!iW
1 4 4 2 2 2 2 2 4 4 4 4 4 4
TTG
aGG’ (G c G T) energy is taken to be 4-5
kcal
16.4 8.2 4.1 4.1 -0a 1.2 -0 -0 8.2 12.6 12.6 6.3 2.45 2.45 2.45 2.3 4.9 4.9 4.9 4.9 4.9 4.9
mol-’ [ 211.
in the IR spectrum of the amorphous state (Table 3). The one at 1073 cm-‘, which is observed in both the IR and the Raman spectra (very very weak) cannot come from a centrosymmetic structure, such as GTG’; because it is polarized in the Raman spectrum 1223, it is assigned to the TTG form, which is more abundant than TGG or GTG, since it would be of B symmetry for TGT (Table 3). The weak bands at 1054 and 1045 cm-‘, observed in the IR spectrum of the amorphous state, belong to a complex group of bands; they can come from the same mode of two other conformers. The relative intensity of these three absorptions agree with the proposed assignment. In the spectral domain 1000-910 cm-’ only one band (A,) exists for !ZY’T (977 cm”), and only one is calculated for each other isomer; it belongs to A symmetry for the TTG, TGT, TGG and GTG forms and to A, symmetry for GTG’. Two IR and Raman-active bands can be assigned to this mode: the higher frequency one at 992 cm-’ to TTG and the lower frequency one at 928 cm-’ to TGT, from the proximity of experimental and calculated frequencies and band intensities (Table 3). A very weak polarized Raman line at 961 cm-‘, which has no equivalent in the IR
252 TABLE
3
Proposed assignments for some bands of n-C,F,,
“& Ill (cm-l) lO”3
IR--R(P)
739 IR 730 IR-R 713 IR
isomers
Calculated frequencies (cm-) TTG
1054 IR 1045 IR 992 IR-R(P) 979 IR 928 961 R(P) IR-R(P) 863 IR 856 IR 818 IR-R 756 790 IR R
gauche
TGT
TGG
GTG
GTG’
1094 (B)
1076
1058(B) 967 (A)
1058 (Au)
1072 970 953 933
855
846 (B)
845 (A,)
769 (A)
770
770 (A)
770 (A,)
730 (B)
739 666
739 (B) 660 (A)
842 (B) 818 769 714 671
968 (A,)
(A)
738 (Au)
aIR frequencies (except those underlined, which refer to the Raman spectrum) of the amorphous state.
spectrum, comes perhaps from the same GTG’ mode calculated at 968 cm-‘. The rather intense IR band at 979 cm-‘, the calculated frequency of which is the same as for TTT, is probably due to TGG. One fundamental vibration is calculated for each isomer in the frequency raigt: 900-780 cm-‘; in addition to the absorptions assigned to the TTT isomer, a B, fundamental at 796 cm-’ and several combination bands, e.g. that at 830 cm-‘, two fairly intense bands at 818 and 856 cm-’ and a weak one at 863 cm-’ are observed in the IR spectrum; the one only 818 cm-l is seen in the Raman spectrum with a very weak intensity. The relative intensity variation of the bands at 818 and 856 cm-’ and of a band of the all-trans isomer as a function of temperature in the gaseous state is consistent with the presence of only one gaudhe bond in the molecule; comparison with calculated frequencies leads to an assignment of 818 cm-’ to TTG and 856 cm-’ to TGT. The other maximum may arise from the same mode, calculated at 845 cm-’ for GTG’ (A,) or 855 cm-l for TGG (A) (Table 3). Two vibrations of A, symmetry, 757 and 715 cm-‘, and one of B, symmetry, 719 cm-l, of the TTT form are located between 790 and 700 cm-‘; three fundamentals are expected in this frequency range for each isomer. Four bands or shoulders which could be due to gauche forms are observed in the IR spectrum, two only in the Raman spectrum. The highest frequency mode, of A, symmelzy for the all-trans form, is calculated at the same frequency for all the conformers; since it is at 757 cm-’ for TTT, the IR frequency of 756 cm-l is assigned to the same mode for all the conformers
except GTG’; indeed, the corresponding vibration of this latter form is not IR active and may give rise to the weak Reman line at 790 cm-‘. The weak absorption at 739 cm-’ which has no equivalent in the Reman spectrum can be assigned to an A, mode of the GTG’ form. This analysis confirms that at least three forms other than TTT exist in liquid and in gaseous n-CsF14; only the TTT isomer is present in both solids
111. n-Petiluorooctane
Based on a consideration of the calculated percentage of the isomers, only the gauche forms TTTTG, TTTGT and TTGTT are expected to show bands of a noticeable intensity in the spectrum of the gas (Table 2). As there is no evidence for the occurrence of new bands on going from the gas to the liquid, and as out force field is roughly approximate for the gauche isomers, we did not look for other forms in the condensed stems; for instance, we did not search for the presence of kinks (GT,,, 1 G’) as in molten alkanes. However, this possibility cannot be excluded. The vibrational representations of the above gauche isomers are r
T!MTG
r TTGT_T
=r =
T’ITGT
37A
=
72A
+ 35B
All the vibrations are IR and Reman active; the A ones are polarized in the Raman spectrum. We shall denote by (i), (ii) and (iii) those isomers present in the liquid which disappear when the temperature is decreased and tend towards the solids I, II and III, respectively. We discuss here only a few spectral domains, in which a small n-umber of fundarnent.al vibrations are expected for each isomer. In the 1110-950 cm-’ spectral range, two fundamental vibrations of the all-tralzs form, one of symmetry B, at 1006 cm-‘, the other of symmetry A, at 1103 cm-‘, are found; two modes are calculated for each isomer TTTTG, TTTGT and TTGTT, at 998 and 1076 cm-‘, 984 and 1089 cm-’ and 1019 and 1058 cm-‘, respectively, corresponding to the motions v(CC) and v,(CF,) coupled with w(CF,) for all three molecules. A polarized Reman line at 1077 cm-’ disappears at the liquid-solid I transition and belongs to the (i) isomer. The absorptions at 1078 and 1100 cm-’ vanish at the solid Isolid II and solid II-solid III transitions, respectively; they arise from the (ii) and (iii) forms. Between 950 and 830 cm-‘, only one A, band at 864 cm-’ exists in the spectrum of the all-tins isomer and only one vibration, IR - and Ramanactive, is expected for each conformer; the PED is the same for all the isomers. In addition to some very weak absorptions, two similarly intense bands at 882 and 833 cm-’ and a shoulder at 890 cm-’ are observed in the spectrum of the liquid or amorphous state; three poIerized Raman lines at 895 (weak), 883 and 834 cm-’ (very weak) correspond to them (Table 4);
254
TABLE 4 Proposed assignments for some bands of gauche range 900-600 cm*
““Lp Cl1
isomers of n-C,F,,
Calculated frequencies (cm*)
Assignment
(cm-‘) 895 883 834 780 753 748 745 741 730 722 712 706
TllTGT
IR-R(P) IR-R(P) IR-R(P) IR-R(P) R(P) (iii) IR (ii) R(P) (i) IR (i) IR (i) IR (i) R(P) (i) IR (ii)
(ii) (iii) (i) (ii)
aRaman frequencies (except liquid state.
within the frequency
884 884
877 877
784 764 764
788 763 763
lTGTT
854 (A)
762 795 701 674 672 674
(A) (8) (B) (B) (A)
673
those underlined, which refer to the IR spectrum) of the
band at 834 cm-’ vanishes at the liqui&solid transition in the two spectra and corresponds to the (i) isomer; the Raman line at 895 cm-’ no longer exists in the solid II spectrum and is due to the (ii) isomer; the intensity of the band at 883 cm-l decreases at every transition and becomes zero at the lowest temperature one, which leads us to attribute it to the (iii) form. These results can be compared with those of normal-mode calculations for the mode expected in this frequency interval: the frequencies obtained for TTTTG and TTTGT are close, 884 and 877 cm-‘, that for TTGTT being lower at 854 cm- I. This frequency difference exists in the experimental assignments and could suggest that the (i) form is TTGTT; polarization of the line at 834 cm-’ agrees with this interpretation. Four vibrations of the all-trans isomer, two of A, symmetry (749 and 725 cm-‘) and two of B, symmetry (769 and 708 cm-‘) are located betr ween 800 and 700 cm-‘. Many maxima exist in the IR and Raman spectra of the liquid and amorphous states in this frequency range. The polarized Raman line at 745 cm-l, the one at 712 cm-’ and three IR bands at 722, 730 and 741 cm-’ vanish on solidification and are assigned to the (i) isomer The line at 780 cm-’ disappears at the solid I-solid II transition and belongs to the (ii) form. Another polarized Raman line at 753 cm-’ is very ternperature dependent; its intensity decreases on passing to the solid state and becomes zero in the solid III spectrum and it can be assigned to the (iii) form. A weak absorption at 748 cm-’ and the band at 706 cm-l seem to disappear at the solid I-solid II tiansition.
the
The disappearance
of two polarized
Raman
lines at 140
and 165 cm-’
at
255
the liquid--solid transition agrees with the hypothesis that the (i) form has TTGTT structure, since two A vibrations having S(CCC) character (LAM modes) are calculated at 144 and 174 cm-’ only for this molecule. Moreover, the TTGTT geometry is the only one which allows one to calculate a normal mode at 104 cm-‘, thus accounting for the weak line at 103 cm-’ in the spectrum of the liquid at -23°C. Thus the spectra of the different physical states can be analysed using the hypothesis of the presence of the four statistically most abundant isomers in the gaseous and the liquid states. It is shown that one of these forms disappears at each transition; it is suggested that the isomer present in the liquid and which does not exist in the solid phases has the TTGTT structure; some of its bands can be assigned. The existence of a conformational disorder in the two solid phases which are stable above 190 and 200 K agrees with the high value of the transition entropy [ 231. ACKNOWLEDGEMENT
The authors discussions.
are grateful
to
Dr
C.
Garrigou-Lagrange for
helpful
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