Investigation of pretransition phenomena in organic crystals by vibrational spectroscopy

Investigation of pretransition phenomena in organic crystals by vibrational spectroscopy

Journal of Molecular Structure, Elsevier Science Publishers 216 (1990) 91-103 B.V., Amsterdam - Printed 91 in The Netherlands INVESTIGATION OF P...

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of Molecular


Elsevier Science Publishers

216 (1990) 91-103 B.V., Amsterdam - Printed

91 in The Netherlands







of Sciences,


Troitsk, Moscow

region, 142092



10 April 1989)

ABSTRACT Some examples illustrate the efficiency of the investigation of reorientational molecular motion and order-disorder phenomena in organic crystals near their points of phase transition and melting by the temperature dependence of low-frequency vibrational spectra combined with simultaneous calculations of the lattice dynamics by the atom-atom potential method.


Because of their negligible intermolecular interactions, organic crystals are extremely rich in polymorphic modifications and disordered states, e.g. statically and conformationally disordered states, liquid and plastic crystals and so on. Processes occurring in a crystal as it approaches the melting point are to a great extent a display of the single complicated process of crystal melting [ 11. As shown in ref. 2, the inclusion in statistical models of molecular crystal melting of anisotropic molecular reorientations with two different barriers u1 and u2 ( u1 < u,) and with the number of allowed orientations D, and D, respectively, leads to one or two phase transitions (depending on the relationship between the model parameters) induced by the orientational melting, and to a phase transition with positional disordering of molecules. For sufficiently large &, three cases can occur depending on u2: activation of anisotropic reorientations of molecules just at the ordered phase and subsequent melting; activation of reorientations only with small barriers u1 leading to one-dimensional plastic crystal; sequential reorientational activation of molecules with different barriers leading to two plastic phases with different degrees of disorder. Changes in the molecular orientational mobility and the stage-by-stage “melting” of the rotational degrees of freedom can be seen in the low-frequency vibrational spectra, because random molecular reorientations between allowed minima of the crystal potential create, in general, irregular oriented molecules


0 1990 Elsevier Science Publishers



which are the source of dephasing and distortion of the correlated external vibrations of molecules. This paper presents a study of low-frequency Raman spectra in a wide temperature range including the closest vicinity of phase transition points for different cases of orientational phase transitions of both plastic crystals and crystals lacking mesophases. For interpretation of spectral data and extraction of the necessary information from them, calculations of frequencies, normal-mode coordinates and relative Raman line intensities were made using atom-atom potentials (6-exp ) (with Williams parameters [ 3,4] ) and the oriented gas approximation [ 5,6]. EXPERIMENTAL

The Raman spectra were measured by means of DFS-12 and DFS-24 spectrometers using 4416 A and 5145 A excitation lines from He-Cd and Ar+ lasers. The observed frequencies are believed to be accurate to within ? 1 cm-‘. For the study of point of phase transition and melting point we used a specially designed optical cell which provided heating of the sample at a rate of l-2 K h-l, and allowed its temperature to be maintained within + 0.01 K. The time taken for sample equilibration at each temperature was 20-30 min. RESULTS AND DISCUSSION

Thiophene Solid thiophene exists in four forms with transition points at 112 K (IVIII), 138 K (III-II), and 171 K (I-II) [ 71. The temperature dependence (77260 K) of the Raman spectra of polycrystalline thiophene is shown in Figs. 1 and 2. The spectrum of the low-temperature phase IV, the lines of which are the most distinct, is typical for “rigid” ordered crystals. The most intense line (54 cm-‘) in the thiophene IV Raman spectrum broadens faster than the others as the crystal approaches its IV-III transition point (Fig. 2)) its intensity decreases and finally it disappears totally from the spectrum in the narrow temperature range of 1 K. The absence of structural data preclude the calculation and reliable assignment of the phonon spectrum, but it may be assumed that this anomalous temperature dependence is connected with the appreciable molecular mobility observed in the NMR spectra of phase IV at 20 K before the IV-III transition [ 71. In this case the 54 cm-l line can be assigned to the thiophene molecular libration around the axis perpendicular to the molecular plane presenting the most probable reorientations. Thus the IV-III phase transition is accompanied by the beginning of the thiophene molecular reorientations in its plane and leads to the formation of a one-dimensional plastic crystal. Subsequent transitions are, apparently, accompanied only by fur-


\ 80

160 vkr


8% 160 v(cm-



Fig. 1. Raman spectra of external modes for four crystalline phases of thiophene: 85 K, phase IV; 128 K, phase III; 158 K, phase II; 213 and 234 K, phase I. Fig. 2. Temperature dependence of the Raman line 54 cm-’ in the vicinity of phase transition IV-III of thiophene.

ther increase of the anisotropic orientational mobility of molecules. This assumption is confirmed by small values of transition entropies [ 71 and slight changes of Raman (Fig. 1) and FIR-absorption [ 81 spectra. Our conclusion about the step-by-step increase of the molecular orientational mobility, which accompanies phase transitions IV-III-II-I in thiophene, was confirmed by Andre et al. [9] who showed on the basis of X-ray studies that in thiophene I orientational jumps around the axis perpendicular to the molecular plane are possible between twenty equivalent orientations, while in thiophene II they are possible only between ten equivalent orientations. Benzene and cyclohexane In solid benzene (space group Pbca, z = 4 [lo] ) and in the low-temperature crystal phase II of cyclohexane (space group C2/c, z = 4 [ 111) NMR data [ 12, 131 indicate the activation of reorientational motion at 110 K and 150 K, which is much lower than both the melting point of benzene (278.5 K) and the point of phase transition of cyclohexane to the plastic phase I (186 K). The barriers of reorientation around molecular axes C, (benzene) and C, (cyclohexane )


calculated by means of atom-atom potentials reach 3.2 and 4.5 kcal mol-l, and demonstrate reasonable agreement with experimental values [ 12,131. If the high molecular symmetries of benzene (DSh) and cyclohexane (D,,) are insignificantly disturbed in the solid state, the molecular jumps from one orientation to others around the U axis (C, and C, axes of free molecules) do not lead to irregularly oriented molecules (allowed orientations will be thermodynamically indistinguishable). Moreover since the polarizability tensor of such highly symmetric molecules is


( ) allo








where cylland cryIare the polarizabilities along the high-symmetry molecular axis U and those axes perpendicular to it (V and W), then the molecular librations around the U axis give zero contribution (within the bounds of the oriented gas approximation) to the intensity of Raman lines [ 141. Thus it would be expected that anisotropic orientational motion of the highly-symmetric molecules will not be manifested in the Raman spectrum. This takes place for benzene crystal the spectrum of which, calculated with the help of atom-atom potential and oriented gas models and assuming molecular symmetry Dsh ( y= 0) (Table 1, Fig. 3)) coincides very well with the experimental spectrum (Fig. 3). Accordingly the 57 cm-l line (140 K) which refers to the normal-mode vibration with the predominant participation of molecular libration around the U axis (Table 1) is observed in the spectrum up to the melting point (Fig. 3). However, for cyclohexane II satisfactory coincidence between calculation and experiment was obtained only for y=O.9 (Fig. 4), i.e. the symmetry of cyclohexane molecules is essentially lowered in phase II by the crystal field and their allowed orientations become thermodynamically distinguishable. In the Raman spectrum the lines 69 (A,) and 92 (B,) cm-l referred to the normal-mode vibrations around the Uaxis (Table 2) coinciding with the direction of reorientational motion broaden and their intensities decrease faster than those of others, with increase of temperature; at 20-30 K before the point of transition to the plastic state they become practically unobservable (Fig. 5 1. These results demonstrate convincingly that some types of thermodynamically distinguishable molecular reorientations (the “melting” of rotational degrees of freedom) can be activated just in the anisotropic phase long before the transition to the plastic modification and that they may be revealed by the temperature dependence of the low-frequency Raman spectrum.



Raman active external modes of benzene crystal Symmetry



B 2z

Line (cm-‘)




(140 K)

(140 K)






- 0.600

0.050 0.810


0.546 0.714


78 46



128 100

139 95

- 0.484


0.865 0.447




- 0.233 0.963


- 0.038




92 a4

- 0.057 0.215



84 62



93 78

V3 V4

V7 90

V8 V9

“L, librations


0.416 -0.036

0.864 0.141

around molecular axes of inertia moments:


-0.219 -0.414 0.884

- 0.453



0.283 0.355

0.823 - 0.567




IV= I,.







120 vkm')



Fig. 3. Raman spectra of benzene crystal: calculated spectrum).


(a) single crystal, (b) polycrystals

(dashed line is the


Fig. 4. Observed (solid line ) and calculated I&man spectra of cyclohexane II polycrystals for (a ) y=O.9 and (b) y=O. TABLE 2 Baman active external modes of cyclohexane II crystal”


Exp (115 K)

Calc. (115 K)





110 85 69

102 86 61

-0.268 0.527 0.807

0.939 - 0.044 0.341

0.215 0.849 - 0.483

V4 V5 %

120 92 62

125 98 59

-0.071 0.879 0.472

-0.246 0.474 0.845

0.967 - 0.056 0.250





Line (cm-‘)


“Inertia moments: Iu> Iv= Zw

Naphtha&e Analogous changes of Raman spectra were observed in the case of solid naphthalene [ 161 (space group P2,/a, z = 2 [ 151)) for which no phase transitions to the orientationally disordered states have previously been detected. The temperature dependence of Raman spectra of a single crystal measured in polarized light in the closest vicinity of the melting point (354 K) are shown in Fig. 6. One can see that the 109 (A,) and 125 (B,) cm-l lines are decreased in intensity and broaden much faster than other Raman lines. Near the melting point they are fully smeared into the Rayleigh line wing. The disappearance


Fig. 5. Temperature dependence of Raman spectra of cyclohexane II and deuterocyclohexane II

Fig. 6. Temperature dependence of the external F&man spectra of naphthalene single crystal near the melting point.

of both lines happens in the temperature interval -0.3 K. Beyond 0.25 K to the melting point these lines become practically unobservable, whereas the other lines are clearly observed. As the temperature decreases from 353.8 K to 353.6 K the 109 and 125 cm-’ lines reappear in the spectrum.


The experiment was repeated with two single crystal specimens in four crystal orientations with excellent reproducibility. The disappearance of the 109 and 125 cm-’ lines in the premelting region is not connected with the presence of impurities or with the probable imperfections of single crystals because it was also observed in the Raman spectra of polycrystals and naphthalene-/3naphthol solid solutions (Fig. 7). According to the normal-mode calculations (Table 3) the 109 and 125 cm-’ lines correspond to the v5 and v6 librations of molecules around their axis of smallest inertia moment ( W). Thus we can say that the premelting region of naphthalene is characterized by disordering of the molecular orientations around the W axis similar to that which occurred at the crystal to plastic phase transitions of thiophene and cyclohexane. It should be noted that this conclusion cannot be made merely on the basis of a simple calculation of orientational barriers around the molecular axis [ 141. Such a calculation at 300 K [ 161, i.e. long before the melting temperature, predicts the smallest reorientational barrier around the other molecular axis U to be 30 kcal mol-l. The presence of some subtransition near the melting point of the naphthalene crystal is confirmed by the existence of maxima on melting and solidifying DTA curves [ 171 and by a weak minimum on the temperature dependence of the spin-lattice relaxation time Tip [ 181.

T. K 355.;





353.5 353.4

353.3 353.0 .s‘z.(, 5'6 0


2C %

5' E 10


Fig. 7. Temperature dependence of Raman spectra of (a) polycrystalline naphthalene solid solution of naphthalene (95%) +j?-naphthol (5%) near the melting point.

and (b)


TABLE 3 Raman active external modes of naphthalene Symmetry




Line (cm-‘)



Exp. (300 K)

Calc. (300 K)






84 y2

74 50

84 56

0.108 0.185 0.973

0.569 0.817 0.092

0.815 0.546 0.192


125 70 46

106 79 41

0.039 0.405 0.914

0.080 0.910 0.407

0.996 0.089 0.003

US v1 “Inertia moments:

I,> I,> Zw

Phenanthrene An interesting case for the investigation of pretransition states is presented by solid phenanthrene undergoing the smeared phase transition at the temperature interval 315-345 K [ 201. In spite of numerous investigations by different methods the elucidation of the mechanism of this transition has not been successful [ 19-221. Characteristic features of the phase transition observed by us and Colombo [ 231 are the anomalous temperature dependence of Raman frequencies in the region of external vibrations (Fig. 8) and, as follows from our calculations, the negligible difference between equilibrium structures of two phases. The structure of the low-temperature phase II (space group P2i, z = 2) has been determined at 293 K by neutron diffraction studies [ 241. We calculated the previously unknown structure of the high-temperature phase I (with the same space group) by means of atom-atom potentials. Unit cell parameters at 353 K were taken from ref. 22. Calculations resulted in two possible packings ( 1) and (2 ) of molecules in phase I with approximately equal lattice energies 22.94 (1) and 22.09 (2) kcal mol- ‘. These packings differ from the structure of phase II by the rotation of molecules by angles of lo ( 1) and 30’ (2). Comparison of the calculated and experimental Raman spectra (Fig. 9) shows convincingly that the real structure of phase I is well described by the calculated molecular packing ( 1)) i.e. the equilibrium molecular orientation is practically unchanged during phase transition. In order to explain the anomalous shifts of Raman line frequencies we performed the calculation of temperature dependence of external vibrational frequencies using the data on the variation of unit cell parameters at phase transition measured by Matsumoto and Fukuda [ 221. Anharmonic corrections of


Fig. 8. Observed (solid line) and calculated frequencies of phenanthrene crystal.




(dashed line) temperature


of the external


Fig. 9. Observed (full line) and calculated (dashed line) Raman spectra of phenanthrene phenanthrene II polycrystals, (1) calculation with packing 1, (2) with packing 2.

I and


the third and fourth orders were taken into account by means of the independent oscillators model proposed in refs. 14 and 25

where vha_ is the harmonic frequency, U(Q) the one-dimensional cross-section of the crystal potential surface by the normal coordinate Q calculated by means of atom-atom potentials, and a3 and cy4 are the constants of anharmonicity. The results of the calculation are displayed in Fig. 8 and clearly show the temperature dependence of frequencies v3 and vIOwhich correspond to the librations of molecules around the W axis (Table 4). However, for other frequencies, corresponding mainly to the molecular librations around U and V axes, the discrepancies with experiment are rather large. This indicates strong anharmonic interaction between the latter normal vibrations in phase I, which was not taken into account by the calculation model used. The investigation in this connection of the potential energy minimum shape showed that two-dimensional cross-sections of the energy surface relative to the symmetric rotation of molecules around their U and Vaxes (Fig. 10) have a “ravine” like shape with the bottom becoming practically flat in phase I. Other cross-sections are of the regular shape changing only slightly during phase transition. Our studies permit us to draw the conclusion that the most probable distinction of phase transition in phenanthrene is a noticeable increase in phase TABLE 4 I&man active external modes of phenanthrene crystal’ Symmetry


Phase II (293 K) (cm-‘)

Phase I (353 K) (cm-‘)







110 82 65 51 35



0.068 0.094 0.910 0.369 - 0.029 0.016 - 0.293 0.941 -0.088 -0.028 -0.011 0.010 0.879 0.312 -0.116

us 106 u1 84 ug 60 v, 47 ur 32





75 63 48 32



53 27

76 48 54


0.012 -0.150 0.183 0.971



0.308 0.830 0.843 -0.282 0.434 - 0.067 0.047 - 0.033

“Inertia moments: ZU>Zv> Zw; contributions of translational and internal non-planar (100 and 114 cm-‘) molecular vibrations to the normal modes are not cited in the table.



y%$md -4





Fig. 10. Cross-sections (kcal mol-‘) of the potential surface of a phenanthrene crystal as functions of molecular rotations around axes U and V by the angles $” and q&.

I of the thermal rotational motion of molecules around the U and V axes with an angular amplitude of - 25 ‘. CONCLUSION

It can be concluded from our data that the low-frequency spectra of the molecular librations in crystals are very sensitive to the different types of orientational disorder predicted by the statistical model of melting [ 21. Activation of the rotational jumps of molecules between their allowed orientations around definite axes leads to the broadening and intensity decrease of the corresponding lines in the Raman spectrum. On this basis, experiments indicate that the step-by-step disordering of the rotational degrees of freedom can occur both at the narrow temperature range near the melting point (naphthalene ) , and long before the phase transition to the plastic state (cyclohexane ), as well as in the appearance of a sequence of orientational phase transitions (thiophene ) . The phase transition in phenanthrene is also caused by activation of the reorientational molecular motion, but here it leads to the angular motion of


molecules with high amplitude without overcoming the potential barriers this is displayed mainly as an anomalous temperature shift of Raman frequencies.

and line


10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

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