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MICROSCOPIC DYNAMICS.END CHAIN MOTION IN THE SOLID PHASE OF TBBA
F. Volino, A. Dianoux, R. Lechner, H. Hervet
To cite this version:
F. Volino, A. Dianoux, R. Lechner, H. Hervet. MICROSCOPIC DYNAMICS.END CHAIN MOTION IN THE SOLID PHASE OF TBBA. Journal de Physique Colloques, 1975, 36 (C1), pp.C1-83-C1-88.
�10.1051/jphyscol:1975113�. �jpa-00215890�
M/CROSCOPIC D YNA MICS.
Classification
Physics Abstracts 7.130 - 7.114
END CHAIN MOTION IN THE SOLID PHASE OF TBBA
F. VOLINO, A. J. DIANOUX, R. E. LECHNER Institut Laue-Langevin, B. P. 156, 38042 Grenoble Cedex, France
and H. HERVET
Collbge de France, Lab. de Physique de la Matike CondensCe, place Marcelin-Berthelot, 75005 Paris, France
R6sum6, - On rapporte des expkriences de diffusion quasi 6lastique de neutrons, a haute reso- lution, dans la phase solide du terephtal-bis-butyl aniline (TBBA). Celles-ci r6vklent que les extrk- mit6s des chaines butyle se reorientent rapidement. Les meilleurs r6suItats sont obtenus en suppo- sant une rotation des derniers groupes m6thylBne et methyle des chaines. Les valeurs des temps de correlation et de 1'6nergie &activation sont compatibles avec celles, obtenues par RMN dans des substances solides contenant des chaines aliphatiques.
Abstract. - High resolution quasielastic neutron scattering experiments on the crystalline phase of terephtal-bis-butyl aniline (TBBA) are reported. The data are discussed in terms of rotational motion of the butyl chain extremities. Best agreement with the experiment is obtained assuming that the last methylene and methyl groups are rotating. Both correlation times and activation energy are consistent with previous NMR work on solid substances containing alkyl chains.
1. Introduction. - In the field of liquid crystalline mesophases, there is an increasing interest in the details of the microscopic molecular motion. Among the various techniques available, high resolution quasi- elastic scattering of neutrons belongs to the most effective ones. With the neutron technique - due to the large incoherent cross-section of the proton - the molecular motion is seen mainly through the motion of the hydrogen atoms. As there are, in general, many hydrogen atoms in such molecules, the spectra will reflect an average of all the individual proton motions.
However, the samples can often be partially deuterated without app~eciably changing their physical properties.
As the deuteron cross-section is relatively small, the spectra will then mainly reflect the motion of the remaining protons. Consequently, by comparing the
results obtained with normal and partially deuterated materials, one is able to separate the motions of diffe- rent parts of the molecule.
In those liquid crystalline systems where the mole- cules, roughly speaking, consist of a body made of phenyl groups and alkyl chains attached to the ends of the body, it is of interest to separate the body motion from the chain motion. With this aim we have under- taken a systematic neutron study of terephtal-bis- butyl aniline [I] (TBBA), using the partial deuteration method. This material is particularly interesting since there exist at least two crystalline phases, three smectic and one nematic phases along with other metastable mesophases [2]. In the present work we have studied the normal material and one partially deuterated deriva- tive, which we call DTBBA. The chemical formulae are
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975113
C1-84 F. VOLINO, A. J. DIANOUX, R. E. LECHNER AND H. HERVET It is seen that DTBBA contains protons only on and
between the phenyl rings, so that with this sample, one will mainly obtain information about the body motion.
Comparison with normal TBBA will give information about the chain motion.
In a previous paper [3] we have presented data obtained from the smectic-B phase (called the smectic H phase by other authors) at 119 OC, and the main result was that the molecules perform a random rotational motion around their long axis, with a correlation time z, of about 1.8 x lo-'' s. Furthermore, the comparison of TBBA to DTBBA spectra suggested a much faster random motion of the butyl chains or of parts of them superimposed on the overall rotation. No further quantitative .results on the chain motion could be extracted, because the various methylene groups and the terminal methyl groups probably have different dynamical behaviour, as suggested by recent NMR measurements on the local order in the chain [4].
We will now present results on the chain motion obtained from high resolution quasielastic neutron scattering experiments in the high temperature crystal- line phase of both TBBA and DTBBA. These results may also lead to a better understanding of the chain dynamics in other phases. We first describe the experi- mental data and give an interpretation in terms of rotational diffusion of the extremities of the butyl chains. Then correlation times and an activation energy for the motion are deduced. Finally, the results are compared to data obtained by other techniques on similar substances. Some details on the method of data analysis are given in the Appendix.
2. Experiment and analysis. - The experiments were carried out with the multichopper time-of-flight spectrometer IN 5 at the cold source of the ILL-HFR.
The experimental conditions have been described in [3]. Spectra were taken simultaneously at 9 different scattering angles, at 25, 104 and 109 OC, the crystalline- smectic B transition being at 114 OC. These tempera- tures were reached starting from room temperature.
Care was taken to avoid Bragg peak positions. The spectra were corrected for detector efficiency, sample holder scattering, absorption and self shielding and properly normalized by comparison to a similarly corrected vanadium run. No multiple scattering correc- tion was applied. Figures 2a, b, c show the corrected spectra (points are measured, full lines calculated) of TBBA .at 25 OC, TBBA at 104 OC and DTBBA at 104 OC, respectively for the scattering angles cp = 64.1, 91.5, 105 and 1340 (incident wavelength : A, = 9.48 The main characteristics of the spectra are the follow- ing : they all exhibit a very large elastic peak (not completely shown on the figure). This peak has the shape of the resolution function and is superimposed on a broader, much smaller peak. Qualitatively similar observations were made in the smectic B phase [3].
However, there are two major quantitative differences ; first the broad peak in crystalline TBBA is much
smaller than the one observed in the smectic B phase, and second it is again much smaller in DTBBA. The first observation suggests that a diffusive rotational motion is taking place also in the solid, but that the number of protons participating in this rotation is smaller than in the smectic B phase. ( A priori, the smaller quasielastic intensity could also be explained by a much smaller gyration radius ; however, as we will see below, this can be excluded.) The second observation permits the conclusion that the protons taking part in a rotation belong to the alkyl chains rather than to the body of the molecules.
Let us now analyze the TBBA data on the basis of a model which takes into account these observations.
Let Pf and Pm be the numbers ofjixed(i. e. not rotating) and moving (i. e. rotating) protons, respectively. If we assume that all the moving protons are equivalent, the scattering function around w = 0 can be written as
K?
PmS(Q, w) = - b(0) + - SR(Q, 0) exp(- Q' u2) .
Pl
I
(1) Here P , = P, + Pm = 32. The b-function comes from the fixed protons, SR(Q, w) is the scattering law for the moving protons and u2 is an average of the mean square vibrational displacements for all the protons including inter- as well as intramolecular vibrations. We have to stress the limitations of these assumptions.
Certainly the motions of the various groups of the chains are not exactly identical. In particular the terminal methyl groups probably are somewhat more free to rotate than the methylene groups. In principle we could include such different dynamical behaviour in our calculation, but the increased number of para- meters would make the fitting procedure much more difficult. On the other hand it is doubtful that the results would be more meaningful. In order to calculate SR(Q, o), we assume that - the broad (quasielastic) contribution underneath the elastic peak observed in solid TBBA is due to a uniaxial rotational motion in which Pm protons of a molecule take part. Such a model (with Pm = P,) was already successfully used for the smectic B phase 131. The protons are pictured as performing instantaneous jumps between N equi- distant sites on a circle of radius a, the mean time between consecutive jumps being z. For large N this model is equivalent with continuous uniaxial rotational diffusion. Obviously the particular assumptions (ins- tantaneous jumps, equidistant sites, strictly uniaxial motion) should not be taken too literally. They are merely necessary in order to make the problem tractable, the essential point being that the protons perform a diffusive motion on a circle. Mathematical details of the model are given in the Appendix. Here we will restrict ourselves to a discussion of its application.
There are five parameters in our model, namely Pm (or P,), a, z, N and u2 (see eq. (I), (A l), (A 2), (A 3)).
In practice, however, many restrictions are imposed on their values :
END CHAIN MOTION IN THE SOLID PHASE OF TBBA C1-85 (i) The choice of Pm is reduced to a few possibilities,
namely Pm = 6 (only the two terminal methyl groups are rotating), Pm = 10 (the same methyl groups plus the two adjacent methylene groups), Pm = 14, etc.
(ii) The value of a must be consistent with the molecular dimensions.
(iii) For the number of jump sites, it turns out that in the Q-range of our experiment (Q < 1.2 AU1) the scattering function depends very little on N as soon as N 2 6. On the other hand N must be chosen 2 4 in order to account for the slight increase with Q of the quasielastic peak width [ 5 ] . We may therefore choose N = 6 and reduce in this manner thenumber of para- meters.
(iv) The value of u2 must be consistent with the Q-dependence of the elastic plus quasielastic peak integrals which we have obtained directly from the measured spectra (see Fig. 1).
T B B A : o 2 5 O C n 104' c
10 X 1 0 9 ' C
FIG. 1. - Semilogarithmic plots of the integrals (in arbi- trary scale) of elastic plus quasielastic scattering versus Q2 ; points are obtained by graphical integration, full lines from fit of
exp[- Q 2 uZ] to the points.
We note that for the fitting procedure as a sixth parameter a factor F is needed in front of the theoretical scattering function, in order to normalize the calculated to the measured intensities.
3. Results and discussion. - In analyzing the data the following procedure was adopted. First the spectra of TBBA, obtained at 104 OC, were considered. N was taken equal to 6 and using the least squares method, expression (1) was fitted to nine spectra simultaneously.
For different values of Pm the following results were obtained :
Although the quality of the fits is almost equally good in the three cases (slightly better for Pm = lo), the only a-value which is well consistent with the chain geo- metry is a = 1.42 A, the two other values being defini- tely too large and too small, respectively.
The values found for the mean square displacements u2 are somewhat different from those obtained directly from integration of the spectra, although not comple- tely inconsistent. It turns out that, due to the intense elastic scattering, the only parameter which depends sensitively on u2, within the possible range of variation of the latter, is the normalization factor F. We there- fore conclude that for further calculations we can fix Pm = 10 and a = 1.42 A and use for u2 the values found in the integration.
Thus we obtain for TBBA at three different tempe- ratures :
T, = 14.3 x s u2=0.210 A2 for T= 25 OC
T, = 7.9 x 10-l2 s u2=0.274 A2 for T= 104OC
T, = 7.9 x s u2 =0.274 A2 for T= 109 OC .
The quality of the fits is practically the same for the three temperatures. Figures 2a, b show the theoretical spectra (full lines) calculated with the above parameter values for 25 OC and 104 OC, as compared to the experimental data. The DTBBA-spectra (1040C), shown in figure 2c, were analysed subsequently. The difficulty here is that the deuterons, which we believe to participate in a rotational motion, scatter neutrons incoherently as well as coherently. Our theory, how- ever, was derived for incoherent scattering only. We have nevertheless obtained an estimate of the rotational correlation time in the following way. Expression (A 6) (see Appendix) was fitted to the DTBBA-spectra after replacing the factor Pm/32 by the parameter
0,. [cD(l - 2)
+
GH. Z]X =
[22 o,(l - z) + o,(10 + 22 z)] '
Here Dm is the number of rotating deuterons, o, and oH are the scattering cross sections of deuteron and hydrogen, respectively ; z is the fraction of remaining protons, if the partial deuteration is not perfect (z = 0, if the 22 protons selected for deuteration in the mole- cule are entirely replaced by deuterons). Fixing a = 1.42 A and u2 = 0.165 A2 (from integration) the fitting procedure gives X=0.089 and z1 = 14 x lo-'' s.
This value of the correlation time seems well consistent with the results found for TBBA.
In order to interpret the value obtained for Xwe have considered several cases :
(a) Assume z = 0 and o, = 7.6 b, i. e. the total deu- teron scattering cross section ; this yields Dm = 1 1.4 ;
(b) Assume Dm = 10 and a, = 7.6 b ; this yields z = 0.019 ;
7
C1-86 F. VOLINO, A. J. DIANOUX, R. E. LECHNER AND' H. HERVET
FIG. 2. - Corrected time-of-flight spectra versus energy trans- fer : (a) TBBA at 25 OC ; (6) TBBA at 104 OC ; (c) DTBBA at 104 OC. Spectra are shown for four scattering angles : y, = 64.1, 91.5, 105 and 134O (from left to right) ; incident wavelength IZo = 9.48 A ; points are measured, full lines are calculated (rotational diffusion). The spectra of different temperatures are given in arbitrary units, but normalized to the same number of incident neutrons. The horizontal straight lines correspond to the inelastic background fitted to the flat part of the scattered intensity
outside the quasielastic region.
(c) Assume Dm = 10 and a, = 2.2 b, i. e. we allow only the incoherent part of the scattering cross section to contribute to the quasielastic scattering ; this gives z = 0.085.
All these results are consistent with each other, but result (c) agrees best with the observations made on TBBA and with the degree of the (partial) deuteration of our DTBBA sample, which was estimated to be 92 %.
Let us now examine the rotational correlation times. Assuming an Arrhenius law for the physi- cal process which produces the rotation, a value of E = 1.7 kcal/mol'e for the activation energy is deduced from the above values of z, versus temperature. We also note'that at all temperatures z, is smaller than the 7,-value found for the body-rotation in the smectic-B phase at 119 OC [3]. We will now compare our results to data obtained on similar substances by other authors using different techniques.
4. Comparison with other experiments. - From the above results it can be concluded that most pro-
bably the motion responsible for the quasielastic neutron scattering observed in the solid phase of TBBA is a rapid reorientational motion of the methyl and the last methylene group of the butyl chain. This conclu- sion is quite consistent with ,recent X-ray work on this substance [6], where the author could not localize the last carbon atom of the butyl chain. It is, however, more instructive to compare our data with other (mainly NMR) results dealing with motions in solid systems containing alkyl chains. The existence of end chain methyl group rotation in solid n-alkanes has been recognized both by second moment considerations and by proton spin-lattice relaxation [7, 8, 91. The activa- tion energies found by the various authors are consis- tent with each other and range from 2.6 to 2.9 kcal/mole. An example of results which are parti- cularly interesting for a comparison with our data are those obtained recently by NMR in the solid phase of ethyl-[p-(p-methoxybenzilidene)-amino]-cinnamate (EMC) [lo]. This substance has 0-CH, ando-C,H, chains and is very similar to TBBA since it presents various crystalline and mesomorphic liquid crystal- line phases in roughly the same range of temperature.
In [lo] the dominant mechanism for the proton spin-lattice relaxation was attributed to a rotation, probably of the ethyl group. The similarity between these and our results is striking. Not only do we find a similar value for the activation energy (1.7 as compared to 2.3 kcal/mole, our value being perhaps not too reliable sinceit was obtained from only two points of the plot of 7, versus inverse temperature) ; but, considering the logarithmic plot of the correlation time z, versus 1/T (Fig. 10 of [lo]), our T,-values are to a very good precision on the same straight line. This suggests that the phenomena observed by the two different tech- niques in the two different substances are of the same physical origin and that the chain motion in such substances is more sensitive to the temperature than to the exact chemical nature of the material. Finally, it is of interest to note that thermodynamical measure- ments [ l l , 12, 131, on similar compounds have also been interpreted in terms of chain disorder. In parti- cular, it has been suggested [13] that the difference between melting entropies of the stable and metastable crystal phases of (p-methoxybenzi1idene)-p'-n-butyl- aniline (MBBA) may be interpreted as being due to the motions of the methoxy and n-butyl tails of the mole- cules.
5. Conclusion. - In summary, the high resolution quasielastic neutron spectra obtained from solid TBBA have proved the existence of a rotational motion of the extremity of the butyl chain, comprising probably the methyl and the last methylene groups. In spite of the crude approximations made, our model is sufficient, not only to describe the experimental observations, but also to obtain good estimates of the rotational correla- tion times and of the activation energy. Our results are completely consistent with recent NMR work on a
END CHAIN MOTION I N THE SOLID PHASE OF TBBA CI-87 similar compound, EMC. The observed end group
rotation in solid TBBA is faster than the body rotation we found previously (at a higher temperature) in the smectic-B phase of TBBA. Deuteration of the rotating groups increases the rotational correlation time by almost a factor of 2.
Acknowledgments. - We are indebted to Prof.
P. G. de Gennes for his interest in this work and for helpful discussions. Thanks are due to Drs. L. Litbert and B. Deloche for their work in the synthesis of the samples.
Appendix
For the jump rotation model described in the text, it can be shown 114, 151 that the incoherent scattering law in the case of a powder sample is given by
where
1 sin C2 ~a sin ( n j / ~ ) I COS (2 Xj,N) (A 2)
= N
z1
2 Qa sin (nj/N)sin2 (n/N) . 7
zl = 71 --- 3 71 =
sin2 (nl/N) 1 - cos (2 n/N) ' (A 3) In the limit of large N, as mentioned in the text, these equations are equivalent with continuous rotational diffusion [12], with the diffusion constant D, given by D, = 117,. It is therefore, even for small N, more useful to compare z1 rather than z to the correlation times obtained with other techniques, e. g. NMR. This is why only 7,-values are given in the text. Introducing relations (A 1) to (A 3) into eq. (I), we obtain the scattering law of our problem. It can be split into two parts, a delta function due to the fixed and the moving protons, and a sum of Lorentzian curves due to the moving protons only. In order to test the model one must fit expression (I), folded with the experimental resolution function, to the experimental spectra, taking into account that the latter are taken not at constant Q, but at constant scattering angle rp. When the shape of the resolution function R(o) is not simple, the convolu- tion must be performed numerically. In our case this procedure can be greatly simplified due to the simple symmetric shape of R(o). This function is quite well approximated by a triangle or by a Gaussian, the latter being preferable for the determination of the full width at half maximum (FWHM), 2 r. Therefore a Gaussian was fitted to R(o) at each scattering angle in order to obtain 2 r. Then the resolution function was replaced by a triangular function R'(o), given by
This function was used for the convolution of the reso- lution with the quasielastic part of the scattering func- tion. The advantage of this approximation is that the convolution of a triangle with a Lorentzian can be expressed in terms of known functions. In our case we have the following result :
1 R'(o - w') dw'
- m O? + or2
2 r - o
+ (2 -
:)
[arctan + arctan 21)
(A 5 )W1
- 1
where we have set o, = zl .
Thereplacement of R(o) by R'(w) is well justified if -
as in our case - the triangle is also a good approxi- mation (only the very small tails are neglected) of the resolution function, and if the widths of the measured spectra are not too small compared to 2 r. The latter condition is, of course, not fulfilled for the elastic term 6(o) ; this term is represented by the measured shape of R(o) in our calculations.
The final expression, with which we compared our corrected experimental data, is the following :
Here the wave vector transfer of the neutron is given by
2 m 112
Q = [F (Eo + E - 2(Eo E)'12 cos rp)]
F i s a normalization factor, cp is the scattering angle, Eo and E are the incident and the scattered neutron energy, respectively ; rn is the mass of the neutron. In the fitting procedure only experimental points with
1 w 1 ,< E0/2 h were considered and a small flat background was subtracted. This background corres- ponds partly to the flat inelastic contribution in the quasielastic region and partly to multiple scattering which is never completely negligible. The fits were performed on all angles simultaneously, so that a total of about 1 000 experimental points were used with only a few parameters as explained in the text.
C1-88 F. VOLINO, A. J. DIANOUX, R. E. LECHNER AND H. HERVET
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