THE NATURE OF THE SMECTIC E PHASE

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THE NATURE OF THE SMECTIC E PHASE

A. Leadbetter, R. Richardson, C. Carlile

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C3, supplkment au no 6, Tome 37, Juin 1976, page C3-65

THE NATURE

OF

THE SMECTIC

E PHASE

A. J. LEADBETTER and R. M. RICHARDSON

Chemistry Department, University of Exeter, Exeter. EX4 4QD, U. K. and

C. J. CARLILE

Neutron Beam Research Unit, Rutherford Laboratory, Chilton, Oxon. OX1 1 OQX: U. K. and ILL, 38-Grenoble, France

Abstract. - Incoherent neutron scattering experiments have been carried out on a powder sample of D-PBABC

(

6 '

/ ~ ' c H = N < ~ > c H = c H COOCIDI : Crystal 77 OC Se 107 'C SB

L A 'L/

172 OC SA 206 "C Isotropic Liquid) in the smectic E phase at 92 OC and 60 OC (supercooled) and in the crystalline phase at 60 OC.

Data were obtained for 0.16 Q/A-1 1.14 with a resolution of 28 peV (FWHM) on a time-of- flight spectrometer at ILL Grenoble.

No molecular motion is observed in the solid phase showing that any relaxations are slower than

-

0.5 GHz. Molecular motions are observed in the smectic E phase and the results have been compared with models of reorientational motion about the long molecular axes. It is concluded that some restricted rotational motion occurs with a correlation time of a few GHz-1. The nature of the rotational motion is not yet established but appears to involve two-fold reorientation through an angle a and the restriction in the motion involves either part of the molecule rotating more slowly than the rest, or a preferred orientation of the molecule as a whole (on the neutron time-scale), or both.

1. Introduction. - As a result of X-ray diffraction studies of single crystals of three smectic E phases formed by molecules of the form

with R = C,Hll ;

CH(CH3)C,H, and CH(CH3)C,H13

Doucet et al. [I] have proposed the following structure for smectic E phases. The long molecular axes are normal to the layers and within the layers the molecules have a chevron structure with orthorhombic symmetry. The molecules have a two-fold orientational disorder about their long axes but the x-ray studies could not determine whether this was static or dynamic. These conclusions have been confirmed for a fourth member of the series with R = C,H9 by Lydon and Gray (*) and by ourselves [2]. There is considerable 3-dimensional ordering in the smectic E phase but clearly also considerable disorder as no high index Bragg reflections are observed, but whether this disorder is simply large amplitude vibrations remains to be established.

We report here a neutron scattering study of a powder sample of

<$

~ > H = N ( ~ = C H C O O C , D ~

( * ) Gray, G and Lydon, J. E.: Private communication.

in the solid phase and in the smectic E phase. The butyl chain was deuteriated in order to avoid compli- cations arising from special internal motions of this chain.

2. Experimental results. - The specimen was 5 x 2.5 x 0.05 cm3 in dimension and was contained in an aluminium can of wall thickness 0.5 mm. The smectic E phase exists between 77 and 1070 but readily supercools and we were able to make measurements at 60 OC and 92 OC in this phase and at 60 OC in the crystalline phase, in all cases on unoriented (powder) samples.

The measurements were made using the multichop- per time-of-flight spectrometer IN5 a t ILL Grenoble. An incident wavelength of 10 was used so as to obtain a high resolution (-- 6.8 GHz

-

28 peV, FWHM) because we believed that any reorientational motion would probably be slow on a neutron time scale. Data were obtained at 9 angles corresponding to Q values between 0.16 and 1.14

A-

'

; angles affected by Bragg reflections are excluded. No mul- tiple scattering corrections were made. In figure l are shown typical data for the scattering law S(Q, w ) at three angles for a temperature of 92 OC. The data for T = 60 OC are similar but narrower and this is illus- trated in figure 2 where the highest angle data are compared for each temperature. In the crystalline phase no broadening is observed (Fig. 2).

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A. J. LEADBETTER, R. M. RIC :HARDSON AND C. J. CARLILE

FIG. 1. - Quasi-elastic scattering law S(Qw) of PBABC at 92 OC

at average Q values of 0.16,0.84 and 1.14 A-1. The lower dashed lines represent the inelastic background and the upper ones separate the elastic and the quasi-elastic components. The solid

lines show S(Qw) for the best fit model (see text).

model first. The scattering law for a powder sample

[3] is

where jo(x) is the zero order spherical Bessel function (sin xjx), 2 a is the jump distance (a is the gyration radius) z is the mean residence time between jumps and L(2/z) is the Lorentzian function.

The scattering law has two components : a central elastic peak and an underlying Lorentzian. The relative intensity of the elastic peak I,/(I,

+

I,) (the elastic incoherent structure factor) is given directly by the model as

Knowing the resolution function of the instrument, which is almost triangular, it is possible to estimate the two components directly from experiment. This experimental separation is shown for 3 angles in figure 1 and the results for R ( Q ) are given in figure 3 for the

~ N E R G \ € l r n e ' d

FIG. 2. - Quasi-elastic scattering law, S(Qw) at an average 4? of

1.15 A-1 of PBABC in its smectic E phase at 92 OC (0) and 60 OC (@) and in its crystalline phase at 60 OC (-). The dashed

line is the inelastic background.

3. The nature of the molecular motions.

-

First we assume that in these experiments the translational motion of the molecules may be neglected and the observed quasi-elastic broadening is attributed to some kind of molecular rotational motion. From the known structure of the phase [I] the simplest model of this motion is a two-fold instantaneous jump reorientation about a long molecular axis, so we consider this

FIG, 3.

-

The elastic incoherent structure factor R(Q) obtained

from the spectra of PBABC in its smectic E phase at 92 OC (0)

and 60 OC (0). The solid lines are calculated values for a two- fold jump model with gyration radius 2.2 acd (a) the following proportions of the protons moving :

A : 0.5 ; B : 0.75 ; C : 1.0 (eq. (2)) or (6) occupancy ratios of the two positions of

A : 0.7510.25 ; B : 0.8510.15 ; C : 0.510.5 (eq. (3)) The dashed lines show the calculated values for a rotational diffusion model with a single preferred direction (eq. (4) with

N > 6 and a = 2.2 A) weighted according to p' values of 2 (curve D) and 4 (curve E).

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NATURE OF THE SMECTIC E PHASE C3-67

especially a t the lower temperature. Perhaps more importantly the experimental R(Q) is different a t the different temperatures.

It could be argued that the direct separation of elastic and quasi elastic components of the scattering is in error due to the narrow width of the quasi elastic component. However, we have also compared the model of eq. (1) with the overall experimental scattering law, without making any such separation. Using a fitting programme and two parameters : a and z (plus a normalisation factor and a Debye Waller factor which we do not consider here) all angles are fitted reasonably well a t both temperatures. The resultant values of the best fit parameters are

Such small values of a are clearly incompatible with

the molecular dimensions and confirm the structure factor results.

An obvious inference from this comparison of experiment with the simple two-fold jump model is that not all the protons are moving, or at least that there are two or more proton motions of different rates. Models of this type have therefore been investigated with the following results. First an estimate of the feasibility of the model and the fraction of moving protons may be obtained from the intensity data of figure 3. By assuming that only a fraction x of the protons in the molecule are reorienting, the experimental structure factors can be fitted t o within the experimentaI uncertainty and in particular the shapes of the experimental curves are compatible with that for a 2 fold reorientation. These results indicate that x

-

0.50 at 60 OC and 0.75 at 92 OC, suggesting that different parts of the molecule acquire reorientational freedom progressively with increasing temperature. A more detailed analysis has been made of the experimental scattering law in terms of such models in which a fraction x of the protons reorient by 2 fold jumps while the rest (1 - x) are stationary (on the neutron time scale, i. e. z M 1 2 0.5 GHz). A number of models have given reasonable fits to the data and the best fit for three Q values at 92 OC is shown in figure 1 ;

similar quality fits are obtained for the 60 OC data. The parameters from the best fit models so far obtained are as follows :

Fraction (x) of

T/OC Protons Moving a / A T-'/GHz

where a is the gyration radius for the protons which

move. Taking the criterion that for a realistic model

a

-

2 A, and that the a values obtained for a given

model represent an average over the rotating protons, then these results suggest again that at 60 OC only about half of the protons are, reorienting. If this is correct it would presumably mean rotation of the two end phenyl groups. At higher temperatures the situation is less satisfactory as the a value obtained suggests

that only 11 of the protons should be moving and while a reasonable fit is indeed still obtained with x = 11/16 the value of a is only 1.87

A,

but more importantly the physical significance of this fraction is obscure. This model however is clearly too simple, even if it were correct in essence, since if different parts of the molecule reorient at different rates (as surely happens for the butyl chain for example) it will be necessary to consider the time constants and activation energies for the motion of each part rather than assuming that it is either stationary or moving at the same rate as the rest of the molecule. Unfortunately this introduces additional parameters so that more data are required. An alternative explanation of the data can be given by assuming that the whole molecule reorients through an angle .n between the two possible positions but that these are no longer equally probable. If the fractional occupancy of the two orientations is y and 1-y then the elastic incoherent structure factor, which is simply the fourier transform of the infinite time (i. e.

t y s for these experiments) correlation function, for a powder sample is given by

sin 2 Qa

R(Q) = Y'

+

(I

-

y)'

+

2 y(l - y)

-

2 Qa (3) which reduces to eq. (2) for y = 0.5. Curves identical with those calculated for the previous model (a fraction x of the molecule rotating) are obtained with y = 0.75 at 92 O C and 0.85 at 60 OC assuming the same average gyration radius of 2.2

A.

The implication of this calcu- lation is an increasing ordering of the molecules with decreasing temperature towards the ordered configura- tion of the crystal. This model again needs further investigation with more extensive data but there are also implications for X-ray diffraction data which should be investigated.

This model of partially frozen rotational motion has been discussed in a genera1,form by Hervet et al. [4].

They consider a jump reorientational motion around a circle with an occupancy weighting of the sites of the form exp cos cp when, for a powder sample, the structure factor is

1 sin Qa sin nj/N

R(Q) = ---

C

N I ; ( F ) j = I 2 Qa sin nj/N

I, is a zero order modified Bessel Function of the first

kind.

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C3-68 A. J. LEADBETTER, R. M. RICHARDSON A N D C. J. CARLILE otational motion about their long axes and about a

preferred direction in space. This direction would need to have some static (on a neutron time scale) 2 fold disorder to satisfy the X-ray structural data. Again assuming a gyration radius a = 2.2

bi

calculated curves for p' = 2 and 4 are shown in figure 3. The fit is fair but not a.s good as for the models considered earlier as the curves have the wrong shape ; good agreement can be obtained with a

--

3.3

A

but this is physically unreasonable.

It may be concluded that the molecules in the smectic E phase certainly undergo some kind of restricted reorientational motion about their long axes. The precise nature of this motion cannot be established

without further experiments but it occurs on a time scale of a few GHz-' and probably involves %-fold reorientation, through an angle n and either different rates for different parts of the molecule or a preferred orientation (on the neutron time scale), or both.

Further experiments with both X-ray and neutron scattering are planned in order to clarify the situation.

Acknowledgments.

-

We are grateful to Dr. G. Gray and Dr. A. Moseley for supplying the sample and for useful discussions, and also to Dr. A. J. Dianoux and Dr. F. Volino for many stimulating discussions and to them and other members of ILL for help and hospitality.

References

DOUCET, I., LEVELUT, A. M., LAMBERT, M., LIEBERT, L

& STRZELECKI, L., J. Physique Colloq. 36 (1975) C 1-13. LEADBETTER, A. J. & RICHARDSON, R. M., Unpublished. [3j BARNES, J. D., Neutron Inelastic Scattering (Proceeding of Grenoble Conference) IAEA Vienna p. 287, 1972. [4] HERVET, F., VOLINO, A. J., DIANOUX, R. E. & LECHNER, Phys.