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The Study of Various Phases of Smectic Chiral Liquid Crystals

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The Study of Various Phases of Smectic Chiral Liquid Crystals

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    The Study of Various Phases of Smectic Chiral Liquid Crystals

    I-Min Jiang(姜一民), Y. S. Lin(林佑松), C. C. Shih(施嘉佶), and H. W. Chen(陳修文)

    Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan

    Tel:(07)5252000#3730, Fax:(07)5253709

    E-mail: jiang@mail.phys.nsysu.edu.tw

    ???3TT024BABSTRACT ????????????? ?fjjjj?1iN????24zi?1 G?A(2)???24j?1??We study the various phases of smectic chiral liquid ???????????b????????aijj?1jj?1????crystals using a phenomenological model. The competition i?1??between the interlayer ferro-( antiferro-) interaction and the chiral interaction is especially concerned in this study. The first two terms are the usual mean-field expansion of the free-energy in terms of the primary order Keywords: smectic liquid crystal, liquid crystal phase, parameter. T is the phase transition temperature into a 0chiral tilted phase for a system of smectic layers without

    interlayer interactions. The three fterms describe i

    effective interlayer chiral interactions up to third-nearest

    neighbors. The four a terms account for effective i interlayer interactions up to fourth-nearest neighbors. They

    are not chiral in nature. The coefficient a affects the 1我們以現象學的模型研究各種手徵層列型液晶相orientation of the order parameter in neighboring layers.

    Depending on its sign, a makes the liquid crystal favors 變化。本文特別專注在研究層間鐵電性(或反鐵電性)1either ferroelectric or antiferroelectric order. The 交互作用與手徵的交互作用間的互相競爭關係。 coefficient a affects the orientation in the next-nearest 2 neighboring layers. The coefficient b corresponds to the

    interactions between quadrupolarly ordered transverse 層列型液晶,液晶相,手徵

    molecular dipoles in two neighboring layers. The effective interactions typically follow |a| > |a| > |a| > |a| and |f| > 12341

    |f| > |f|, although this rule does not need to be strictly 23Model and Phases followed. 2According to the study of Skarabot et al. the phases

    of smectic chiral liquid crystals are devided into four There has much interesting in the various phases of **classes: Sm-C, Sm-C, Sm-C*, and Sm-C*. The smectic chiral liquid crystals aroused by the paper of Aαγ1Sm-C*is subdivided into Sm-C* and Sm-C* Huang et al. α α1α2

    according to Huangs paper. And the variant distorted In order to describe the order of the director field of

    phases Sm-C* and Sm-C* are attributed to Sm-C*. smectic chiral liquid crystals, the two-dimensional tilt d3d4γ

    The various phases are described in the following figure 1. order parameter is defined as follows:

     ξ=θ[cos(α),sin(α)] (1) jjj

ξ describes the magnitude and the direction of the j

    molecular tilt in jth smectic layer. θ and α are the tilt j

    magnitude and azimuthally orientation, respectively. The

    free energy (G) of a smectic chiral liquid crystal sample of

    N layers is as follows:

    Figure 1 Various phases of smectic chiral LC

    Different phases present various tilt orientation (c

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    Sm-C* phase become larger than that in the figure 2. In director) projected on the layer plane, as shown in figure 1. region, the 1the left part of the phase diagram, negative aFigure 1(a) describes the c director for the Sm-C* phase. ferroelectric interactions of a and a tend to enhance the c 23The α angle for this phase is (0, φ, 2φ, 3φ, …). The angle director’s alignment, and make the φ small. The , Aφ is small in Sm-C* phase. The angle α of Sm-C*competition from the chiral interaction would be small. Sm-C*, Sm-C* phase are shown in figure 1(b), figure α1α2

    1(c), and figure 1(d), respectively. As φ ? π, the phase is

    denoted as Sm-C*. As for | φ | < π/2 and | φ | > π/2, they A

    are Sm C* and Sm C*, respectively. Figure 1(e) and α1α2

    figure 1(f) describe the c director for the Sm-C* and d4

    Sm-C*, respectively. The angle α of the Sm-C*and d3d4

    Sm-C* are (0, δ, π+2φ, π+2φ+δ, 4φ, …) and (0, π-δ/2 +φ, d3π+δ/2 +2φ, 3φ, …), respectively. As for the Sm-C*phase, γ

    there are two alternative phase angles, φ and δ. Figure 1(g)

    displays that the phase angle increase by φ first, then it

    flips back close to the original direction, as the c director

    makes another rotation by δ. The phase angles are (0, φ,

    φ-δ, 2φ-δ, 2φ-2δ, …). Simulation and analysis Figure 3. a= -|a/4| and a= -|a/9| 2 13 1

     Figure 4 shows the variation of angle φ as function of The competition between the interlayer the coefficient a and f on the phase diagram, while a= 112 ferro-( antiferro-) interaction and the chiral interaction is -|a/4| and a= |a/9|. There are four different phases that 13 1especially concerned in this study. We explore the phase are Sm-C*, Sm-C*, Sm-C*, and Sm-C* in the α1Aα2diagram as function of the coefficient a and f. The 11diagram. We found that the region of Sm-C* phase Acoefficients a, f and f would be small. In the following 423become larger than that in the figure 2. In the right part of 2 studies, we set a= f= f= 0, and = -0.2 according to 4 2 3 the phase diagram, positive a region, the alternative 1Huangs work. interactions of a, a and a tend to make the 123In the first case, we set a = a = 0. Figure 2 shows 23antiferroelectric phase. Although the chiral interaction is the variation of angle φ as function of the coefficient a 1the disturbance out of the ferroelectric and antiferrolectric and f on the phase diagram. There are four different 1interaction, the competition is still small in this case. phases which are Sm-C*, and Sm-C*, Sm-C*, and α1A Sm-C* in the diagram. α2

     Figure 4. a= -|a/4| and a= |a/9| 2 13 1

     Figure 2. a = a = 0 23We then study the cases that the next-nearest neighboring interaction is antiferro-interaction. Figure 5

    shows the variation of angle φ as function of the We further include the interaction from the

    coefficient a and f in the phase diagram, while a= |a/4| next-nearest neighbor. The interaction coefficient is a. 112 12and a= |a/9|. There are four different phases that are Because the distance from original layer to the 3 1Sm-C*, Sm-C*, Sm-C*, and Sm-C* in the diagram. next-nearest neighbor is twice to that of the nearest α1Aα2

    In the left part of the phase diagram, negative a region, neighbor, so we set the strength of a is |a/4|. And we also 121the competition from the chiral interaction would be large set the strength of ais |a/9|. Figure 3 shows the variation 3 1enough to restrict the the region of Sm-C* phase. of angle φ as function of the coefficient a and f in the 11 phase diagram, while a= -|a/4| and a= -|a/9|. There are 2 13 1four different phases that are Sm-C*, Sm-C*, Sm-C*, α1Aand Sm-C* in the diagram. We found that the region of α2

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     = |a/4| and a= |a/9| 2 13 1Figure 5. a

    Figure 6 shows the variation of angle φ as function of the coefficient a and f on the phase diagram, while a= 112 |a/4| and a= -|a/9|. There are four different phases that 13 1

    are Sm-C*, Sm-C*, Sm-C*, and Sm-C* in the α1Aα2diagram. In the right part of the phase diagram, positive a 1region, the competition from the chiral interaction would

    be large enough to restrict the the region of Sm-C* phase. A

     Figure 6. a= |a/4| and a= -|a/9| 2 13 1 2 We also explore various parameter domains, such 2as positive coefficients, small negative and small 2positive coefficients. It is noted that in case we dont restrain the strength of the coefficient a, the variant 2Sm-C* and Sm-C* of smectic chiral liquid crystal d3d4

    phases appear as a close to the a or even exceeding a. 211ACKNOWLEDGEMENT

    We are grateful to professors C. C. Huang and

    Chi-Yu Chao for valuable discussions.

    REFERENCES

    [1] D. A. Olson, X. F. Han, A. Cady, and C. C. Huang,

    Phys. Rev. E 66, 021702 (2002).

    [2] M. Skarabot, M. Cepic, B. Zeks, R. Blinc, G. Heppke,

    A. V. Kityk, and I. Musevic, Phys. Rev. E 58, 575

    (1998).

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