Abstract

A significant advance in sensitivity of liquid-crystal (LC)-based chemical and biological sensors can be achieved by actively monitoring anchoring energy change. We simulate the deformation of a LC director with different anchoring energies using the finite element method and the optical properties of the LC film using the finite-difference time-domain method. Polarizing micrographs are collected and compared with simulated textures. Measurement of optical transmission is used to monitor the anchoring change. Experimental and simulation results both demonstrate the optical method can effectively monitor the surface anchoring change due to the presence of targeted analytes.

© 2010 Optical Society of America

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References

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  1. V. K. Gupta and N. Abbott, “Design of surface for patterned alignment of liquid crystals on planar and curved substrates,” Science 276, 1533-1536 (1997).
    [CrossRef]
  2. J. J. Skaife and N. Abbott, “Influence of molecular-level interactions on the orientations of liquid crystals supported on surfaces presenting specially bound proteins,” Langmuir 17, 5595-5604 (2001).
    [CrossRef]
  3. J. Brake, M. Daschner, and N. Abbott, “Biomolecular interactions at phospholipids-decorated surfaces of thermotropic liquid crystals,” Science 302, 2094-2098 (2003).
    [CrossRef] [PubMed]
  4. T. Govindaraju, P. J. Bertrics, N. L. Abbott, and R. T. Raines, “Using measurements of anchoring energies of liquid crystals on surfaces to quantify proteins captured by immobilized ligands,” J. Am. Chem. Soc. 129, 11223-11231 (2007).
    [CrossRef] [PubMed]
  5. A. Abu-Abed, R. G. Lindquist, and Woo-Hyuck Choi, “Capacitive transduction for liquid crystal-based sensors, Part I: ordered system,” IEEE Sens. J. 7, 1617-1624 (2007).
    [CrossRef]
  6. A. Abu-Abed and R. G. Lindquist, “Capacitive transduction for liquid crystal-based sensors, Part II: partially disordered system,” IEEE Sens. J. 8, 1557-1564 (2008).
    [CrossRef]
  7. R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296-1299 (2001).
    [CrossRef] [PubMed]
  8. I. W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals (Taylor & Francis, 2004).
  9. D. W. Berreman, “Numerical modeling of twisted nematic devices,” Phil. Trans. R. Soc. London A 309, 203-216 (1983).
    [CrossRef]
  10. E. Willman, F. A. Fernandez, R. James, and S. E. Day, “Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory,” IEEE Trans. Electron Devices 54, 2630-2637 (2007).
    [CrossRef]
  11. I. C. Khoo, Liquid Crystal (Wiley, 2007).
    [CrossRef]
  12. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).
  13. I. Dierking, Textures of Liquid Crystals (Wiley-VCH, 2003).
    [CrossRef]

2008 (1)

A. Abu-Abed and R. G. Lindquist, “Capacitive transduction for liquid crystal-based sensors, Part II: partially disordered system,” IEEE Sens. J. 8, 1557-1564 (2008).
[CrossRef]

2007 (3)

E. Willman, F. A. Fernandez, R. James, and S. E. Day, “Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory,” IEEE Trans. Electron Devices 54, 2630-2637 (2007).
[CrossRef]

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

A. Abu-Abed, R. G. Lindquist, and Woo-Hyuck Choi, “Capacitive transduction for liquid crystal-based sensors, Part I: ordered system,” IEEE Sens. J. 7, 1617-1624 (2007).
[CrossRef]

2003 (1)

J. Brake, M. Daschner, and N. Abbott, “Biomolecular interactions at phospholipids-decorated surfaces of thermotropic liquid crystals,” Science 302, 2094-2098 (2003).
[CrossRef] [PubMed]

2001 (2)

R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296-1299 (2001).
[CrossRef] [PubMed]

J. J. Skaife and N. Abbott, “Influence of molecular-level interactions on the orientations of liquid crystals supported on surfaces presenting specially bound proteins,” Langmuir 17, 5595-5604 (2001).
[CrossRef]

1997 (1)

V. K. Gupta and N. Abbott, “Design of surface for patterned alignment of liquid crystals on planar and curved substrates,” Science 276, 1533-1536 (1997).
[CrossRef]

1983 (1)

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Phil. Trans. R. Soc. London A 309, 203-216 (1983).
[CrossRef]

Abbott, N.

J. Brake, M. Daschner, and N. Abbott, “Biomolecular interactions at phospholipids-decorated surfaces of thermotropic liquid crystals,” Science 302, 2094-2098 (2003).
[CrossRef] [PubMed]

J. J. Skaife and N. Abbott, “Influence of molecular-level interactions on the orientations of liquid crystals supported on surfaces presenting specially bound proteins,” Langmuir 17, 5595-5604 (2001).
[CrossRef]

V. K. Gupta and N. Abbott, “Design of surface for patterned alignment of liquid crystals on planar and curved substrates,” Science 276, 1533-1536 (1997).
[CrossRef]

Abbott, N. L.

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

R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296-1299 (2001).
[CrossRef] [PubMed]

Abu-Abed, A.

A. Abu-Abed and R. G. Lindquist, “Capacitive transduction for liquid crystal-based sensors, Part II: partially disordered system,” IEEE Sens. J. 8, 1557-1564 (2008).
[CrossRef]

A. Abu-Abed, R. G. Lindquist, and Woo-Hyuck Choi, “Capacitive transduction for liquid crystal-based sensors, Part I: ordered system,” IEEE Sens. J. 7, 1617-1624 (2007).
[CrossRef]

Berreman, D. W.

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Phil. Trans. R. Soc. London A 309, 203-216 (1983).
[CrossRef]

Bertrics, P. J.

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

Brake, J.

J. Brake, M. Daschner, and N. Abbott, “Biomolecular interactions at phospholipids-decorated surfaces of thermotropic liquid crystals,” Science 302, 2094-2098 (2003).
[CrossRef] [PubMed]

Choi, Woo-Hyuck

A. Abu-Abed, R. G. Lindquist, and Woo-Hyuck Choi, “Capacitive transduction for liquid crystal-based sensors, Part I: ordered system,” IEEE Sens. J. 7, 1617-1624 (2007).
[CrossRef]

Daschner, M.

J. Brake, M. Daschner, and N. Abbott, “Biomolecular interactions at phospholipids-decorated surfaces of thermotropic liquid crystals,” Science 302, 2094-2098 (2003).
[CrossRef] [PubMed]

Day, S. E.

E. Willman, F. A. Fernandez, R. James, and S. E. Day, “Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory,” IEEE Trans. Electron Devices 54, 2630-2637 (2007).
[CrossRef]

Dierking, I.

I. Dierking, Textures of Liquid Crystals (Wiley-VCH, 2003).
[CrossRef]

Fernandez, F. A.

E. Willman, F. A. Fernandez, R. James, and S. E. Day, “Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory,” IEEE Trans. Electron Devices 54, 2630-2637 (2007).
[CrossRef]

Govindaraju, T.

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

Gupta, V. K.

V. K. Gupta and N. Abbott, “Design of surface for patterned alignment of liquid crystals on planar and curved substrates,” Science 276, 1533-1536 (1997).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

James, R.

E. Willman, F. A. Fernandez, R. James, and S. E. Day, “Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory,” IEEE Trans. Electron Devices 54, 2630-2637 (2007).
[CrossRef]

Khoo, I. C.

I. C. Khoo, Liquid Crystal (Wiley, 2007).
[CrossRef]

Lindquist, R. G.

A. Abu-Abed and R. G. Lindquist, “Capacitive transduction for liquid crystal-based sensors, Part II: partially disordered system,” IEEE Sens. J. 8, 1557-1564 (2008).
[CrossRef]

A. Abu-Abed, R. G. Lindquist, and Woo-Hyuck Choi, “Capacitive transduction for liquid crystal-based sensors, Part I: ordered system,” IEEE Sens. J. 7, 1617-1624 (2007).
[CrossRef]

Raines, R. T.

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

Shah, R.

R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296-1299 (2001).
[CrossRef] [PubMed]

Skaife, J. J.

J. J. Skaife and N. Abbott, “Influence of molecular-level interactions on the orientations of liquid crystals supported on surfaces presenting specially bound proteins,” Langmuir 17, 5595-5604 (2001).
[CrossRef]

Stewart, I. W.

I. W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals (Taylor & Francis, 2004).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

Willman, E.

E. Willman, F. A. Fernandez, R. James, and S. E. Day, “Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory,” IEEE Trans. Electron Devices 54, 2630-2637 (2007).
[CrossRef]

IEEE Sens. J. (2)

A. Abu-Abed, R. G. Lindquist, and Woo-Hyuck Choi, “Capacitive transduction for liquid crystal-based sensors, Part I: ordered system,” IEEE Sens. J. 7, 1617-1624 (2007).
[CrossRef]

A. Abu-Abed and R. G. Lindquist, “Capacitive transduction for liquid crystal-based sensors, Part II: partially disordered system,” IEEE Sens. J. 8, 1557-1564 (2008).
[CrossRef]

IEEE Trans. Electron Devices (1)

E. Willman, F. A. Fernandez, R. James, and S. E. Day, “Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory,” IEEE Trans. Electron Devices 54, 2630-2637 (2007).
[CrossRef]

J. Am. Chem. Soc. (1)

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

Langmuir (1)

J. J. Skaife and N. Abbott, “Influence of molecular-level interactions on the orientations of liquid crystals supported on surfaces presenting specially bound proteins,” Langmuir 17, 5595-5604 (2001).
[CrossRef]

Phil. Trans. R. Soc. London A (1)

D. W. Berreman, “Numerical modeling of twisted nematic devices,” Phil. Trans. R. Soc. London A 309, 203-216 (1983).
[CrossRef]

Science (3)

J. Brake, M. Daschner, and N. Abbott, “Biomolecular interactions at phospholipids-decorated surfaces of thermotropic liquid crystals,” Science 302, 2094-2098 (2003).
[CrossRef] [PubMed]

V. K. Gupta and N. Abbott, “Design of surface for patterned alignment of liquid crystals on planar and curved substrates,” Science 276, 1533-1536 (1997).
[CrossRef]

R. Shah and N. L. Abbott, “Principles for measurement of chemical exposure based on recognition-driven anchoring transitions in liquid crystals,” Science 293, 1296-1299 (2001).
[CrossRef] [PubMed]

Other (4)

I. W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals (Taylor & Francis, 2004).

I. C. Khoo, Liquid Crystal (Wiley, 2007).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

I. Dierking, Textures of Liquid Crystals (Wiley-VCH, 2003).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic model of the analyte detection at the ppb concentration compared to the parts in 10 12 (ppt) concentration. Vertically aligned LC film deforms in the fringing electric field with (b) stronger anchoring and (c) weaker anchoring.

Fig. 2
Fig. 2

LC director and potential distribution. Strong anchoring is assumed on the upper interface between LC and air. The different anchoring energy on lower interface: (a) strong anchoring and (b) weak anchoring w = 50 × 10 6 J / m 2 . (Less grid density than the ones used in simulation.)

Fig. 3
Fig. 3

Electric field at the observation line immediately after the LC film: (a) extraordinary electric field and (b)  ordinary electric field. The ordinary electric field remains uniform, while the extraordinary electric field shows some interference due to the periodic refractive index.

Fig. 4
Fig. 4

Theoretically reproduced polarization photomicrographs. (a) Weak anchoring w = 50 × 10 6 J / m 2 at 4 V applied voltage. (b) Strong anchoring at 4 V applied voltage. The white bar is 20 μm long.

Fig. 5
Fig. 5

Photomicrographs taken by Nikon E600 polarizing microscopy for LC film (thickness 4 μm ) coated on ITO patterned glass substrate with different applied voltages. The white bar is 100 μm long. The white arrows show the directions of polarizer and analyzer.

Fig. 6
Fig. 6

Photomicrographs taken by Nikon E600 polarizing microscopy for LC film (thickness 4 μm ) coated on ITO patterned glass substrate with different applied voltages. (a)  0.01 wt . % CTAB solution as an alignment layer. (b)  0.1 wt . % CTAB solution as alignment layer. The white bar is 20 μm long. The white arrows show the directions of polarizer and analyzer.

Fig. 7
Fig. 7

Optical power depends on applied voltage for different concentrations of CTAB.

Fig. 8
Fig. 8

Schematic illustration of different packing densities of the CTAB layer making different surface anchoring: (a) weaker anchoring with high packing density and (b) stronger anchoring with low packing density.

Equations (19)

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n = n ( x , y , z ) with     n · n = 1.
w e = 1 2 K 1 ( · n ) 2 + 1 2 K 2 ( n · × n ) 2 + 1 2 K 3 ( n × × n ) 2 .
n = n ( x , z ) = ( sin θ , 0 , cos θ ) .
( · n ) 2 = n i , i n j , j = ( sin θ θ , z cos θ θ , x ) 2 ,
( n · × n ) 2 = n j , k n j , k n j , k n k , j n i n j , k n k n j , i = 0 ,
( n × × n ) 2 = n j n k n i , j n i , k = ( cos θ θ , z + sin θ θ , x ) 2 ,
w d = 1 2 ε a ( n · E ) 2 = 1 2 ε a ( E x sin θ + E z cos θ ) 2 ,
w s = 1 2 w sin 2 θ ,
W = 0 x 0 z w ( θ , θ , i ) d z d x + 0 x w s ( θ ) d x with     w = w e + w d .
· D = · [ ε 0 ε ˜ e E ] = 0 ,
· [ ε 0 ε ˜ e Φ ] = 0 ,
D t = × H , μ 0 H t = × E , D = ε ˜ o E ·
ε ˜ o = ( ε x x ε x y ε x z ε x y ε y y ε y z ε z x ε z y ε z z ) = ε 0 ( n o 2 cos 2 θ + n e 2 sin 2 θ 0 ( n e 2 n o 2 ) sin θ cos θ 0 n o 2 0 ( n e 2 n o 2 ) sin θ cos θ 0 n o 2 sin 2 θ + n e 2 cos 2 θ ) ·
D x m + 1 ( i , k ) = D x m ( i , k ) + Δ t [ H y m ( i , k ) H y m ( i , k 1 ) Δ z ] ,
D y m + 1 ( i , k ) = D y m ( i , k ) + Δ t [ H x m ( i , k ) H x m ( i , k 1 ) Δ z H z m ( i , k ) H z m ( i 1 , k ) Δ x ] ,
D z m + 1 ( i , k ) = D z m ( i , k ) + Δ t [ H y m ( i , k ) H y m ( i 1 , k ) Δ x ] ,
H x m + 1 ( i , k ) = H x m ( i , k ) + Δ t μ [ E y m ( i , k ) E y m ( i 1 , k ) Δ z ] ,
H y m + 1 ( i , k ) = H y m ( i , k ) + Δ t μ [ E z m ( i , k ) E z m ( i 1 , k ) Δ x E x m ( i , k ) E x m ( i , k 1 ) Δ z ] ,
H z m + 1 ( i , k ) = H z m ( i , k ) + Δ t μ [ E y m ( i , k ) E y m ( i 1 , k ) Δ x ] ,

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