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A controlled helix pitch modulation in the in-plane direction of a planarly aligned cholesteric liquid crystal cell is demonstrated by using photopolymerizable cholesteric liquid crystals. By fabricating artificial domains with a closed volume via two-photon excitation laser-lithography, the degree of pitch modulation could be controlled by adjusting the surface area to volume ratio of the domain. A pitch modulation of over 60 nm was realized by designing the shape of the artificial domain.
©2008 Optical Society of America
1. Introduction
Liquid crystals (LCs) are categorized into a number of different phases, depending on the symmetry exhibited by the comprising molecules. In materials with chiral constituents, the cholesteric (Ch) phase is exhibited where the LC director assumes a helical configuration along a single helical axis. Depending on the pitch of the helix, ChLCs show selective reflection of light over a certain wavelength region [1], and this property has been utilzed in a number of optical and photonic devices, such as thermometers [2], optical polarizers [3], and more recently, photonic crystal devices [4–7]. The optical properties of ChLCs are caused as a result of a highly birefringent rodlike molecules twisting into a helical structure. The resultant periodic modulation of the dielectric constant along the helical axis causes circularly polarized light within a certain spectral range (described by λ=nop-nep, where no and ne are the ordinary and extraordinary refractive indices, and p is the pitch of the ChLC) to be selectively reflected. The ChLC pitch can be controlled relatively easily over a wide range, owing to the external field sensitivity of the molecules: control of the ChLC pitch has been demonstrated by varying the concentration of the chiral dopant [8]; heating [9]; applying electric field [10]; or in specific cases, by irradiating UV light [11]. The spectral position of the reflection band can therefore be tuned throughout the visible spectrum: but since the typical birefringence of LCs in the optical region is Δn=n e-n o~0.15-0.2, the typical reflection bandwidth is limited to 50–100 nm.
Several strategies have been proposed in an attempt to exploit the optical properties of ChLCs over a broader spectrum. Theoretical studies have revealed that introducing multiple structural defects within the ChLC helix would cause multiple reflection bands to appear [12], or simply gradually changing the pitch would produce an elongated reflection band [13]. However, experimental demonstrations of these systems were only possible through the use of photopolymerizable ChLC materials [14]. The environmental sensitivity of ChLCs only allows a temporary change in the pitch, since, for a particular environmental (thermal) condition, the ChLC phase can only take a single pitch length. By using photopolymerizable materials, a particular LC director configuration can be “frozen” upon irradiating UV light, and become thermally and mechanically stable. Applications of photopolymerized ChLCs have been studied extensively [15–17], as well as various other LC phases, such as smectic [18] and ferroelectric [19] LCs that have been photopolymerized.
Photopolymerizable ChLCs are interesting also because, by choosing appropriate materials, phenomena other than just “freezing” the orientation can be observed. In ChLCs comprised of monomers with a different reactivity, monomer diffusion occurs as a result of polymerization. Fabrication of molecular architectures has been demonstrated by causing an in-plane diffusion of high and low or non-reactive monomers [20]. The diffusion of monomers in the depth direction of the cell has been used to create a ChLC material with a pitch gradient, so that the reflection band would cover the entire visible spectrum [3].
We have previously reported the effect of local polymerization on the helix pitch of a photopolymerizable ChLC material comprised of a chiral monoacrylate and a nematic diacrylate [6]. Upon polymerization, the non-chiral diacrylates are consumed in the polymerization process at a faster rate than the chiral monoacrylates, and decreases the concentration of the non-chiral monomers in the polymerized region. As a result, molecular diffusion causes the concentration of the chiral monomers to decrease in the polymerized region, causing the pitch to elongate. In our previous report, an elongation factor of approximately 15 % was obtained in the polymerized region, while no obvious change was seen in the surrounding, unpolymerized region. Here, we show that a controlled degree of pitch modulation can be induced in the unpolymerized region by forming polymer “frames” within the cell to prepare artificial domains. Changing the size of the domain allows us to control the effective monomer diffusion taking place, and thus the resultant pitch length within the domain. We will show that ChLCs with pitch lengths varying by more than 60 nm (corresponding to selective reflection wavelength > 100 nm) can be made to coexist in a single cell by designing the surface area to volume ratio of the artificial domain. The degree of pitch modulation can also be varied while keeping the effective domain size constant by engineering the surface shape of the frames.
2. Fabrication of the artificial domains
The material used was a right-handed, photopolymerizable ChLC mixture comprised of achiral diacrylate and chiral monoacrylate monomers provided by Merck KGaA, with 1 wt% of Irgacure 1850 [Ciba] added as a photoinitiator. The material absorbs light with wavelength < 430 nm and polymerizes into a solid film. A small amount (0.01 wt%) of N,N’-bis(2,5-ditert-butylphenyl)-3,4,9,10-perylenedicarboximide [Sigma-Aldrich: BTBP], which has a weak absorption peak at λ=488 nm and 532 nm was doped in the mixture for observation purposes. The ChLC material was infiltrated in a LC cell with cell-gap of ~6 µm at 76°C which is above the ChLC-isotropic phase transition temperature and was cooled slowly to room temperature, after which the “frames” were fabricated by laser-lithography on a confocal laser scanning microscope system [Zeiss: LSM-510]. A mode-locked titanium sapphire laser [Spectra Physics: Maitai] with λ=800 nm, pulse width 150 fs and a repetition rate of 80 MHz was scanned by a galvanometer over a desired pattern. As the laser light is scanned through the material, photopolymerization induced by two-photon absorption occurrs in the vicinity of the laser focus, allowing structures of arbitrary shape to be fabricated. The scanning conditions which gave optimum results were laser intensity of several MW cm-2 and scan speed of approximately 0.02 µm µs-1. The scan was also performed in the depth direction of the cell also to polymerize frames thoroughly in the depth direction.
After the frame patterns had been made, optical measurements were performed under an optical polarization microscope, while keeping the temperature at 30°C on a hotstage [Mettler: FP-90]. The transmittance spectra were measured upon right circular polarization incidence by a CCD multichannel spectrometer [Hamamatsu Photonics: PMA-11] with a spectral resolution of 3 nm. A color filter cutting out light with wavelength below 480 nm was inserted where possible when handling the sample, to avoid spontaneous polymerization.
3. Observation and modelling of pitch shortening in the artificial domains
Figure 1(a) represents the frame pattern and the associated domains. A polymer frame approximately 10 µm wide was fabricated and four isolated domains were formed. Figures 1(b) and 1(c) are the polarized optical micrograph and the confocal laser-scanning fluorescence micrograph of fabricated structure (fabricated at 3.8 MW cm-2), where the number “02” is a label. The polarized optical micrograph shows a clear change in texture at the photopatterned frame and at each of the domains confined by the frame: the changing process started soon after photopolymerization until reaching an equilibrium state after several hours. The different colors correspond to a different pitch of the ChLC helix, as seen in the optical transmittance spectrum measured at each domain (Fig. 2). The selective reflection wavelength is distinctively different at each confined region and is also different from the surrounding (bulk) ChLC; a larger blue-shift of the selective reflection wavelength is observed in domains with a smaller confined volume. The estimated pitch lengths calculated from the transmittance spectra, assuming n e=1.716 and n o=1.544 are 332, 317, 302, 290 and 267 nm respectively (using selective reflection band: λs=n o p-n e p), which means that 4 completely different helix configurations are stably coexisting in a single cell. Upon heating the sample, the ChLC in each domain showed pitch shortening (which is the same behavior as the original ChLC material), whereas the pitch of the polymerized region remained almost constant, due to molecular fixation [6]. The pitch-shortened ChLC could be photopolymerized into a film in the same manner as the ChLC without pitch-shortening, by irradiating UV light on the material.
Fig. 1. (a). Schematic of the fabricated pattern where the units is µm. (b). Polarized optical micrograph of the fabricated structure. In a ChLC, the color observed under crossed polarizers corresponds to the selective reflection wavelength; the different colors in each domain correspond to a different pitch length. (c). Confocal laser-scanning fluorescence micrograph of the structure, giving information of the distribution of the doped DCM dye.
Fig. 2. Transmittance spectrum upon right circularly polarized light incidence at each of the domains prepared in Fig. 1. A color filter (cutting light with wavelength below 480 nm, shaded in figure) was inserted when obtaining the spectra for domains 1 and 2, to avoid spontaneous photopolymerization.
The pitch shortening in the artificial domains is caused as a result of the molecular diffusion of the chiral monomers from the polymer frames into the unpolymerized ChLC, as shown schematically in Fig. 3. The molecular diffusion observed in this system is one where the chiral monomers are pushed out of the polymer matrix into the unpolymerized ChLC, as a result of the concentration gradient formed by the difference in the consumption rate of the achiral diacrylates (which have a higher reactivity) and the chiral monoacrylates, upon photopolymerization. The confocal laser-scanning fluorescence micrograph (Fig. 1(c)) gives evidence of the molecular diffusion occurring between the polymerized and the unpolymerized regions, since the fluorescence from the DCM dye, which does not take part in the polymerization process, decreases in the polymerized structure. This indicates that the DCM dye (and therefore other unreacted monomers) diffuse out of the polymer matrix. We observed that the diffusion of both the dye and the monomers occur over a certain amount of time after polymerization, but the time required to reach steady state was longer for the monomers than that for the dye, since the decrease in the fluorescence was observed in a few seconds after polymerization, whereas the change in the pitch took several hours until completion.
Fig. 3. A schematic representation of the molecular diffusion process which causes a pitch shortening in the artificial domains with size x and y, fabricated in a LC cell with thickness t.
The various degrees of pitch modulation are achieved by controlling the effective increase in the chiral concentration within each artificial domain. Usually, the chiral monomers pushed into the unpolymerized region are not sufficient to change the pitch of the whole unpolymerized region, because only a small increase in the chiral concentration occurs compared to the volume. This region showing no change corresponds to the unpolymerized region outside the frame in Figs. 1 and 3. However, within the artificial domains–which are confined regions with a small volume, the concentration increase of the chiral monomers become sufficient to cause pitch modulation. For a rectangular domain with sizes x, y and t where t is the thickness of the cell, as shown in Fig. 3, the volume V of the domain is given by V=xyt, whereas the surface area S of the polymer wall is given by S=2(x+y)t. Assuming that the amount of chiral molecules which diffuse out of the polymer matrix per unit area of the polymer/monomer interface upon reaching equilibrium is D, the effective increase in the chiral concentration ΔCchiral within a particular domain can be modeled as a simple two-dimensional problem,
The selective reflection wavelength λs(=n o p or n e p at the short and long-wavelength bandedge wavelengths respectively) is in general inversely proportional to the concentration Cchiral of the chiral molecules [21]. The pitch shortening in a single domain can therefore be described by
where C 0 is the initial concentration, and A is a constant. According to Eq. (2), the domains with a larger pitch modulation should be the domains with a larger S/V ratio: this is found to be true for the fabricated domains, as shown in Table 1. Plotting the ratio of the shortened pitch length of each domain to the pitch of the ChLC surrounding the frame (p 0=332 nm) as a function of the S/V ratio (Fig. 4), it is found that the best fit is obtained when D/C 0=1.4 is used as the fitting parameter in Eq. (2). The graph of Eq. (2) plotted with various D/C 0 values also reveals that a larger pitch shortening effect is obtained by using materials with a large D/C 0, i.e. large diffusion and strong chirality.
Table 1. The Surface area (S) to Volume (V) ratio of each of the domains prepared in Fig. 1. t is the thickness of the cell.
Fig. 4. The S/V ratio dependence of pitch shortening (filled circles) and theoretical fits (dashed lines) with various D/C 0 values. D/C 0=1.4 gives the best fit for the studied material.
4. Pitch modulation by engineering the frame shape
In the final part of this paper, we will show how polymer frames with engineered surface shapes can cause different degrees of pitch modulation. This is useful since artificial domains with approximately the same size can be made to exhibit different selective reflection wavelengths, and has potential applications for display devices when, for example, an array of domains exhibiting Red, Green and Blue colors are fabricated to function as reflective pixels. The idea is to increase the S/V ratio of the domain by introducing small patterns in the frame of the domain. Assuming n rectangular slits with dimensions a×b in the frame of a square domain with sides x and thickness t (Fig. 5(a)), the S/V ratio of the new domain becomes
which is always greater than the value without the slits, since a,b ≪ x. An example is shown in Fig. 5(b), where different degrees of pitch modulation are observed in three domains with effective size 80 µm×80 µm (fabricated at 5.0 MW cm-2): the domain with the slits in the frame has a shorter pitch than the domain without. A single rectangular slit with size 2 µm×10 µm introduced in the frame increases the S/V ratio of the domain by 5.9 %, which becomes a 112 % and 211 % increase respectively with 20 and 40 slits. The transmittance spectrum of each domain shown in Fig. 5(c) reveals that the ChLC pitch can be shortened to reach even the UV region: thus designing the shape and the number of slits allows arbitrary control of the pitch in the domain, all with the same effective domain size.
Estimating the pitch length using the same n e and n o used in section 3 and plotting the shortened pitch length against the S/V ratio of the engineered domains (Fig. 6), one finds that in this case the best fit is given using the parameter D/C 0=3.0. The large offset in the D/C 0 values used for the fitting of the data obtained in sections 3 and 4 are possibly due to the change in the diffusion parameter D. The presented model is a simplified model only considering the total number of molecules diffusing out of the polymerized matrix: physical factors influencing the diffusion such as the degree of polymerization and the diffusion constant of the material are only incorporated in the model as a change in the value of D. In the current situation, since the diffusion is driven by a polymerization induced gradient in the local chirality, the total number of diffusing molecules increases when a larger volume is polymerized (i.e. when the gradient in the local chirality is induced over a larger volume). The width of the frames fabricated in Fig. 5(b) is ~23 µm, which is approximately double the width of the frames in Fig. 1(b). Hence, the volume of the polymerized region in Fig. 5(b) is greater than the case in Fig. 1(b) by a factor of ~2, which is comparable to the difference between the D/C 0 values used to fit the data. Although the presented model is capable of describing the pitch shortening phenomenon, physical parameters such as the degree of polymerization, volume of the polymerized frame and the diffusion constant should be incorporated in the model for it to be capable of predicting the pitch shortening phenomena for given experimental conditions.
Fig. 5. (a). Effects of introducing a slit pattern in the domain frame. (b). Polarized optical micrograph of three domains with a normal frame (top), frame with 20 slits (middle) and 40 slits (bottom). Note the difference in the colors, corresponding to the pitch observed in each domain. (c). The transmittance spectra of the ChLC within each domain at λ ≥ 400 nm, which is the limit upon observing the structure on a microscope. No stop-band is observed in the domain with 40 slits, because the pitch has shortened enough to shift the band-gap into the UV region.
Fig. 6. The S/V ratio dependence of pitch shortening (filled circles) and its theoretical fit (dashed lines) for the ChLC confined by the engineered frames in Fig. 5.
To further exploit the effect of engineering the frames to enhance the S/V ratio, one can think of employing a fractal geometry. We give numerical estimates on the effect of employing such complex surfaces. Illustrated in Fig. 7 are possible designs of slits which themselves have self-similar slits recurring once (Fig. 7(b)) or twice (Fig. 7(c)). Assuming the dimensions of the second-generation slits to be 1 µm×2 µm and that each first-generation slit has 10 second-generation slits as in Fig. 7(b), the S/V ratio of the frame considered in Fig. 5 increases by 322% and 580% upon introducing 20 and 40 slits, respectively. If thirdgeneration slits are further introduced, the increase in the S/V ratio becomes 934% and 1610% (for 20 slits and 40 slits respectively, assuming third-generation slit size 0.33 µm×0.66 µm and 10 third-generation slits in each second-generation slit), compared to the 112% and 211% increase when no recurring slits are introduced. Figure 8 shows the slit-number dependence of the actual S/V values when second and third generation slits are introduced. When third-generation slits are introduced, the S/V ratio exceeds 0.9 for 40 slits, shortening the pitch by approximately 75% (from Fig. 6): this is more than enough to cover the entire visible spectrum and will also be useful in realizing broadband devices. The fractal surface is therefore very effective in enhancing the pitch shortening effect.
Fig. 7. Schematic illustration of fractal slits with recurring self-similar slits. (a) first-generation slit, (b) first-generation slit with 10 second-generation slits, (c) first-generation slit with 10 second-generation slits each possessing 10 third-generation slits.
Fig. 8. Slit number dependence of the S/V ratio for fractal slits with different generations. Assumed dimensions are 10 (1 µm×2 µm) second generation slits in each (2 µm × 10 µm) first generation slit, and 10 (0.33 µm×0.66 µm) third generation slits in each second generation slit, in a square frame with sides 80 µm.
5. Conclusion
We demonstrated controlled pitch modulation in the in-plane direction of a planarly aligned ChLC cell by fabricating artificial domains and controlling the effective diffusion of chiral monomers taking place. In the particular material we used comprised of chiral monoacrylates and achiral diacrylates, a pitch shortening of more than 60 nm was observed by varying the surface area to volume ratio of the domain by either changing the size, or engineering the frame shape. We also discussed on some approaches to effectively enhance the pitch shortening effect.
While the structures studied in this paper were all fabricated on a laser-scanning microscope system, similar results should be obtained by one-step photopolymerization using conventional UV exposure systems. The use of appropriate photomasks will allow one to fabricate ChLC arrays functioning as RGB domains, or mirrors with particular patterns or designs exhibiting rich colors. Since the pitch-shortened region is unpolymerized, the system can be further tuned by external fields, making them useful for photonic applications. This simple technique relying on the amazing self-organizing ability of liquid crystals provides a novel approach to fabricate new types of optical and photonic components.
Acknowledgments
The authors thank Merck KGaA for providing the photopolymerizable ChLC mixture used in the study. H. Yoshida appreciates Dr. J. Nakanowatari for valuable discussions. This work is partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
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