Korean Journal of Optics and Photonics (한국광학회지)

Optical Society of Korea (한국광학회)
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The Explicitly Quasi-linear Relation Between the Order Parameter and Normalized Birefringence of Aligned Uniaxially Anisotropic Molecules Determined Using a Numerical Method

수치해석적인 방법으로 규명한 정렬된 단축이방성 분자들의 질서변수와 상대 복굴절의 준선형 관계식

  • Received : 2016.10.11
  • Accepted : 2016.11.29
  • Published : 2016.12.25
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Abstract

The birefringence of distributed, uniaxially anisotropic molecules like liquid crystals is calculated as the degree of ordering is varied. The relation between the normalized birefringence ${\Delta}n_{rel}$ and the orientational order parameter S is investigated. The distribution function, which enables one to monitor the degree of ordering of liquid crystals including randomly distributed ones, is introduced. Using this distribution function, a series of distributed liquid crystals with order parameters ranging from 0 to 1 are generated, and ${\Delta}n_{rel}$ and S of the correspondingly distributed liquid crystals are calculated. Based on the calculated data, it is revealed that ${\Delta}n_{rel}$ and S satisfy the quasi-linear relation of $S=(1+a){\Delta}n_{rel}-a{\Delta}n^2_{rel}$, where a can be approximated as $n_o{\frac{{\Delta}n}{4}}$. The anisotropy of molecular polarizability is also calculated, using the birefringence, and separately following Vuks' method and Neugebauer's method, and it is shown that the relations between S and the molecular-polarizability anisotropy are also quasi-linear.

액정과 같은 단축 이방성 분자들의 정렬 정도에 따라 달라지는 복굴절으로부터 상대 복굴절 ${\Delta}n_{rel}$를 구하고 ${\Delta}n_{rel}$과 방향질서변수(orientational order parameter) S의 관계를 탐색하였다. 무질서한 분포를 하고 있는 경우를 포함하여 액정의 정렬정도를 달리 표현할 수 있는 분포함수를 도입하고 이 분포함수를 사용하여 질서변수 S가 0부터 1까지 변하도록 액정분자들의 정렬정도를 달리하며 ${\Delta}n_{rel}$과 S를 수치계산 하였다. 이 계산 결과로부터 s와 ${\Delta}n_{rel}$는 $S=(1+a){\Delta}n_{rel}-a{\Delta}n^2_{rel}$와 같이 준선형적인 관계를 만족하며 a는 $n_o{\frac{{\Delta}n}{4}}$으로 근사할 수 있음을 확인하였다. 또한 복굴절으로부터 Vuks의 방법에 따라 구한 분자분극의 이방성과 Neugebauer의 방법에 따라 구한 분자분극의 이방성이 각각 질서변수 S와 또 다른 준선형 관계식들을 따름을 보였다.

Keywords

References

  1. P. Yeh and C. Gu, Optics of Liquid Crystal Display (John Wiley & Sons, Inc., New York, 1999) chap. 1 & chap. 5.
  2. P. G. de Gennes, "Short range order effects in the isotropic phase of nematics and cholesterics," Molecular Crystals and Liquid Crystals 12, 193-214 (1971). https://doi.org/10.1080/15421407108082773
  3. D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystal Devices (John Wiley & Sons, Ltd., 2006) chap.1 & chap. 5-7.
  4. M. Simoes, D. S. Simeao, A. de Campos, and A. J. Palangana, "Corresponding states of nematic birefringence: an order parameter universality," Philosophical Magazine 87(33), 5237-5247 (2007). https://doi.org/10.1080/14786430701642282
  5. V. G. K. M. Pisipati, D. Madhavi Latha, P. V. Datta Prasad, and G. Padmaja Rani, "Order parameter studies from effective order geometry in a number of liquid crystals of different homologous series," J. Molecular Liq. 174, 1-4 (2012). https://doi.org/10.1016/j.molliq.2012.07.009
  6. H. Ozbek, S. Ustunel, E. Kutlu, and M. C. Cetinkaya, "A simple method to determine high-accuracy refractive indices of liquid crystals and the temperature behavior of the related optical parameters via high-resolution birefringence data," J. Molecular Liq. 199, 275-286 (2014). https://doi.org/10.1016/j.molliq.2014.09.003
  7. Sangita Patari, T. K. Devi, and Aparna Nath, "Studies of optical texture, birefringence, order parameter, normalized polarizability and validation of the four-parameter model of a thermotropic mesogen 7OAOB," J. Molecular Liq. 215, 244-252 (2016). https://doi.org/10.1016/j.molliq.2015.12.026
  8. A. Kumar, "Calculation of optical parameters of liquid crystals," Acta Physica Polonica A 112(6), 1213-1221 (2007). https://doi.org/10.12693/APhysPolA.112.1213
  9. P. G. de Gennes, The Physics of Liquid Crystals (2nd ed., Oxford Science Publications, Oxford 1993).
  10. M. G. Robinson, J. Chen and G. D. Sharp, Polarization Engineering for LCD Projection (John Wiley & Sons, Ltd., 2005) Chapter 5.
  11. M. N. Akimov, O. F. Bezrukov, M. F. Vuks, and A. V. Struts, "The study of birefringence and orientational order in plastic tert-butyl bromide," Molecular Cryst. and Liq. Cryst. Inc. Nonlinear Opt. 192(1), 197-201 (1990). https://doi.org/10.1080/00268949008035630
  12. M. F. Vuks, "Determination of the optical anisotropy of aromatic molecules from the double refraction of crystals," Opt. Spectrosc. 20, 361-364 (1966).
  13. M. F. Vuks, N. B. Rozhdestvenskaya, and K. Eidner, "Determination of the optical anisotropy of the molecules of various liquid crystals based on tolan and benzylideneaniline," Opt. Spectrosc. 45(5), 768-769 (1978).
  14. M. Mitra, S. Paul, and R. Paul, "Optical birefringence and order parameter of three nematogens," J. Physics 29(4), 409-417 (1987).
  15. V. S. Chandel, R. Manohar, and J. P. Shukla, "Refractive indices, order parameter and density study of BKS/B07 nematic liquid crystal," Anal. Univ. Bucuresti-Chimie 20(2), 155-163 (2011).
  16. A. Kanwar, "Measurement of order parameter, birefringence and polarizability of liquid crystals," J. Optics 42(4), 311-315 (2013). https://doi.org/10.1007/s12596-013-0141-1
  17. S. Y. Kim, "Ellipsometric expressions for two uniaxially anisotropic layers coated on a multilayered substrate," Korean J. Opt. Photon. 26(2), 115-120 (2015). https://doi.org/10.3807/KJOP.2015.26.2.115
  18. Jun Li, "Refractive Indices of Liquid Crystals and Their Applications in Display and Photonics Devices," Ph.D. Thesis, University of Central Florida, Orlando, USA (2005), chap. 4.