Abstract

Two external-field-free methods are presented for measuring the azimuthal anchoring strength in twisted nematic liquid crystal (TNLC) cells. For asymmetrical TNLC samples, the twist angle is derived from the phase of the detected signal in a phase-sensitive heterodyne polarimeter and is then used to calculate the weak anchoring strength directly. The measurement resolution which is found to be about 0.01μJ/m2 makes the present method sensitive enough for the LC-based bio-sensing application. Using the proposed method, the weak azimuthal anchoring strength of a composite liquid crystal mixture (40% LCT-061153 + 60% MJO-42761) in contact with a plasma-alignment layer is found to be 7.19 μJ/m2. For symmetrical TNLC samples, the liquid crystals are injected into a wedge cell, and the two-dimensional distributions of the twist angle and cell gap are extracted from the detected phase distribution using a genetic algorithm (GA). The azimuthal anchoring strength is then obtained by applying a fitting technique to the twist angle vs. cell gap curve. Utilizing the proposed approach, it is shown that the strong anchoring strength between a rubbed polyimide (PI) alignment layer and E7 liquid crystal is around 160 μJ/m2 while that between a rubbed PI alignment layer and MLC-7023 liquid crystal is approximately 32 μJ/m2.

©2010 Optical Society of America

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References

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  1. S. Faetti and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2), 026601 (2003).
    [Crossref] [PubMed]
  2. S. Faetti and G. C. Mutinati, “An improved reflectometric method to measure the azimuthal anchoring energy of nematic liquid crystals,” Eur Phys J E Soft Matter 10(3), 265–279 (2003).
    [Crossref]
  3. G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
    [Crossref] [PubMed]
  4. T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(Part 1, No. 8), 4434–4437 (1996).
    [Crossref]
  5. Y. Zhou, Z. He, and S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
    [Crossref]
  6. Y. Zhou, Z. He, and S. Sato, “Generalized relation theory of torque balance method for azimuthal anchoring measurements,” Jpn. J. Appl. Phys. 38(Part 1, No. 8), 4857–4858 (1999).
    [Crossref]
  7. J. G. Fonseca and Y. Galerne, “Simple method for measuring the azimuthal anchoring strength of nematic liquid crystals,” Appl. Phys. Lett. 79(18), 2910–2912 (2001).
    [Crossref]
  8. T. Govindaraju, P. J. Bertics, R. T. Raines, and N. L. Abbott, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129(36), 11223–11231 (2007).
    [Crossref] [PubMed]
  9. J. H. Kim and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
    [Crossref]
  10. S. Faetti, K. Sakamoto, and K. Usami, “Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 051704 (2007).
    [Crossref] [PubMed]
  11. T. C. Yu and Y. L. Lo, “A novel heterodyne polarimeter for the multiple-parameter measurements of twisted nematic liquid crystal cell using a genetic algorithm approach,” J. Lightwave Technol. 25(3), 946–951 (2007).
    [Crossref]
  12. W. L. Lin, T. C. Yu, Y. L. Lo, and J. F. Lin, “A hybrid approach for measuring the parameters of twisted-nematic liquid crystal cells utilizing the Stokes parameter method and a genetic algorithm,” J. Lightwave Technol. 27(18), 4136–4144 (2009).
    [Crossref]
  13. Y. Sato, K. Sato, and T. Uchida, “Relationship between Rubbing Strength and Surface Anchoring of Nematic Liquid Crystal,” Jpn. J. Appl. Phys. 31(Part 2, No. 5A), L579–L581 (1992).
    [Crossref]
  14. P. Yeh, and C. Gu, Optics of liquid crystal displays. New York: John Wiley & Sons, Inc. (1999).
  15. S. S. Lin and Y. D. Lee, “Orientational microgrooves generated by plasma beam irradiation at surface of polymer films to align liquid crystals,” Jpn. J. Appl. Phys. 45(27), 24–28 (2006).
    [Crossref]
  16. T. C. Yu and Y. L. Lo, “A two-dimentional heterodyne polarimeter for determination of parameters in twisted nematic liquid crystal cells,” J. Lightwave Technol. 27(23), 5500–5507 (2009).
    [Crossref]
  17. Y. L. Lo, H. W. Chih, C. Y. Yeh, and T. C. Yu, “Full-field heterodyne polariscope with an image signal processing method for principal axis and phase retardation measurements,” Appl. Opt. 45(31), 8006–8012 (2006).
    [Crossref] [PubMed]
  18. F. Z. Yang, H. F. Cheng, H. J. Gao, and J. R. Samples, “Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique,” Liq. Cryst. 28(1), 51–57 (2001).
    [Crossref]
  19. S. Faetti and P. Marianelli, “Strong azimuthal anchoring energy at a nematic-polyimide interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051708 (2005).
    [Crossref] [PubMed]

2009 (2)

2007 (4)

T. Govindaraju, P. J. Bertics, R. T. Raines, and N. L. Abbott, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129(36), 11223–11231 (2007).
[Crossref] [PubMed]

J. H. Kim and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
[Crossref]

S. Faetti, K. Sakamoto, and K. Usami, “Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 051704 (2007).
[Crossref] [PubMed]

T. C. Yu and Y. L. Lo, “A novel heterodyne polarimeter for the multiple-parameter measurements of twisted nematic liquid crystal cell using a genetic algorithm approach,” J. Lightwave Technol. 25(3), 946–951 (2007).
[Crossref]

2006 (2)

Y. L. Lo, H. W. Chih, C. Y. Yeh, and T. C. Yu, “Full-field heterodyne polariscope with an image signal processing method for principal axis and phase retardation measurements,” Appl. Opt. 45(31), 8006–8012 (2006).
[Crossref] [PubMed]

S. S. Lin and Y. D. Lee, “Orientational microgrooves generated by plasma beam irradiation at surface of polymer films to align liquid crystals,” Jpn. J. Appl. Phys. 45(27), 24–28 (2006).
[Crossref]

2005 (1)

S. Faetti and P. Marianelli, “Strong azimuthal anchoring energy at a nematic-polyimide interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051708 (2005).
[Crossref] [PubMed]

2004 (1)

G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
[Crossref] [PubMed]

2003 (2)

S. Faetti and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2), 026601 (2003).
[Crossref] [PubMed]

S. Faetti and G. C. Mutinati, “An improved reflectometric method to measure the azimuthal anchoring energy of nematic liquid crystals,” Eur Phys J E Soft Matter 10(3), 265–279 (2003).
[Crossref]

2001 (2)

J. G. Fonseca and Y. Galerne, “Simple method for measuring the azimuthal anchoring strength of nematic liquid crystals,” Appl. Phys. Lett. 79(18), 2910–2912 (2001).
[Crossref]

F. Z. Yang, H. F. Cheng, H. J. Gao, and J. R. Samples, “Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique,” Liq. Cryst. 28(1), 51–57 (2001).
[Crossref]

1999 (1)

Y. Zhou, Z. He, and S. Sato, “Generalized relation theory of torque balance method for azimuthal anchoring measurements,” Jpn. J. Appl. Phys. 38(Part 1, No. 8), 4857–4858 (1999).
[Crossref]

1997 (1)

Y. Zhou, Z. He, and S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[Crossref]

1996 (1)

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(Part 1, No. 8), 4434–4437 (1996).
[Crossref]

1992 (1)

Y. Sato, K. Sato, and T. Uchida, “Relationship between Rubbing Strength and Surface Anchoring of Nematic Liquid Crystal,” Jpn. J. Appl. Phys. 31(Part 2, No. 5A), L579–L581 (1992).
[Crossref]

Abbott, N. L.

T. Govindaraju, P. J. Bertics, R. T. Raines, and N. L. Abbott, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129(36), 11223–11231 (2007).
[Crossref] [PubMed]

Akahane, T.

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(Part 1, No. 8), 4434–4437 (1996).
[Crossref]

Barbero, G.

G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
[Crossref] [PubMed]

Bertics, P. J.

T. Govindaraju, P. J. Bertics, R. T. Raines, and N. L. Abbott, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129(36), 11223–11231 (2007).
[Crossref] [PubMed]

Cheng, H. F.

F. Z. Yang, H. F. Cheng, H. J. Gao, and J. R. Samples, “Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique,” Liq. Cryst. 28(1), 51–57 (2001).
[Crossref]

Chih, H. W.

Choi, H.

J. H. Kim and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
[Crossref]

Faetti, S.

S. Faetti, K. Sakamoto, and K. Usami, “Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 051704 (2007).
[Crossref] [PubMed]

S. Faetti and P. Marianelli, “Strong azimuthal anchoring energy at a nematic-polyimide interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051708 (2005).
[Crossref] [PubMed]

S. Faetti and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2), 026601 (2003).
[Crossref] [PubMed]

S. Faetti and G. C. Mutinati, “An improved reflectometric method to measure the azimuthal anchoring energy of nematic liquid crystals,” Eur Phys J E Soft Matter 10(3), 265–279 (2003).
[Crossref]

Fonseca, J. G.

J. G. Fonseca and Y. Galerne, “Simple method for measuring the azimuthal anchoring strength of nematic liquid crystals,” Appl. Phys. Lett. 79(18), 2910–2912 (2001).
[Crossref]

Galerne, Y.

J. G. Fonseca and Y. Galerne, “Simple method for measuring the azimuthal anchoring strength of nematic liquid crystals,” Appl. Phys. Lett. 79(18), 2910–2912 (2001).
[Crossref]

Gao, H. J.

F. Z. Yang, H. F. Cheng, H. J. Gao, and J. R. Samples, “Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique,” Liq. Cryst. 28(1), 51–57 (2001).
[Crossref]

Govindaraju, T.

T. Govindaraju, P. J. Bertics, R. T. Raines, and N. L. Abbott, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129(36), 11223–11231 (2007).
[Crossref] [PubMed]

He, Z.

Y. Zhou, Z. He, and S. Sato, “Generalized relation theory of torque balance method for azimuthal anchoring measurements,” Jpn. J. Appl. Phys. 38(Part 1, No. 8), 4857–4858 (1999).
[Crossref]

Y. Zhou, Z. He, and S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[Crossref]

Kaneko, H.

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(Part 1, No. 8), 4434–4437 (1996).
[Crossref]

Kim, J. H.

J. H. Kim and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
[Crossref]

Kimura, M.

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(Part 1, No. 8), 4434–4437 (1996).
[Crossref]

Lee, Y. D.

S. S. Lin and Y. D. Lee, “Orientational microgrooves generated by plasma beam irradiation at surface of polymer films to align liquid crystals,” Jpn. J. Appl. Phys. 45(27), 24–28 (2006).
[Crossref]

Lin, J. F.

Lin, S. S.

S. S. Lin and Y. D. Lee, “Orientational microgrooves generated by plasma beam irradiation at surface of polymer films to align liquid crystals,” Jpn. J. Appl. Phys. 45(27), 24–28 (2006).
[Crossref]

Lin, W. L.

Lo, Y. L.

Marianelli, P.

S. Faetti and P. Marianelli, “Strong azimuthal anchoring energy at a nematic-polyimide interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051708 (2005).
[Crossref] [PubMed]

Mutinati, G. C.

S. Faetti and G. C. Mutinati, “An improved reflectometric method to measure the azimuthal anchoring energy of nematic liquid crystals,” Eur Phys J E Soft Matter 10(3), 265–279 (2003).
[Crossref]

S. Faetti and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2), 026601 (2003).
[Crossref] [PubMed]

Olivero, D.

G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
[Crossref] [PubMed]

Raines, R. T.

T. Govindaraju, P. J. Bertics, R. T. Raines, and N. L. Abbott, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129(36), 11223–11231 (2007).
[Crossref] [PubMed]

Sakamoto, K.

S. Faetti, K. Sakamoto, and K. Usami, “Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 051704 (2007).
[Crossref] [PubMed]

Samples, J. R.

F. Z. Yang, H. F. Cheng, H. J. Gao, and J. R. Samples, “Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique,” Liq. Cryst. 28(1), 51–57 (2001).
[Crossref]

Sato, K.

Y. Sato, K. Sato, and T. Uchida, “Relationship between Rubbing Strength and Surface Anchoring of Nematic Liquid Crystal,” Jpn. J. Appl. Phys. 31(Part 2, No. 5A), L579–L581 (1992).
[Crossref]

Sato, S.

Y. Zhou, Z. He, and S. Sato, “Generalized relation theory of torque balance method for azimuthal anchoring measurements,” Jpn. J. Appl. Phys. 38(Part 1, No. 8), 4857–4858 (1999).
[Crossref]

Y. Zhou, Z. He, and S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[Crossref]

Sato, Y.

Y. Sato, K. Sato, and T. Uchida, “Relationship between Rubbing Strength and Surface Anchoring of Nematic Liquid Crystal,” Jpn. J. Appl. Phys. 31(Part 2, No. 5A), L579–L581 (1992).
[Crossref]

Scaramuzza, N.

G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
[Crossref] [PubMed]

Strangi, G.

G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
[Crossref] [PubMed]

Uchida, T.

Y. Sato, K. Sato, and T. Uchida, “Relationship between Rubbing Strength and Surface Anchoring of Nematic Liquid Crystal,” Jpn. J. Appl. Phys. 31(Part 2, No. 5A), L579–L581 (1992).
[Crossref]

Usami, K.

S. Faetti, K. Sakamoto, and K. Usami, “Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 051704 (2007).
[Crossref] [PubMed]

Versace, C.

G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
[Crossref] [PubMed]

Yang, F. Z.

F. Z. Yang, H. F. Cheng, H. J. Gao, and J. R. Samples, “Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique,” Liq. Cryst. 28(1), 51–57 (2001).
[Crossref]

Yeh, C. Y.

Yu, T. C.

Zhou, Y.

Y. Zhou, Z. He, and S. Sato, “Generalized relation theory of torque balance method for azimuthal anchoring measurements,” Jpn. J. Appl. Phys. 38(Part 1, No. 8), 4857–4858 (1999).
[Crossref]

Y. Zhou, Z. He, and S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

J. G. Fonseca and Y. Galerne, “Simple method for measuring the azimuthal anchoring strength of nematic liquid crystals,” Appl. Phys. Lett. 79(18), 2910–2912 (2001).
[Crossref]

J. H. Kim and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
[Crossref]

Eur Phys J E Soft Matter (1)

S. Faetti and G. C. Mutinati, “An improved reflectometric method to measure the azimuthal anchoring energy of nematic liquid crystals,” Eur Phys J E Soft Matter 10(3), 265–279 (2003).
[Crossref]

J. Am. Chem. Soc. (1)

T. Govindaraju, P. J. Bertics, R. T. Raines, and N. L. Abbott, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129(36), 11223–11231 (2007).
[Crossref] [PubMed]

J. Lightwave Technol. (3)

Jpn. J. Appl. Phys. (5)

Y. Sato, K. Sato, and T. Uchida, “Relationship between Rubbing Strength and Surface Anchoring of Nematic Liquid Crystal,” Jpn. J. Appl. Phys. 31(Part 2, No. 5A), L579–L581 (1992).
[Crossref]

S. S. Lin and Y. D. Lee, “Orientational microgrooves generated by plasma beam irradiation at surface of polymer films to align liquid crystals,” Jpn. J. Appl. Phys. 45(27), 24–28 (2006).
[Crossref]

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(Part 1, No. 8), 4434–4437 (1996).
[Crossref]

Y. Zhou, Z. He, and S. Sato, “A novel method for determining the cell thickness and twist angle of a twisted nematic cell by Stokes parameter measurement,” Jpn. J. Appl. Phys. 36(Part 1, No. 5A), 2760–2764 (1997).
[Crossref]

Y. Zhou, Z. He, and S. Sato, “Generalized relation theory of torque balance method for azimuthal anchoring measurements,” Jpn. J. Appl. Phys. 38(Part 1, No. 8), 4857–4858 (1999).
[Crossref]

Liq. Cryst. (1)

F. Z. Yang, H. F. Cheng, H. J. Gao, and J. R. Samples, “Determination of the torsional anchoring of a twisted nematic liquid crystal using the half-leaky guided mode technique,” Liq. Cryst. 28(1), 51–57 (2001).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (4)

S. Faetti and P. Marianelli, “Strong azimuthal anchoring energy at a nematic-polyimide interface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 051708 (2005).
[Crossref] [PubMed]

S. Faetti and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2), 026601 (2003).
[Crossref] [PubMed]

G. Barbero, D. Olivero, N. Scaramuzza, G. Strangi, and C. Versace, “Influence of the bias-voltage on the anchoring energy for nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 021713 (2004).
[Crossref] [PubMed]

S. Faetti, K. Sakamoto, and K. Usami, “Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(5), 051704 (2007).
[Crossref] [PubMed]

Other (1)

P. Yeh, and C. Gu, Optics of liquid crystal displays. New York: John Wiley & Sons, Inc. (1999).

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Figures (13)

Fig. 1
Fig. 1 Schematic illustration of heterodyne polarimeter used to measure twist angle of asymmetrical TNLC cell.

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Fig. 2
Fig. 2 (a) Variation of σ as function of ϕ t and dΔn, (b) alternative view of phase variation shown in (a). (Note that α = 0°).

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Fig. 3
Fig. 3 (a) Variation of σ as function of dΔn in range 0.30μm ~0.38μm for twist angles of ϕt = −180° ~180°, (b) alternative view of phase σ variation shown in (a). (Note that α = 0°).

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Fig. 4
Fig. 4 Variation of weak azimuthal anchoring strength wϕ with real twist angle ϕt for asymmetrically-aligned TNLC cell with ϕe = 120°, K 22 = 7.35 pN, and d = 3μm.

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Fig. 5
Fig. 5 Correlation between measured phase and extracted twist angle in asymmetrical TNLC cell for azimuthal angles of (a) α = 0°; (b) α = 1°; and (c) α = −1°.

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Fig. 6
Fig. 6 Simulated twist angle vs. thickness (ϕt - d) curves for symmetrical TNLC cells with different azimuthal anchoring strengths in the range 30 μJ/m2 (lower) to 150 μJ/m2 (upper).

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Fig. 7
Fig. 7 Schematic illustration of heterodyne polarimeter used to measure parameters of TNLC wedge cell containing symmetrically-aligned LCs.

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Fig. 8
Fig. 8 Block diagram showing interface between CCD and CPLD [16].

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Fig. 9
Fig. 9 (a) Typical image acquired by CCD camera of wedge cell containing E7 liquid crystals, (b)~(d): phase distributions σ1 ~σ3 for sample shown in (a).

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Fig. 10
Fig. 10 Variations of A and B in Eq. (9) as function of cell gap d.

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Fig. 11
Fig. 11 Cell parameter distributions of E7 wedge cell: (a) azimuthal angle, (b) twist angle (ϕ e = 60° ± 2°), and (c) cell gap (1.8 μm ~4.5 μm).

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Fig. 12
Fig. 12 Cell parameter distributions of MLC-7023 wedge cell: (a) azimuthal angle, (b) twist angle (ϕ e = −60° ± 2°), and (c) cell gap (7.3μm ~9.5 μm).

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Fig. 13
Fig. 13 Variation of twist angle with cell thickness and fitted values of azimuthal anchoring strength for: (a) E7 wedge cell, and (b) MLC-7023 wedge cell.

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Equations (11)

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F = F b + 2 F s ,
F b = K 22 2 d ( ϕ t − ϕ 0 ) 2 ,
F s = 1 2 w ϕ sin 2 ( Δ ϕ ) ,
w ϕ = 2 K 22 ( ϕ t ) d sin 2 Δ ϕ = 2 K 22 ϕ t d sin ( ϕ e − ϕ t ) ,
w ϕ = 2 K 22 ϕ t d sin 2 ( ϕ e − ϕ t ) .
E ⇀ = [ ​     1 2 − 1 2 − 1 2 1 2 ] [ e − i π / 4   0 0   e i π / 4 ] [ cos α − sin α sin α cos α ] M T N L C ( ϕ ) [ cos α sin α − sin α cos α ] [ cos ( ω t 2 ) i sin ( ω t 2 ) i sin ( ω t 2 ) cos ( ω t 2 ) ] [ 1 0 ] ,
M T N L C ( ϕ t ) = [ cos ϕ t − sin ϕ t sin ϕ t cos ϕ t ] [ cos X − i ⋅ Γ ⋅ sin X 2 X ϕ t ⋅ sin X X − ϕ t ⋅ sin X X cos X + i ⋅ Γ ⋅ sin X 2 X ] ,
{ X = ϕ t 2 + ( Γ / 2 ) 2 Γ = 2 π d Δ n / λ ,
I ∝ E ⇀ ⋅ E ⇀ * = [ ( 8 X 2 + 2 Γ 2 − 2 Γ 2 cos 2 X + 8 X 2 cos 2 X + 8 ϕ t 2 − 8 ϕ t 2 cos 2 X ) ︷ I D C + cos ( ω t ) ⋅ ( − 8 ϕ t Γ cos 2 α + 8 ϕ Γ cos 2 X cos 2 α − 8 Γ X sin 2 X sin 2 α ) ︷ A + sin ( ω t ) ⋅ ( 8 X 2 ( 1 + cos 2 X ) + ( 1 − cos 2 X ) ( 8 ϕ t 2 − 2 Γ 2 ) ) ︷ B ] = I D C + A cos ω t + B sin ω t = I D C + A 2 + B 2 sin ( ω t + σ ) = I D C + K sin ( ω t + σ ) , σ = tan − 1 ( A B )
σ 1 , 2 , 3 = tan − 1 [ ( ∫ 0 T 4 I 1 , 2 , 3 ( t ) d t − ∫ T 4 T 2 I 1 , 2 , 3 ( t ) d t ) ( ∫ T 4 T 2 I 1 , 2 , 3 ( t ) d t − ∫ T 2 3 T 4 I 1 , 2 , 3 ( t ) d t ) ] .
{ 0 ° ≤ α ≤ 180 ° 45 ° ≤ ϕ t ≤ 65 ° 1 μ m ≤ d ≤ 4 μ m , 4 μ m ≤ d ≤ 7 μ m , or 7 μ m ≤ d ≤ 10 μ m .

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