Thickness Dependent Phase Behavior of Antiferroelectric Liquid Crystal Films

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Thickness Dependent Phase Behavior of Antiferroelectric Liquid Crystal Films

LiDong Pan,1Shun Wang,1C. S. Hsu,2and C. C. Huang1

1_{School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA} 2_{Department of Applied Chemistry, National Chiao Tung University, Hsinchu 30050, Taiwan}

(Received 8 June 2009; published 30 October 2009)

Free standing films of a liquid crystal compound with simple surface enhanced order were studied. The resultant phase diagram demonstrates that (1) the short helical pitch smectic-Cphase disappears below a

film thickness of 10 layers, and (2) the temperature window of a distorted 4 layer smectic-CFI2 phase

increases dramatically upon decreasing film thickness. The experimental findings were attributed to the reduced dimensionality and enhanced surface effects in thin films. The results of the smectic-Cphase are

consistent with what have been reported for helically ordered magnetic thin films, with a noticeable difference due to the opposite effect of the surface on ordering in the two systems.

DOI:10.1103/PhysRevLett.103.187802 PACS numbers: 61.30.Hn, 64.70.M, 77.84.Nh

With the discovery of chiral antiferroelectric liquid crystal (AFLC) materials, several new smectic phases be-low smectic-A (SmA, in which long axes of the molecules are parallel to the layer normal) were identified [1]. Since in those new phases, molecules are all tilted, they are usually referred to as the smectic-C (SmC) variant phases. The successful application of a resonant x-ray diffraction technique [2] and optical probes [3] established the molecular arrangements called the ‘‘distorted clock model.’’ Different SmC variant phases are characterized with different azimuthal arrangements of tilt directions among layers. Within each layer, the tilt directions are uniform if no defects are present. For example, smectic-C(SmC) andSmC phases are featured with a

helical structure with pitch on the order of nanometers and micrometers, respectively, while smectic-C_FI2 (SmC_FI2) and smectic-CFI1 (SmCFI1) phases have 4-layer and

3-layer unit cell with structures discussed in detail in Ref. [3]. In order to understand the physical origins and the interactions responsible for theSmCvariant phases, sev-eral theoretical models have been proposed [4–9]. However, there is still no theory that provides a compre-hensive picture of the origin of theSmCvariant phases, or the nature of the interactions responsible for them.

In this Letter, we reported our study on the thickness dependence of SmC variant phases from free standing films of one chiral AFLC compound. To the best of our knowledge, this is the first systematic study of thickness dependence of the stability of SmC variant phases. Previous studies of this kind either did not involveSmC variant phases [10] or used nondeterministic method [11]. Thus, we believe the results will provide new insight into our understanding of the nature of SmC variant phases and the interactions responsible for them.

The AFLC compound chosen for this study is (R)-MHPBC. Its molecular structure is shown at the top of Fig.1. Phase sequence in bulk is isotropicð109CÞ SmA ð76_{CÞ SmC}

ð71CÞ SmCFI2 ð66CÞ SmCFI1

ð63_{CÞ SmC}

A. This compound was chosen for its

sim-ple surface structure. Previous study reported that MHPBC free standing films above the SmA SmC transition show a simple surface induced tilt transition and have the surface phase thicknessðL_SÞ 2 layers [12]. As compari-son, some other AFLCs have LS 9 layers [13] or

mul-tiple surface transitions [14]. Thus, using MHPBC allows us to minimize the complicated surface effects.

In our null transmission ellipsometer (NTE) [15], optical parameter is acquired. measures the phase difference between the p and s component of the incident light necessary to produce linearly polarized transmitted light. The liquid crystal free standing films are prepared over a cover glass slide with a 4-mm diameter hole. Applying a proper set of voltages to eight evenly spaced electrodes

FIG. 1 (color online). as a function of temperature upon cooling from films with thickness N ¼ 6, 10, and 34 layers with ¼ 90 (black squares) and 270 (red dots). T0, T1, T2, T3, and T4 mark the transitions into SmC, SmC, SmC_FI2, SmC

FI1, andSmCAphase. On the top is the chemical structure

of MHPBC.

PRL 103, 187802 (2009) P H Y S I C A L R E V I E W L E T T E R S 30 OCTOBER 2009week ending

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around the film hole creates a rotatable uniform in-plane dc electric field over the film. For films with nonzero in-plane polarization, the whole structure can be rotated smoothly about the layer normal by changing the direction of the electric field (E). Variable denotes the angle between E and the projection of the laser’s wave vectork onto the film plane.

Figure 1 shows the ellipsometric parameter as a function of temperature upon cooling from theSmA phase. The temperature ramp rate was60 mK= min. Data with E field orientation ¼ 90 (black squares) and ¼ 270 (red dots) are presented for films with thickness N ¼ 6, 10, and 34 layers. In the figure, T0, T1, T2, T3, and T4 marks the transition into SmC, SmC, SmC_FI2, SmC_FI1, and SmC

A phase. These phases have the following

character-istic features for parameter . Above T0=T1, surface induced tilt produce a discernible difference between₉₀ and₂₇₀ðj₂₇₀ ₉₀j_SurfÞ. Between T1 and T2, character-istic oscillation in₉₀ and₂₇₀ is the signature ofSmC phase [16]. Because of the optically uniaxial structure of SmC

phase, j270 90jSmC j270 90jSurf. For

the data between T0 and T2 of the 6-layer film, j270

90jT0 to T2> j270 90jSurfindicates that it is theSmC

phase. For data between T2 and T3; and data below T4, 90matches270 as temperature changes, this indicates a

twofold rotational symmetry in the structure. Thus, the phases in these two regions are SmC_FI2 and SmC_A. For data between T3 and T4, a noticeable difference between 90and270 was observed since the films were in a

ferri-electric phase (SmC_FI1). Because the transitions at T2, T3, and T4 are all first order transitions, variations in transition temperatures are observed between different runs and are treated as uncertainties for the transition temperatures.

In order to study the symmetries and structures of the phases in more detail and to confirm the results obtained from the temperature ramp, data were taken as a function ofE field orientation at various temperatures for several films. Shown in Figs. 2(a)–2(c) are as a function of from the 6-layer film at temperatures T ¼ 80:3C, 67:6_{C, and 65:7}_{C. The solid lines are fitting results}

using a4 4 matrix method [17]. Values of the principal indices of refraction and layer spacing used in the fitting are no¼ 1:481 0:002, ne ¼ 1:626 0:01, and d ¼

3:44 0:05 nm [12].

The structure used for the fitting in Fig. 2(a) is SmC with an anticlinic arrangement between two outermost layers. The tilt angle profile from surface to interior is: 11₂_{(1st and 6th layer),}₉₂_{(2nd and 5th layer),}

and8 2(3rd and 4th layer). For Fig.2(b), the structure used isSmC_FI2with an anticlinic surface [a top view of the SmC

FI2 phase is shown in Fig.2(d)]. For the fitting, 2 ¼

10₂ _{is used and an overall helix with pitch}_{¼ 72}

layers is added to the structure. The tilt angle profile used is: 18 2, 16 2, and 15 2 for Fig. 2(b) and 20₂_,₁₇₂_{, and}₁₆₂_{for Fig.}_2(c)_{. The}

struc-ture used for Fig. 2(c) is SmC_FI1 with 1 ¼ 60 10.

Parameters 1 and 2 used for fitting the SmCFI1 and

SmC

FI2structure are consistent with results from previous

studies [3].

Free standing films of MHPBC with thicknesses ranging from 6 to 106 layers were studied. The resultant thickness dependent phase diagram obtained upon cooling from the SmA phase is shown in Fig.3. To avoid complications due to even-odd effect, for N 60 layers, only films with even number of layers were chosen and studied. From the phase diagram, it is clear that all the transition temperatures show trends of increases upon decreasing N. T1 (transition into the SmC phase) shows a slight increase until N < 10 layers, where the SmC phase disappears and theSmC

FIG. 2 (color online). data (symbols) and fitting (lines) as a function of from the 6-layer film at (a) T ¼ 80:3C (SmC phase), (b) T ¼ 67:6C (SmCFI2 phase), (c) T ¼ 65:7C

(SmC

FI1 phase). (d) Top views of structures for SmCFI2 and

SmC

FI1phase, arrows represent the tilt direction of each layer,

numbers represent the layer index within the unit cell.

FIG. 3 (color online). Thickness dependent phase diagram of MHPBC free standing films obtained from cooling runs. PRL 103, 187802 (2009) P H Y S I C A L R E V I E W L E T T E R S 30 OCTOBER 2009week ending

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is observed instead. Upon decreasing N, T2 (transition into theSmC_FI2phase) increases dramatically, while T3 (tran-sition into theSmC_FI1 phase) and T4 (transition into the SmC

Aphase) stay almost constant.

Figure4(a)shows the temperature window of theSmC phase [TðSmCÞ] as a function of N. TðSmCÞ shows an overall trend of decrease upon decreasing N till below the 10 layer film, where theSmCphase completely dis-appears. The disappearing of theSmCphase in thin films has been observed in two other compounds [18,19]. However, in the 6-layer film of MHPBC,SmC structure is observed belowSmA. A similar result was reported for the helical magnetic ordering temperatures (TN) in Ho thin

films [20]. E. Weschke et al. studied TN as a function of

film thickness by resonant magnetic soft x-ray and neutron diffraction. They found that TNdecreases with decreasing

film thickness L and reaches 0 below a film thickness L0

(10 monolayers) which is of the order of bulk helix period P0 (7 to 12 monolayers as a function of temperature). The

result was attributed to the reduced coordination number at the surface. A mean field model was employed to explain the results. From the calculation, it was also found that when TN reaches 0 for L L0, the film is still

magneti-cally ordered. A ferromagnetic structure exists below TC,

which is distinguishable from TN only below L0. Later,

another group performed Monte Carlo simulations on the same system. The results agree with the mean-field calcu-lation [21]. So far, the ferromagnetic structure in the films with TN equals 0 has not been observed experimentally.

Because of the structural similarities between helically ordered magnetic films and liquid crystal films in the SmC

phase, our results can be viewed as an experimental

confirmation of the prediction made for magnetic systems. Although due to the finite size effect, the ordering tem-perature for magnetic thin films is predicted to decrease as film thickness decreases; this is not observed for AFLC films. The most important reason for this is that for AFLC films, surfaces are usually more ordered than the interior

and stronger surface interactions prevent the ordering tem-perature from decreasing.

The helical pitch of theSmCstructure of MHPBC was previously determined to be about 7 layers [22]. Taking into account the surface layers, the film thickness at which the SmC phase disappears is of the order of the bulk helical pitch. In thinner films, the SmC structure is ob-served belowSmA instead of SmC. Free energy of an N layer film having a helical structure can be written as

F ¼ ðN 1ÞJ1cos þ ðN 2ÞJ2cos2 (1)

with J1 and J2 being the coupling constants between the

nearest-neighboring layers (NN) and next-nearest-neighboring layers (NNN), and being 2 divided by the helical pitch P0. For the case of MHPBC, J1¼ 2:5J2

gives a pitch value of 7 layers. Figure4(b)shows the free energy per layer calculated from Eq. (1) with J1¼ 2:5J2

for ¼ 51:4(SmC, black squares) and ¼ 0 (SmC,

red dots). As shown in the figure, above a thickness of 6 layers, theSmCstructure has lower energy, while below 6 layers, the SmC structure has lower energy, which is consistent with the experimental results. An intuitive ex-planation would be that in thin films, the weight of J1 is

more pronounced than J2since there are fewer NNN bonds

than NN bonds, so that a longer helix is favored.

Figure 5(a) shows the temperature window of the SmC

FI2 phase [TðSmCFI2Þ] as a function of N.

TðSmC

FI2Þ increases dramatically as N decreases,

espe-cially for N < 20 layers.

In order to understand the enhanced stability ofSmC_FI2 phase in thin films, we studied the behavior of free energy per layer as a function of N. jFj=N is an estimate of the average energy required to flip the orientation of a random layer in the structure; thus, it is a rough calculation of the

FIG. 4 (color online). (a) TðSmCÞ as a function of N (b) free energy per layer of theSmCstructure (black squares) andSmC structure (red dots) as a function of film thickness calculated from Eq. (1).

FIG. 5 (color online). (a) TðSmC_FI2Þ as a function of N (black square) and free energy per layer calculated with Eq. (2) (red line). (b) Cartoon of a film with even number of layers in theSmC_FI2phase.

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stability of the phase. Figure5(b)shows a cartoon of the SmC

FI2 structure of a film with even number of layers.

Since the distortion angle 2 of MHPBC is small (10

2_{), a planar structure (Ising-like) is a good approximation.}

The two outermost surface layers are assumed to be anti-clinic with the neighboring layers as obtained from the fitting shown in Fig.2(b).

Taking into account the fact that surface bonds are usually stronger than interior bonds, we write the coupling strength between the surface and the adjacent layer to be J1[in theSmCFI2phase J1< 0, so here a negative sign

is needed to produce the anticlinic surface arrangement shown in Fig.5(b)]and J2stands for the coupling strength

between the surface and the NNN, with (a constant) representing the level of surface enhancement. Thus, for the structure shown in Fig.5(b), including a NN and NNN interaction, we have jFðSmC FI2Þj=N ¼ XN2 i¼2 J1i iþ1þ X N3 i¼2 J2i iþ2 2J11 2þ 2J21 3 N ¼ J2þ ½2ðJ2 J1Þ ð4J2þ J1Þ =N ¼ a þ b=N (2)

with J1 (J2) term standing for the interior NN (NNN)

interaction, and_i representing the tilt direction of layer i, a ¼ J2, and b ¼ ½2ðJ2 J1Þ ð4J2þ J1Þ . The red

line in Fig.5(a)was obtained with a ¼ 3:9 0:3 and b ¼ 43 3. Using J1 ¼ 2:5J2 as determined from theSmC

structure, we obtain ¼ 1:8. If, however, we follow the constrains in the ANNNI model for theSmC_FI2 structure, J1< 2J2 [4], then we have > 2:2, which is reasonable

for the case of AFLC [23]. These results show that the dramatic increase ofTðSmC_FI2Þ in thin films is the result of enhanced coupling strength at the surface. Structure of theSmC_FI2phase allows both the NN bonds and the NNN bonds of the surfaces to contribute to the enhancement of stability of this phase, causing the effect to be more pro-nounced. For the case ofSmC_A which also has an Ising-like structure, these two interactions will work against each other, causing the effect to be less obvious. With J1 ¼

2:5J2 and ¼ 2, we get TðSmCAÞ increases for about

26% in decreasing N from 100 to 6 layers, much less compared to about 200% forSmC_FI2. Since inSmC_A, J1>

0, the J1 term will not need a negative sign. Note the

current model [Eq. (2)] does not apply to the case ofSmC. More advanced models are required to explain all the experimental findings.

In summary, we studied the thickness dependent phase diagram of free standing films of AFLC compound MHPBC. TheSmCphase disappears below a film thick-ness of 10 layers, which is of the order of the bulk helix. In

thinner films the SmC structure is observed belowSmA. This result is attributed to the reduced coordination number of the surface layers and is consistent with studies on helically ordered magnetic system. The temperature win-dow of the SmC_FI2 phase increases dramatically upon reducing the film thickness. Surface enhanced couplings are found to be the key reason. The ratio of the enhanced surface couplings to the bulk ones is found to be around 2. Because of the similar structures in both systems, studies on magnetic thin films are proven to be valuable resources for our understanding of SmC variant phases. However, the relatively easy preparation of AFLC films with desired thicknesses and the rich phase behaviors make them more accessible for experimental studies. Also, the completely different surface effects in the two systems (surface in-duced order for AFLC films and surface inin-duced disorder for magnetic thin films) make the comparison between the two systems even more interesting, and will enhance our understanding of the roles of surface in systems having layered structures.

This research was supported in part by the National Science Foundation, Solid State Chemistry Program, under Grant No. DMR-0605760.

[1] A. D. L. Chandani et al., Jpn. J. Appl. Phys. 28, L1265 (1989).

[2] P. Mach et al., Phys. Rev. Lett. 81, 1015 (1998). [3] P. M. Johnson et al., Phys. Rev. Lett. 84, 4870 (2000); D.

Konovalov et al., Phys. Rev. E 64, 010704(R) (2001); M. Sˇkarabot et al., Phys. Rev. E 58, 575 (1998).

[4] M. E. Fisher and W. Selke, Phys. Rev. Lett. 44, 1502 (1980).

[5] A. Roy and N. V. Madhusudana, Eur. Phys. J. E 1, 319 (2000).

[6] D. A. Olson et al., Phys. Rev. E 66, 021702 (2002). [7] M. Cˇ epicˇ et al., J. Chem. Phys. 117, 1817 (2002). [8] P. V. Dolganov et al., Phys. Rev. E 67, 041716 (2003). [9] M. B. Hamaneh and P. L. Taylor, Phys. Rev. Lett. 93,

167801 (2004); Phys. Rev. E 72, 021706 (2005). [10] C. Y. Chao et al., Phys. Rev. Lett. 86, 4048 (2001). [11] E. I. Demikhov, JETP Lett. 61, 977 (1995). [12] L. D. Pan et al., Phys. Rev. E 79, 031704 (2009). [13] P. M. Johnson et al., Phys. Rev. Lett. 83, 4073 (1999). [14] B. K. McCoy et al., Phys. Rev. E 73, 041704 (2006). [15] D. A. Olson et al., Liq. Cryst. 29, 1521 (2002). [16] D. Schlauf et al., Phys. Rev. E 60, 6816 (1999). [17] D. W. Berreman, J. Opt. Soc. Am. 62, 502 (1972). [18] A. Fera et al., Phys. Rev. E 64, 021702 (2001). [19] P. V. Dolganov et al., Phys. Rev. E 65, 031702 (2002). [20] E. Weschke et al., Phys. Rev. Lett. 93, 157204 (2004). [21] F. Cinti et al., Phys. Rev. B 78, 020402(R) (2008). [22] D. A. Olson et al., Phys. Rev. E 63, 061711 (2001). [23] K. Binder and P. C. Hohenberg, Phys. Rev. B 9, 2194

(1974).