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Anisotrophy of X-ray critical scattering in liquid NPOB crystal
Solid State Communications, Vol. 41, No. 1, pp, 111-113, 1982. Printed in Great Britain.
0038-1098/82/010111-03502.00/0 Pergamon Press Ltd.
ANISOTROPHY OF X-RAY CRITICAL SCATTERING IN LIQUID NPOB CRYSTAL B. Pura, J. Przedmojski and W. Nazarewicz Institute of Physics, Warsaw Technical University, 00-662 Warszawa, Koszykowa 75, Poland
(Received 9 July 1981 by P. H. Dederichs) We have carried out a high-resolution X-ray critical scattering experiment in the nematic phase connected with the nematic ~ smectic A transition in 4-nitrophenyl-4-n-octyloxybenzoate (Ca Hi7 O-C6 H a - C O O - C 6 H 4 NO2)-NPOB. The measurements yielded the following parameter values: d = 30.20,8,, qo = 0.205 A -~ and the critical exponts ~/= 1.31 -+ 0.11, vii = 0.69 -+0.06, v± = 0.49 -+ 0.08, for 1.5 × 10 -4 ~< (1 -- T/Tc) <~ 10-2. The ratio of the longitudinal to the transverse correlation lengths ~11/~± increases gradually with decreasing reduced temperature and it changes by a factor of about two within the above temperature range. 1. INTRODUCTION INVESTIGATIONS of X-ray critical scattering in liquid crystals undergoing smectic A ~ nematic phase transition which were carried out firstly by McMiUan [1] and subsequently by means of high resolution method by Als-Nielsen et al. [2] allowed for a precise determination of critical exponents. The measurements reported in [3] and [4] yielded significantly different values of critical exponents for the longitudinal ~11 and transverse ~± correlation lengths. The numerical values are vii = 2/3 and vI = 1/2. The interpretation given by De Gennes [5] based upon the analogy between the situation in a liquid crystal and in superfluid helium failed in giving a satisfactory explanation due to differences in the values v±. Besides that the exponents differ with various materials. In the quoted papers the longitudinal ~11 and transverse ~_Lcorrelation lengths were found to be different and a significant change of the ratio ~11/~± with temperature was observed. The present paper contains the results of critical X-ray scattering at temperatures above T~ for smectic A -~ nematic transition in 4-nitrophenyl-4-n-octyloxybenzoate. 2. EXPERIMENTAL The measurements of anistrophy of X-ray critical scattering in NPOB were carried out on a two-crystal spectrometer by using Cura radiation monochromatized with the help of two flat LiF monochromators. Our spectrometer was analogous to that described by AlsNielsen [6]. Slits of 0.25 mm and Soller slits were used. The instrumental spatial resolution expressed as half-widths at half-maximum (HWHM) was I 0 -a A -1 in the longitudinal direction 10 -4 A -t in the transverse direction and 10 -2 A -l in the direction perpendicular
to the scattering plane. The parameters of the primary beam were 20 mA and 40 kV. The liquid crystal was placed in a copper container in the form of a box of size 3 x 4.5 x 1.5 mm. The X-rays penetrated through Mylar windows. The copper container was electrically heated and temperature of the sample was stabilized and controlled automatically within -+ 0.01°C. During the measurements of scattering the magnetic field of 1.8 kG was applied. Only the center of the crystal of dimensions 0.5 × 3 mm was illuminated with X-rays. The scattered radiation was registered by a scintillation counter. The NPOB used in the experiment was synthesized in the Chemical Department of the Martin-Luther Universitiit in Halle (DDR). Scanning calorimetry measurements of NPOB yielded the following phase diagram: Solid II, 47.5°C, Solid I, 50.4°C, SA 61 .I°C I. The nematic phase has a strong tendency toward the homotropic orientation which is preserved in the smectic state. Sometimes the nematic state occurs in a marbled texture and then the smectic modification appears in the simple texture which is typical for smectic A [71. 3. EXPERIMENTAL RESULTS By measuring of the Bragg scattering in the smectic phase we determined d = 30.20 A and with qo = 0.205 A -1 (qo = 2n/d). As the transition temperature T c = 61.33°C was accepted this temperature at which the transverse scan showed the minimal linewidth. We carried out longitudinal scans (q± = O, qJI = varying) and transverse scans (q = qo, q± = varying) for the same fixed temperature. The results are presented in Figs. 1-3. 111
X-RAY CRITICAL SCATTERING IN LIQUID NOPB CRYSTAL
112
The error bars in Fig. 4 refer to standard deviation statistical errors. At the temperature t = 0.00015 the correlation lengths are equal to ~11 = 8 0 0 A , ~± = 1 0 0 A and for t = 0.01 they are equal to ~li = 5 0 A , ~± = 12A. In the same figure is represented the ratio ~11/~± which changes from4-+ 1, a t t = 10 -2 , t o 8 + l a t t = 1.5x 10 -~.
NPOB T~+O 25"C tO000 %o o
o
0
o
o
ee° qll oooq
o
em
2
5oo~
q~=O 205 A
%
ooiio o°
: % : :
o o° ooO o
04
.... ~ o3
~"
I
o.2
°o %0
i %°r •
o,
t
oo
*
"i"
o
I °°°~°°°°~
02
o,
03
Tc+ 0 " 7 ° c oo,:~o 'IF o
o •
o oo
o°
o°° :"
I~o°:t°°°°l ~ I 0.4 0.5 0.2 0.1
:
•
~
o
"'o%
oooCl ~z
~
oO.• ~%o
oO ° °oo°d ooo~oOo I .... r 04 05 02 0 I
°° oo o
I I " " I°°°°?°°°°1 0 0.1 0.2 05 0.4 q/qo
Fig. 2. Longitudinal (qu - qo) and transverse scans in units o f q o = 0.205 A - ' , for the 1.8 kG experiment at the temperature T = Tc + 0.7°C.
=
Oo/[1 - - ~ l ( q l l - - q o ) 2 + ~ q ~
+C~q'*]
0 0.1 q/qo
02
0.5
0.4
NPOB I00(
The data for each scan were analyzed using the cross-section proposed by Als-Neilsen [8] which is o f the form
o(q)
%", °°°°°o Oo T'".. I °~ °°o I
I
The iso-intensity contours in ( q , , q±) plane at temperature T = (Tc + 0.3)°C and T = (Te + 1.2)°C are given respectively in Figs. 5 and 6. The theoretical curves in Figs. 5 and 6 follow from the cross-section (1).
: %0
t
,500
"''qu o o o q.l.
Fig. 3. Longitudinal (qu - - q o ) and transverse scans in units o f qo = 0.205 A -~ , for the 1.8 kG experiment at the temperature T = (Tc + 1.2)°C.
NPOB
2500
Tc+12*C oee%Oo °
O 5000 ro
Fig. 1. Longitudinal (qJl - qo) and transverse scans in units o f q o = 0.205 A -1 , for the 1.8 kG experiment at the temperature T = Tc + 0.25°C.
5000
NPOB
o4
q/qo
I
Vol. 41, No. 1
"
~
q °--0205~'Tc =61.33°C
I0( (1) g
in which the constant Oo corresponds to qo = (0, 0, qo)The data were analyzed in terms o f the cross-section (1) convoluted with the instrumental resolution function and the mosaic spread. The mosaic spread was measured from limiting transverse linewidth for the reduced temperature t ~ 0. This limiting transverse width is much larger than the transverse instrumental width and therefore represents the macroscopic misorientation o f the smectic planes in different regions o f the sample. The mosaicities were 0.6 deg FWHM (full-width at half-maximum) for the 1.8 kG magnetic alignment field. In Fig. 4. we show the values o f ~11 and ~1 for fluctuations o f the smectic in the nematic phase o f NPOB. The dependence o f the correlation length on temperature in the interval 1.5 × t 0 'a ~< t ~< 10 -1 is given by: ~tlqo = 0.41 t -0"69-+0"°6 ~lqo = 0-26t-°'49-+°'°8,
Oo
= at-l.31 +-O.ll
10 0
I 0 0001
I 0001
J 00~
(T -T c ) / T c
Fig. 4. Longitudinal ~tt and transverse ~± correlation lengths as functions of reduced temperatures. Mosaic corrections are indicated by vertical lines. 4. DISCUSSION AND CONCLUSIONS The critical exponents determined from our data are: 7 = 1.31 -4-0.11, Pll = 0.69 ~ 0.06, v± = 0.49 + 0.08. The values for b and vii are close to those o f helium 3' = 1.32, v = 0.67 [9]. However, the transverse correlation length exponent vI = 0.49 -+ 0.08, markedly disagrees with that for helium. The difference in the exponents vll -- v I = 0.20 leads to a change in the ratio o f the correlation lengths by the factor o f about 2 over the reduced temperature range from t = 1.5 x 10 -2 . The difference in the exponents Vii - - Pj. is similar to that observed in CB00A [6], 80CB [8], 8CB [4].
X-RAY SCATTERING IN LIQUID NOPB CRYSTAL
Vol. 41, No. 1
The values of the correlation lengths are connected with the dimensions of clausters of molecules. The latter form fluctuations of the smectic A phase in the nematic phase above the critical temperature. The correlation lengths ~11and ~± for transverse and longitudinal direction respectively are different and they decrease with increasing temperature. The observed temperature dependences of the correlation lengths ~11and ~l are different. This leads to a decrease of the anistrophy of scattering when temperature increases (Figs. 5 and 6). NPOB Tc + 0 . 3 ° C qll/qo
Therefore starting from several degres above Tc scattering is practically isotropic.
Acknowledgement - We wish to thank Professor J. Kocinski for several helpful discussions.
REFERENCES 1. 2. 3. 4. 5.
I 3oo
To%. . . .
6.
O. I --
- '"-"
"--
. . . . . .
7. 8. 01-- --
9.
Theoretical Experimental
Fig. 5. Iso-intensity contour of X-ray critical scattering observed at T = (Te + 1.2)°C. NPOB Tc + I. 2°C
qu/qo
Ol Theoretical Experimen?ol
Fig. 6. Iso-intensity contour of X-ray critical scattering obsrved at T = (Tc + 1.2)°C.
113
W.L. McMillan,Phy~ Rev. A6, 936 (1972). J. Als-Nielsenetat, Phys. Rev. Lett. 39, 1668 (1977). J.D. Litsteretal.,J. dePhys. 40, C3-339 (1979). D. Davidov etaL Phy~ Rev. B19, 1657 (1979). P.G. de Gennes, Solid State CommurL 10, 753 (1972). J. Als-Nielsen et al., Phy~ Rev. Lett. 39,352 (1977). H. Sackmann & D. Demus, MoL Cryst. Liq. Cryst. 21,239 (1973). J. Als-Nielsen & R.J. Birgeneau, AM. J. Phys. 45,554 (1977). J.C. Le Guillou & J. Zinn-Justin, Phys. Re},. 39, 95 (1977).
0038-1098/82/010111-03502.00/0 Pergamon Press Ltd.
ANISOTROPHY OF X-RAY CRITICAL SCATTERING IN LIQUID NPOB CRYSTAL B. Pura, J. Przedmojski and W. Nazarewicz Institute of Physics, Warsaw Technical University, 00-662 Warszawa, Koszykowa 75, Poland
(Received 9 July 1981 by P. H. Dederichs) We have carried out a high-resolution X-ray critical scattering experiment in the nematic phase connected with the nematic ~ smectic A transition in 4-nitrophenyl-4-n-octyloxybenzoate (Ca Hi7 O-C6 H a - C O O - C 6 H 4 NO2)-NPOB. The measurements yielded the following parameter values: d = 30.20,8,, qo = 0.205 A -~ and the critical exponts ~/= 1.31 -+ 0.11, vii = 0.69 -+0.06, v± = 0.49 -+ 0.08, for 1.5 × 10 -4 ~< (1 -- T/Tc) <~ 10-2. The ratio of the longitudinal to the transverse correlation lengths ~11/~± increases gradually with decreasing reduced temperature and it changes by a factor of about two within the above temperature range. 1. INTRODUCTION INVESTIGATIONS of X-ray critical scattering in liquid crystals undergoing smectic A ~ nematic phase transition which were carried out firstly by McMiUan [1] and subsequently by means of high resolution method by Als-Nielsen et al. [2] allowed for a precise determination of critical exponents. The measurements reported in [3] and [4] yielded significantly different values of critical exponents for the longitudinal ~11 and transverse ~± correlation lengths. The numerical values are vii = 2/3 and vI = 1/2. The interpretation given by De Gennes [5] based upon the analogy between the situation in a liquid crystal and in superfluid helium failed in giving a satisfactory explanation due to differences in the values v±. Besides that the exponents differ with various materials. In the quoted papers the longitudinal ~11 and transverse ~_Lcorrelation lengths were found to be different and a significant change of the ratio ~11/~± with temperature was observed. The present paper contains the results of critical X-ray scattering at temperatures above T~ for smectic A -~ nematic transition in 4-nitrophenyl-4-n-octyloxybenzoate. 2. EXPERIMENTAL The measurements of anistrophy of X-ray critical scattering in NPOB were carried out on a two-crystal spectrometer by using Cura radiation monochromatized with the help of two flat LiF monochromators. Our spectrometer was analogous to that described by AlsNielsen [6]. Slits of 0.25 mm and Soller slits were used. The instrumental spatial resolution expressed as half-widths at half-maximum (HWHM) was I 0 -a A -1 in the longitudinal direction 10 -4 A -t in the transverse direction and 10 -2 A -l in the direction perpendicular
to the scattering plane. The parameters of the primary beam were 20 mA and 40 kV. The liquid crystal was placed in a copper container in the form of a box of size 3 x 4.5 x 1.5 mm. The X-rays penetrated through Mylar windows. The copper container was electrically heated and temperature of the sample was stabilized and controlled automatically within -+ 0.01°C. During the measurements of scattering the magnetic field of 1.8 kG was applied. Only the center of the crystal of dimensions 0.5 × 3 mm was illuminated with X-rays. The scattered radiation was registered by a scintillation counter. The NPOB used in the experiment was synthesized in the Chemical Department of the Martin-Luther Universitiit in Halle (DDR). Scanning calorimetry measurements of NPOB yielded the following phase diagram: Solid II, 47.5°C, Solid I, 50.4°C, SA 61 .I°C I. The nematic phase has a strong tendency toward the homotropic orientation which is preserved in the smectic state. Sometimes the nematic state occurs in a marbled texture and then the smectic modification appears in the simple texture which is typical for smectic A [71. 3. EXPERIMENTAL RESULTS By measuring of the Bragg scattering in the smectic phase we determined d = 30.20 A and with qo = 0.205 A -1 (qo = 2n/d). As the transition temperature T c = 61.33°C was accepted this temperature at which the transverse scan showed the minimal linewidth. We carried out longitudinal scans (q± = O, qJI = varying) and transverse scans (q = qo, q± = varying) for the same fixed temperature. The results are presented in Figs. 1-3. 111
X-RAY CRITICAL SCATTERING IN LIQUID NOPB CRYSTAL
112
The error bars in Fig. 4 refer to standard deviation statistical errors. At the temperature t = 0.00015 the correlation lengths are equal to ~11 = 8 0 0 A , ~± = 1 0 0 A and for t = 0.01 they are equal to ~li = 5 0 A , ~± = 12A. In the same figure is represented the ratio ~11/~± which changes from4-+ 1, a t t = 10 -2 , t o 8 + l a t t = 1.5x 10 -~.
NPOB T~+O 25"C tO000 %o o
o
0
o
o
ee° qll oooq
o
em
2
5oo~
q~=O 205 A
%
ooiio o°
: % : :
o o° ooO o
04
.... ~ o3
~"
I
o.2
°o %0
i %°r •
o,
t
oo
*
"i"
o
I °°°~°°°°~
02
o,
03
Tc+ 0 " 7 ° c oo,:~o 'IF o
o •
o oo
o°
o°° :"
I~o°:t°°°°l ~ I 0.4 0.5 0.2 0.1
:
•
~
o
"'o%
oooCl ~z
~
oO.• ~%o
oO ° °oo°d ooo~oOo I .... r 04 05 02 0 I
°° oo o
I I " " I°°°°?°°°°1 0 0.1 0.2 05 0.4 q/qo
Fig. 2. Longitudinal (qu - qo) and transverse scans in units o f q o = 0.205 A - ' , for the 1.8 kG experiment at the temperature T = Tc + 0.7°C.
=
Oo/[1 - - ~ l ( q l l - - q o ) 2 + ~ q ~
+C~q'*]
0 0.1 q/qo
02
0.5
0.4
NPOB I00(
The data for each scan were analyzed using the cross-section proposed by Als-Neilsen [8] which is o f the form
o(q)
%", °°°°°o Oo T'".. I °~ °°o I
I
The iso-intensity contours in ( q , , q±) plane at temperature T = (Tc + 0.3)°C and T = (Te + 1.2)°C are given respectively in Figs. 5 and 6. The theoretical curves in Figs. 5 and 6 follow from the cross-section (1).
: %0
t
,500
"''qu o o o q.l.
Fig. 3. Longitudinal (qu - - q o ) and transverse scans in units o f qo = 0.205 A -~ , for the 1.8 kG experiment at the temperature T = (Tc + 1.2)°C.
NPOB
2500
Tc+12*C oee%Oo °
O 5000 ro
Fig. 1. Longitudinal (qJl - qo) and transverse scans in units o f q o = 0.205 A -1 , for the 1.8 kG experiment at the temperature T = Tc + 0.25°C.
5000
NPOB
o4
q/qo
I
Vol. 41, No. 1
"
~
q °--0205~'Tc =61.33°C
I0( (1) g
in which the constant Oo corresponds to qo = (0, 0, qo)The data were analyzed in terms o f the cross-section (1) convoluted with the instrumental resolution function and the mosaic spread. The mosaic spread was measured from limiting transverse linewidth for the reduced temperature t ~ 0. This limiting transverse width is much larger than the transverse instrumental width and therefore represents the macroscopic misorientation o f the smectic planes in different regions o f the sample. The mosaicities were 0.6 deg FWHM (full-width at half-maximum) for the 1.8 kG magnetic alignment field. In Fig. 4. we show the values o f ~11 and ~1 for fluctuations o f the smectic in the nematic phase o f NPOB. The dependence o f the correlation length on temperature in the interval 1.5 × t 0 'a ~< t ~< 10 -1 is given by: ~tlqo = 0.41 t -0"69-+0"°6 ~lqo = 0-26t-°'49-+°'°8,
Oo
= at-l.31 +-O.ll
10 0
I 0 0001
I 0001
J 00~
(T -T c ) / T c
Fig. 4. Longitudinal ~tt and transverse ~± correlation lengths as functions of reduced temperatures. Mosaic corrections are indicated by vertical lines. 4. DISCUSSION AND CONCLUSIONS The critical exponents determined from our data are: 7 = 1.31 -4-0.11, Pll = 0.69 ~ 0.06, v± = 0.49 + 0.08. The values for b and vii are close to those o f helium 3' = 1.32, v = 0.67 [9]. However, the transverse correlation length exponent vI = 0.49 -+ 0.08, markedly disagrees with that for helium. The difference in the exponents vll -- v I = 0.20 leads to a change in the ratio o f the correlation lengths by the factor o f about 2 over the reduced temperature range from t = 1.5 x 10 -2 . The difference in the exponents Vii - - Pj. is similar to that observed in CB00A [6], 80CB [8], 8CB [4].
X-RAY SCATTERING IN LIQUID NOPB CRYSTAL
Vol. 41, No. 1
The values of the correlation lengths are connected with the dimensions of clausters of molecules. The latter form fluctuations of the smectic A phase in the nematic phase above the critical temperature. The correlation lengths ~11and ~± for transverse and longitudinal direction respectively are different and they decrease with increasing temperature. The observed temperature dependences of the correlation lengths ~11and ~l are different. This leads to a decrease of the anistrophy of scattering when temperature increases (Figs. 5 and 6). NPOB Tc + 0 . 3 ° C qll/qo
Therefore starting from several degres above Tc scattering is practically isotropic.
Acknowledgement - We wish to thank Professor J. Kocinski for several helpful discussions.
REFERENCES 1. 2. 3. 4. 5.
I 3oo
To%. . . .
6.
O. I --
- '"-"
"--
. . . . . .
7. 8. 01-- --
9.
Theoretical Experimental
Fig. 5. Iso-intensity contour of X-ray critical scattering observed at T = (Te + 1.2)°C. NPOB Tc + I. 2°C
qu/qo
Ol Theoretical Experimen?ol
Fig. 6. Iso-intensity contour of X-ray critical scattering obsrved at T = (Tc + 1.2)°C.
113
W.L. McMillan,Phy~ Rev. A6, 936 (1972). J. Als-Nielsenetat, Phys. Rev. Lett. 39, 1668 (1977). J.D. Litsteretal.,J. dePhys. 40, C3-339 (1979). D. Davidov etaL Phy~ Rev. B19, 1657 (1979). P.G. de Gennes, Solid State CommurL 10, 753 (1972). J. Als-Nielsen et al., Phy~ Rev. Lett. 39,352 (1977). H. Sackmann & D. Demus, MoL Cryst. Liq. Cryst. 21,239 (1973). J. Als-Nielsen & R.J. Birgeneau, AM. J. Phys. 45,554 (1977). J.C. Le Guillou & J. Zinn-Justin, Phys. Re},. 39, 95 (1977).