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For experimental data showing the tilt response θ (E) and birefringence response Δn (E) in a system with a continuous Sm- A -Sm- C transition, see, for example, Ref..
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For experimental data showing the tilt response θ (E) and birefringence response Δn (E) in a system with a continuous Sm- A -Sm- C transition, see, for example, Ref..
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10
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68949095905
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For experimental data showing the tilt response θ (E) and birefringence response Δn (E) in a system with a first-order Sm- A -Sm- C transition, see, for example, Ref..
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For experimental data showing the tilt response θ (E) and birefringence response Δn (E) in a system with a first-order Sm- A -Sm- C transition, see, for example, Ref..
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N. A. Clark, T. Bellini, R. Shao, D. Coleman, S. Bardon, D. R. Link, J. E. Maclennan, X. H. Chen, M. D. Wand, D. M. Walba, P. Rudquist, and S. T. Lagerwall, Appl. Phys. Lett. 80, 4097 (2002). 10.1063/1.1480472
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68949148095
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It should be noted that here, and throughout this article, exponents are calculated within mean-field theory, and do not include the effects of fluctuations. For example, it is known that when fluctuation effects are included in analysis of the three-dimensional XY transition, θ scales like (1- T TC) β, with β 0.35, whereas in mean-field theory β=0.5. The use of mean-field theory is justified by the fact that virtually all continuous AC transitions are observed to be mean field like.
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It should be noted that here, and throughout this article, exponents are calculated within mean-field theory, and do not include the effects of fluctuations. For example, it is known that when fluctuation effects are included in analysis of the three-dimensional XY transition, θ scales like (1- T TC) β, with β 0.35, whereas in mean-field theory β=0.5. The use of mean-field theory is justified by the fact that virtually all continuous AC transitions are observed to be mean field like.
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68949095904
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We deviate slightly from the notation used in, dropping the subscript 0 on the b, g, h, and s coefficients. We also use rn and rs, instead of tn and ts, for the coefficients of M2 and |ψ| 2, respectively. This is done to avoid confusion with the reduced temperature t.
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We deviate slightly from the notation used in, dropping the subscript 0 on the b, g, h, and s coefficients. We also use rn and rs, instead of tn and ts, for the coefficients of M2 and |ψ| 2, respectively. This is done to avoid confusion with the reduced temperature t.
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23
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0000623511
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See for example, 10.1103/PhysRevA.25.3385
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See for example, C. C. Huang and J. M. Viner, Phys. Rev. A 25, 3385 (1982). 10.1103/PhysRevA.25.3385
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Phys. Rev. A
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Huang, C.C.1
Viner, J.M.2
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24
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0000841663
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10.1103/PhysRevA.31.2621
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C. C. Huang and S. C. Lien, Phys. Rev. A 31, 2621 (1985). 10.1103/PhysRevA.31.2621
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Huang, C.C.1
Lien, S.C.2
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25
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68949152077
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Of course, different materials will also have different values of κ. It is not clear how strongly these parameters will vary from material to material.
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Of course, different materials will also have different values of κ. It is not clear how strongly these parameters will vary from material to material.
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26
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41349112254
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10.1103/PhysRevE.71.041704
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M. Krueger and F. Giesselmann, Phys. Rev. E 71, 041704 (2005). 10.1103/PhysRevE.71.041704
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Krueger, M.1
Giesselmann, F.2
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27
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68949100761
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In a separate analysis, which we do not present here, we have found that the layering order at the Iso-Sm- A transition is indeed larger in systems with smaller orientational order. However, we have also found that for a given decrease in orientational order, the increase in layering required at the Sm- A -Sm- C transition was larger than the increase in layering at the Iso-Sm- A transition. This would imply that a wider temperature window for the Sm- A phase will result as the orientational order is reduced.
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In a separate analysis, which we do not present here, we have found that the layering order at the Iso-Sm- A transition is indeed larger in systems with smaller orientational order. However, we have also found that for a given decrease in orientational order, the increase in layering required at the Sm- A -Sm- C transition was larger than the increase in layering at the Iso-Sm- A transition. This would imply that a wider temperature window for the Sm- A phase will result as the orientational order is reduced.
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0000736169
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Assuming P z ×c reflects the fact that the polarization P is a secondary order parameter, with the tilt c being the primary order parameter. However, the relationship between P and c may be more complicated than the linear one assumed here. See 10.1103/PhysRevA.34.5010;
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Assuming P z ×c reflects the fact that the polarization P is a secondary order parameter, with the tilt c being the primary order parameter. However, the relationship between P and c may be more complicated than the linear one assumed here. See S. Dumrongrattana, C. C. Huang, G. Nounesis, S. C. Lien, and J. M. Viner, Phys. Rev. A 34, 5010 (1986) 10.1103/PhysRevA.34.5010
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Dumrongrattana, S.1
Huang, C.C.2
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29
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10.1103/PhysRevA.36.1484
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T. Carlsson, B. Zeks, A. Levstik, C. Filipic, I. Levstik, and R. Blinc, Phys. Rev. A 36, 1484 (1987). With a view to making our analysis manageable, we avoid introducing another order parameter P and assume the simplest linear relationship. 10.1103/PhysRevA.36.1484
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Carlsson, T.1
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41349110184
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10.1103/PhysRevE.65.061704
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R. B. Meyer and R. A. Pelcovits, Phys. Rev. E 65, 061704 (2002). 10.1103/PhysRevE.65.061704
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Pelcovits, R.A.2
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32
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68949140127
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It should be noted that in the Landau theory of, there was a coupling between tilt and polarization. This coupling leads to an innocuous renormalization of the continuous Sm- A -Sm- C transition temperature.
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It should be noted that in the Landau theory of, there was a coupling between tilt and polarization. This coupling leads to an innocuous renormalization of the continuous Sm- A -Sm- C transition temperature.
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33
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68949130372
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Nature of Sm- A -Sm- C phase transitions in a series of ferroelectric liquid crystal with little smectic layer shrinkage. S. Bezner, M. Krueger, and F. Giesselmann, presented at the 32nd Arbeitstagung Fluussigkristalle, Halle, Germany
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Nature of Sm- A -Sm- C phase transitions in a series of ferroelectric liquid crystal with little smectic layer shrinkage. S. Bezner, M. Krueger, and F. Giesselmann, presented at the 32nd Arbeitstagung Fluussigkristalle, Halle, Germany, 2004 (unpublished).
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