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Electrically tunable soft photonic gel formed by blue phase liquid crystal for switchable colour reflecting mirror Vimala Sridurai, Manoj Mathews, Channabasaveshwar V. Yelamaggad, and Geetha G Nair ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b10952 • Publication Date (Web): 25 Oct 2017 Downloaded from http://pubs.acs.org on October 27, 2017
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Electrically tunable soft photonic gel formed by blue phase liquid crystal for switchable colour reflecting mirror Vimala Sridurai1, Manoj Mathews2, Channabasaveshwar V. Yelamaggad1 and Geetha G. Nair1* 1 2
Centre for Nano and Soft Matter Sciences, Jalahalli, Bangalore - 560013, India St.Joseph's College, Devagiri, University of Calicut, Kerala – 673008, India
KEYWORDS: Soft photonic crystals, blue phase liquid crystal, photonic band gap, selective reflection, liquid crystal gels
ABSTRACT: We report a robust soft photonic crystal system, fabricated using blue phase (BP) liquid crystal, which can efficiently filter visible light. The BP gel system is obtained without surface treatment or polymerization and thus is facile and cost effective to fabricate. Perfect monodomain with vivid colour is achieved with a low electric field, which can be further tuned to reflect a second colour. Most importantly, apart from the field induced colour switching, a dark / transparent state is also achieved due to complete unwinding of the BP helical structure. A
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potential application as a tunable colour reflecting mirror which can be switched between ‘reflecting’ and ‘transparent’ states is proposed. INTRODUCTION
Photonic crystals are periodic dielectric structures with periodicity modulation of the order of the wavelength of light. The Bragg reflection1 due to this periodicity causes a range of frequencies (or wavelength) called the ‘photonic band gap’ being selectively blocked from passing through the system leading to interesting applications2,3 like colour filters, optical waveguides, lasers and innovative devices like photonic integrated ciruits4, optically coupled biosensors2 etc. Soft photonic crystals have attracted immense research interest recently due to simple bottom-up self-assembly fabrication and soft-stimuli responsive photonic band gaptunability (see for eg. Ref 5 & 6) with potential applications in tunable filters, sensors and optical switches7,8. Blue phase (BP), a unique liquid crystalline phase that exists between the isotropic and cholesteric, can be considered as photonic crystal owing to the cubic lattice formed by its molecular arrangement9. Among the three blue phases BPIII, BPII and BPI obtained on cooling from the isotropic, BPII with a simple cubic lattice and the BPI with a body centred cubic lattice have been studied extensively10. The lattice sizes are of the order of a few hundred nm which facilitates BPs to act as 3-dimensional photonic crystals with photonic stop band (band gap) for visible light due to selective (Bragg) reflection10. As the BPs are soft systems, their lattice and thereby, the selective reflection wavelength can be tuned8 by temperature, electric field, optical field, etc. Electric field is known to provide the widest range of possibilities for the wavelength tuning especially due to the field induced lattice distortion/reorientation or electrostriction11,12.
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Although blue phases have interesting physical properties, from application point of view, stabilizing the phase is a huge technological challenge owing to their highly frustrated nature leading to narrow thermal range13. Among the various techniques14 that have been employed to stabilize BPs over wide temperature ranges, polymer stabilization15 has been highly successful especially for electric field induced photonic band gap tuning16. Once the desired colour is achieved with electric field, the system is polymerized and the rigid polymer network preserves the lattice structure17. But as the polymer strands almost freeze the BP lattice, AC electric field driven electrostriction effect is hardly observed. This is overcome by applying DC field and a lattice expansion is reported18. However DC field has undesirable effects such as increased conductivity and resultant electro-hydrodynamic instabilities19. Also polymer network is known to restrict the lattice size growth and thereby formation of truly perfect monodomains20. On the other hand, thermo-reversible liquid crystal (LC) physical gels formed by low molecular weight organogelators (LMOG) are functional soft matter systems in which the LC medium is trapped by the 3-dimensional fibrous gel network.21 This leads to attractive phenomena like enhanced mechanical strength and fast electro-optic response22. BP gels that are reported in literature are formed in liquid crystalline, polymers23,24, elastomers25 and aerosil network26. In the present work, the BP gel obtained by the addition of a very small concentration (1 wt %) of LMOG is a physical gel and hence thermo-reversible. Additionally, we find that flexibility of the gel network in spite of the mechanical strength, aids in facile tunability of the photonic band gap with electric field. MATERIALS AND METHODS The host nematic liquid crystal (RLC) is a eutectic mixture consisting of rod-like molecules, whose composition is given in Figure (S1-a). The host RLC is doped with 30% of a chiral 3 ACS Paragon Plus Environment
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dopant (S811, Merck) to induce blue phase (BP). To further enhance the range of BP, 15% of a bent core compound (BLC) is added to the mixture. The blue phase gel composite is obtained with further addition (1%) of a LMOG 12-hydroxystearic acid (HSA). Thus the optimized composition of the BP gel composite is 1% HSA in (15% BLC in (30% S811 in RLC)). The chemical structures and phase transition temperatures of all components are given in Figure S1. The components were taken by weight %, heated to 120 °C and stirred continuously for ~ 5 mins followed by cooling below gelation temperature to form the gel. The host LC mixture consisting of RLC and BLC exhibits a positive dielectric anisotropy (∆ε) which was confirmed by a planar to homeotropic switching with electric field (sine-1KHz-20V). The sample was filled (at 110 °C) into a ~11µm thick LC test cell fabricated using two ITO coated glass plates without any surface treatment. The thickness of the cell was measured by interferometric technique (see section 2 of SI) and was found to be uniform over the entire active area of 5 mm x 5mm to an accuracy of 0.05 µm. All the observations were done by cooling the system at 0.2 °C/min. The temperature was controlled using a hotstage (Mettler ToledoHS82/HS1) with a precision of 0.1 °C. The various phase transitions and textures of the phases were obtained by a polarizing optical microscope (POM) (Leica - DM4500P) in the reflection mode (R-POM) along with Lumenera –Infinity camera. The reflected wavelength spectra from the BP were obtained by attaching the detector head of a portable UV-visible spectrometer (Ocean Optics-USB2000) to one of the eye pieces of the microscope so as to simultaneously capture the spectra and visually observe the textures. The spectra were fit to a Pearson function and the fit profile was considered for analysis. AC electric field (sine-1KHz) was applied normal to the glass substrates using a function generator (HP-33120A) along with an amplifier (Trek – PZD700A) and the voltage was measured using a precision digital multimeter (Keithley - 2000).
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RESULTS AND DISCUSSION
Figure 1. POM texture of BP Gel mixture exhibiting (a) BPII, (b) BPI and (c) BPGel. The regions denoted by white squares and yellow ellipses indicate the red shift in selective reflection wavelength from the platelets. Scale bar is 50 µm. On cooling from the isotropic, the mixture exhibits a very low birefringent BPIII phase over a rather short temperature range of 0.1 °C. Below that bright green coloured crystallites corresponding to BPII start appearing. On further cooling by 1 °C, the green coloured platelets abruptly transform to BPI with red coloured crystallites (Figure 1). The raw selective reflection spectra obtained for BPII and BPI (see Figure S4 in SI) have peak wavelengths (λ) at ~510 nm and ~ 620 nm respectively. Although it is well established that the lattice planes of the BPII and BPI crystallites, with the above mentioned platelet colours, correspond to (100) plane of simple cubic lattice and (110) plane of body centred cubic lattice,27 it is explained in more detail in the following paragraphs. According to Bragg’s law, the selective reflection wavelength (λ100) corresponding to the (h k l) plane is given as λhkl = 2 n a (h2 + k2 + l2)-1/2 (Eq. 1), where, n is the average refractive index of the medium, a is the lattice constant and (hkl) are the Miller indices. For BPII with a simple cubic lattice, the lattice constant is half of the cholesteric pitch, P.9 Thus eq.1 becomes λ100 = n P = λCh (Eq. 2), where, λCh is the selective reflection wavelength of cholesteric phase. This equality holds good at the BPII to BPI transition.10
In order to verify this, selective reflection studies
are carried out in the cholesteric (Ch) phase. The BP gel composite is sandwiched between a pair of glass plates with the LC molecules aligned parallel to the substrates, such that the helix axis is 5 ACS Paragon Plus Environment
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orthogonal to the substrate plane. In this configuration, the Ch phase selectively reflects green colour with a reflection central wavelength (λ) of 534 nm (Figure S3 in SI), which is very close to the selective reflection wavelength at the BPII- BPI transition, i.e., 526 nm (as seen from Figure S4-b&c). As, λCh ~ λ100 (from eq.2) it is clear that, the BPII platelets possess (100) plane parallel to the substrates. It is well known that, for a bcc lattice according to the Bragg reflection selection rules, the sum of Miller indices h+k+l should be even. Thus there are four prominent reflection planes allowed for BPI: (110), (200), (211) and (220)10,26, amongst which, the (110), which has longest wavelength in BPI,28 is known to preferably grow parallel to the substrates.29,30,31,32 For the BP gel system, in BPI, red is the prominent platelet colour, and hence these platelets are assigned to (110) plane. Further, Wang et al31 have established that, at the BPII to BPI transition, the red coloured platelets with (110) lattice plane are switched to the green coloured platelets with (200) plane when a pulsed voltage enough to reorient the lattice is applied across the sample. Similar feature is seen in the current BP gel system with a pulsed voltage of 30V (2.7V/µm). Moreover the authors31 have used same chiral dopant S811 in a similar concentration, as in the case of current BP gel system. Hence it is inferred that, in the BP gel system, the red coloured platelets of BPI have (110) plane parallel to substrates. Thus, the green crystallites of BPII correspond to (100) plane of simple cubic lattice and the red crystallites of BPI to (110) plane of body centred cubic lattice. Cooling further, in BPI, results in the platelets turning from red to pinkish with some grey patches (see Figure 1c). This phase is denoted as BPGel and the transition temperature as TGel hereafter. The selective reflection spectrum (raw data) corresponding to BPGel is given in Figure S3-a. Further cooling results in cholesteric phase with focal conic texture. The phase sequence of 6 ACS Paragon Plus Environment
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the system is Iso (45.2 °C) BPIII (45.1 °C) BPII (44.1 °C) BPI (43.5 °C) BPGel (35 °C) Ch as obtained from POM, which is also confirmed by the temperature dependence of reflection spectra (see Figure S3-c). The average mono-domain platelet size obtained in the BPI phase is 125 µm long and 75 µm wide (Figure 2), which does not change upon gelation. From Figure S3-c it can also be seen that, in the BPII, the selective reflection wavelength (λ) is thermally invariant. The BPI sol range is so short that even before the λ could saturate, gelation occurs. At the transition to BPGel, there is a step-like increase in λ (~30 nm) and after transforming to BPGel, there is hardly any thermal dependence seen for λ. As no other phase transition is observed in this thermal regime, the red shift of 30 nm could be readily attributed to gelation. Also, from R-POM textures (Figure 1), the following colour changes are observed in BP platelets as the composite transforms from the BPI sol to BPGel state: (i) Orange to red, (ii) Blackish blue to bluish green (region marked by white squares) and (iii) Blackish green to pale green (region marked by yellow ellipses). Against this backdrop, the presence of prominent black patches on the red platelets of BPGel (Figure 1) would mean shifting of λ towards infrared. In a similar cubic BP system with polymer network, it has been established that, the polymer strands grow through the disclination lines of the BP lattice18. Moreover, organogels are known to swell upon gelation, due to the micro-phase separation of the gelator molecules (responsible for formation of the gel fibres) from the surrounding medium21,33. From the above mentioned features, it is clear that, the red shift seen in BPGel is caused by the lattice expansion due to the growth of gel network through the BP lattice. Rheologically the BPGel shows two distinct regimes, (i) the mechanically weaker BPGel1 followed by (ii) the stronger gel BPGel2 at lower temperatures (Figure S5), the latter featuring
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increased number of grey patches as observed by POM. Thus, a wide BP range of ~ 10 °C is obtained by simple physical mixing without the need for polymerization. As the system gelates in BPI, we have studied electric field dependence of the selective reflection wavelength in the BPI and BPGel phases, which are the sol and gel states of BPI respectively. With increasing field (sine – 1 KHz), the BPI which initially exhibited red coloured platelets, changes to yellow and subsequently to green for 2.7 V/µm (Figure 2). The reflection peak wavelength (λ) continuously varies with applied electric field (Figure 3) giving a blue shift of ~ 95 nm (from ~ 620 nm to ~ 525 nm). According to Bragg’s condition (eq.1), λ is directly proportional to the lattice constant, a.
Figure 2. POM textures of BPI at various electric fields. The top and bottom rows correspond to increasing and decreasing field steps respectively. Scale bar is 50 µm.
For cubic BP systems with positive dielectric anisotropy (+ve ∆ε), electric field applied along the two fold axis [110] of BPI results in lattice expansion.11 In such cases, λ increases with increase in electric field. But in the present case, which is also a system with +ve ∆ε, the behavior is opposite i.e. λ decreases upon increase in electric field (Figure 3), suggesting that, there is some other mechanism apart from lattice size change, governing this interesting phenomenon.
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Reflection Wavelength (nm)
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1.5
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Figure 3. Electric field (E) dependence of the reflection peak wavelength in BPI phase. The filled and open circles correspond to increasing and decreasing field steps respectively. The inset shows the reflection spectra i.e., wavelength (λ) dependence of reflection intensity (R) for different values of E in the increasing step. The numbers next to the spectra denote the applied electric field in V/ µm. B & F are the initial and final wavelengths on increasing and decreasing field steps respectively. Lattice reorientation, i.e. switching between different facets of the lattice, is another well known electric field induced phenomenon in BPs34. When the BP platelets are not grown from isotropic, as in the case of BP gel system, lattice reorientation is expected to occur due to field induced torque, from the domain walls35. The POM images corresponding to field of 2.16 and 2.34 V/µm (Figure 3) show a colour change from orange-yellow to green occurring from the edges of platelet domains, confirming lattice reorientation. This causes the blue shift in λ for field up to 2.34 V/ µm, and λ decreases by 30 nm in this electric field regime. Also, it is well established that, in the presence of electric field, the (200) plane with four fold axis along the field direction is more stable compared to (110).9,35,36 Thus, in the reoriented state, the green coloured platelets are due to (200) plane parallel to the substrates. Interestingly a plateau-like region (denoted as ‘Pl’ in Figure 4) is seen for electric fields ranging from 1.96 to 2.34 V/µm, which could be attributed to a regime where the lattice plane remains unaltered at (200). 9 ACS Paragon Plus Environment
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Increasing the electric field beyond 2.34 V/µm, leads to a further blue shift in λ. This is consistent with the electrostriction (lattice shrinkage) behaviour of the (200) plane along [100] axis of BPI with a +ve ∆ε, as extensively investigated by Heppke et al11. Therefore we attribute the overall blue shift (~ 95 nm) to the combined effect of lattice reorientation and lattice shrinkage as schematically represented in Figure 4.
Figure 4. Schematic representation of the lattice reorientation and shrinkage occurring due to the electric field induced effect in BPI.
In the BPGel1, similar electric field dependent measurements were carried out, the results of which are given in Figure 5. An important observation in this case is that, up to 2.16 V/µm (the same field which gave a blue shift of ~ 30 nm for the non-gelated BPI) the peak wavelength remains unaffected (Figure 6). This shows that the gel fibres of HSA, which have grown through the BP lattice hold it strongly such that electrostriction is prevented at least with AC field, an effect similar to polymer stabilized blue phase (PSBP) systems20. Upon increasing the field to 3.42 V/µm, platelets which are initially oriented along [110] axis get pinned by gel network resulting in red coloured domains throughout the field of view (Figure 5).
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Figure 5. POM textures of BPGel1 at various electric fields. The top and bottom rows correspond to increasing and decreasing field steps respectively. The texture for 4.14 V/µm shows the homeotropic dark state (top) confirmed by conoscopy (bottom). Scale bar is 50 µm. 690
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Figure 6. Electric field dependence of the reflection peak wavelength for BPGel1. The filled and open circles correspond to increasing and decreasing field steps respectively. The inset shows the reflection spectra i.e., wavelength (λ) dependence of reflection intensity (R) for different values of E in the increasing step. The numbers next to the spectra denote the applied electric field in V/ µm. B & F are the initial and final wavelengths on increasing and decreasing field steps respectively. Interestingly, for this field, the intensity of the reflected peak is much higher than the value without any field, unlike in the case of PSBP systems, wherein the reflectivity decreases with field37,38. The increased intensity in the present gel system could be because, the fibres, in spite of the cross-linked network, are flexible enough to allow lattice reorientation resulting in better alignment of the platelets. Further increase in the field overcomes the pinning effect of gel fibres,
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and results in abrupt blue shift (see Figure 6), with the lattice plane change from (110) to (200) and all the domains turn green for 3.96 V/µm (Figure 5). It has to be mentioned here that in both BPI and BPGel1, the monodomain platelets are perfectly tuned between red and green as a function of applied field. The tuning between the two reflective colours are tested over 10 consecutive electric field cycles, and the data obtained in the BPGel1 phase are presented in the Supporting Information (Figure S6). Here, we would like to emphasize that the selective reflection studies are repeated at least 16 times over a period of 4 months and the phenomenon is found to be highly reproducible. Also, in the BPGel1 (see Figure 6), the final wavelength at the end of the decreasing field step (say state ‘F’) does not coincide with the initial value of the increasing field step (state ‘B’) unlike in the case of sol BPI (Figure 3). As the field is decreased, the state ‘F’ saturates with a λ value corresponding to that of the plateau region ‘Pl’, which is ~ 30 nm lower (see Figure 6) than the initial value. The hysteretic behaviour could be explained as follows. When the platelets start reorienting with electric field in the increasing field step, the gel fibres spread out such that the fibre bundles are more concentrated in the domain boundaries of the BP platelets probably due to lateral stretching. This could have also led to the increased peak intensity in this regime (orange coloured peak in the inset of Figure 6). This spread gel network is pinned by the BPI lattice and therefore remains at the domain boundaries even when the field is completely removed (state ‘F’) resulting in decreased λ. Essentially this process leads to perfect monodomain (110) red platelets over a larger electric field range (Figure 5) compared to BPI. Nevertheless, this hysteretic behaviour exists only in the first electric field cycle, as confirmed from the cyclic test measurement (Figure S6).
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An important requirement for selectively reflecting surfaces and display devices is vividness of colour. It can be quantified by calculating the peak intensity and full width at half maximum (FWHM) of the reflection spectra. In the BPGel1 phase, once the lattice reorients from (110) to (200), the reflected colour is more pronounced for subsequent electric fields, both in the increasing and decreasing field steps, as compared to the pristine state. From the reflection spectra (see Figure S7 in SI), it is clear that the peak intensity increases by a factor of ~ 2.7 and the FWHM decreases by 0.4 at the end of the electric field cycle (Figure S7-f) compared to the intial zero-field state (Figure S7-a). A similar decrease in FWHM is seen for the reflection from (200) plane (Figure S7-c&d) as compared to the pristine state (a). Also, upon lattice reorientation, the mono-domain size increases to the extent that it fills the entire field of view limited only by the size of the circular glass window (2 mm diameter) of the hotstage. Thus, vividness of the selective reflection colour gets enhanced upon application of electric field. Increasing the field to 4.2 V/µm leads to a state that appears dark between the crossed polarizers. This is confirmed to be a nematic phase oriented homeotropically from conoscopic measurements (see the bottom extreme right image in Figure 5). This field driven nematic is due to the complete unwinding of double helix structure of the BP. This phenomenon is especially surprising because, in the BPI (the sol state), when the green platelets were obtained (with a field of 2.7 V/µm), further increase in the field, only resulted in melting of the platelets which ultimately led to their collapse. This is due to the ions, which are inherently present in a LC being set to oscillation by the applied electric field causing electro-hydrodynamic instabilities19. In the BPGel1, this undesirable effect is not observed indicating that the ions are trapped by the gel network39. So it is quite evident that gelation has enhanced the robustness (against electric field) of the BPI. Upon lowering the field to 4V/µm, the selective reflection is regained with the
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corresponding green platelets. This process of switching the selective reflection colour “on” (BPGel1) and “off” (nematic) was also highly reversible over several cycles. It has to be noted that, the overall wavelength tunability is enhanced in the BPGel1 (~120 nm) as compared to the BPI (~95 nm). Here it is worth mentioning that, the operating field used to obtain ~120 nm wavelength shift in the BPGel1 is a mere 4V/µm, which is ~ 4.5 times smaller than that reported for a similar +∆ε system which gives only a 80 nm blue shift.40 This is also comparable to a field induced red shift (~160 nm with 4V/µm) seen in a PSBP system20. More importantly, perfect monodomain BP and homeotropic states are almost impossible (at least with the current understanding) in the PSBPs due to the rigid polymer network. Very recently, such monodomain BP alignment has been reported by using substrate treatment41 and nano-patterning 42
. But, in the present thermo-reversible BP gel system, electric field induced monodomains are
easily achieved due to flexible gel fibres incorporated in the BP liquid crystal itself. Apart from the shift in the selective reflection wavelength, another feature that is observed in both BPI and BPGel1 phases (Insets of Figures 3 & 6) is, the decrease in the reflection intensity itself with increase in electric field. This intensity decrease from the (110) plane (red colour) can be attributed to the deviation from the normal incidence (of light) with respect to the platelets (as discussed in the section 7 of SI). However one of the components (BLC) of the BP gel composite, absorbs in the green spectral regime i.e., ~ 540 nm (Figure S8). This leads to a quenching effect with a marked decrease in the selective reflection intensity from the (200) plane (green colour) as compared to the red ones. The BPGel2, which has a stronger gel network, as confirmed from rheological data, (Figure S5), also shows selective reflection colour (see Figure S9) and the wavelength is unaffected up to 2.7 V/µm (see Figure S10-a). This is because the thermo-reversible gel with its enhanced
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strength comparable to polymer melts43 holds the BP lattice. Further increase in field to 2.8 V/µm leads to a cholesteric phase with focal conic texture (Figure S10-b) as the double twisted cylindrical state of the BP is transformed to a single twisted structure44. At 6 V/µm, helix completely unwinds leading to a homeotropic nematic texture (Figure S10-b). Thus in the BP gel system, perfect and reversible tunability of colors (and hence the photonic band gap) between vivid red and green reflecting states is achieved by varying the operating electric field. Interestingly, at higher fields the gelated BPI additionally gives rise to a homeotropic nematic state which appears dark (light completely blocked) or transparent (light completely passes through) with and without crossed polarizers respectively. This phenomenon clearly exhibits the enhanced electrical robustness (apart from higher mechanical strength) of the gel state. The process of switching between the reflecting and transparent states brings in the possibility to fabricate a tunable mirror device (see Figure 7) using the BP composite.
Figure 7. The proposed BP gel switchable mirror device exhibiting (a) Green reflection with electric field (b) Transparent homeotropic state with further higher field and (c) Red reflection when the field is completely removed CONCLUSION Gelation of BPI using a LMOG stabilizes the electrostriction regime and also provides robustness to platelets withstanding higher voltages which eventually leads to an unwound-helix state of nematic. Also, BPI gel exhibits enhanced mechanical strength comparable to that of polymer stabilized systems and unlike the latter, the flexibility of gel fibres enables facile 15 ACS Paragon Plus Environment
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reorientation between BP lattice planes even after the formation of 3D network. Thus the softstimuli responsive nature of the BPI phase in conjunction with the ion-trapping nature of the gel fibers enable tuning between reflective color and transparent states by the application of electric field. Based on the electrostriction phenomena occurring in the gelated BPI, a tunable mirror device switching between green and red reflecting states and a transparent state is proposed. The system also has potential application in tunable colour filters and waveguides where the reflected colours can not only be tuned but also be switched ‘off’. ASSOCIATED CONTENT Supporting Information (SI) Chemical structures and phase transition temperatures of the components of BP gel mixture Uniformity of cell thickness by interferometry POM texture and selective reflection spectrum of the Ch phase Reflection spectra at various temperatures of the BP gel composite and thermal dependence of the reflection peak wavelength Temperature dependence of storage (G′) and (G″) of the BP gel system exhibiting various phases Cyclic test measurements performed in the BPGel1 phase Electric field dependence of selective reflection spectrum of the BPGel1 Discussion about decrease of reflection intensity with electric field in the BPI and BPGel1 phases Absorbance spectrum of the BLC component
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Electric field dependence of reflection wavelength of the BPGel2 and corresponding POM textures This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Email:
[email protected] Author Contributions S.V carried out the experiments. M.M and C.V.Y were involved in synthesizing the BLC compound. G.G.N supervised the entire work. S.V and G.G.N prepared the manuscript. Notes Authors declare no competing financial interest. ACKNOWLEDGMENT The authors are thankful to Dr. S. Krishna Prasad, CeNS, for his valuable suggestions in preparing the manuscript. REFERENCES 1. Yariv, A.; Yeh, P. Optical Waves in Crystals; Wiley: Newyork, 1984; Ch.5, pp. 155 – 219. 2. Gong, Q.; Hu, X. Photonic Crystals Principles and Applications; CRC press: Florida, 2013. 3. Ozaki, M. ; Kasano, M. ; Ganzke, D.; Haase, W.; Yoshino, K.. Mirrorless Lasing in a Dye-Doped Ferroelectric Liquid Crystal. Adv. Mater. 2002, 14, 4, 306-309.
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