OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 23954–23959
« Show journal navigation

Simulation of the in-plane-switching blue-phase liquid crystal using the director model

Shui-Shang Hu, Jin-Jei Wu, Chia-Chun Hsu, Tien-Jung Chen, and King-Lien Lee  »View Author Affiliations


Optics Express, Vol. 20, Issue 21, pp. 23954-23959 (2012)
http://dx.doi.org/10.1364/OE.20.023954


View Full Text Article

Acrobat PDF (972 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We analyze the non-uniform electric field distribution in an in-plane-switching blue phase liquid crystal (IPS-BPLC) cell and use the director model to simulate the electro-optical properties of an IPS-BPLC cell using a commercial simulator. The calculated results are in good agreement with the experimental data.

© 2012 OSA

1. Introduction

Polymer-stabilized blue-phase liquid crystal (BPLC) [1

1. H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002). [CrossRef] [PubMed]

6

6. M. Jiao, Y. Li, and S. T. Wu, “Low voltage and high transmittance blue-phase liquid crystal displays with corrugated electrodes,” Appl. Phys. Lett. 96(1), 011102 (2010). [CrossRef]

] is emerging as a viable material for use in display applications because it exhibits some attractive properties. (1) It has no threshold driving voltage. (2) It does not require any alignment layer. (3) Its gray-to-gray response time is in the sub-millisecond range. (4) The dark state is optically isotropic, and its viewing angle is wide and symmetric [7

7. K. M. Chen, S. Gauza, H. Xianyu, and S. T. Wu, “Submillisecond gray-level response time of a polymer-stabilized blue-phase liquid crystal,” J. Disp. Technol. 6(2), 49–51 (2010). [CrossRef]

]. Previously, BPLCs were often observed in a very narrow temperature range (about 2°C) [8

8. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (New York: Oxford Univ., 1993), pp. 320–336.

]. However when it is polymerized with a mixture of monomers, the stable temperature range has been extended to over 60°C [1

1. H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002). [CrossRef] [PubMed]

], such that it makes BPLC a strong candidate for display applications. Accordingly, Samsung Co. demonstrated a BPLC display prototype at the 2008 SID exhibition.

In this paper, we use the director model to simulate and analyze the observed electro-optical properties of an IPS-BPLC cell. The BPLC cell is modelled by the stacking of a number of high pretilt nematic (HPN) liquid crystal layers. The results are in good agreement with the experimental results.

2. Theory

It is well known that the director is used to describe the molecular orientation of nematic liquid crystal (NLC). For a polymer-stabilized BPLC cell, liquid crystal molecules are constrained by polymer in crystal lattices. We consider the BPLC cell as a stacking of a number of NLC layers and can be simulated by the director model. It can describe the two facts of a BPLC cell: (1) the cell is optically isotropic without an external field and then becomes anisotropic when the field increased, (2) there is no threshold voltage.

In the voltage-off state, n is considered to be randomly distributed in the bulk of the cell shown in Fig. 1(a). The average direction cosine on the z-axis can be calculated by
1VbVb|nz|dVb=|cos(π2θ)|=0.5
(2)
where Vb is the integral volume in the bulk of the BPLC cell, and z is the unit vector on the z-axis. The average tilt angle (θ = 30°) of n is then obtained, so the pretilt angle of the HPN cell can be set as 30° shown in Fig. 1(b).

T=sin2(ϕbp2)
(5)

Now, we consider the difference between normal electric field E (simulation) in Fig. 2(a)
Fig. 2 (a) A normal electric field is applied on the BPLC cell (simulation). (b) A parallel electric field is applied on the IPS-BPLC cell (experiment).
and parallel electric field E (IPS in experiment) in Fig. 2(b). Normal electric field E results in refractive index δn and parallel electric field E results inΔn, so we can obtain the relationship of δnand Δn asΔn=3δn [15

15. J. Yan, M. Jiao, L. Rao, and S.-T. Wu, “Direct measurement of electric-field-induced birefringence in a polymer-stabilized blue-phase liquid crystal composite,” Opt. Express 18(11), 11450–11455 (2010). [CrossRef] [PubMed]

].

Next, we consider the substitution of the IPS-BPLC cell in Fig. 1(a) with multiple HPN cells. The IPS-BPLC cell with electrode spacing D is divided into Mz layers with each layer thickness (2dh) in Fig. 3
Fig. 3 An IPS-BPLC cell is substituted with multiple HPN cells.
. The applied voltage on each IPS-BPLC layer is Vh = Vbp /M, because of the series connection. Here, the voltage multiplier M is the fitting parameter and M = 3Mz [13

13. J.-J. Wu, S.-S. Hu, C.-C. Hsu, T.-J. Chen, K.-L. Lee, and Q. Li, “A director Model for the Electro-Optics of Blue Phase Liquid Crystal,” IEEE Photon. Technol. Lett. 24(6), 503–505 (2012). [CrossRef]

].

Vbp=MVh=3MzVh=3(D2dh)Vh
(6)

We adjust the parameter M to fit the experimental data. Because the polymer network increases the anchoring energy, the magnitude of M indicates the influence of the polymer network. In this simulation, we assume that the polymer network is not distorted with the increase of the electric field.

3. Simulation and discussion

In this study, the experimental result is retrieved from Ref [7

7. K. M. Chen, S. Gauza, H. Xianyu, and S. T. Wu, “Submillisecond gray-level response time of a polymer-stabilized blue-phase liquid crystal,” J. Disp. Technol. 6(2), 49–51 (2010). [CrossRef]

]. The BPLC is a mixture consisting of high birefringence cyanates, chiral dopants (Merck CB15 and R-1011) and monomers (EHA and RM257). The mixture has an intrinsic birefringence of 0.272 and 100°C clearing temperature. The BPLC mixture was used to fill in an in-plane-switching (IPS) cell. The cell gap is about 13μm, the electrode width is 5μm, and the electrode spacing is 10μm. The light source is an unpolarized 10-mw He-Ne laser (λ = 633nm). The voltage-dependent transmittance (V-T) curves are depicted in Fig. 4(a)
Fig. 4 (a) Measured normalized transmittance vs. Vbp. (b) Experimental result and simulation results of the BPLC cell. The voltage multiplier M = 103 is adopted in the simulation.
. Using the experimental data of Fig. 4(a) and Eq. (5), the phase retardation can be obtained as ϕbp=2sin1(T). The experimental data of ϕbp are depicted in Fig. 4(b).

In the simulation, a commercial simulator (TechWiz LCD) was used. To simulate the experimental results, we adjusted the value of dbp = 3deff and the voltage multiplier M to fit the experimental results. Here, deff is the effective penetration depth of the electric field andϕbp is the total phase retardation of the IPS-BPLC cell with thickness deff. The simulation results are shown in Fig. 4(b). A set of values,dbp=7.0μm,deff=3.2μm and M = 103, is found to fit the experimental results well.

The effective BPLC cell thickness (deff=2.3μm) obtained from the simulation is smaller than the real cell thickness (d=13μm). The fact that deff = d/5 indicates that the penetration depth is about one-fifth the cell gap of the BPLC cell. This means that the E field distribution is about one-fifth of the whole cell if we assume that the distribution of the E field is uniform. The simulated results are consistent with the results in the paper reported by Professor Shin-Tson Wu’s Laboratory [4

4. Z. Ge, L. Rao, S. Gauza, and S. T. Wu, “Modeling of blue phase liquid crystal displays,” J. Disp. Technol. 5(7), 250–256 (2009). [CrossRef]

]. The other result is the voltage multiplier (M = 103). From the theoretical discussion, the result means that there are 103 vertical BPLC layers in the electrode spacing D (=10μm) such that the driving voltage is 103 times the value of Vh. For 3-dim structure consideration, the layer thickness is D/Mz = 3D/M = 291nm . If we think of it as a lattice unit, the dimension is under the double twist cylinder (DTC) diameter of 300 nm such that the BPLC cell will be thermodynamically stable.

Although the simulation results fit the experimental data well atdeff=2.3μm and M = 103, and we can obtain the effective penetration depth of the electric field in the IPS-BPLC cell and the layer thickness considered as the dimension of the BPLC lattice, the electrode spacing D (=10μm) of the IPS-BPLC cell is not equal to the electrode spacing dbp=7.0μm in the simulation. The fact that dbp < D indicates the dilution of the liquid crystal by the polymer in the blue phase liquid crystal cell [13

13. J.-J. Wu, S.-S. Hu, C.-C. Hsu, T.-J. Chen, K.-L. Lee, and Q. Li, “A director Model for the Electro-Optics of Blue Phase Liquid Crystal,” IEEE Photon. Technol. Lett. 24(6), 503–505 (2012). [CrossRef]

]. The unmoving polymer layers makes dbp smaller than D.

4. Conclusion

We have used the director model to successfully simulate the electro-optical properties of the IPS-BPLC cell, and the theoretical calculations match the experimental results well. We have also analyzed the distribution of the electric field in the IPS-BPLC cell. This is a valuable study which uses a simple model to simulate the electro-optical behaviors of the polymer-stabilized IPS-BPLC cell with a commercial simulator.

Acknowledgment

The work is supported by the National Science Council of the Republic of China under Grant NSC 99-2221-E-027-049-MY3.

References and links

1.

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002). [CrossRef] [PubMed]

2.

H. Kikuchi, Y. Haseba, S. Yamamoto, T. Iwata, and H. Higuchi, “Optically isotropic nano-structured liquid crystal composites for display applications,” in SID Symp. Dig. 40, 578–581 (2009).

3.

Z. Ge, S. Gauza, M. Jiao, H. Xianyu, and S. T. Wu, “Electro-optics of polymer-stabilized blue phase liquid crystal displays,” Appl. Phys. Lett. 94(10), 101104 (2009). [CrossRef]

4.

Z. Ge, L. Rao, S. Gauza, and S. T. Wu, “Modeling of blue phase liquid crystal displays,” J. Disp. Technol. 5(7), 250–256 (2009). [CrossRef]

5.

L. Rao, Z. Ge, S. T. Wu, and S. H. Lee, “Low voltage blue-phase liquid crystal displays,” Appl. Phys. Lett. 95(23), 231101 (2009). [CrossRef]

6.

M. Jiao, Y. Li, and S. T. Wu, “Low voltage and high transmittance blue-phase liquid crystal displays with corrugated electrodes,” Appl. Phys. Lett. 96(1), 011102 (2010). [CrossRef]

7.

K. M. Chen, S. Gauza, H. Xianyu, and S. T. Wu, “Submillisecond gray-level response time of a polymer-stabilized blue-phase liquid crystal,” J. Disp. Technol. 6(2), 49–51 (2010). [CrossRef]

8.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (New York: Oxford Univ., 1993), pp. 320–336.

9.

J. Kerr, “A new relation between electricity and light: Dielectrified media birefringent,” Philos. Mag. 50, 337–348 (1875).

10.

P. R. Gerber, “Electro-optical effects of a small-pitch blue-phase system,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 116(3-4), 197–206 (1985). [CrossRef]

11.

J. Philip and T. A. Prasada Rao, “Kerr-effect investigations in a nematic liquid crystal,” Phys. Rev. A 46(4), 2163–2165 (1992). [CrossRef] [PubMed]

12.

J. Yan, H.-C. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S.-T. Wu, “Exteded Kerr effect of polymer-stabilized blue-phase liquid crystals,” Appl. Phys. Lett. 96(7), 071105 (2010). [CrossRef]

13.

J.-J. Wu, S.-S. Hu, C.-C. Hsu, T.-J. Chen, K.-L. Lee, and Q. Li, “A director Model for the Electro-Optics of Blue Phase Liquid Crystal,” IEEE Photon. Technol. Lett. 24(6), 503–505 (2012). [CrossRef]

14.

D. Demus, J. Goodby, G. W. Gray, H. W. Spiess, and V. Vill, Handbook of Liquid Crystals (Wiley-VCH. Weinheim. New York. Chichester Brisbane. Singapore. Toronto., 1998), 1, p. 269.

15.

J. Yan, M. Jiao, L. Rao, and S.-T. Wu, “Direct measurement of electric-field-induced birefringence in a polymer-stabilized blue-phase liquid crystal composite,” Opt. Express 18(11), 11450–11455 (2010). [CrossRef] [PubMed]

OCIS Codes
(120.2040) Instrumentation, measurement, and metrology : Displays
(160.3710) Materials : Liquid crystals
(160.4760) Materials : Optical properties

ToC Category:
Optical Devices

History
Original Manuscript: August 13, 2012
Revised Manuscript: September 28, 2012
Manuscript Accepted: September 28, 2012
Published: October 4, 2012

Citation
Shui-Shang Hu, Jin-Jei Wu, Chia-Chun Hsu, Tien-Jung Chen, and King-Lien Lee, "Simulation of the in-plane-switching blue-phase liquid crystal using the director model," Opt. Express 20, 23954-23959 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23954


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater.1(1), 64–68 (2002). [CrossRef] [PubMed]
  2. H. Kikuchi, Y. Haseba, S. Yamamoto, T. Iwata, and H. Higuchi, “Optically isotropic nano-structured liquid crystal composites for display applications,” in SID Symp. Dig. 40, 578–581 (2009).
  3. Z. Ge, S. Gauza, M. Jiao, H. Xianyu, and S. T. Wu, “Electro-optics of polymer-stabilized blue phase liquid crystal displays,” Appl. Phys. Lett.94(10), 101104 (2009). [CrossRef]
  4. Z. Ge, L. Rao, S. Gauza, and S. T. Wu, “Modeling of blue phase liquid crystal displays,” J. Disp. Technol.5(7), 250–256 (2009). [CrossRef]
  5. L. Rao, Z. Ge, S. T. Wu, and S. H. Lee, “Low voltage blue-phase liquid crystal displays,” Appl. Phys. Lett.95(23), 231101 (2009). [CrossRef]
  6. M. Jiao, Y. Li, and S. T. Wu, “Low voltage and high transmittance blue-phase liquid crystal displays with corrugated electrodes,” Appl. Phys. Lett.96(1), 011102 (2010). [CrossRef]
  7. K. M. Chen, S. Gauza, H. Xianyu, and S. T. Wu, “Submillisecond gray-level response time of a polymer-stabilized blue-phase liquid crystal,” J. Disp. Technol.6(2), 49–51 (2010). [CrossRef]
  8. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (New York: Oxford Univ., 1993), pp. 320–336.
  9. J. Kerr, “A new relation between electricity and light: Dielectrified media birefringent,” Philos. Mag.50, 337–348 (1875).
  10. P. R. Gerber, “Electro-optical effects of a small-pitch blue-phase system,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)116(3-4), 197–206 (1985). [CrossRef]
  11. J. Philip and T. A. Prasada Rao, “Kerr-effect investigations in a nematic liquid crystal,” Phys. Rev. A46(4), 2163–2165 (1992). [CrossRef] [PubMed]
  12. J. Yan, H.-C. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S.-T. Wu, “Exteded Kerr effect of polymer-stabilized blue-phase liquid crystals,” Appl. Phys. Lett.96(7), 071105 (2010). [CrossRef]
  13. J.-J. Wu, S.-S. Hu, C.-C. Hsu, T.-J. Chen, K.-L. Lee, and Q. Li, “A director Model for the Electro-Optics of Blue Phase Liquid Crystal,” IEEE Photon. Technol. Lett.24(6), 503–505 (2012). [CrossRef]
  14. D. Demus, J. Goodby, G. W. Gray, H. W. Spiess, and V. Vill, Handbook of Liquid Crystals (Wiley-VCH. Weinheim. New York. Chichester Brisbane. Singapore. Toronto., 1998), 1, p. 269.
  15. J. Yan, M. Jiao, L. Rao, and S.-T. Wu, “Direct measurement of electric-field-induced birefringence in a polymer-stabilized blue-phase liquid crystal composite,” Opt. Express18(11), 11450–11455 (2010). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited