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Dependence of viscoelastic parameters of nematic liquid crystals on pretilt angle and temperature
Current Applied Physics 10 (2010) 561–564
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Dependence of viscoelastic parameters of nematic liquid crystals on pretilt angle and temperature Yao-Xiong Huang *, Mei Tu Institute of Biomedical Engineering, Jinan University, Guangzhou 510632, China
a r t i c l e
i n f o
Article history: Received 9 May 2008 Received in revised form 11 July 2009 Accepted 27 July 2009 Available online 30 July 2009 PACS: 61.30.Hn 61.30.Eb
a b s t r a c t The viscoelastic parameters of nematic liquid crystal (LC) E7 in both splay and twist relaxation modes are investigated as functions of pretilt angle and temperature by the technique of dynamic laser light scattering. The results show that the elastic constants of the liquid crystal in the two modes not only depend on temperature, but also depend on pretilt angle. There is a critical pretilt angle (bC) at which nematic LC begins exhibiting elastic property, and beyond which the elastic constants increase with pretilt angle, then keep constant after exceeding another angle (bS, with bS > bC). This phenomenon is observed to be universal for different nematic LC’s, and significant not only in the understanding of the molecular mechanism of exhibiting viscoelastic properties in nematic LC, but also for their practical purpose. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Nematic liquid crystal Relaxation mode Viscoelastic parameters Pretilt angle
1. Introduction Liquid crystals (LC) are the kinds of mesomorphic substances possess the characters of low dimension and order between liquids and crystals. They have not only flow properties of liquids, but also anisotropic optical properties of crystals. In the applications of liquid crystals, mainly the optical anisotropy is utilized to achieve optical modulation. The condition for a LC to exhibit optical anisotropy is that it must be in regular and ordered alignment. The regularity of a liquid crystal is characterized by its vector director n, which in turn can be represented by the pretilt angle of the LC molecules [1,2]. Generally, the alignment of LC molecules is achieved by a thin alignment layer which is applied to a glass plate substrate. The most popular method of forming the alignment layer is to coat an inorganic or organic film on the inner surface of the glass plate substrate, then rub the surface by velvet textures or cloths. When the LC molecules are placed on this layer, they are automatically aligned in the direction made by rubbing and become regularity. However, the regularity can be distorted by thermal effect or other external forces. For example, thermal effect can induce spontaneous fluctuations of n, thus lead to dynamic distortions of the nematic structure. The dynamic distortions implicate the information about the LCs elastic parameters such as twist, * Corresponding author. Tel.: +86 20 85220469; fax: +86 20 85223742. E-mail address: [email protected] (Y.-X. Huang). 1567-1739/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2009.07.022
splay and bend elastic constants. The dynamic distortion behavior of liquid crystals induced by thermal effect and its relation with pretilt angle are very important in basic investigation and for display applications, for both the elastic constants and pretilt angle are the key parameters of LC devices. From the dependence of the elastic constants on pretilt angle and temperature, the relation between the distortional ability of LC molecules and their pre-confinement at different thermal conditions, and the balance among different interactions can be revealed. Based on our knowledge, no research about this relation has been reported previously. One of the most probable reasons for such a situation is that it is difficult to determine the elastic constants in situ for a LC device. Since the spontaneous thermal fluctuations of the vector director n of a defect-free nematic domain, light scattering in nematic liquid crystals is strong enough and can give the information about the dynamic distortions of the nematic structure, such as twist, splay and bend elastic deformation. Several authors have shown [3–5] that the technique of dynamic light scattering (or called photon correlation spectroscopy) can simultaneously determine the viscoelastic deformations for both the splay and twist relaxation modes without disturbance on the LC device. Therefore, it is an ideal tool to measure the viscoelastic parameters of LC’s with different pretilt angles and temperature in situ. For this reason, we used dynamic light scattering to determine the splay and twist elastic constants K11 and K22, and the viscosity coefficients gsplay and gtwist of LC as functions of pretilt angle and temperature.
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Y.-X. Huang, M. Tu / Current Applied Physics 10 (2010) 561–564
In this paper, the nematic liquid crystal E7 is selected as the object of study. This LC is an eutectic mixture of four low molecular weight liquid crystals but has a single nematic-isotropic transition temperature tNI = 58 °C. Since the optical anisotropy (Dn = neno) of E7 molecules is large enough to be used in polymer dispersed LC for many applications such as to reduce the driving voltage, rise time and to augment the contrast ratio [6], the blends of polymers and E7 are widely employed in display devices, light shutters, privacy windows, tunable photonic band gap [7–9] etc. Accordingly the polymer dispersed E7 composites, consisting of LC microdroplets embedded in a transparent polymer matrix, have recently attracted a great deal of interest for their potential in a variety of applications. In view of this, the study on the dynamic distortion behavior and their dependence on pretilt angle and temperature will possess theoretic instructional significance for the developments and applications of E7. 2. Experimental 2.1. Preparation of the samples Mixture E7 was purchased from Slichem Liquid Crystal Material Co. in Shijiazhuang City, China. The liquid crystal is nematic at room temperature, its tXN < 20 °C, tNI = 58 °C. Two clean glasses were used to prepare a homogeneously aligned nematic cell, with coated polyvinyl alcohol (PVA) alignment layers on the inner surfaces of the glass plate substrates. After the PVA has been dried, the two glass surfaces were rubbed uni-directionally with a velvet cloth, which was wrapped on a rotation wheel. The thickness of the cell gap was 25 lm. It was sealed with epoxy resin after the sample (E7) is filled in. 2.2. Method and equipment The crystal rotation method [10,11] was used for the measurement on the pretilt angle of E7. All the measurements were performed at room temperature (t = 23 °C). The laser light scattering apparatus used for the measurement on the dynamic distortion of E7 in these experiments is the same as that described previously [12]. It consists of an argon laser (Iron Co., working at k0 = 514 nm), a goniometer (BI200SM); a single photon recording system with high sensitivity and low dark current; a Brookhaven BI9000AT autocorrelator, and a temperature controlling system. The experimental setup was so configured that the incident light was vertically polarized and the scattered light horizontally polarized with the vector director n, and perpendicular to the plane of the incident and scattered directions. For such an experimental geometry, only q\, the wave vector component perpendicular to the director n should be considered. In experiment, the scattered angle (h) was set at the range from 15° to 65°. The autocorrelation function of the scattered intensity was analyzed using the autocorrelator. The autocorrelation function is given by:
h 2 i Gð2Þ ðq; tÞ ¼ B 1 þ aA1 ðqÞeC1 ðqÞt þ A2 ðqÞeC2 ðqÞt
and C2(q) are also related to the viscoelastic coefficients of the LC respectively as follows [3]:
C1 ðqÞ ¼ Csplay ðqÞ ¼ C2 ðqÞ ¼ Ctwist ðqÞ ¼
K 11 q2?
gsplay K 22 q2?
gtwist
ð3Þ
where q\ = (2p/k0)[n02sin2h + (ne n0cosh)2]1/2. Therefore, one can obtain gsplay and gtwist from C1(q) and C2(q) upon knowing the values of K11 and K22 from A1(q) and A2(q). For E7, the values of ne and no are 1.720 and 1.521, respectively [13]. Since the scattering is taken at optical frequency, the dielectric anisotropy contains no contribution from permanent dipoles and can be expressed as the optical anisotropy: De = n//2 n\2 = ne2 n02 [1], thus De 0.6450. In experiment, each set of A1(q), A2(q), C1(q) and C2(q) were determined by averaging the autocorrelation functions measured in five times, then K11, K22, gsplay and gtwist were deduced from the values of A and C with different q (or h) and pretilt angles. The calibration of the light scattering setup and the detail process of autocorrelation function analysis can be referred to Refs. [3,12]. To make a comparison between the values of gsplay and gtwist, and that of the bulk or capillary flow viscosity gbulk, an Ubbelohde viscometer was also used in the experiment to measure gbulk. 3. Results and discussions Fig. 1 is a typical curve of the autocorrelation function of E7 LC. A1 and A2 (or Asplay and Atwist) obtained from the autocorrelation function as a function of scattering angle at temperature t = 40 °C and b = 3.4° are illustrated in Fig. 2. It can be seen that, in the range of scattering angles from 15° to 65°, the dynamic distortion displays the two dynamic modes simultaneously. For 20° < h < 40°, the amplitude of the twist mode is very small and the splay mode dominates the dynamics. Especially at the angle of h = 35°, the amplitude of the twist mode vanishes, the dynamic behavior of E7 is only described by the splay mode. For h > 40°, the twist mode emerges gradually, and becomes more important as h is increased. The similar behaviors are also observed at other temperatures (t = 25, 30, 35 °C) and pretilt angles (b = 2.1, 4.7°), as well as in other nematic LC such as 5CB Redouane Borsali [3]. So the scattering angles suggested to observe the relaxation modes of E7 are in the ranges of 15° < h < 25° and 45° < h < 5°. Fig. 3 shows the variation of C of the two relaxation modes with q\2 at 25 and 40 °C, respectively. We can see that both Csplay and Ctwist increase linearly against q\2 but with different slopes. The values of Csplay are much greater than those of Ctwist in most values
ð1Þ
where B is the base line, a is the spatial coherence factor that depends on the detection geometry, A1(q) and A2(q) are the amplitudes of the normal modes called splay-bend and twist-bend modes, having frequencies C1(q) and C2(q), respectively. According to Redouane Borsali and co-workers [3], the amplitudes of the two light scattering modes in turn give the information of the splay and twist elastic constants K11 and K22, if the values of the ordinary and extraordinary refractive indices of the LC, ne and no; the scattered angle h; the absolute temperature T and the dielectric anisotropy De = e// e\ are known. On the other hand, the parameters C1(q)
ð2Þ
Fig. 1. A typical autocorrelation function of E7.
Y.-X. Huang, M. Tu / Current Applied Physics 10 (2010) 561–564
563
Fig. 2. Variation of amplitudes of the splay and twist modes as a function of the scattering angle (b = 3.4°, t = 40 °C). () Twist mode and (j) splay mode.
Fig. 4. Variation of K11 and K22 with pretilt angle in different temperatures. t = 25 °C; jt = 30 °C; Nt = 35 °C and dt = 40 °C.
Fig. 3. Variation of C with q\ in the two modes. : Splay mode at t = 40 °C; N: splay mode at t = 25 °C; j: twist mode at t = 40 °C and d: twist mode at t = 25 °C.
of q\ so that the two modes can be easily distinguished in a wide range of scattering angle. The elastic constants of E7 in different pretilt angles and temperatures are shown in Fig. 4. The value of K11 at 20 °C (11.25 1012 N) agrees well with the value taken by the method of Frederiks deformation (11.1 1012 N) at the same temperature [14], showing that the technique of dynamic light scattering can give accurate and reliable result. From Fig. 4 we can see that both K11 and K22 decrease with temperature, and increase with pretilt angles then keep constant after exceeding the angle b = 5°. On the other hand, when b < 1°, the elastic constants of E7 become immeasurable, so the lowest values of the elastic constants showing in Fig. 4 were taken at b = 1.1°. The pretilt angle of a nematic LC is caused by the anisotropic alignment of the first LC monolayer molecules on the rubbed polyimide film. Such an anisotropic alignment is induced through a short range interaction between the rubbed polyimide film and the first LC monolayer molecules. During the process of rubbing, a large deformation of the polymer backbone works with its side chains [15]. The greater the rubbing strength, the larger is the deformation, thus a greater pretilt angle is resulted. The anisotropic molecular orientation then propagates into the bulk LC via a long range (elastic) interaction among the LC molecules, makes the whole bulk of the liquid crystal also in orientation order [16– 18]. The elastic constants of a nematic LC are the apparent parameters of the molecular orientation order, or in other wards, they are the physical properties which depend on its molecular orientation
order. Therefore, for a LC to exhibit the property of crystal, its molecules must be in alignment. When pretilt angle is very small (e.g., <1° for E7), the E7 molecules can not align steadily on the rubbed surfaces at small friction strength, only very few first LC monolayer molecules are in alignment, thus almost none of the bulk LC molecules are induced in orientation order. Consequently, no elastic property exhibits. As pretilt angle increase, more and more the first LC monolayer molecules are in alignment, and correspondingly more and more bulk LC molecules are induced in orientation order. When the orientation order parameter increases to a certain value, the elastic constants become apparent and increase with pretilt angle until b P 5°. At this angle, almost all the bulk LC molecules have become aligned completely, so the elastic parameters keep constant after exceeding the angle. To see if other nematic LC’s also have a critical pretilt angle for exhibiting elastic properties, and another angle for the elastic constants to become saturated. We performed a less comprehensive study on nematic LC Z7 (phenylcyclohexane system), D6 (cyclohexanecarboxylphenyl system) and R5 (pyrimidine system) also obtained from Slichem Liquid Crystal Material Co., the result shows that similar phenomena are observed in these nematic LC’s (data not shown). It is reasonable that the elastic constants decrease with temperature at a certain pretilt angle, since thermal perturbation disrupts the orientation order of the LC molecules, so elastic constants decrease. Fig. 5 illustrates the dependence of three viscosities on temperature. They are the gsplay and gtwist measured by light scattering and the bulk viscosity measured by Ubbelohde viscometer. Obviously, all the viscosities decrease with temperature in the range from 20 to 40 °C. In this temperature range, the magnitude of gsplay is slightly greater than gtwist, and the later is almost the same as the bulk viscosity gbulk. No pretilt angle dependence of both gsplay and gtwist is observed in the experiment. This is understandable, for the viscosity of a LC device is mainly a bulk property but without/or little correlation with the first monolayer. It should be noted
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Fig. 5. Variation of viscosity of E7 with temperatures (: gsplay, j: gtwist and N: gbulk).
the technique of dynamic laser light scattering. We observe that the elastic constants of the nematic LC are functions of pretilt angle in the range of small pretilt angles. There is a critical pretilt angle (bC) at which nematic LC begins exhibiting elastic property, and beyond which the elastic constants increase with pretilt angle, then keep constant after exceeding another angle (bS). This phenomenon seems universal for different nematic LC’s. Based on our knowledge, this is the first time such a phenomenon is reported. It is believed to be significant not only in the understanding of the molecular mechanism of exhibiting viscoelastic properties in nematic LC, but also for the practical purpose of the LC’s. Our finding about the relation between elastic constants and pretilt angle indicates that the elastic parameters of LC devices can be adjusted to some extent by varying pretilt angle, and to guarantee LC devices work with steady elastic parameters, a certain pretilt angle (>bS) has to be preset. No dependence of viscosity on pretilt angle is observed. Both elastic constants and viscosities of E7 decrease with increasing in temperature, while the viscoelastic parameters K11/gsplay and K22/ gtwist increase with increasing in temperature. Though the splay mode has a steeper slope than the twist mode in their dependence on temperature, both the curves are linear and provide the information about the temperature range in which the LC is of stability of nematic phase. Acknowledgments This work was supported in part by the Chinese National Natural Science Foundation (Grant No.: 30227001) and by the Guang Dong Provincial Natural Science Fund (Grant No.: 9803162). References
Fig. 6. Variation of the viscoelastic parameters with temperatures (: K11/gsplay; j: K22/gtwist).
that owing to their strong temperature dependence, both gsplay and gtwist decrease with temperature faster than elastic constants, so the viscoelastic parameters K11/gsplay and K22/gtwist increase linearly with temperature, as is shown in Fig. 6. We can see that the splay mode has a steeper slope than the twist mode in their dependence on temperature, for K11 decreases with temperature faster than K22. Similar behavior was also found in other nematic LCs [7]. 4. Conclusion We have studied the dependence of the viscoelastic parameters of nematic liquid crystal E7 on pretilt angle and temperature, using
[1] L. Pohl, E. Merck, Physical properties of liquid crystals, in: B. Bahadur (Ed.), Liquid Crystals, World Scientific, Singapore, 1990. [2] X.I.E. Yuzhang, Liquid Crystal Physics, Science Press, Beijing, 1998. [3] Redouane Borsali, Do Yoon, R. Pecora, J. Phys. Chem. B102 (1998) 6337. [4] D. Gu, C. Rosenblatt, Macromolecules 24 (1991) 2385. [5] D. Gu, A. Jamieson, M. Kawasumi, Macromolecules 25 (1992) 2151. [6] Kubota Satoru, Displays 18 (1998) 79. [7] P. Yeh, C. Gu, Displays 21 (2000) 31. [8] A. Eringen, C. Cemal, Int. J. Eng. Sci. 38 (2000) 959. [9] S.T. Wu, C.S. Wu, Displays 20 (2000) 231. [10] R. Shun, X. Huang, Z. Wang, K. Ma, Transaction of Optical Exact Machine Academy in Changchun 15 (1992) 15. [11] T.J. Scheffer, J. Nehring, J. Appl. Phys. 48 (1977) 1783. [12] Yao Xiong Huang, J. Chem. Phys. 107 (1997) 9141. [13] Values provided by the Silicon LC Materials Co. in Shijiazhuang. [14] V. Frederiks, V. Zolina, Z. Kristallogr. 79 (1931) 255. [15] J.H. Park et al., J. Polym. Sci. Part A: Polym. Chem. 39 (2001) 3622. [16] K. Sakamoto, N. Ito, R. Arafune, S. Ushioda, Vib. Spectrosc. 19 (1999) 61. [17] H. Lange, F. Schmid, Comput Phys Commun 147 (2002) 276. [18] G. Barbero, A.K. Zvezdin, Phys. Lett. A 270 (2000) 331.
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Dependence of viscoelastic parameters of nematic liquid crystals on pretilt angle and temperature Yao-Xiong Huang *, Mei Tu Institute of Biomedical Engineering, Jinan University, Guangzhou 510632, China
a r t i c l e
i n f o
Article history: Received 9 May 2008 Received in revised form 11 July 2009 Accepted 27 July 2009 Available online 30 July 2009 PACS: 61.30.Hn 61.30.Eb
a b s t r a c t The viscoelastic parameters of nematic liquid crystal (LC) E7 in both splay and twist relaxation modes are investigated as functions of pretilt angle and temperature by the technique of dynamic laser light scattering. The results show that the elastic constants of the liquid crystal in the two modes not only depend on temperature, but also depend on pretilt angle. There is a critical pretilt angle (bC) at which nematic LC begins exhibiting elastic property, and beyond which the elastic constants increase with pretilt angle, then keep constant after exceeding another angle (bS, with bS > bC). This phenomenon is observed to be universal for different nematic LC’s, and significant not only in the understanding of the molecular mechanism of exhibiting viscoelastic properties in nematic LC, but also for their practical purpose. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Nematic liquid crystal Relaxation mode Viscoelastic parameters Pretilt angle
1. Introduction Liquid crystals (LC) are the kinds of mesomorphic substances possess the characters of low dimension and order between liquids and crystals. They have not only flow properties of liquids, but also anisotropic optical properties of crystals. In the applications of liquid crystals, mainly the optical anisotropy is utilized to achieve optical modulation. The condition for a LC to exhibit optical anisotropy is that it must be in regular and ordered alignment. The regularity of a liquid crystal is characterized by its vector director n, which in turn can be represented by the pretilt angle of the LC molecules [1,2]. Generally, the alignment of LC molecules is achieved by a thin alignment layer which is applied to a glass plate substrate. The most popular method of forming the alignment layer is to coat an inorganic or organic film on the inner surface of the glass plate substrate, then rub the surface by velvet textures or cloths. When the LC molecules are placed on this layer, they are automatically aligned in the direction made by rubbing and become regularity. However, the regularity can be distorted by thermal effect or other external forces. For example, thermal effect can induce spontaneous fluctuations of n, thus lead to dynamic distortions of the nematic structure. The dynamic distortions implicate the information about the LCs elastic parameters such as twist, * Corresponding author. Tel.: +86 20 85220469; fax: +86 20 85223742. E-mail address: [email protected] (Y.-X. Huang). 1567-1739/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2009.07.022
splay and bend elastic constants. The dynamic distortion behavior of liquid crystals induced by thermal effect and its relation with pretilt angle are very important in basic investigation and for display applications, for both the elastic constants and pretilt angle are the key parameters of LC devices. From the dependence of the elastic constants on pretilt angle and temperature, the relation between the distortional ability of LC molecules and their pre-confinement at different thermal conditions, and the balance among different interactions can be revealed. Based on our knowledge, no research about this relation has been reported previously. One of the most probable reasons for such a situation is that it is difficult to determine the elastic constants in situ for a LC device. Since the spontaneous thermal fluctuations of the vector director n of a defect-free nematic domain, light scattering in nematic liquid crystals is strong enough and can give the information about the dynamic distortions of the nematic structure, such as twist, splay and bend elastic deformation. Several authors have shown [3–5] that the technique of dynamic light scattering (or called photon correlation spectroscopy) can simultaneously determine the viscoelastic deformations for both the splay and twist relaxation modes without disturbance on the LC device. Therefore, it is an ideal tool to measure the viscoelastic parameters of LC’s with different pretilt angles and temperature in situ. For this reason, we used dynamic light scattering to determine the splay and twist elastic constants K11 and K22, and the viscosity coefficients gsplay and gtwist of LC as functions of pretilt angle and temperature.
562
Y.-X. Huang, M. Tu / Current Applied Physics 10 (2010) 561–564
In this paper, the nematic liquid crystal E7 is selected as the object of study. This LC is an eutectic mixture of four low molecular weight liquid crystals but has a single nematic-isotropic transition temperature tNI = 58 °C. Since the optical anisotropy (Dn = neno) of E7 molecules is large enough to be used in polymer dispersed LC for many applications such as to reduce the driving voltage, rise time and to augment the contrast ratio [6], the blends of polymers and E7 are widely employed in display devices, light shutters, privacy windows, tunable photonic band gap [7–9] etc. Accordingly the polymer dispersed E7 composites, consisting of LC microdroplets embedded in a transparent polymer matrix, have recently attracted a great deal of interest for their potential in a variety of applications. In view of this, the study on the dynamic distortion behavior and their dependence on pretilt angle and temperature will possess theoretic instructional significance for the developments and applications of E7. 2. Experimental 2.1. Preparation of the samples Mixture E7 was purchased from Slichem Liquid Crystal Material Co. in Shijiazhuang City, China. The liquid crystal is nematic at room temperature, its tXN < 20 °C, tNI = 58 °C. Two clean glasses were used to prepare a homogeneously aligned nematic cell, with coated polyvinyl alcohol (PVA) alignment layers on the inner surfaces of the glass plate substrates. After the PVA has been dried, the two glass surfaces were rubbed uni-directionally with a velvet cloth, which was wrapped on a rotation wheel. The thickness of the cell gap was 25 lm. It was sealed with epoxy resin after the sample (E7) is filled in. 2.2. Method and equipment The crystal rotation method [10,11] was used for the measurement on the pretilt angle of E7. All the measurements were performed at room temperature (t = 23 °C). The laser light scattering apparatus used for the measurement on the dynamic distortion of E7 in these experiments is the same as that described previously [12]. It consists of an argon laser (Iron Co., working at k0 = 514 nm), a goniometer (BI200SM); a single photon recording system with high sensitivity and low dark current; a Brookhaven BI9000AT autocorrelator, and a temperature controlling system. The experimental setup was so configured that the incident light was vertically polarized and the scattered light horizontally polarized with the vector director n, and perpendicular to the plane of the incident and scattered directions. For such an experimental geometry, only q\, the wave vector component perpendicular to the director n should be considered. In experiment, the scattered angle (h) was set at the range from 15° to 65°. The autocorrelation function of the scattered intensity was analyzed using the autocorrelator. The autocorrelation function is given by:
h 2 i Gð2Þ ðq; tÞ ¼ B 1 þ aA1 ðqÞeC1 ðqÞt þ A2 ðqÞeC2 ðqÞt
and C2(q) are also related to the viscoelastic coefficients of the LC respectively as follows [3]:
C1 ðqÞ ¼ Csplay ðqÞ ¼ C2 ðqÞ ¼ Ctwist ðqÞ ¼
K 11 q2?
gsplay K 22 q2?
gtwist
ð3Þ
where q\ = (2p/k0)[n02sin2h + (ne n0cosh)2]1/2. Therefore, one can obtain gsplay and gtwist from C1(q) and C2(q) upon knowing the values of K11 and K22 from A1(q) and A2(q). For E7, the values of ne and no are 1.720 and 1.521, respectively [13]. Since the scattering is taken at optical frequency, the dielectric anisotropy contains no contribution from permanent dipoles and can be expressed as the optical anisotropy: De = n//2 n\2 = ne2 n02 [1], thus De 0.6450. In experiment, each set of A1(q), A2(q), C1(q) and C2(q) were determined by averaging the autocorrelation functions measured in five times, then K11, K22, gsplay and gtwist were deduced from the values of A and C with different q (or h) and pretilt angles. The calibration of the light scattering setup and the detail process of autocorrelation function analysis can be referred to Refs. [3,12]. To make a comparison between the values of gsplay and gtwist, and that of the bulk or capillary flow viscosity gbulk, an Ubbelohde viscometer was also used in the experiment to measure gbulk. 3. Results and discussions Fig. 1 is a typical curve of the autocorrelation function of E7 LC. A1 and A2 (or Asplay and Atwist) obtained from the autocorrelation function as a function of scattering angle at temperature t = 40 °C and b = 3.4° are illustrated in Fig. 2. It can be seen that, in the range of scattering angles from 15° to 65°, the dynamic distortion displays the two dynamic modes simultaneously. For 20° < h < 40°, the amplitude of the twist mode is very small and the splay mode dominates the dynamics. Especially at the angle of h = 35°, the amplitude of the twist mode vanishes, the dynamic behavior of E7 is only described by the splay mode. For h > 40°, the twist mode emerges gradually, and becomes more important as h is increased. The similar behaviors are also observed at other temperatures (t = 25, 30, 35 °C) and pretilt angles (b = 2.1, 4.7°), as well as in other nematic LC such as 5CB Redouane Borsali [3]. So the scattering angles suggested to observe the relaxation modes of E7 are in the ranges of 15° < h < 25° and 45° < h < 5°. Fig. 3 shows the variation of C of the two relaxation modes with q\2 at 25 and 40 °C, respectively. We can see that both Csplay and Ctwist increase linearly against q\2 but with different slopes. The values of Csplay are much greater than those of Ctwist in most values
ð1Þ
where B is the base line, a is the spatial coherence factor that depends on the detection geometry, A1(q) and A2(q) are the amplitudes of the normal modes called splay-bend and twist-bend modes, having frequencies C1(q) and C2(q), respectively. According to Redouane Borsali and co-workers [3], the amplitudes of the two light scattering modes in turn give the information of the splay and twist elastic constants K11 and K22, if the values of the ordinary and extraordinary refractive indices of the LC, ne and no; the scattered angle h; the absolute temperature T and the dielectric anisotropy De = e// e\ are known. On the other hand, the parameters C1(q)
ð2Þ
Fig. 1. A typical autocorrelation function of E7.
Y.-X. Huang, M. Tu / Current Applied Physics 10 (2010) 561–564
563
Fig. 2. Variation of amplitudes of the splay and twist modes as a function of the scattering angle (b = 3.4°, t = 40 °C). () Twist mode and (j) splay mode.
Fig. 4. Variation of K11 and K22 with pretilt angle in different temperatures. t = 25 °C; jt = 30 °C; Nt = 35 °C and dt = 40 °C.
Fig. 3. Variation of C with q\ in the two modes. : Splay mode at t = 40 °C; N: splay mode at t = 25 °C; j: twist mode at t = 40 °C and d: twist mode at t = 25 °C.
of q\ so that the two modes can be easily distinguished in a wide range of scattering angle. The elastic constants of E7 in different pretilt angles and temperatures are shown in Fig. 4. The value of K11 at 20 °C (11.25 1012 N) agrees well with the value taken by the method of Frederiks deformation (11.1 1012 N) at the same temperature [14], showing that the technique of dynamic light scattering can give accurate and reliable result. From Fig. 4 we can see that both K11 and K22 decrease with temperature, and increase with pretilt angles then keep constant after exceeding the angle b = 5°. On the other hand, when b < 1°, the elastic constants of E7 become immeasurable, so the lowest values of the elastic constants showing in Fig. 4 were taken at b = 1.1°. The pretilt angle of a nematic LC is caused by the anisotropic alignment of the first LC monolayer molecules on the rubbed polyimide film. Such an anisotropic alignment is induced through a short range interaction between the rubbed polyimide film and the first LC monolayer molecules. During the process of rubbing, a large deformation of the polymer backbone works with its side chains [15]. The greater the rubbing strength, the larger is the deformation, thus a greater pretilt angle is resulted. The anisotropic molecular orientation then propagates into the bulk LC via a long range (elastic) interaction among the LC molecules, makes the whole bulk of the liquid crystal also in orientation order [16– 18]. The elastic constants of a nematic LC are the apparent parameters of the molecular orientation order, or in other wards, they are the physical properties which depend on its molecular orientation
order. Therefore, for a LC to exhibit the property of crystal, its molecules must be in alignment. When pretilt angle is very small (e.g., <1° for E7), the E7 molecules can not align steadily on the rubbed surfaces at small friction strength, only very few first LC monolayer molecules are in alignment, thus almost none of the bulk LC molecules are induced in orientation order. Consequently, no elastic property exhibits. As pretilt angle increase, more and more the first LC monolayer molecules are in alignment, and correspondingly more and more bulk LC molecules are induced in orientation order. When the orientation order parameter increases to a certain value, the elastic constants become apparent and increase with pretilt angle until b P 5°. At this angle, almost all the bulk LC molecules have become aligned completely, so the elastic parameters keep constant after exceeding the angle. To see if other nematic LC’s also have a critical pretilt angle for exhibiting elastic properties, and another angle for the elastic constants to become saturated. We performed a less comprehensive study on nematic LC Z7 (phenylcyclohexane system), D6 (cyclohexanecarboxylphenyl system) and R5 (pyrimidine system) also obtained from Slichem Liquid Crystal Material Co., the result shows that similar phenomena are observed in these nematic LC’s (data not shown). It is reasonable that the elastic constants decrease with temperature at a certain pretilt angle, since thermal perturbation disrupts the orientation order of the LC molecules, so elastic constants decrease. Fig. 5 illustrates the dependence of three viscosities on temperature. They are the gsplay and gtwist measured by light scattering and the bulk viscosity measured by Ubbelohde viscometer. Obviously, all the viscosities decrease with temperature in the range from 20 to 40 °C. In this temperature range, the magnitude of gsplay is slightly greater than gtwist, and the later is almost the same as the bulk viscosity gbulk. No pretilt angle dependence of both gsplay and gtwist is observed in the experiment. This is understandable, for the viscosity of a LC device is mainly a bulk property but without/or little correlation with the first monolayer. It should be noted
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Fig. 5. Variation of viscosity of E7 with temperatures (: gsplay, j: gtwist and N: gbulk).
the technique of dynamic laser light scattering. We observe that the elastic constants of the nematic LC are functions of pretilt angle in the range of small pretilt angles. There is a critical pretilt angle (bC) at which nematic LC begins exhibiting elastic property, and beyond which the elastic constants increase with pretilt angle, then keep constant after exceeding another angle (bS). This phenomenon seems universal for different nematic LC’s. Based on our knowledge, this is the first time such a phenomenon is reported. It is believed to be significant not only in the understanding of the molecular mechanism of exhibiting viscoelastic properties in nematic LC, but also for the practical purpose of the LC’s. Our finding about the relation between elastic constants and pretilt angle indicates that the elastic parameters of LC devices can be adjusted to some extent by varying pretilt angle, and to guarantee LC devices work with steady elastic parameters, a certain pretilt angle (>bS) has to be preset. No dependence of viscosity on pretilt angle is observed. Both elastic constants and viscosities of E7 decrease with increasing in temperature, while the viscoelastic parameters K11/gsplay and K22/ gtwist increase with increasing in temperature. Though the splay mode has a steeper slope than the twist mode in their dependence on temperature, both the curves are linear and provide the information about the temperature range in which the LC is of stability of nematic phase. Acknowledgments This work was supported in part by the Chinese National Natural Science Foundation (Grant No.: 30227001) and by the Guang Dong Provincial Natural Science Fund (Grant No.: 9803162). References
Fig. 6. Variation of the viscoelastic parameters with temperatures (: K11/gsplay; j: K22/gtwist).
that owing to their strong temperature dependence, both gsplay and gtwist decrease with temperature faster than elastic constants, so the viscoelastic parameters K11/gsplay and K22/gtwist increase linearly with temperature, as is shown in Fig. 6. We can see that the splay mode has a steeper slope than the twist mode in their dependence on temperature, for K11 decreases with temperature faster than K22. Similar behavior was also found in other nematic LCs [7]. 4. Conclusion We have studied the dependence of the viscoelastic parameters of nematic liquid crystal E7 on pretilt angle and temperature, using
[1] L. Pohl, E. Merck, Physical properties of liquid crystals, in: B. Bahadur (Ed.), Liquid Crystals, World Scientific, Singapore, 1990. [2] X.I.E. Yuzhang, Liquid Crystal Physics, Science Press, Beijing, 1998. [3] Redouane Borsali, Do Yoon, R. Pecora, J. Phys. Chem. B102 (1998) 6337. [4] D. Gu, C. Rosenblatt, Macromolecules 24 (1991) 2385. [5] D. Gu, A. Jamieson, M. Kawasumi, Macromolecules 25 (1992) 2151. [6] Kubota Satoru, Displays 18 (1998) 79. [7] P. Yeh, C. Gu, Displays 21 (2000) 31. [8] A. Eringen, C. Cemal, Int. J. Eng. Sci. 38 (2000) 959. [9] S.T. Wu, C.S. Wu, Displays 20 (2000) 231. [10] R. Shun, X. Huang, Z. Wang, K. Ma, Transaction of Optical Exact Machine Academy in Changchun 15 (1992) 15. [11] T.J. Scheffer, J. Nehring, J. Appl. Phys. 48 (1977) 1783. [12] Yao Xiong Huang, J. Chem. Phys. 107 (1997) 9141. [13] Values provided by the Silicon LC Materials Co. in Shijiazhuang. [14] V. Frederiks, V. Zolina, Z. Kristallogr. 79 (1931) 255. [15] J.H. Park et al., J. Polym. Sci. Part A: Polym. Chem. 39 (2001) 3622. [16] K. Sakamoto, N. Ito, R. Arafune, S. Ushioda, Vib. Spectrosc. 19 (1999) 61. [17] H. Lange, F. Schmid, Comput Phys Commun 147 (2002) 276. [18] G. Barbero, A.K. Zvezdin, Phys. Lett. A 270 (2000) 331.