An experimental investigation of electrically induced-birefringence of Kerr effect in
polymer-stabilized blue phase liquid crystals resulting from orientations of liquid
crystals
Hung-Shan Chen, Shih-Ya Ni, and Yi-Hsin Lin
Citation: Applied Physics Letters 101, 093501 (2012); doi: 10.1063/1.4748117
View online: http://dx.doi.org/10.1063/1.4748117
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/101/9?ver=pdfcov Published by the AIP Publishing
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orientations of liquid crystals
Hung-Shan Chen, Shih-Ya Ni, and Yi-Hsin Lina)
Department of Photonics, National Chiao Tung University, Hsinchu 30010, Taiwan
(Received 7 July 2012; accepted 10 August 2012; published online 27 August 2012)
The electrically induced-birefringence (EIB) of Kerr effect of polymer-stabilized blue phase liquid crystals (PSBP-LCs) is experimentally investigated by discussing the orientations of liquid cryastal (LC) molecules. The results show that the EIB of Kerr effect of PSBP-LCs mainly results from the orientations of LC molecules when the voltage is larger than the voltage of disappearance of the lattice deformation; otherwise, lattice deformation is also involved in the contribution of EIB besides the orientations of LC molecules. This study proves that the orientations of liquid crystals indeed play roles in the EIB of Kerr effect in PSBP-LCs.VC 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4748117]
Polymer-stabilized blue phase liquid crystal (PSBP-LC) has many versatile photonic applications including tunable lenses, electro-optical switches, lasers, and color filters.1The attractive features of PSBP-LCs include electrically induced-birefringence (EIB) or so called Kerr effect, submillisecond response time (lsec), and optical isotropy at a voltage-off state.2 The origins of electrically induced-birefringence in the quadratic electro-optic effect of an optically isotropic medium are proposed. A. Yariv proposed the electrically induced-birefringence of an optically isotropic medium is caused by the charge re-distributions and the alignment of the molecules in the presence of an electric field.3 In the model of Kerr effect, the EIB of PSBP-LCs is proportional to the square of the electric field; however, such a model is only adequate when the electric field is small. Yanet al. pro-posed the model of the extended Kerr effect to correct the Kerr effect.4However, the physical meanings of “the satura-tion electric field” and “the saturated refractive index change” in the extended Kerr effect are still not clear. Chen et al. attributed the fast response time of a blue phase liquid crystal display (BP-LCD) to the local molecular reorienta-tion without any experimental evidence.5 Therefore, the physical origins of electrically induced-birefringence in an optically isotropic medium, such as PSBP-LCs and BPLCs, still need to be investigated.
Recently, we demonstrated a reflective electro-optical switch based on a guest-host liquid crystal system, named dye-doped polymer-stabilized blue phase liquid crystals (DDPSBP-LC).6The mechanism of such an electro-optical switch of DDPSBP-LCs results from the Bragg reflection and the light absorption. The experimental results of DDPSBP-LCs seem to indicate that the liquid crystal (LC) molecules are re-orientated by the applied electric field locally and then bring the dye molecules to rotate with the LC molecules. This inspires us to investigate the EIB in PSBP-LCs which might result from orientations of liquid crystals. In this paper, we investigate the EIB of extended Kerr effect in PSBP-LCs by experimentally exploring the
orientational angles of dye molecules and LC molecules under the applied voltages. The results show that the change of refractive index or EIB of extended Kerr effect in PSBP-LCs mainly results from the orientations of LC molecules when the applied voltage (V) exceeds the voltage of disap-pearance of the lattice deformation (Vdef) which results from
the breakdown of the cubic symmetry. When V < Vdef, the
EIB is contributed not only by the orientations of LC mole-cules but also by the lattice deformation. This study can prove that the orientations of liquid crystals indeed play roles in the EIB in PSBP-LCs.
To prove the orientations of LC molecules in PSBP-LCs, we adopt a guest-host PSBP-LC which means the dichroic dye is added into PSBP-LCs. When LC molecules are reorientate by the applied electric field, the guest dye molecules are reorientated by the LC molecules (or the host). Figure 1 illustrates the structure of the guest-host PSBP-LC. The structure consists of two ITO glass substrates, BPLC, dichroic dye molecules, and polymer networks. The polymer networks locate in the disclination lines of the blue phase structure to stabilize the BPLC. The dye molecules are locally aligned with host LC to form the double twist cylin-ders. The structure of the double twist cylinders can be treated as a locally nematic arrangement.7 Here we define that / and h are the orientational angle of the dye molecular director with respect to z-axis and the orientational angle of the liquid crystal molecular director with respect to z-axis, respectively. When the order parameter (S) of dye molecules is high, the dye molecules tend to align with LC molecules which also means / h. In Fig.1, the transmittance (I) of guest-host PSBP-LCs following the Beer’s law can be expressed as6
IðVÞ ¼ I0ðVÞ ecaaveð/ðVÞÞd; (1)
where I0is the transmittance of PSBP-LCs without dye
mol-ecules, V is an applied voltage, c is the concentration of dye molecules, d is the cell gap, and aave is the average
absorp-tion coefficient of dye molecules. When the light propagates along z-axis, the dye molecules are distributed three-a)
Electronic mail: [email protected].
dimensionally in guest-host PSBP-LCs, and aavecan be
writ-ten as8
aaveð/ðVÞÞ ¼
2 a?þ aef fð/ðVÞÞ
3 ; (2)
where a? and a== are the absorption coefficients when the
linear polarization of incident light is perpendicular and par-allel to the dye molecules, respectively. The effective absorption coefficient aef f in Eq.(2)can also be written as9
aef fð/ðVÞÞ ¼
ajj a?
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ajj2 cos2/ðVÞ þ a?2 sin2/ðVÞ
q : (3)
From Eqs.(2)and(3), when V is large, aaveis closed to a?
which means /ðVÞ 08. At V ¼ 0, aave is ð2a?þ ajjÞ=3
which is related to the absorption in x, y, and z-axes. Owing to the absorption in z-axis is fixed under an applied voltage, /ðV ¼ 0Þ approximately equals to 908.
As to the LC directors, the average refractive index of the guest-host PSBP-LCs can be expressed as10
naveðhðVÞÞ ¼
2noþ nef fðhðVÞÞ
3 ; (4)
where nef f is effective refractive index which follows Eq. (5). nef fðhðVÞÞ ¼ ne no ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ne2 cos2hðVÞ þ no2 sin2hðVÞ q ; (5)
where neand noare the extraordinary refractive index and the
ordinary refractive index of host liquid crystals, respectively. The change of the refractive index of the guest-host PSBP-LCs (dn) between V¼ 0 and V ¼ V0 is naveðhðV ¼ 0ÞÞ
naveðhðV0ÞÞ. In addition, naveðhðV ¼ 0ÞÞ equals to ðneþ
2noÞ=3 at V ¼ 0 and naveðhðV0ÞÞ n0 when V is large
enough. By measuring the transmittance I(V) of the guest-host PSBP-LCs, / can be obtained from Eq.(1). By utilizing the features of the guest-host LC system (i.e., / h ), dn can be obtained as well. Therefore, by comparing measured dn of the guest-host PSBP-LCs and the results of dn based on LC orientations, we can then discuss the influence of the orienta-tions of LC molecules in PSBP-LCs.
In the experiments, we prepared two samples: a PSBP-LC and a guest-host PSBP-PSBP-LC. We mixed a positive nematic
host LC (JC1041-XX, Dn¼ 0.142) with two UV-curable monomers, EHA (2-Ethylhexyl, Fluka) and RM257 (Merck), a chiral molecules CB15 (Merck), dye molecules S428 (Mit-sui Chemicals Inc.), and photo-initiator DMPAP (Aldrich) at 55:3.5:3.5:37:0:1 wt. % ratios for the PSBP-LC and at 54.3:2.8:3.6:36.7:1.5:1 wt. % ratios for the guest-host PSBP-LC. Each mixture at isotropic state was filled into an empty LC cells consisting of two ITO glass substrates only with the cell gap of 5.56 lm. The sample of the guest-host PSBP-LC was cooled down at the cooling rate of 0.1C/min and then exposed by UV light at 33C with intensity1.5 mW/cm2 for 1 h for photo-polymerization. After that, the guest-host PSBP-LC appeared blue phase when the temperature (T) was between 20C and 40C. Similarly, the sample of PSBP-LC was photo-polymerized at T¼ 29.5C and appeared the blue phase at 20C < T < 37.9C after photo-polymerization.11Both the structures of samples were BPII according to the observations of Bragg fringes of the Kossel diagram.
To measure the voltage-dependent transmittance of sam-ples, we used a spectrophotometer (Jasco, V-670 UV-Vis Spectrophotometers) to measure the voltage-dependent trans-mittance at a single wavelength of 633 nm. The light source was an unpolarized light. The samples were normalized by the sample of BP-LC at the isotropic state in order to calibrate the multiple reflections from the interfaces. The chosen wave-length of 633 nm is to minimize the Bragg reflection. Fig. 2(a) shows the voltage-dependent transmittance of the guest-host PSBP-LCs (blue diamonds) and the PSBP-LCs (red squares). In Fig.2(a)the transmittance of the PSBP-LCs increases slightly from 91% to 95%. That means the Bragg reflection of PSBP-LC is not only weak but also decreases slightly with the applied voltage at k¼ 633 nm. This also rep-resents I0(V) in Eq.(1)can be determined. The transmittance
of the guest-host PSBP-LCs increases from49% to 67% with the applied voltage because of an increase of light absorption and weak Bragg reflection. That also means the change of the reorientations of dye molecules and then also indicates the reorientations of LC molecules. We measured the phase difference (DdðVÞ) of samples between V and V¼ 0 by adopting Mach-Zehnder interferometer. The phase difference can be converted to the change of refractive index (dnðVÞ) according to the relation: DdðVÞ ¼ 2p d dnðVÞ=k, where k is the wavelength. The changes of the re-fractive index as a function of voltage of samples are shown in Fig. 2(b). In Fig.2(b), the total changes of the refractive
FIG. 1. The structure of guest-host PSBP-LCs. The incident light (the yellow arrow) propagates along þz direction.
index for guest-host PSBP-LCs and PSBP-LCs are similar 0.04. This represents the phase is not affected by the light absorption which is induced by dye molecules.
From Fig. 2(a) and Eq. (1), the calculated a? is
4.28 lm1and a== is 13.93 lm1on a basis of the statistical
estimations of the absorption coefficients ofð2a?þ ajjÞ=3
at V¼ 0 and a?at 100 Vrms. According to Fig. 2(a) and
Eqs. (1)–(3), the orientational angle of the dye molecular directors (/) as a function of the applied voltage is plotted in Fig.3. In Fig. 3, / decreases slowly when V < 60Vrms, /
decreases dramatically when V > 60Vrms, and / remains
almost the same orientational angle after V > 80Vrms. This
means the dye molecular directors tend to tilt up from x-y plane to the direction along z-axis with the applied voltage. When V > 80Vrms, the long axis of the dye molecular
directors are almost parallel to the z-axis.
tive index of the guest-host PSBP-LC (dn) between V¼ 0 and V¼ V0isnaveð/ðV ¼ 0ÞÞ naveð/ðV0ÞÞ in which h(V)
is replaced by /(V). According to Eqs. (4) and(5), Fig.3, and the relationnaveð/ðV ¼ 0ÞÞ ¼ ðneþ 2noÞ=3, we can plot
the change of the refractive index of the guest-host PSBP-LCs as a function of the applied voltage, as shown in Fig.4 (blue squares). In addition, the measured no and ne of the
guest-host PSBP-LCs were 1.51 and 1.63 by the method of rotating the samples under a Mach-Zenhder interferometer.12 Compared the measured results of the guest-host PSBP-LCs in Fig.2(or the black dots in Fig.4) with the results analyz-ing based on the reorientations of LC directors (blue squares in Fig. 4), the changes of refractive index are similar when V > 60 Vrms. However, the results are mismatch when
V < 60 Vrms. In Fig.3, the LC directors and the dye directors
change somehow dramatically at V > 60 Vrms. To understand
more, we performed the observation of the Kossel diagram of PSBP-LCs under the applied voltages, as shown in Figs.5(a)–5(c). The PSBP-LCs shows hyperbolic fringes of the Kossel diagram at V¼ 0 and at V ¼ 48 Vrms, but the
brightness of fringes decreases and the distance between two hyperbolic fringes increases slightly when the voltage increases. That might result from the lattice deformation and the change of the orientations of LC directors in PSBP-LCs when V < 60 Vrms. When V > 60 Vrms, the hyperbolic
fringes disappear. The results in Figs.5(a)–5(c)can help us to explain the reason why the mismatch of the results at V < 60 Vrms. This is because the guest-host PSBP-LCs tends
to preserve the cubic symmetry and hence results in a slight lattice deformation. The net effect then influences a change in the optical impermeability tensor and the refractive index of the guest-host PSBP-LC. Therefore, the induced change of refractive index or electrically induced-birefringence should be the combinations of liquid crystal orientations and the lattice deformation. The similar result has been simulated in blue phase LCs.13
FIG. 2. (a) Voltage-dependent transmittance for the guest-host PSBP-LCs (blue diamonds) and the PSBP-LCs (red squares). k¼ 633 nm. (b) The change of refractive index as a function of applied voltage for the guest-host PSBP-LCs (blue diamonds) and the PSBP-LCs (red squares). k¼ 633 nm.
FIG. 3. The orientational angle of the dye molecular directors as a function of the applied voltage.
FIG. 4. The change of refractive index of guest-host PSBP-LC as a function of the applied voltage. Black dots represent the experimental results, blue squares represent the results analyzed from the measured transmittance and reorientations of LC directors, blue hollow squares represent the results ana-lyzed from the measured transmittance and modified orientational angles of LC directors and dye directors, gray dotted line represents the calculated result of the conventional Kerr effect, and red solid line represents the calcu-lated result of the extended Kerr effect. k¼ 633 nm.
Besides, at V > 60 Vrms the liquid crystal orientations
are in charge of the change of the refractive index, and the lattice deformation disappears owing to the breakdown of cubic symmetry. Since the orientational angle of LC direc-tors remains almost a constant at V > 80 Vrms, the change of
the refractive index, therefore, remains almost the same at V > 80 Vrms. We also plotted extended Kerr effect (red line
in Fig. 5) based on the equation dnextendðEÞ ¼ dnsat
½1 expððE=ESÞ 2
Þ, where E is electric field, dnsatis the
saturated refractive index change, and Es is the saturated
electric field.4To fit the measured results, dnsatis 0.041 and
Esis 9.99 V/m (which also means voltage is56 Vrms). The
Kerr constant (K) is 1:9 109m/V2which is calculated by following the relation K¼ 3 dnsat=k Es2. We also
plotted the change of refractive index of Kerr effect which can be expressed as dnKerrðEÞ ¼ ðk K E2Þ=3, as shown
in Fig. 4 (gray dotted line).4 As expected, the Kerr effect only validate at a small voltage region. From Fig.4, we con-clude that the meaning of Esand dnsatof the extended Kerr
effect: dnsatis mainly contributed from the reorientation of
LC when E > Esand Es is kind of a critical electric field at
which the lattice deformation disappears.
The above discussion is based on features of the guest-host LC system: the orientational angle of dye molecular directors (/) is the orientational angle of LC directors (h). However, the / and h actually are not identical because of the limitation of order parameter (S). The calculated order param-eter of dye molecules, defined as (a== a?)/ða==þ 2a?Þ, is
0.429.8Generally, the order parameter of LC is around 0.7– 0.8.14The relation between the order parameter and the time-averaged orientational angle (w) of LC directors (or dye direc-tors) with respect to x-axis is S¼< ð3cos2ðwÞ 1Þ=2 >.14 As a result, the orientational angles of LC directors and dye directors should be 24.1 and 38.1 with respect to x-axis in Fig.1, respectively. / and h should be 51.9 and 68.6 with respect to z-axis in Fig.1. As a result, / equals to0:8 h. By considering the modified orientational angles, we re-calculated the change of refractive index of guest-host PSBP-LC as a function of the applied voltage and plotted in blue hollow squares in Fig.4. The results based on the modified orientational angles are slightly close to the experimental results, but the mismatch still exists when V < 60 Vrms. That
means we can still conclude that the orientation of LC direc-tors play a major role in EIB of extended Kerr effect when the voltage (V) exceeds the voltage of disappearance of the lattice deformation (Vdef) and play a minor role when V < Vdef.
In conclusion, we experimentally investigated the EIB of Kerr effect of PSBP-LCs by discussing the orientations of LC molecules. The results show that the EIB of Kerr effect of PSBP-LCs mainly results from the orientations of LC
molecules when the voltage (V) exceeds the voltage of dis-appearance of the lattice deformation (Vdef). Besides the
ori-entations of LC molecules, lattice deformation is also involved in contribution of EIB when V < Vdef. We also
observed the change of Bragg fringes of Kossel diagram of PSBP-LCs at V⭌ Vdef which means the lattice deformation
of PSBP-LCs disappears. We also explain the physical meanings of the saturation electric field and the saturated re-fractive index change in the extended Kerr effect. This study proves that the orientations of liquid crystals indeed play roles in the EIB of Kerr effect in PSBP-LCs.
The authors would like to thank Dr. Hsu-Kuan Hsu (CMI) for the discussions and Professor Ru-Pin Pan (National Chiao Tung University) for Kossel Diagrams. The authors also thank Hung-Yuan Chen for the technical assis-tance. This research was supported partially by Chimei-Innolux Corp. and partially by the National Science Council (NSC) in Taiwan under the Contract (No. NSC 1012112 -M-009 -011 -MY3).
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FIG. 5. Kossel diagrams of PSBP-LCs at (a) 0 Vrms,
(b) 48 Vrms, and (c) 60 Vrms.
