- Email: [email protected]
Anisotropy of X-ray critical scattering in 4,4-di-n-hexyl-biphenyl liquid crystal
Volume 96A, number 2
PHYSICS LETTERS
13 June 1983
ANISOTROPY OF X-RAY CRITICAL SCATTERING IN
4,4-DI-n-HEXY~BIPHENYLLIQUIDCRYSTAL
B. PURA and J. PRZEDMOJSKI Institute o f Physics, Warsaw Technical University, Koszykowa 75, 00-662 Warsaw, Poland
Received 7 July 1982
We have carried out a high-resolution X-ray critical scattering experiment in the isotropic phase connected with the isotropic-smectic-B transition in 4,4-di-n-hexyl-biphenyl. The measurements yield the following parameter values: d = 23.92 A, qo = 0.268 A -I and the critical exponents 7 = 1.51 ~ 0.12, vii = 0.65 ± 0 . 0 6 , v ± = 0.70 ± 0.08. At the temperature t = 10 -a (t = TIT c - 1) the correlation lengths are ~1~= 390A and ~± = 1080A.
I n t r o d u c t i o n . The liquid-crystal B phase is a layered phase with the molecules oriented perpendicular to the layer planes and hexagonally ordered with. in each layer. Recent X-ray structural studies [ 1 - 3 ] have led to the conclusion that this hexagonal order involves positional correlations which are three-dimensional and long range. Using free-standing liquidcrystal film techniques Pindak et al. [4] have found that the B phase exhibits short-range order in the plane of the layer and also long-range three-dimensional sixfold bond-orientational order. This B phase is, therefore, quasi-crystalline. The aim of our measurements is to obtain more information concerning the three-dimensional molecular arrangement. To this end we have carried out the critical scattering in the smectic-B 4,4-di-hexyl-biphenyl liquid crystal with hexagonal arrangement in the smectic layer for a temperature above the smectic-B-isotropic phase transition. E x p e r i m e n t . The measurements of X-ray critical scattering were carried out on a two-crystal spectrometer by using Cu Ka radiation monochromatized with the help of two flat Ge single crystals having a small density of dislocations. Slits of 0.1 mm and Soller slits were used. The instrumental spatial resolution expressed as HWHM (half width at half maximum) was 6 X 10 - 4 A -1 in the longitudinal direction,
98
5 × 10 -5 A -1 in the transverse direction and 2 × 10 - 2 A -1 in the direction perpendicular to the scattering plane. The parameters of the primary beam were 40 kV and 40 mA. The liquid crystal was placed in a copper container in the form of a box of sizes 4 × 15 × 1.5 ram, with beryllium windows. The copper container was electrically heated and the temperature of the sample was stabilized and controlled automatically within -+0.01°C. The sample was ordered with the help of a magnetic field of intensity 5 kG. The X-ray illuminated area of the sample had size 0.4 ×4mm. The 4,4-di-n-hexyl-biphenyl liquid crystal used in our investigations has the phase diagram 35.2°C 3 9 . 1 ° C 53.3°c solid* > S E* > S• < ~ I. Our measurements yielded the following parameter values for the smectic E and B phases;d E = 23.21 A, qB = 23.92 )~, qE = 0"272)k-1 and qB = 0"268 A - I " Results. T h e smectic-B-isotropic-liquid phase transition is a first-order transition (fig. 1). The temperature of this phase transition is T c = 53.30°C. We have measured the change of the X-ray critical scattering intensity for the directions (q u - q0, q varying) and (q varying, ql = 0) at the temperature T = (T c + 0.2)°C (fig. 2).
0 031-9163]83/0000-0000/$ 03.00 © 1983 North-Holland
Volume 96A, number 2
PHYSICS LETTERS
13 June 1983 0.3 °C
100 •
zT-
, i0 $ 0
0.02
- .~
la°°\~-,~
SMECH£ B I
SNECrlC E
_
40
50
~
r ('C)
Fig. 1. Measured X-ray scattered intensity versus temperature at the Bragg angle in the smectic E and B phases.
At the temperature t = 10 - 3 (t = TIT c - 1) the correlation lengths are ~ II = 390 A. and ~.t = 1080 A. The critical exponents 1, = 1.51 + 0.12, Vii = 0.65 + 0.06, V± = 0.70 -+ 0.08 were extracted from our data. We have also investigated the anisotropy of the Xray critical scattering. The equi-intensity contour maps drawn in the (q,, q±) plane at the temperature T = (T c + 0.3)°C are given in fig. 3. By using the cross section given by Ms-Nielsen et al. [5] which is of the form 2 o(q) = oo(qo)l[1 + (qll - q0) 2 ~II + q±2 2~± + cq4~4], (1) we have calculated the correlation lengths ~, and ~±, qll and q±.
Analysis and discussion. The values of the critical exponents vii , V.L and 3' are similar within errors with
"
t
%+0.2°C
• tO3 l
o o - - OtI • . --q~
0.02
Fig. 3. Iso-intensity contour of X-ray critical scattering observed at T = (Tc + 0.3) °C. The dotted lines follow from the cross section (1) convoluted with the instrumental resolution function.
the corresponding exponents for the n e m a t i c smectic-A phase transition in CBOOA [5,6], 8OCB [7], 8CB [8], NPOB [9], EEBAC [10]. Analogous results have been observed for the longitudinal correlation length ~11, the magnitude of which is of the same order as that in smectic A. The transverse correlation length ~l is by almost an order of magnitude larger than in the smectic-A liquid crystal. The anisotropy of the critical scattering iso-intensity contour maps in fig. 3 deviates from that observed with neutrons in CBOOA [6] and with X-rays in NPOB [9], EEBAC [10]. The theoretical curves in fig. 3 calculated from the cross section proposed by Als-Nielsen et al. [5] have an elliptical shape. In spite of this discrepancy between the experimental and theoretical contours the two correlation lengths, which correspond to the direction q u/q0 and q±/qo in fig- 3 have been calculated on the basis of the cross section (1). The shape of the experimental iso-intensity curves strongly resembles that o f the isointensity curves of critical X-ray scattering in single crystals [ 1 1 - 1 3 ] . It seems, therefore, that our resuits support the suggestion of Moncton and Pindak. We wish to thank Professor J. Kocifiski for Several helpful discussions.
0.0~
0.02
0.02
0.04
q/¢.
Fig. 2. Longitudinal (q II- qo) and transverse scans in units of qo = 0.268 A -1, for the 5 kG experiment at temperature T = (T c + 0.2)°C.
References [1] A. de Vries, J. Chem. Phys. 70 (1979) 2705. [2] D.E. Moncton and R. Pindak, Phys. Rev. Lett. 43 (1979) 701. 99
Volume 96A, number 2 [3] [4] [5] [6]
PHYSICS LETTERS
A.J. Leadbetter et al., Phys. Rev. Lett. 43 (1979) 630. R. Pindak et al., Phys. Rev. Lett. 46 (1981) 1135. J. Als-Nielsen et al., Phys. Rev. Lett. 39 (1977) 352. A.M. Conrad et al., Solid State Commun. 23 (1977) 571. [7] J.D. Litster et al., J. Phys. (Paris) 40 (1979) C3-339. [8] D. Davidov et al., Phys. Rev. B19 (1979) 1657. [9] B. Pura et al., Solid State Commun. 41 (1982) 111.
100
13 June 1983
[10] A. Rajewska et al., J. Phys. (Paris), to be published. [11] B. Pura and J. Przedmojski, Phys. Lett. 43A (1973) 217. [12] B. Pura and J. Przedmojski, Phys. Star. Sol. 69b (1975) K37. [13] J. Przedmojski and B. Pura, Ferroelectrics 21 (1978) 545.
PHYSICS LETTERS
13 June 1983
ANISOTROPY OF X-RAY CRITICAL SCATTERING IN
4,4-DI-n-HEXY~BIPHENYLLIQUIDCRYSTAL
B. PURA and J. PRZEDMOJSKI Institute o f Physics, Warsaw Technical University, Koszykowa 75, 00-662 Warsaw, Poland
Received 7 July 1982
We have carried out a high-resolution X-ray critical scattering experiment in the isotropic phase connected with the isotropic-smectic-B transition in 4,4-di-n-hexyl-biphenyl. The measurements yield the following parameter values: d = 23.92 A, qo = 0.268 A -I and the critical exponents 7 = 1.51 ~ 0.12, vii = 0.65 ± 0 . 0 6 , v ± = 0.70 ± 0.08. At the temperature t = 10 -a (t = TIT c - 1) the correlation lengths are ~1~= 390A and ~± = 1080A.
I n t r o d u c t i o n . The liquid-crystal B phase is a layered phase with the molecules oriented perpendicular to the layer planes and hexagonally ordered with. in each layer. Recent X-ray structural studies [ 1 - 3 ] have led to the conclusion that this hexagonal order involves positional correlations which are three-dimensional and long range. Using free-standing liquidcrystal film techniques Pindak et al. [4] have found that the B phase exhibits short-range order in the plane of the layer and also long-range three-dimensional sixfold bond-orientational order. This B phase is, therefore, quasi-crystalline. The aim of our measurements is to obtain more information concerning the three-dimensional molecular arrangement. To this end we have carried out the critical scattering in the smectic-B 4,4-di-hexyl-biphenyl liquid crystal with hexagonal arrangement in the smectic layer for a temperature above the smectic-B-isotropic phase transition. E x p e r i m e n t . The measurements of X-ray critical scattering were carried out on a two-crystal spectrometer by using Cu Ka radiation monochromatized with the help of two flat Ge single crystals having a small density of dislocations. Slits of 0.1 mm and Soller slits were used. The instrumental spatial resolution expressed as HWHM (half width at half maximum) was 6 X 10 - 4 A -1 in the longitudinal direction,
98
5 × 10 -5 A -1 in the transverse direction and 2 × 10 - 2 A -1 in the direction perpendicular to the scattering plane. The parameters of the primary beam were 40 kV and 40 mA. The liquid crystal was placed in a copper container in the form of a box of sizes 4 × 15 × 1.5 ram, with beryllium windows. The copper container was electrically heated and the temperature of the sample was stabilized and controlled automatically within -+0.01°C. The sample was ordered with the help of a magnetic field of intensity 5 kG. The X-ray illuminated area of the sample had size 0.4 ×4mm. The 4,4-di-n-hexyl-biphenyl liquid crystal used in our investigations has the phase diagram 35.2°C 3 9 . 1 ° C 53.3°c solid* > S E* > S• < ~ I. Our measurements yielded the following parameter values for the smectic E and B phases;d E = 23.21 A, qB = 23.92 )~, qE = 0"272)k-1 and qB = 0"268 A - I " Results. T h e smectic-B-isotropic-liquid phase transition is a first-order transition (fig. 1). The temperature of this phase transition is T c = 53.30°C. We have measured the change of the X-ray critical scattering intensity for the directions (q u - q0, q varying) and (q varying, ql = 0) at the temperature T = (T c + 0.2)°C (fig. 2).
0 031-9163]83/0000-0000/$ 03.00 © 1983 North-Holland
Volume 96A, number 2
PHYSICS LETTERS
13 June 1983 0.3 °C
100 •
zT-
, i0 $ 0
0.02
- .~
la°°\~-,~
SMECH£ B I
SNECrlC E
_
40
50
~
r ('C)
Fig. 1. Measured X-ray scattered intensity versus temperature at the Bragg angle in the smectic E and B phases.
At the temperature t = 10 - 3 (t = TIT c - 1) the correlation lengths are ~ II = 390 A. and ~.t = 1080 A. The critical exponents 1, = 1.51 + 0.12, Vii = 0.65 + 0.06, V± = 0.70 -+ 0.08 were extracted from our data. We have also investigated the anisotropy of the Xray critical scattering. The equi-intensity contour maps drawn in the (q,, q±) plane at the temperature T = (T c + 0.3)°C are given in fig. 3. By using the cross section given by Ms-Nielsen et al. [5] which is of the form 2 o(q) = oo(qo)l[1 + (qll - q0) 2 ~II + q±2 2~± + cq4~4], (1) we have calculated the correlation lengths ~, and ~±, qll and q±.
Analysis and discussion. The values of the critical exponents vii , V.L and 3' are similar within errors with
"
t
%+0.2°C
• tO3 l
o o - - OtI • . --q~
0.02
Fig. 3. Iso-intensity contour of X-ray critical scattering observed at T = (Tc + 0.3) °C. The dotted lines follow from the cross section (1) convoluted with the instrumental resolution function.
the corresponding exponents for the n e m a t i c smectic-A phase transition in CBOOA [5,6], 8OCB [7], 8CB [8], NPOB [9], EEBAC [10]. Analogous results have been observed for the longitudinal correlation length ~11, the magnitude of which is of the same order as that in smectic A. The transverse correlation length ~l is by almost an order of magnitude larger than in the smectic-A liquid crystal. The anisotropy of the critical scattering iso-intensity contour maps in fig. 3 deviates from that observed with neutrons in CBOOA [6] and with X-rays in NPOB [9], EEBAC [10]. The theoretical curves in fig. 3 calculated from the cross section proposed by Als-Nielsen et al. [5] have an elliptical shape. In spite of this discrepancy between the experimental and theoretical contours the two correlation lengths, which correspond to the direction q u/q0 and q±/qo in fig- 3 have been calculated on the basis of the cross section (1). The shape of the experimental iso-intensity curves strongly resembles that o f the isointensity curves of critical X-ray scattering in single crystals [ 1 1 - 1 3 ] . It seems, therefore, that our resuits support the suggestion of Moncton and Pindak. We wish to thank Professor J. Kocifiski for Several helpful discussions.
0.0~
0.02
0.02
0.04
q/¢.
Fig. 2. Longitudinal (q II- qo) and transverse scans in units of qo = 0.268 A -1, for the 5 kG experiment at temperature T = (T c + 0.2)°C.
References [1] A. de Vries, J. Chem. Phys. 70 (1979) 2705. [2] D.E. Moncton and R. Pindak, Phys. Rev. Lett. 43 (1979) 701. 99
Volume 96A, number 2 [3] [4] [5] [6]
PHYSICS LETTERS
A.J. Leadbetter et al., Phys. Rev. Lett. 43 (1979) 630. R. Pindak et al., Phys. Rev. Lett. 46 (1981) 1135. J. Als-Nielsen et al., Phys. Rev. Lett. 39 (1977) 352. A.M. Conrad et al., Solid State Commun. 23 (1977) 571. [7] J.D. Litster et al., J. Phys. (Paris) 40 (1979) C3-339. [8] D. Davidov et al., Phys. Rev. B19 (1979) 1657. [9] B. Pura et al., Solid State Commun. 41 (1982) 111.
100
13 June 1983
[10] A. Rajewska et al., J. Phys. (Paris), to be published. [11] B. Pura and J. Przedmojski, Phys. Lett. 43A (1973) 217. [12] B. Pura and J. Przedmojski, Phys. Star. Sol. 69b (1975) K37. [13] J. Przedmojski and B. Pura, Ferroelectrics 21 (1978) 545.