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Rayleigh scattering induced by static bends of layers in a smectic A liquid crystal
Solid State Communications
Vol. 12, pp. 27—29, 1973.
Pergamon Press
Printed in Great Britain
RAYLEIGH SCA11~ERINGINDUCED BY STATIC BENDS OF LAYERS IN A SMECTIC A LIQUID CRYSTAL* R. Ribotta,t G. Durand and J. D. Litsterl Laboratoire de Physique des Solides, § Faculté des Sciences, 91405—Orsay (Received 2 October 1972; in revisedform 15 October 1972 by F. G. de Gennes)
We observe the anisotropy and the polarization properties of the Rayleigh scattered light for a planar smectic A texture of butoxyl benziledene-p-n anilino-acetophenone (BBAA). This scattering is attributed to static bends of the smectic layers, with wave vectors parallel to the smectic planes. This effect gives a simple method to measure the ratio of the extraordinary to the ordinary indices: fle/flO = 1.18 at 89°C.
DE GENNES has suggested1 that in smectic A liquid crystal, the smectic layers could undergo thermally excited bend of formations of wave vector q, parallel to the layers. The reason for this geometric condition is simple: in that case the bend deformation does not imply a compression of the layers and should cost less elastic energy. However this geometry favours also the development of static bends in the material; looking for the thermally excited fluctuations in smectic A single crystals, we have in fact observed a Rayleigh scatteringsignal, having all the polarization and intensity properties implied by the De Gennes’ condition, but which does not fluctuate in time. We attribute this scattering to the existence of small random static bends of the smectic layers in our sample.
b~’~
\ (ic~ d /
b) ,
Let us first summarize the characteristics of the Rayleigh scatteringwhen q is restricted to remain *
FIG. 1. Geometry for Rayleigh scattering of laser light by a sample of smectic A, BBAA liquid crystal (T = 89°C).The scattering pattern appears as portions of circles (see text). am is proportional to the critical q~for which the penetration depth of defects equals the sample thickness.
Work partially supported by French Delegation Generale la Recherche Scientifique et Technique, Under Contract No. 68.01.194.
a
t On leave from Institut d’Electromque Fondamentale Orsay.
parallel to the layers. A planar smectic A sample is illuminated by an ordinary (or extraordinary) light beam, making an angle a with the common normal to
1 John Simon Guggenheim Memorial Fellow. Perma~ nent Address: Dept. of Physics, M.I.T., Cambridge, Mass. 02139, USA.
the layers and the glass boundaries (Fig. 1). Inside the crystal the wave vector of this beam is k~,(or ke).
§ Assoclé au CNRS. 27
28
RAYLEIGH SCATTERING IN A SMECTIC A LIQUID CRYSTAL
Vol. 12, No. 1
A smectic plane bend corresponds to a molecular splay which causes Rayleigh scattering as in nematic crystals The scattered wave may be split up mto ordinary and extraordinary waves of wave vectors k, and k.~.A simple application of the polarization selection rules for splay in nematic crystals2 gives a zero cross section for the(k 0 k~,)configurationThe following three possibilities are left (k0 k~),(Ice k~) (kek,) In the medium k0 and k~,have their ends located on a sphere of radius n0 (ordinary index of refraction), while Ice and k~terminate on an ellipsoid of revolution about the optic axis (also the molecular axis). This ellipsoid comes from the sphere by an affinity of ratio ~e/~o around the molecular axis (; is the principal extraordinary index). With q restricted to the plane of the layers, k and k’ must terminate on one of two concentric circles formed by the intersections of the the sphere and ellipsoid with a plane normal to the molecular axis (and containing q); one circle corresponds to the ordinary ray and the other to the extraordinary ray. The ratio of the components of extraordinary to ordinary wave vectors in this plane is ne/no. This ratio is conserved in the refraction process so that, in air, all the possible scatteringbeams must be on two coaxial cones of well defined angles; let us call (a + i3) the half angle of the extraordinary cone k~scattered from the ordinary wave k0, and (a y) the half angle of the ordinary cones k, scattered from the extraordinary wave ice; one has the simple relationship. —
sin (a + 13) sin a
=
sin a sin (a ‘y) —
=
fl~
~
~
/
Obviously, in the (ke,k~)configuration, the scattered beam must be on the cone of half angle a. Let us assume now a bend amplitude independent ofq and a fixed angle a. The scattered intensity depends on the relative angles between the incident wave polarization, the q direction and the scattered light vibration (tangent or normal to its cone, for ordinary or extraordinary waves). This intensity should vanish for scattering in the plane of symmetry, close to the laser beam. Our experimental set up is sketched on Fig. 1. A 60 mW He—Ne laser beam (X = 6328 A) with an ordinary (o) or extraordinary (e) polarization illuminates a smectic A sample of BBAA. (Butoxy-benzilidene-p-n-
FIG. 2. Two pictures of the scattering patterns showing the two portions of circles corresponding to: (a) extraordinary output for ordinary input, (b) ordinary output for extraordinary attenuated laser beam.input. The spot represents anilino acetophenone). In our experiment a can vary from 0 to 70°.We observe the scattered pattern on a screen (ground glass) of arbitrary orientation, behind an analyser, by eye. The sample is prepared in its smectic A planar texture at T = 89°Cby cooling from the homeotropic nematic phase. The uniformity of the texture is checked by observation under a polarizing microscope. The glass plate against the temperatureregulated oven is a microscope cover-glass of standard quality, and the upper one is a thick (5mm) ?~/10 optically polished window. With mica spacers the thickness of the sample can be adjusted from 50 to 500~um.Figure 2 shows two pictures of the screen for the (ke, k~)and (k0, k’e) configurations. We do find that the scattered light is distributed on the predicted cones, but concentrates in the lower q region. The circularity of the cone is easily checked by using as a reference a simultaneously conoscopic pattern of the sample on the same screen. The scattering pattern is found to remain parallel to the neighbouring conoscopic circular fringes, as long as visible. The two portions of the scattered circles show the central intensity extinction. The polarization of the scattered light is found tangent to the inner ‘circle’ (ordinary wave) and normal to the external one (extraordinary wave). The position of the cones is not dependent on the sample thickness, but the thickness of the circles (typically l0~rad) decreases with samples of better quality. We did not find the scattering for the (Ice, k~)configuration, probably because fmding a region
Vol. 12, No. 1
RAYLEIGH SCATTERING IN A SMECTIC A LIQUID CRYSTAL
29
maximum q extension of the scattered pattern increases as d decreases. This kind of variation would be expected in nematics where defects induced, for in-
~(o)
~
—
B BAA 1=89°C
30\
(i~L)
depth of the order of their transverse wave length. The surprising observation is that now, in the smectic A, the penetration of these defects seems to extend stance, from the plates, extend inlarger the bulk to thicknesses two orderswould of magnitude thanto a their wave length. Possible models to describe this effect are given in references 3 and 4.
COS~ 25 20
~
/
rn Sifl~(!i*~)
o 0
~(o)
~
IC
20
30
£0
50
50
70
SO
90
FIG. 3. Angular dependence of 13 and 1 vs. the mcidence angle a. The angle a = sin_i (no/ne), corresponds to a situation for which the scattered extraordinary wave is at the limit angle and cannot emerge from the material, where the geometrical factor is non zero necessitates the existence of bends of large q. These bends seem to have a very weak amplitude in the sample. We now vary a and measure 13 and Our results are shown on Fig. 3. We find a very good fit of our measurements on the relationship (1) with the value ~e/flo = 1.18 (solid line). This value is to be compared with the birefringence measurement deduced from the conoscopic simultaneous observation: = 0.26. Assumingn 0 = 1.52, one obtains ~e/flo = 1.17, in reasonable agreement with the previous figure. ~.
Finally we have to mention that the scattered signal, analysed on a light beat spectrometer, has not shown any time fluctuation in the range of our capability (l—lO8sec). This can be understood easily: the scattered bends of the layers prevent thermal fluctuations from having a detectable amplitude, the mean angular distortion of the layers being larger than the tolerance on the alignment of q in the smectic planes, as defined in reference 1. To summarise, we have observed in apparently defect free samples of smectic A, small static bends of the smectic layers, which give rise to a strongly anisotropic Rayleigh light scattering. We can deduce from this experiment the ratio of the indices of refraction of the liquid crystal, the origin of the observed bends is not yet dear; their penetration in the bulk is found anomalously large.
Acknowledgements We wish to thank Dr. Liebert and Dr. Strezleski for the synthesis of good quality BBAA, and Dr. P. G. de Gennes for stimulating dis. cussions. —
Using the same plates, we now vary the sample thickness d from 50 to 500 pm; we observe that the
REFERENCES 1.
DE GENNES P.G., J. Phys. C4—65, 30(1969).
2. 3.
DE GENNES P.G., C. r. hebcL Séanc. Acad. ScL, Paris, 15, 266 (1968). DURAND G., C. r. hebd. Séanc. Acad. ScL, Paris, to be published.
4.
DE GENNES P.G., C r. hebd. Séanc. Acad. ScL, Paris, to be published.
Nous avons observe I’anisotropie et les lois de polarisation de l’intensité de la lumlére Rayleigh diffusde par une texture smectique A planaire de butoxyl Benziidéne-p-n anilino-acétophénone (BBAA). Cette diffusion est attribuée a des ondulations statiques des couches smectiques, de vecteur d’onde paralléle aux plans smectiques. Cet effet constitue une méthode simple de mesure du rapport des indices: he/fib = 1, 18 a T = 89°C(ne: indice extraordinaire principal, n0 indice ordinaire).
Vol. 12, pp. 27—29, 1973.
Pergamon Press
Printed in Great Britain
RAYLEIGH SCA11~ERINGINDUCED BY STATIC BENDS OF LAYERS IN A SMECTIC A LIQUID CRYSTAL* R. Ribotta,t G. Durand and J. D. Litsterl Laboratoire de Physique des Solides, § Faculté des Sciences, 91405—Orsay (Received 2 October 1972; in revisedform 15 October 1972 by F. G. de Gennes)
We observe the anisotropy and the polarization properties of the Rayleigh scattered light for a planar smectic A texture of butoxyl benziledene-p-n anilino-acetophenone (BBAA). This scattering is attributed to static bends of the smectic layers, with wave vectors parallel to the smectic planes. This effect gives a simple method to measure the ratio of the extraordinary to the ordinary indices: fle/flO = 1.18 at 89°C.
DE GENNES has suggested1 that in smectic A liquid crystal, the smectic layers could undergo thermally excited bend of formations of wave vector q, parallel to the layers. The reason for this geometric condition is simple: in that case the bend deformation does not imply a compression of the layers and should cost less elastic energy. However this geometry favours also the development of static bends in the material; looking for the thermally excited fluctuations in smectic A single crystals, we have in fact observed a Rayleigh scatteringsignal, having all the polarization and intensity properties implied by the De Gennes’ condition, but which does not fluctuate in time. We attribute this scattering to the existence of small random static bends of the smectic layers in our sample.
b~’~
\ (ic~ d /
b) ,
Let us first summarize the characteristics of the Rayleigh scatteringwhen q is restricted to remain *
FIG. 1. Geometry for Rayleigh scattering of laser light by a sample of smectic A, BBAA liquid crystal (T = 89°C).The scattering pattern appears as portions of circles (see text). am is proportional to the critical q~for which the penetration depth of defects equals the sample thickness.
Work partially supported by French Delegation Generale la Recherche Scientifique et Technique, Under Contract No. 68.01.194.
a
t On leave from Institut d’Electromque Fondamentale Orsay.
parallel to the layers. A planar smectic A sample is illuminated by an ordinary (or extraordinary) light beam, making an angle a with the common normal to
1 John Simon Guggenheim Memorial Fellow. Perma~ nent Address: Dept. of Physics, M.I.T., Cambridge, Mass. 02139, USA.
the layers and the glass boundaries (Fig. 1). Inside the crystal the wave vector of this beam is k~,(or ke).
§ Assoclé au CNRS. 27
28
RAYLEIGH SCATTERING IN A SMECTIC A LIQUID CRYSTAL
Vol. 12, No. 1
A smectic plane bend corresponds to a molecular splay which causes Rayleigh scattering as in nematic crystals The scattered wave may be split up mto ordinary and extraordinary waves of wave vectors k, and k.~.A simple application of the polarization selection rules for splay in nematic crystals2 gives a zero cross section for the(k 0 k~,)configurationThe following three possibilities are left (k0 k~),(Ice k~) (kek,) In the medium k0 and k~,have their ends located on a sphere of radius n0 (ordinary index of refraction), while Ice and k~terminate on an ellipsoid of revolution about the optic axis (also the molecular axis). This ellipsoid comes from the sphere by an affinity of ratio ~e/~o around the molecular axis (; is the principal extraordinary index). With q restricted to the plane of the layers, k and k’ must terminate on one of two concentric circles formed by the intersections of the the sphere and ellipsoid with a plane normal to the molecular axis (and containing q); one circle corresponds to the ordinary ray and the other to the extraordinary ray. The ratio of the components of extraordinary to ordinary wave vectors in this plane is ne/no. This ratio is conserved in the refraction process so that, in air, all the possible scatteringbeams must be on two coaxial cones of well defined angles; let us call (a + i3) the half angle of the extraordinary cone k~scattered from the ordinary wave k0, and (a y) the half angle of the ordinary cones k, scattered from the extraordinary wave ice; one has the simple relationship. —
sin (a + 13) sin a
=
sin a sin (a ‘y) —
=
fl~
~
~
/
Obviously, in the (ke,k~)configuration, the scattered beam must be on the cone of half angle a. Let us assume now a bend amplitude independent ofq and a fixed angle a. The scattered intensity depends on the relative angles between the incident wave polarization, the q direction and the scattered light vibration (tangent or normal to its cone, for ordinary or extraordinary waves). This intensity should vanish for scattering in the plane of symmetry, close to the laser beam. Our experimental set up is sketched on Fig. 1. A 60 mW He—Ne laser beam (X = 6328 A) with an ordinary (o) or extraordinary (e) polarization illuminates a smectic A sample of BBAA. (Butoxy-benzilidene-p-n-
FIG. 2. Two pictures of the scattering patterns showing the two portions of circles corresponding to: (a) extraordinary output for ordinary input, (b) ordinary output for extraordinary attenuated laser beam.input. The spot represents anilino acetophenone). In our experiment a can vary from 0 to 70°.We observe the scattered pattern on a screen (ground glass) of arbitrary orientation, behind an analyser, by eye. The sample is prepared in its smectic A planar texture at T = 89°Cby cooling from the homeotropic nematic phase. The uniformity of the texture is checked by observation under a polarizing microscope. The glass plate against the temperatureregulated oven is a microscope cover-glass of standard quality, and the upper one is a thick (5mm) ?~/10 optically polished window. With mica spacers the thickness of the sample can be adjusted from 50 to 500~um.Figure 2 shows two pictures of the screen for the (ke, k~)and (k0, k’e) configurations. We do find that the scattered light is distributed on the predicted cones, but concentrates in the lower q region. The circularity of the cone is easily checked by using as a reference a simultaneously conoscopic pattern of the sample on the same screen. The scattering pattern is found to remain parallel to the neighbouring conoscopic circular fringes, as long as visible. The two portions of the scattered circles show the central intensity extinction. The polarization of the scattered light is found tangent to the inner ‘circle’ (ordinary wave) and normal to the external one (extraordinary wave). The position of the cones is not dependent on the sample thickness, but the thickness of the circles (typically l0~rad) decreases with samples of better quality. We did not find the scattering for the (Ice, k~)configuration, probably because fmding a region
Vol. 12, No. 1
RAYLEIGH SCATTERING IN A SMECTIC A LIQUID CRYSTAL
29
maximum q extension of the scattered pattern increases as d decreases. This kind of variation would be expected in nematics where defects induced, for in-
~(o)
~
—
B BAA 1=89°C
30\
(i~L)
depth of the order of their transverse wave length. The surprising observation is that now, in the smectic A, the penetration of these defects seems to extend stance, from the plates, extend inlarger the bulk to thicknesses two orderswould of magnitude thanto a their wave length. Possible models to describe this effect are given in references 3 and 4.
COS~ 25 20
~
/
rn Sifl~(!i*~)
o 0
~(o)
~
IC
20
30
£0
50
50
70
SO
90
FIG. 3. Angular dependence of 13 and 1 vs. the mcidence angle a. The angle a = sin_i (no/ne), corresponds to a situation for which the scattered extraordinary wave is at the limit angle and cannot emerge from the material, where the geometrical factor is non zero necessitates the existence of bends of large q. These bends seem to have a very weak amplitude in the sample. We now vary a and measure 13 and Our results are shown on Fig. 3. We find a very good fit of our measurements on the relationship (1) with the value ~e/flo = 1.18 (solid line). This value is to be compared with the birefringence measurement deduced from the conoscopic simultaneous observation: = 0.26. Assumingn 0 = 1.52, one obtains ~e/flo = 1.17, in reasonable agreement with the previous figure. ~.
Finally we have to mention that the scattered signal, analysed on a light beat spectrometer, has not shown any time fluctuation in the range of our capability (l—lO8sec). This can be understood easily: the scattered bends of the layers prevent thermal fluctuations from having a detectable amplitude, the mean angular distortion of the layers being larger than the tolerance on the alignment of q in the smectic planes, as defined in reference 1. To summarise, we have observed in apparently defect free samples of smectic A, small static bends of the smectic layers, which give rise to a strongly anisotropic Rayleigh light scattering. We can deduce from this experiment the ratio of the indices of refraction of the liquid crystal, the origin of the observed bends is not yet dear; their penetration in the bulk is found anomalously large.
Acknowledgements We wish to thank Dr. Liebert and Dr. Strezleski for the synthesis of good quality BBAA, and Dr. P. G. de Gennes for stimulating dis. cussions. —
Using the same plates, we now vary the sample thickness d from 50 to 500 pm; we observe that the
REFERENCES 1.
DE GENNES P.G., J. Phys. C4—65, 30(1969).
2. 3.
DE GENNES P.G., C. r. hebcL Séanc. Acad. ScL, Paris, 15, 266 (1968). DURAND G., C. r. hebd. Séanc. Acad. ScL, Paris, to be published.
4.
DE GENNES P.G., C r. hebd. Séanc. Acad. ScL, Paris, to be published.
Nous avons observe I’anisotropie et les lois de polarisation de l’intensité de la lumlére Rayleigh diffusde par une texture smectique A planaire de butoxyl Benziidéne-p-n anilino-acétophénone (BBAA). Cette diffusion est attribuée a des ondulations statiques des couches smectiques, de vecteur d’onde paralléle aux plans smectiques. Cet effet constitue une méthode simple de mesure du rapport des indices: he/fib = 1, 18 a T = 89°C(ne: indice extraordinaire principal, n0 indice ordinaire).