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p s scurrent topics in solid state physics

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caphys. stat. sol. (c) 5, No. 5, 1257–1260 (2008) / DOI 10.1002/pssc.200777804

Fréedericksz transition in homeotropically aligned liquid crystals: a photopolarimetric characterization

C. Vena*, C. Versace**, G. Strangi, St. D’Elia, and R. Bartolino

Dipartimento di Fisica, Università della Calabria, 87036 Rende, Cosenza, Italy

Received 27 August 2007, revised 28 January 2008, accepted 29 January 2008

Published online 20 March 2008

PACS 78.20.Ci, 78.66.Qn

* Corresponding author: e-mail cvena@fis.unical.it ** e-mail versace@fis.unical.it

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction In this paper we report an ellipsomet-ric study of the Fréedericksz transition (FT) in ho-meotropically aligned nematic liquid crystal samples. We use a new theoretical approach to explain our experimental results and gain further understandings. During the transi-tion we observed an unexpected light depolarization of the transmitted light beam [1]. Recently, it was observed a substantial difference between the homeotropic and planar cases of initial configuration of the nematic film [1]. The depolarization effects during Fréedericksz transition occurs only in the homeotropic case. In the planar case the orien-tational director dynamics is established by the geometry of the system, which unambiguously fixes the initial and the final directions of the director. In homeotropic case only the initial director orientation is fixed (perpendicular to the cell plates), then, during the transition, the director is free to revolve in all the directions around the initial one. This is a further degree of freedom which is not present in the planar case. This symmetry breaking produces a local director orientation which is different in the various points of the cell. As a consequence the wave-front of the tran-smitted light undergoes a local phase displacement and light depolarization occurs [1]. In Ref. [2] it was essentially studied the depolarization effects due to different polarization states between differ-

ent regions of the same light wave-front. In this case Stokes parameters are averaged across the wave-front sur-face and accounted in the model as a simple plane wave-front. In this model the wave-front is divided in N regions. Every region has well defined polarization, but there is no correlation between the polarization states of different re-gions. By this model the wave front depolarization can be expressed as a easy function on N, i.e N=(1/P)2. In this work we compare the theoretical results and the experi-mental data and we tend to understand the complex sce-nario that occurs during FT. 2 Experimental We applied an alternate electric voltage (1000 Hz) to a nematic liquid crystal film (M7 nematic mixture [3]) confined between two transparent electrodes (glass slides coated by an ITO layer), being 25µm the cell thickness, each ITO electrode was coated by a surfactant (DMOAP) to induce a homeotropic alignment. The M7 parameters values reported in the literature are the following: the rotational viscosity isγ

1=41cP; the dielectric

anisotropy is ∆ε=-0.31 and the bend elastic costant is 7

338.1 10K

−

= ⋅ dyne. Because M7 has a negative dielec-tric anisotropy (ε║ < ε┴), the nematic molecular director tends to align itself perpendicular to the electric field and, above a certain threshold voltage, the Fréedericksz transi-

This work is aimed to the photopolarimetric characterization

of the disorder evolution occurring in homeotropically

aligned nematic liquid crystal films during the Fréedericksz

transition. This order-disorder transition is studied by moni-

toring the depolarization effects of the transmitted light. De-

polarization mainly occurs because light undergoes random

and local phase displacements. The measurements reveal un-

expected depolarization effects at the transition, which we in-

terpret in terms of director field unhomogeneity.

1258 C. Vena et al.: Fréedericksz transition in homeotropically aligned liquid crystals

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tion occurs. We characterized the transient regime by ana-lyzing the polarization of the transmitted light by the same experimental set-up described in our previous article [4]. The light emitted by the laser (λ = 632.6 nm) was focused on the cell (0.5 mW/0.008 mm2). The transmitted light is collected and collimated into the photopolarimeter by a three lenses system. The polarization state of the transmit-ted light was measured by a home made Four Detector Photopolarimeter (FDP), which simultaneously measures the Stokes parameters [5] of the electromagnetic wave. The FDP is described in Ref. [5] in particular the in-strument calibration has been executed as reported in Ref. [6, 7]. The measurement of the Stokes parameters

iS not only

provides information on polarization ellipse, for example the ellipticity E and the azimuthal angle Θ, but also the de-gree on the degree of polarization P of the light beam can be determined. Let us recall some relations:

( )

2

1

3

1/ 22 2 2

1 2 3

23

1 0

1arctan ,

2

1E tan arcsin ,

2

P .K

k

S

S

S

S S S

S

S=

⎛ ⎞Θ = ⎜ ⎟

⎝ ⎠

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟=⎢ ⎥⎜ ⎟+ +⎝ ⎠⎣ ⎦

⎛ ⎞= ⎜ ⎟

⎝ ⎠∑

P ranges from zero (completely unpolarized light) to unity (totally polarized light) and it holds any intermediate val-ues for partially polarized light. In all the experiment reported here, the sample has been illuminated with left-handed circular polarized light and the temperature of the sample was kept at (25±1)°C, except where we specify otherwise.

Figure 1 Time behavior of the degree of polarization. The ap-

plied voltage was switched between 0 V (for 2 sec) and 5.8 V

RMS (for 60 sec). P decreases at OFF→ON transients and returns

to 1 at ON→OFF transients.

3 Results and discussion In Figure 1 we report the time behavior of the degree of polarization P meanwhile an alternate voltage was applied at the sample. The applied voltage was continuously switched between 0 V (duration

= 2 sec) and 5.8 V RMS (duration = 60 sec). As soon the voltage V is turned on the Fréedericksz transition occurs. At the Fréedericksz transition the degree of polariza-tion decreases and then it increases. We define PMIN as the minimum value of P, and ∆t, the time elapsed between the transition occurrence and PMIN. In Figure 2 we report the statistical analysis of PMIN at V =5.8 V RMS, which matches well to a Poisson distribution.

Figure 2 Histogram of PMIN at 5.8 V RMS.

Figure 3 Mean values of PMIN as function of the voltage, to-

gether with the fit (solid line).

Finally in Figure 3 we report the behavior of the mean value of PMIN that have been obtained by repeating these measurements at different voltages. In Ref. [1] PMIN was matched to an exponential decay and the minimum matched values is 0.16±0.03 for large V . This is not real-istic behavior, because PMIN can be lower than 0.16. We fit these data using the interpretation reported in Ref. [2]. In Fréedericksz transition for homeotropically aligned sample the symmetry breaking produces a local director orienta-tion, which is different in the various domains of the cell. Interacting with these domains, the wave-front of the trans-mitted light undergoes a local phase displacement, and we obtain light depolarization. Following Ref. [2]

MIN

2

1N=

P

.

We found a best fit of N by a simple linear fit

N =A+B V× where A=190±40 and B=34±8 Volt-1. We re-port in Fig. 3 the function

MIN

1P =

A+B V

⋅

,

phys. stat. sol. (c) 5, No. 5 (2008) 1259

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and we obtain a perfect agreement with experimental data. N varies from about 2 at V = 5.6 V RMS to about N = 40 at V = 7 V RMS.

Figure 4 D (defined in the text) vs. V and exponential de-

cay fit (solid line).

According to Ref. [1] and related references we sup-pose that the domains director relaxation time is

2 2

33∆t D / ,Kτ γ π

12∼ ∼

where D is the domain size, γ1

denotes the rotational vis-cosity and

33K is the bend elastic modulus. We have per-

formed a statistical analysis of ∆t at different voltages. We use the ∆t mean value and the standard deviation for obtain D. We fit these data by exponential decay and we report the D behavior and the relative fit in Figure 4. The domains size is of about 1µm at V = 7 V RMS. The illuminated area of the sample is larger than 100 µm. By hypothesizing that all the illuminated area of the sam-ple is formed by 1µm domains it would lead to about M = 2500 domains at V = 7 V RMS. This is about 60 times the values of N at V = 7 V RMS. Therefore, we can speculate that the whole bulk is not formed by correlated domains. The domains correlation length is

ξ= M/N D.

In this case ξ = (7 ± 1) µm. Increasing the voltage the do-mains size tends to keep constant while the number of these uncorrelated domains increases inducing a stronger depolarization effect. Moreover, while domains disappear, it forms the well known defect-antidefect pattern (see Fig. 7). In Fig. 5 we report the time behavior of P at 12 V RMS with a sampling time of 200 µs. So we can obtain great number of points around the first minimum. In Figure 6 we report the time behavior of the degree of polarization and of ellipticity around PMIN. Ellipticity increases from E=-1 (left-handed circular polarized incident light) to about E=1 due to the molecular director reorientation processes (the Fréedericksz transition). When P assume the minimum value of the fluctuations the ellipticity rapidly increase. These fluctuations around the regular behaviour are due to the domains formation and PMIN ~ 0.05 corresponds to ξ = (2 ± 1) µm.

Figure 5 Time behavior of the degree of polarization

(12 Volt RMS).

Figure 6 Time behavior of the degree of polarization and of

ellipticity around PMIN of the Fig. 5.

Figure 7 Observation by orthoscopic optical microscopy of de-

fect-antidefect pattern at V = 7 V RMS.

We observe depolarization in presence of defect-antidefect pattern [1]. We show an image of this pattern in Fig. 7. In order to further characterize this phenomenon we report P time behavior for two events at the same applied voltage (12 Volt RMS) and at temperature of 26 °C (see Fig. 8). We note that the P curves present a second mini-mum due to defects formation and this second minimum is always present. In Fig. 9 we report time behavior of P for two events at the same applied voltage (12 Volt RMS) and at the temperature of 43 °C. We note that the light is much less depolarized (after the first minimum) despite the fact that defects anti-defects patterns appear. Finally, in Figure 10 we report P and intensity time behavior of the transmit-ted light in the same experimental condition of Fig. 8 (26 °C and 12 Volt RMS), but we remove the lens system by our set-up. In this case the scattered light is not collect in the polarimeter and after the transition the light intensity decreases. The scattering persists for long time. The light which is not scattered is not depolarized. Using Figure 8 we deduce that only scattered light is depolarized, but the first minimum is still present.

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Figure 8 Two P curves measured by the repetition of the

same observation (12 VRMS) at the temperature of 26 °C

(12 Volt RMS).

Figure 9 The same of Fig. 8 but at the temperature of 43 °C.

Figure 10 P and the light intensity same of Fig. 8 (26 °C

and 12 Volt RMS), but there are not lens in the set-up.

We deduce that the defect-defect pattern does not de-polarize the light, but it is the perturbation that the sample undergoes in presence of this pattern that is responsible for this effect. The perturbation depends on the visco-elastic properties of the liquid crystal. This hypothesis could ex-plain the temperature dependence of P. In fact, by varying the temperature, the visco-elastic properties also change. We suppose that this perturbation generates weak defects in the sample bulk, but further investigations are required.

4 Conclusion In this work we report the characteri-zation of disorder evolution that occurs during the Fréede-ricksz transition in homeotropically aligned nematic liquid crystals films. The study was carried out by measuring the Stokes parameters of the light transmitted by the sample during the transient. These measurements have been per-formed by a four detectors photopolarimeter that provides the Stokes parameters of the radiation. In particular we fo-cus our attention on the time behavior of the degree of po-

larization which reveals interesting characteristics of the disorder due to domains having different orientation. We demonstrate that the depolarization effects occurs mainly because the transmitted light undergoes local phase displacements during FT. We have estimated both the number and the size of the orientational domains which are responsible for the depolarization of both the scattered and not scattered light. We have introduced and evaluated a domain correlations length. A second depolarization mechanism affects only the scattered light during the for-mation of the defect-antidefect pattern. Moreover, this se-cond depolarization effect is less evident at higher tem-peratures when the defect pattern is still present. We think that depolarization arises from the sample perturbation coming from this pattern, but this matter remains open to discussions.

References

[1] C. Vena, C. Versace, G. Strangi, S. D’Elia, and R. Bartolino,

Optics Express 15(25), 17063 (2007).

[2] C. Vena, C. Versace, G. Strangi, and R. Bartolino, unpub-

lished.

[3] N. Scaramuzza, G. Strangi, and C. Versace, Liq. Cryst. 28,

307 (2001).

[4] C. Vena, C. Versace, G. Strangi, V. Bruno, N. Scaramuzza,

and R. Bartolino, Mol. Cryst. Liq. Cryst. 441, 1 (2005).

[5] R. M. A. Azzam, Opt. Acta 32, 1407 (1985).

[6] R. M. A. Azzam, E. Masetti, I. M. Elminyawi, and F. G.

Grosz, Rev. Sci. Instrum. 59, 84 (1988).

[7] E. Masetti and M. P. de Silva, Thin Solid Films 264, 47

(1994).