Abstract

The Maier–Saupe theory for liquid crystals is extended to describe poling by an electric field of side-chain polymers with π-conjugated acceptor–donor molecules as pendant groups. Applications of the theory are in the field of nonlinear-optical materials. By using a quasi-one-dimensional description of the acceptor–donor molecules, our model is capable of going beyond the linear approximation and is intended for the strong-field regime. The theory takes both the dipole moment and the anisotropic polarizability of the side chains into account. A field-induced phase transition to the nematic phase is predicted for isotropic materials. This leads to enhanced polar order and thus to a larger nonlinear susceptibility than is predicted by the simpler isotropic model. The difference between initially liquid-crystalline and initially isotropic materials becomes smaller if the field-induced axial order is taken into account.

© 1990 Optical Society of America

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  1. D. J. Williams, Angew. Chem. 96, 637 (1984).
    [Crossref]
  2. G. R. Meredith, J. G. van Dusen, and D. J. Williams, Am. Chem. Soc. Symp. Ser. 233, 109 (1983);Macromolecules 15, 1385 (1982).
  3. P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).
  4. K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
    [Crossref]
  5. K. D. Singer, M. G. Kuzyk, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
    [Crossref]
  6. A. C. Griffin, A. M. Bhatti, and R. S. L. Hung, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 65 (1986).
  7. J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).
  8. C. P. J. M. van der Vorst and S. J. Picken, Proc. Soc. Photo-Opt. Instrum. Eng. 866, 99 (1987).
  9. G. R. Möhlmann and C. P. J. M. van der Vorst, in Side Chain Liquid Crystal Polymers, C. B. McArdle, ed.(Blackie, Glasgow, 1988), Chap. 12.
  10. W. Maier and A. Saupe, Z. Naturforsch. 13A, 564 (1958);Z. Naturforsch. 14A, 882 (1959);Z. Naturforsch. 15A, 287 (1960).
  11. E. F. Gramsbergen, L. Longa, and W. H. de Jeu, J. Phys.-Phys. Rep.135(4), 195 (1986).
    [Crossref]

1987 (2)

K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
[Crossref]

C. P. J. M. van der Vorst and S. J. Picken, Proc. Soc. Photo-Opt. Instrum. Eng. 866, 99 (1987).

1986 (4)

K. D. Singer, M. G. Kuzyk, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

A. C. Griffin, A. M. Bhatti, and R. S. L. Hung, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 65 (1986).

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

1984 (1)

D. J. Williams, Angew. Chem. 96, 637 (1984).
[Crossref]

1983 (1)

G. R. Meredith, J. G. van Dusen, and D. J. Williams, Am. Chem. Soc. Symp. Ser. 233, 109 (1983);Macromolecules 15, 1385 (1982).

1958 (1)

W. Maier and A. Saupe, Z. Naturforsch. 13A, 564 (1958);Z. Naturforsch. 14A, 882 (1959);Z. Naturforsch. 15A, 287 (1960).

Bhatti, A. M.

A. C. Griffin, A. M. Bhatti, and R. S. L. Hung, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 65 (1986).

Buckley, A.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Calundan, G.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Choe, E. W.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

de Jeu, W. H.

E. F. Gramsbergen, L. Longa, and W. H. de Jeu, J. Phys.-Phys. Rep.135(4), 195 (1986).
[Crossref]

De Martino, R.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Dubois, J. C.

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

Gramsbergen, E. F.

E. F. Gramsbergen, L. Longa, and W. H. de Jeu, J. Phys.-Phys. Rep.135(4), 195 (1986).
[Crossref]

Griffin, A. C.

A. C. Griffin, A. M. Bhatti, and R. S. L. Hung, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 65 (1986).

Hung, R. S. L.

A. C. Griffin, A. M. Bhatti, and R. S. L. Hung, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 65 (1986).

Khanarian, G.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Kuzyk, M. G.

K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
[Crossref]

K. D. Singer, M. G. Kuzyk, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

Lalama, S. J.

K. D. Singer, M. G. Kuzyk, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

le Barny, P.

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

Legrand, C.

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

Leslie, T.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Levelut, A. M.

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

Longa, L.

E. F. Gramsbergen, L. Longa, and W. H. de Jeu, J. Phys.-Phys. Rep.135(4), 195 (1986).
[Crossref]

Maier, W.

W. Maier and A. Saupe, Z. Naturforsch. 13A, 564 (1958);Z. Naturforsch. 14A, 882 (1959);Z. Naturforsch. 15A, 287 (1960).

Meredith, G. R.

G. R. Meredith, J. G. van Dusen, and D. J. Williams, Am. Chem. Soc. Symp. Ser. 233, 109 (1983);Macromolecules 15, 1385 (1982).

Möhlmann, G. R.

G. R. Möhlmann and C. P. J. M. van der Vorst, in Side Chain Liquid Crystal Polymers, C. B. McArdle, ed.(Blackie, Glasgow, 1988), Chap. 12.

Nelson, G.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Njeumo, R.

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

Parneix, J. P.

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

Picken, S. J.

C. P. J. M. van der Vorst and S. J. Picken, Proc. Soc. Photo-Opt. Instrum. Eng. 866, 99 (1987).

Ravaux, G.

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

Saupe, A.

W. Maier and A. Saupe, Z. Naturforsch. 13A, 564 (1958);Z. Naturforsch. 14A, 882 (1959);Z. Naturforsch. 15A, 287 (1960).

Singer, K. D.

K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
[Crossref]

K. D. Singer, M. G. Kuzyk, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

Sohn, J. E.

Stamatoff, J. B.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Stuetz, D.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Teng, C. C.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

van der Vorst, C. P. J. M.

C. P. J. M. van der Vorst and S. J. Picken, Proc. Soc. Photo-Opt. Instrum. Eng. 866, 99 (1987).

G. R. Möhlmann and C. P. J. M. van der Vorst, in Side Chain Liquid Crystal Polymers, C. B. McArdle, ed.(Blackie, Glasgow, 1988), Chap. 12.

van Dusen, J. G.

G. R. Meredith, J. G. van Dusen, and D. J. Williams, Am. Chem. Soc. Symp. Ser. 233, 109 (1983);Macromolecules 15, 1385 (1982).

Williams, D. J.

D. J. Williams, Angew. Chem. 96, 637 (1984).
[Crossref]

G. R. Meredith, J. G. van Dusen, and D. J. Williams, Am. Chem. Soc. Symp. Ser. 233, 109 (1983);Macromolecules 15, 1385 (1982).

Yoon, H. N.

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

Am. Chem. Soc. Symp. Ser. (1)

G. R. Meredith, J. G. van Dusen, and D. J. Williams, Am. Chem. Soc. Symp. Ser. 233, 109 (1983);Macromolecules 15, 1385 (1982).

Angew. Chem. (1)

D. J. Williams, Angew. Chem. 96, 637 (1984).
[Crossref]

Appl. Phys. Lett. (1)

K. D. Singer, M. G. Kuzyk, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

J. Opt. Soc. Am. B (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

P. le Barny, G. Ravaux, J. C. Dubois, J. P. Parneix, R. Njeumo, C. Legrand, and A. M. Levelut, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 56 (1986).

A. C. Griffin, A. M. Bhatti, and R. S. L. Hung, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 65 (1986).

J. B. Stamatoff, A. Buckley, G. Calundan, E. W. Choe, R. De Martino, G. Khanarian, T. Leslie, G. Nelson, D. Stuetz, C. C. Teng, and H. N. Yoon, Proc. Soc. Photo-Opt. Instrum. Eng. 682, 85 (1986).

C. P. J. M. van der Vorst and S. J. Picken, Proc. Soc. Photo-Opt. Instrum. Eng. 866, 99 (1987).

Z. Naturforsch. (1)

W. Maier and A. Saupe, Z. Naturforsch. 13A, 564 (1958);Z. Naturforsch. 14A, 882 (1959);Z. Naturforsch. 15A, 287 (1960).

Other (2)

E. F. Gramsbergen, L. Longa, and W. H. de Jeu, J. Phys.-Phys. Rep.135(4), 195 (1986).
[Crossref]

G. R. Möhlmann and C. P. J. M. van der Vorst, in Side Chain Liquid Crystal Polymers, C. B. McArdle, ed.(Blackie, Glasgow, 1988), Chap. 12.

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Figures (5)

Fig. 1
Fig. 1

Axial-order parameters 〈P2〉 and 〈P4〉, using our model, as a function of the local poling field for m(0) = 7 D, Δα = 47 Å3, Tg = 380 K, and Tc, as indicated. The exact solution for 〈P2〉 in the isotropic model is also shown.

Fig. 2
Fig. 2

〈cos3(θ)〉 as a function of the electric field E using the same values of m(0), Δα, Tg, and Tc as for Fig. 1. The thick solid curves are from the exact solutions of the Ising and isotropic models, as indicated. The thin solid curves are from our model. The dotted and dashed curves show the results of the SKS model [Eq. (16)]. The required axial-order parameters are calculated by using our model at zero field strength (dotted curves) and at the actual field strength (dashed curves). The upper curves correspond to Tc = 420 K, and the lower ones to Tc = 340 K.

Fig. 3
Fig. 3

Polar-order parameter 〈½ cos(θ)sin2(θ)〉, using our model, as a function of the local poling field E, for the same values of m(0), Δα, Tg, and Tc as in Figs. 1 and 2.

Fig. 4
Fig. 4

Ratio of polar-order parameters as a function of the field strength, as calculated from our model for the same parameter setting as in Figs. 13.

Fig. 5
Fig. 5

P2〉 -order parameter as a function of the poling temperature for different values of the local poling field from our model for m(0) = 7 D, Δα = 47 Å3, Tc = 380 K. The occurrence of a tricritical point between E = 90 and E = 100 V/μm is shown.

Tables (1)

Tables Icon

Table 1 Energy Terms in the Four Modelsa

Equations (16)

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P ( ω ) I = χ ( 1 ) ( ω ; ω 1 ) I J E ( ω 1 ) J + χ ( 2 ) ( ω ; ω 1 , ω 2 ) I J K E ( ω 1 ) J E ( ω 2 ) K + .
P ( ω ) i = α ( ω ; ω 1 ) i j E ( ω 1 ) j + β ( ω ; ω 1 , ω 2 ) i j k E ( ω 1 ) j E ( ω 2 ) K + .
χ ( 2 ) ( ω ; ω 1 , ω 2 ) I J K = N f ( ω ) f ( ω 1 ) f ( ω 2 ) × β ( ω ; ω 1 , ω 2 ) i j k O I i O J j O K k .
χ Z Z Z ( 2 ) = N F β z z z cos 3 ( θ ) ,
χ X X Z ( 2 ) = χ Y Y Z ( 2 ) = χ X Z X ( 2 ) = χ Y Z Y ( 2 ) = χ Z X X ( 2 ) = χ Z Y Y ( 2 ) = N F β z z z ½ cos ( θ ) sin 2 ( θ ) ,
A = 1 1 d [ cos ( θ ) ] A ( θ ) G ( θ ) ,
G ( θ ) = 1 Z exp [ U ( θ ) / k T ] ,
Z = 1 1 d [ cos ( θ ) exp [ U ( θ ) / k T ] .
U ( θ ) = U 0 ( θ ) + U 1 ( θ ) + U 2 ( θ ) ,
½ α Z Z E 2 = ½ [ α cos 2 ( θ ) + α sin 2 ( θ ) ] E 2 = ½ α ¯ E 2 Δ α E 2 P 2 [ cos ( θ ) ] ,
cos 3 ( θ ) Ising = e a e a e a + e a = tanh ( a ) a ,
cos 3 ( θ ) isotropic = e a ( a 3 3 a 2 + 6 a 6 ) + e a ( a 3 + 3 a 2 + 6 a + 6 ) ( e a e a ) a 3 a / 5 ,
P 2 isotropic = 1 3 a coth ( a ) + 3 a 2 a 2 15 .
U 0 ( θ ) = P 2 P 2 [ cos ( θ ) ] .
k T c 0.22 .
cos 3 ( θ ) SKS = a ( 1 / 5 + 4 P 2 / 7 + 8 P 4 / 35 ) ,

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