ISSN 10637850, Technical Physics Letters, 2010, Vol. 36, No. 10, pp. 885–888. © Pleiades Publishing, Ltd., 2010. Original Russian Text © O.A. Skaldin, Yu.I. Timirov, Yu.A. Lebedev, 2010, published in Pis’ma v Zhurnal Tekhnicheskoі Fiziki, 2010, Vol. 36, No. 19, pp. 23–30.
Effect of Anchoring Energy on Results of Helix Pitch Determination in Nematocholesteric Liquid Crystals O. A. Skaldin*, Yu. I. Timirov, and Yu. A. Lebedev Institute of Molecular and Crystal Physics, Russian Academy of Sciences, Ufa, Bashkortostan, 450075 Russia Ufa State Aircraft Technology University, Ufa, Bashkortostan, 450000 Russia *email:
[email protected] Received May 4, 2010
Abstract—The method of liquid crystal (LC) helix pitch determination from the critical voltage of transition from a homeotropic orientation to a translationinvariant structure in a nematocholesteric LC mixture is considered. It is shown that, in the case of nonrigid homeotropic boundary conditions under which there is azimuthal degeneracy of the director rotation relative to the normal to the LC layer, the helix pitch deter mined from the critical voltage can significantly differ from the true value. DOI: 10.1134/S1063785010100044
An important but sometimes difficult task of applied physics is the development of adequate meth ods for determining physical characteristics of con densed media. The situation is complicated in cases where the media – e.g., liquid crystals (LCs) – are multifunctional and characterized by a large number of parameters. In particular, for the mixtures of cho lesteric and nematic LCs it is important to evaluate the step in the spatial supramolecular winding of the structure – the socalled helix pitch P. The measure ments of P may be affected by various factors, in par ticular – geometric, whereby a wedgelike cell can feature either extension or contraction of the spatial winding at the boundaries of the Kano–Grangin zones [1]. Deformation of the surface of substrates confining the cells and/or their nonlinear configura tion can also introduce significant errors in the deter mination of the helix pitch [2]. There are methods for calculating P based on the notions about physico chemical properties of LC mixtures [3], but these also require experimental verification. Another aspect that determines the importance of this knowledge consists in that cholesteric and nema tocholesteric LCs (NCLC) exhibit a large variety of structure–orientation transitions and dynamic effects in external fields and even without these fields [4, 5], the threshold parameters of which depend on the helix pitch. This factor is especially important for the orien tation transitions in LC layers with an initial homeo tropic orientation of molecules at the boundary [6, 7]. It was established [8] that a threshold (critical) voltage for the transition from a homeotropic orientation to a translationinvariant configuration (TIC) [9] in the
limiting case of rigid boundary conditions is inversely proportional to the helix pitch. In the present Letter, we demonstrate that, in the case of nonrigid homeo tropic boundary conditions under which there is azi muthal degeneracy of the director rotation relative to the normal, allowance for the LC anchoring energy is of key importance for correct determination of the helix pitch. LC cells were assembled using glass substrates with a conducting indium–tin oxide (ITO) layer. A homeo tropic orientation in the nematocholesteric LC layers was set by applying [10] an aqueous solution of surfac tant [3(trimethoxysilyl)propyl]octadecyldimethy lammonium chloride (DMOAP) (purchased from Sigma–Aldrich Inc.) onto the ITO film. The surfac tant application also changed the LC anchoring energy. The thickness of LC layer in the cell was con trolled by Mylar spacers. The air gap width d was mea sured by an interferometric technique [11] on a Shi madzu UV3600 spectrophotometer. The nematocho lesteric LC mixture was prepared from MBBA (Actos Inc.) with a cholesteric additive (cholesteryl chloride, Reakhim Co.) at an amount of 0.22, 0.165, or 0.11 wt %. The equilibrium helix pitch of the nematocholes teric LC mixture was calculated using the wellknown method [3] as 1, P = Cβ
(1)
where C is the concentration of the cholecteric addi tive and β is the molecular force of winding (for the given chiral additive). According to formula (1), the helix pitch for the LC mixtures studied was P0.22% ≈
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(a)
3.6 3.3 3.0 2.7 0.22 wt % 0.165 wt % 0.11 wt %
2.4 (а) 2.1 0
2
4
6
8
10
12
14 (b)
P, µm 110 100 90 80 70
(b)
60
Fig. 1. Transient structures observed using crossed polariz ers in a polarization microscope: (a) translationinvariant configuration (TIC); (b) spatially periodic structure.
50 40
0
1
2
3 4 5 6 7 DMOAP concentration, wt %
54 μm, P0.165% ≈ 72 μm, and P0.11% ≈ 108 μm. Orienta tion transitions in the nematocholesteric LC layers were studied using an Axio Image A1m polarization microscope (Carl Zeiss). The transitions were observed by applying an alternating voltage with a fre quency of f ~ 1 kHz. The threshold (critical) voltage amplitudes U were determined from electrooptical response curves measured in crossed polarizers as described in [6].
dependent on the DMOAP treatment of the ITO coated substrates.
Let us consider the orientation transitions in nem atocholesteric LC cells with initial homeotropic ori entation of molecules on glass substrates covered by ITO layers and treated with DMOAP at various con centrations. Figure 1 shows transient patterns observed for different control voltages applied to the cell. As the voltage is increased, the initial homeotro pic orientation changes at U = Uc to a TIC state (Fig. 1a) and then (at Uc1) to a spatiallyperiodic struc ture (Fig. 1b). Theoretical investigations [4, 9] of the possibility of formation of a twist structure with a homeotropic orientation at the boundary predicted a Freedericksz transition in the absence of the field. We are considering the transition from homeotrope to TIC (characterized by the critical voltage Uc) as
Figure 2a shows plots of the critical voltage Uc ver sus DMOAP concentration for three nematocholes teric mixtures with the P values indicated above. As can be seen, Uc exhibits rapid growth as the DMOAP concentration increases to 5%, after which the growth of Uc slows down and it exhibits saturation. Since the surfactant treatment leads to an increase in the anchoring energy Ws of LC molecules at the boundary, this behavior implies that Ws also tends to saturation at DMOP concentration above 10%. According to [6], the transition from a homeotropic orientation to TIC takes place at Uc ~ 2.2 V for the ratio of the sample thickness d to the equilibrium calculated helix pitch O within 0.25 ≤ d/P ≤ 0.5, which corresponds to the ITOcoated surface treatment by small DMOAP con centrations. However, as will be shown below, this sit
Fig. 2. Plots of (a) critical voltage amplitude Uc for nema tocholesteric LC cells with various concentrations of cho lesteryl chloride and (b) calculated helix pitch P calculated from Uc versus DMOAP concentration.
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uation does not correspond to the limiting case of a rigid anchoring (Ws ∞) for which the following dependence of P∞ on the critical voltage Uc for the homeotrope—TIC transition was derived in [6, 8]: 2πK 22 d P ∞ = , 2 2 2 U c ε 0 ε α K 33 + π K 33
Ws, 10−5 J/m2 6
4
(2)
where εa = –0.5 is the anisotropy of the dielectric per mittivity of the medium; ε0 is the permittivity of vac uum, K22 = 5.5 × 10–12 N the twist constant, and K33 = 7.1 × 10–12 N is the longitudinal bending constant. We have calculated the helix pitch as a function of Uc for the homeotrope–TIC transition using formula (2) and the experimental dependence of Uc on the DMOAP concentration. The results of calculations are presented in Fig. 2b. As can be seen, both calcu lated and true values of P in all three mixtures are attained at a rather large concentration of DMOAP. In addition, the given experimental geometry is charac terized by the azimuthal degeneracy for the rotation of molecules about the normal in the initial homeotropic orientation (prior to the transition to TIC) and, in contrast to [1], the boundary conditions cannot lead to distortions of the P value. The helix pitch in this case is determined by relation (1). That is, the real helix pitch in the LC mixture depends only on the force β (determined by the intermolecular interaction between cholesteric molecules and their concentra tion in the nematic matrix) and cannot be determined (in the given geometry) by external factors – in partic ular, by the anchoring energy. From this it follows that the observed decrease in P at small DMOAP concen trations (Fig. 2b) is only apparent and explained by a change in the anchoring energy that is not taken into account by formula (2). Using the dependences of the critical voltage Uc for the homeotrope–TIC transition on the DMOAP con centration, we have calculated the dependence of Ws on this concentration (Fig. 3) for the given material param eters of the liquid crystal and true values P∞ given by for mula (1). For calculating Ws (DMOAP, wt %), we used an expression obtained in [12, 13] for a magnetic field. Making the justified substitution –1 1 μ 0 χaH2 2
1 ε0εaE2 2
and talking into account that distortions of the director field in the critical field are small, we obtain the fol lowing expression: TECHNICAL PHYSICS LETTERS
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2
0
0.22 wt % 0.165 wt % 0.11 wt % 2
4
6 8 10 12 14 DMOAP concentration, wt %
Fig. 3. Dependence of the anchoring energy Ws of LC molecules on the DMOAP concentration in three nemato cholesteric mixtures.
2
Ws =
2
2
4π K 22 ε α ε 0 U K 33 – 2 2 P d
(3)
⎛ d 4π 2 K 222 ε a ε 0 U 2c K 33⎞ – ⎟ , × tan ⎜ 2 2 ⎝ 2K 33 ⎠ P d where P is the true helix pitch given by formula (1). Estimates show that Ws varies from ~10–6 J/m2 on pure ITO surfaces to 10–4 J/m2 for surfactant concen trations about 15 wt %. It the latter value of the anchoring energy that corresponds to the case described in [6]. In conclusion, it was demonstrated that, for the helix pitch in nematocholesteric LC mixtures to be correctly determined from the critical voltage of the homeotrope–TIC transition, it is necessary to take into account the finitness of the anchoring energy of LC molecules at the boundary. Acknowledgments. This study was supported by the Russian Foundation for Basic Research, project no. 080297008. REFERENCES 1. V. G. Chigrinov, V. V. Belyaev, S. V. Belyaev, and M. F. Grebenkin, Zh. Éksp. Teor. Fiz. 77, 2081 (1979) [Sov. Phys. JETP 50, 994 (1979)]. 2. T. Kosa, V. H. Bodnar, B. Taheri, and P. PaffyMuhoray, Mol. Cryst. Liq. Cryst. 369, 129 (2001). 3. C. S. Bak and M. M. Labes, J. Chem. Phys. 62, 3066 (1975). 4. B. Ya. Zel’dovich and N. V. Tabiryan, Zh. Éksp. Teor. Fiz. 83, 998 (1982) [Sov. Phys. JETP 56, 563 (1982)]. 2010
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5. P. Oswald and P. Pieranski, Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illus trated by Experiments (Taylor and Francis–CRC Press, Boca Raton, 2005). 6. I. I. Smalyukh, B. I. Senyuk, P. PaffyMuhoray, O. D. Lavrentovich, et al., Phys. Rev. E 72, 067707 (2005). 7. P. Ribiere, S. Pirkl, and P. Oswald, Phys. Rev. A 44, 8198 (1991). 8. K. A. Crandall, M. R. Fisch, R. G. Petchek, and C. Rosenblatt, Appl. Phys. Lett. 64, 1741 (1994). 9. M. J. Press and A. S. Arrott, J. Phys. 37, 387 (1976).
10. R. J. Kahn, Appl. Phys. Lett. 22, 386 (1973). 11. H. Mada and S. Kobayashi, Mol. Cryst. Liq. Cryst. 33, 47 (1976). 12. A. N. Zakhlevnykh and V. S. Shavkunov, Vestnik Perm. Gos. Univ., Ser. Fiz., No. 6, 50 (2000). 13. V. S. Shavkunov, Effect of Anchoring Energy on Phase Transitins in Cholesteric Liquid Crystals, Candidate Dis sertation in Physics and Mathematics (Perm, 2000) [in Russian].
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