THE DYNAMICS OF THE CRYSTAL SE, SB AND SA PHASES OF IBPBAC

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THE DYNAMICS OF THE CRYSTAL SE, SB AND SA PHASES OF IBPBAC

A. Leadbetter, R. Richardson, J. Frost

To cite this version:

A. Leadbetter, R. Richardson, J. Frost. THE DYNAMICS OF THE CRYSTAL SE, SB AND SA PHASES OF IBPBAC. Journal de Physique Colloques, 1979, 40 (C3), pp.C3-125-C3-131.

�10.1051/jphyscol:1979326�. �jpa-00218722�

THE DYNAMICS OF THE CRYSTAL S

^E

, S

^B

AND S

^A

PHASES OF IBPBAC

A. J. LEADBETTER (*), R. M. RICHARDSON (**) and J. C. FROST (*)

(*) Department of Chemistry, Exeter University, Stocker Rd., Exeter, EX4 4QD United Kingdom (**) Institut Laue-Langevin, 156X Centre de Tri, 38042 Grenoble, France

Abstract. — Incoherent quasi-elastic neutron scattering experiments have been done on aligned samples of D-IBPBAC

The end chains have been deuterated so that only the diffusive motions of the rigid molecular cores are seen. In all three smectic phases a bound motion perpendicular to the layers has been observed. This has been interpreted in terms of diffusion in a periodic potential. (For example at 150 °C in the SB phase the diffusion constant Z) || = 3 x 10~8 cm2 s_ 1 and the height of the potential, V^l = 8 KT.) In the S^E phase the molecules undergo overdamped librations about their long axes but are not free to reorient by n on the observable time scale (10~10 s). In the SB and SA phases the molecules undergo uniaxial rotational diffusion which is restricted in the S^B. In the S^A there is in addition some other motion with a component perpendicular to the long molecular axes. This is probably fluctuations of the directions of the molecular axes.

1. Introduction.—We report here incoherent quasi- elastic neutron scattering (QENS) results from the crystal and smectic phases of two cinnamate ester compounds. We have previously reported [1] on investigations into the structure and dynamics of their S^B phases which showed that the dominant

diffusive molecular motions on a time scale faster than 1 0_ 1 0s are rotation about the long molecular axes and a bound motion perpendicular to the layers.

The results presented here allow us to extend our understanding of the single particle molecular dyna- mics to the SE and SA phases. The structure of the Résumé. — On a effectué des expériences de diffusion quasi élastique incohérente de neutrons sur des échantillons alignés de D-IBPBAC

Les chaînes terminales ont été deutériées de façon à ne voir que les mouvements du corps rigide.

Dans les trois phases smectiques, on a observé un mouvement d'amplitude limité perpendiculaire aux coucbîs, qui a été interprété en termes d'un mouvement de diffusion dans un potentiel pério- dique (par exemple, à 150 °C en phase SmB, le coefficient de diffusion D , = 3 x 1 0- 8 cm2 s- 1

et la hauteur de la barrière de potentiel est V1 = 8 KT). Dans la phase SmE, les molécules font des oscillations hyperamorties autour de leur axe long, mais ne se réorientent pas par sauts de % autour de cet axe sur l'échelle de temps de l'expérience (10~10 s). Dans les phases SmB et SmA, les molécules tournent autour de leurs axes longs, cette rotation n'étant pas uniforme en phase SmB. Dans la phase SmA, il existe un mouvement supplémentaire dont une composante est per- pendiculaire aux axes longs. Ce mouvement correspond probablement aux fluctuations de l'orien- tation de ces axes.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979326

C3-126 A. J. LEADBETTER, R. M. RICHARDSON AND J. C. FROST

crystal and the ordered smectic phases are reported hydrogenous versions to within a degree

seperately. (This conference.) H

We have made QENS measurements on two /

partly deuterated compounds in order to avoid

complications due to the motion of the alkyl chains. -CH=CHCOR

7

Their transition temperatures were the same as the

R. Name Initials

- - -

CD2 CD2 CD2 CD, n-butyl4(4' phenylbenzylidineamino) cinnamate D-BPBAC CDz CD (CD3)2 iso-butyl4(4' phenylbenzylidineamino) cinnamate D-IBPBAC

Both these compounds exhibit three smectic phases (i) Cooling to the S, phase generally gave a single but only D-IBPBAC has a nematic phase : peaked distribution in the direction in which the

D-BPBAC : magnetic field (H) was originally applied. The tails

of this distribution would not die even at 900 to H

77°C 108°C 172°C 208°C

Cr

s

^SS,

-

^SB

-

^S,

-

¹ and so the static order parameter for the layers was generally :

supercools -

D-IBPBAC : P2

-

^0.5

^.

86°C 1 1 4 ° C 162°C 206°C 214°C

Cr*SE-SB-S,-N-I supercools

An aligned liquid crystal sample can potentially give more information about the molecular motions than a powder sample. In this paper we therefore concentrate on results from aligned samples of D-IBPBAC but we'c refer to powder sample results [I], [2] from D-BPBAC in order to show that our model for the molecular motions is able to explain both types of data. However to analyse the QENS results unambiguously it is necessary to know how well the sample is aligned. The experi- mental alignment process and measurement are therefore discussed in section 2. In section 3 the QENS results are given and they are discussed in terms of models of the molecular motions in section 4.

2. Alignment. ^- The slab shaped samples were contained in an aluminium can of dimensions

and the interior walls were slightly scored in the 2.5 cm direction as a result of the manufacturing process. The samples of D-IBPBAC were aligned by cooling from the isotropic phase with a 0.2 T magnetic field applied along the 2.5 cm dimension. Once in a smectic phase the sample would retain its alignment indefinitely (at least a week) and the magnet could be removed.

The alignment of the sample was originally checked by doing rocking curves (using the guide tube dif- fractometer at Harwell) on the 001 and 002 Bragg reflections from the layers. The results can be sum- marised as follows :

(ii) Cooling to the SE or S, phase often gave two peaks in the rocking curve at 60 to

+

200 from H in the field direction. The details of their temperature behaviour will not be discussed here but they strongly suggest that the walls are the major influence in the alignment of the sample. Fortunately in this case the walls effect is assisting the magnetic alignment so well aligned samples can be prepared (F2 from 0.3-0.7). A typical rocking curve is shown in figure 1.

FIG. 1. - A typical rocking curve obtained by rotating the D- IBPBAC sample (in the S, phase at 120 OC) about an axis normal to the scattering plane and monitoring the intensity of the 001 Bragg reflection. The dashed line represents the incoherent background.

Perfect alignment in the original field direction would have given a single, sharp peak at 1090,In fact the alignment corresponds to

P,

-

^0.7.

(iii) Although there may be one to three maxima in the distribution of the layers for j? < 200 (j? being the angle between the average layer normal and H), there is always a monotonic decay for 200 <

P <

900.

This has been confirmed by rocking curves on the

110 and 200 reflections which would easily detect any domains with

p -

900. Although the behaviour was found to be reproducable, in situ rocking curves were also made on the QENS spectrometers. The results were the same.

3. Experimental results. -All the QENS experi- ments have been done at the Institut Laue-Langevin, Grenoble using the IN5 and INlO spectrometers.

The multichopper time of flight spectrometer IN5 is able to measure over the energy transfer range

- 0.5 to 100 meV with good resolution (12-20 peV for this work). The backscattering spectrometer INlO gives complementary information since it covers the near elastic energy range (+ 15 peV) with very high resolution (- 1 pew.

3.1 IN10. - In principle the translational dif- fusion constants of a sample can be measured by the Lorentzian broadening, AE, of the monochromatic incident beam, provided that the tip of the scattering vector, Q, lies well within the first Brillouin zone (i.e. Q

<

2 n/d where d is the unit cell dimension or the appropriate molecular dimension).

The sample of D-IBPBAC was aligned as described in 2 above. The magnetic field was left in place for the S, and N phases but removed for the S, and S,.

Measurements were made at Q values that avoided any coherent Bragg scattering with both Q

I

m and Q //. n. For Q ,< 0.31 A-' the Lorentzian broa- dening~, AE, of the resolution function were measured and converted to the translational diffusion constants, D, using the formula :

The results are shown in table I but the results for Q // n in the smectic phases are at best only approximate since the condition that Q 6 2 n/d is not fulfilled. The other values are accurate to

+

^{20 0/,.}

Observed translational dzfusion constants of D-1 BPBAC

Temperature Phase D11/10-6 cm2 s-

'

D,/10-6 cm2 s-'

- - - -

150 OC B 0.08 0.12

172 OC A 1.2 0.76

190 OC A 1.3 1.6

208 OC N 3.6 4.4

3.2 IN5. - The energy range of this spectrometer allows the rapid localized diffusive motions in liquid crystals to be seen and at this stage of the analysis we have assumed them to be independent of the trans- lational diffusion. The raw data has been corrected and converted to the scattering law using standard programs and then seperated into elastic, I,, and quasi-elastic, ZQ, components in order to obtain the experimental elastic incoherent structure factor

(EZSF) of the localized motions as described else- where [I], [3]

EZSF = --- ZE

.

ZE

+

^ZQ

Typical seperations into elastic and quasi-elastic components are shown in figure 2 and the values of the EZSF are shown in figure 3.

For the S, and S, phases, the translational diffusion is so slow that the elastic component is only broadened by the instrumental resolution. For the S, phase a contribution, AE (where AE = 2 hD, Q '), to the width of both the elastic and quasi-elastic components has been assumed when extracting the EZSF. However, for Q // n, the Q 2 proportionality is not valid (since

Q > 2 nld) and so the EZSF (for S,, Q // n) must be

treated as approximate.

The error bars in figure 3 correspond to the uncer- tainty in the measured values of D, (table I). In all except the S, phase the EZSF for Q // n is less than for Q I n and we discuss this in the next section.

The widths of the quasi-elastic components give an estimate of the correlation time of the motion (table 111) using the formula :

In the crystal phases of D-BPBAC and D-IBPBAC no quasi-elastic broadening was observed indicating that there are no diffusive motions of the cores of the molecules on a time scale faster than z

-

^{lo-'' s.}

The crystalline phase of the fully hydrogenous BPBAC at 600C gave spectra with a broadened component and the EZSF was consistent with a diffusive motion of the last 2 or 3 links of the butyl chain.

4. Discussion. ^- QENS is capable of observing any diffusive molecular motion on a sufficiently rapid time-scale (z

-

^{2 x 10- l o} s for 20 peV FWHM reso- lution). In this section we discuss which molecular motions are compatible with the experimental EZSF.

4.1 THE SE AND SB PHASES. - In these phases the EZSF for Q // n is much less than the EZSF for Q I n. This cannot be explained by a model of rotation about the long molecular axes with any physically reasonable static distribution of the mole- cular directions ([I], [3] and D. H. Bonsor private communication 1977). Two further pieces of evidence suggest that there is another motion in addition to rotation about the long axes.

(i) The EZSF from powder samples of D-BPBAC in the S, phase fall well below that expected for rotation about the long molecular axes [I].

(ii) In the aligned sample the time constants for Q // n and Q I n are different.

C3-128 A. J. LEADBETTER, R. M. RICHARDSON AND J. C. FROST

FIG. 2. - The quasi-elastic scattering law ( S ( Q , o), arbitrary units) of D-IBPBAC. Spectra are shown with Q/n and Q I n for the three smectic phases : (i) S, phase at 100 OC (12 p V FWHM resolution), (ii) S, phase at 150 OC (20 ~ e v FWHM resolution) and (iii) S, phase at 172 OC (20 peV FWHM resolution). The upper dashed lines represent the separation into elastic and quasi- elastic components and the lower one represents a flat inelastic

background.

, . 1

Fluctuations of the direction of the long molecular axes must occur on some time scale but we have

..fe shown that they cannot explain the S, data of

..,*.,."

...- - - -

^.W'

^... ... . _. ...- ...

D-IBPBAC [I] or the S, phase of D-EABAC [3].

-0.15 0 . 0 0.25 It is probable that in these phases they take place

k u ~ / - a V on a rather slower times scale (say z

-

lO-'s) than

'('J~)

-0.15 0.0 0.25 of the measured distribution of molecular orientations R U/.U+V as described in 2 above is a refinement which will be

(iil added in a more detailed publication.

0 = o . s 3 A 4

1

; L A

1 I

I ^I

.p' 1-1

'$,

. .

L...,

- - -

"...""--*

-. ... ..'... ... -. .

the rotation about the long axes. (Such a motion would not be observable with 20 peV resolution but might influence higher Q spectra from IN10.)

The only model that can explain the Q // n and Q l n data simultaneously is a rotation about the long molecular axes which is restricted at least in the S , phase, and a localized diffusive motion in a direction perpendicular to the layers.

At this preliminary stage in the analysis we have assumed that the sample of D-IBPBAC was perfectly aligned

(6

⁼ 1 .O) in order to estimate the parameters in this model which explain the data. Incorporation

FIG. 3. - EISF of D-IBPBAC in its three smectic phases. For B(p, = 1) and C(pz = 0). If the molecules undergo uniaxed rota- Q I n line A corresponds to no molecular motion, line B to jump tional diffusion plus some other motion with a component per- rotation by x about the long molecular axes and line C to uniaxial pendicular to n the EISF will be below C. For Q/n the angle rotational diffusion. If the molecules are undergoing uniaxial between Q and n was always less than 15O. The EISF given by rotation with one site preferred the EISFmust lie between A(pl = 1) equation (6) with

<

^{Z Z )'IZ = 0.9} A (D) and 1.6 A ^(E) are also and C(B1 = 0). If two sites are preferred the EISF lies between shown.

For the rotational model we have used a model of rotational-diffusion in an N-fold cosine potential [4]

which for perfect alignment (F2 = 1.0) and Q l n gives :

x

1;'

^{Jo(Z Qa sin x) I. (2}

^{P I I}

^{cos nx}

¹⁾

^{dx (3)}

where cc a ⁾⁾ is the radius of gyration, N is the number of wells and /I& is related to the orientational order parameter

B,

for rotation about the long axes :

where the brackets ( ) indicate a time average over the angle of rotation cp about the long axes.

Figure 3 shows three limiting cases for this model (which have been calculated using values of c< a ⁾⁾ measured from a model molecule). Inspection of the figure suggests that in the S, phase the molecules are undergoing uniaxial rotational diffusion about their long axes with either one or two preferred orientations. Table 111 gives the estimated values of

the rotational diffusion constant which have been obtained by fitting the data with a model of a six-fold reorientation as described in reference [I]. In the S, phase the EISF is much higher and the molecules can only be performing some overdamped libration about one preferred orientation on the neutron time scale. The values of

PN

which give the best fit to

the data are given in table 11.

Temptrature Phase

b2 8,

( Z 2 )'I2

A

- - - - -

100 OC E - 0.83 0.9

108 OC E ^- 0.78 1 .O

118 OC B 0.85 0.45 1.3

150 OC B 0.6 0.35 1.6

172 OC A 0.0 0.0 1.6

For the motion perpendicular to the layers we have assumed that the molecules are only weakly constrained to the layers by a periodic potential V ( Z ) :

V(Z) =

3

/1

+

^cos

=)

⁽⁵⁾

2 \ d

where d is the layer spacing.

C3-130 A. J. LEADBETTER, R. M. RICHARDSON AND J. C. FROST

For V, > 4 KT the EZSF for Q // n is given EZSF = exp[- Q 2 ( Z 2

)I

(6) where

The values of ( Z2 )'I2 which give the best fit to the data are given in table 11. Some trial calculations have shown that averaging the above formulae over the real static distributions (with

F2 -

0.5) tends to increase both ( 2' )'I2 and

B,

but does not change the basic model.

Average correlation times corresponding to the widths of the quasi-elastic components

and the rotational dzjjiusion constants

Performing a complete powder average with these parameters gives a good agreement with the powder sample results [I], [2] from D-BPBAC once the temperatures are scaled appropriately. This demons- trates how easy it is to misinterpret data from a powder sample. In [2] we suggested that the molecules were able to reorient by 71 about their long axes with z

-

^{3 x} lo-" s but in fact the EISF for an aligned sample with Q

I

n is much too high for this. The dominant motions in the S, phase appear to be an overdamped libration (- 300) plus a bound motion perpendicular to the layers.

In fact the full dynamics for diffusion in a periodic potential have been solved [5] and we have found that for the S, phase of D-IBPBAC at 150 OC the Q 1 n data can be fitted with the following para- meters

and

3 x lo-* G Dll/cm2 s-'

<

1 x lo-'.

Figure 4 shows a fit of the data from IN5 and IN10 with this model. A similar fit can be obtained for the S, data with V1/2 K T

-

^{20 and}

4.2 THE SA ^PHASE. - In the SA phase the EZSF for Q I n is below that for unizxial rotation. This suggests that an additional motion is becoming fast enough or of large enough amplitude to be obser- vable. Two possibilities exist :

FIG. 4. - The scattering law of D-IBPBAC at 150° in it S, phase with Q H n measured with resolutions of 20 peV FWHM (i) and 1 peV FWHM (ii). The solid lines show fits of the model of dif- fusion in a periodic potential with V1/2 KT = 4 and

Dll = 3 x lo-' cm2 s-'.

(i) Fluctuations of the long molecular axes.

(ii) Neighbouring molecules push each other aside in order to rotate but these cannot be distinguished with only QENS data.

The EZSF for Q // n in the S, phase is identical with that of the S,. It turns out that the data from both IN5 and IN10 can be fitted with V1/2 KT

-

³

and Dll

-

^{3 x cm2 s-'.}

We also point out that the values of ( Z 2 )'I2 are quite consistant with those obtained by treating the Q behaviour of the intensity of the 001 reflections from the smectic layers as a Debye Waller factor as described in [I]. As shown in table IV the diffraction

TABLE IV

Showing the values of

<

^{ZZ )'12} obtainedfrom QENS and from dzfraction experiments as mentionned in text

TempCrature

<

^{Z 2 (QENS) ( Z 2 )'I2} (Diffraction)

- - -

100 O C 0.9 2.0

150 O C 1.6 3.0

172 O C 1.6 4.0

measurements give somewhat larger values than the diffusive motion of 1-2

A

perpendicular to the smectic QENS because they see disorder on any time scale layers. In the S, phase the molecules only undergo whereas the QENS only sees the more rapid compo- some overdamped libration about their long axes

nents. on this time scale. In the SB and S, phases there is

uniaxial rotational diffusion which is somewhat 5. Conclusion. - An important feature of the mole- restricted in the S,. In the S, phase there is probably cular dynamics in the

S,,

SB and S, phases of IBPBAC also some fluctuation of the long molecular axes on is that there is always a rapid (z -- lo-" s) localized the observable time scale.

References

[I] RICHARDSON, R. M., LEADBETTER, A. J. and FROST, J. C., [3] LEADBETTER, A. J. and RICHARDSON, R. M., Mol. Phys. 35

Ann. Phys. 3 (1978). (1978) 1191.

[2] LEADBETTER, A. J., RICHARDSON, R. M. and CARLILE, C. J., [4] DIANOUX, A. J. and V O L ~ , F., Mol. Phys. 34 (1977) 1263.

J. Physique Colloq. 37 (1976) C3-65. [5] VOLINO, F. and DIANOUX, A. J., MoI. Phys. 36 (1978) 389.