Preparation of optical waveplates from cellulose nanocrystal nematics on patterned polydimethylsiloxane substrates

Chenxi Li; Nan Wang; Nan Wang; Tingbiao Guo; Julian Evans; Julian Evans; Sailing He; Sailing He; Sailing He

doi:10.1364/OME.9.004614

1. Introduction

Optical waveplates, which are widely used to modify the state of polarization of light [1,2], are key components in optical systems for various applications, such as DVD/CD players [3], LCoS projectors [4], polarization microscopes [5,6] and so on. Traditional optical waveplates are made from anisotropic crystals (quartz, calcite, etc.) and anisotropic polymer films [7]. Compared with the waveplates manufactured by crystals, which are usually fragile, difficult to polish and make into thin plates or small components, waveplates made by stretching polymer films are flexible, have better processability and can be conveniently made into zeroth-order phase retarder at low cost [8]. In general, materials with sufficient birefringence can be used to produce waveplates [9,10]. Among them, cellulose nanocrystal (CNC) liquid crystal (LC) films are good candidates, because they basically share the same merits of flexibility and good processability with polymer waveplates [11–13] and can even further reduce the cost, since their raw materials cellulose is the most abundant biopolymer on the planet and is an inexpensive renewable resource [14,15]. CNCs, obtained through acid hydrolyzing native cellulose, can show LC phases when the concentration of the CNC suspension exceeds the specific critical value [16]. CNCs made from common sources such as cotton [17,18], woods [19], bacteria [20,21], and so on usually present a rod-like shape with a charged surface [22,23], and generally form chiral nematic phases with a left-handed helical ordering [24]. CNC films made from chiral nematic phase are well known to be used as reflection films [25,26], while they are also reported to serve as birefringent films or optical waveplates [27]. Chiral nematic phase, however, is not an ideal candidate for the preparation of optical waveplates, because liquid crystal directors tend to deviate from being uniformly aligned due to the helical ordering. Therefore, the prepared waveplates usually have a small volume fraction of the anisotropic phase [28–30] and a low optical birefringence [31]. In contrast, nematic phase is naturally more desirable for the application of optical waveplates, since it can generally provide larger optical birefringence, which leads to thinner thickness and lower loss of the waveplates and also allows for adding sufficient polymers to CNC suspensions to improve the mechanical property of the CNC films. However, preparation of nematic phase of CNC LCs is more difficult because it generally needs additional requirements, such as large CNC aspect ratios [32], further pH control [33,34], and so on. As a result, the application of CNC nematic LCs is far less explored compared with that of the chiral nematic phase. The most remarkable feature of CNC LCs is that the orientation ordering of CNCs in both nematic and chiral nematic phases can be preserved in CNC films after complete evaporation of solvent [35]. The obtained nematic CNC film with a relatively large birefringence is very promising for waveplate applications.

In this paper, we present optical waveplates made from CNC nematic liquid crystals, which are prepared by our recently published method of pH control [34]. We doped the CNC nematic LC with polyethylene glycol (PEG) and align it on patterned polydimethylsiloxane (PDMS) substrates by shearing forces and fabricated a 1/4 λ and a 1/2 λ CNC waveplate for 530 nm. The patterned substrates are used to control the thickness of the CNC film and to improve the quality of the liquid crystal alignment. Compared with controlling withdrawal speeds [28–31] or the number of layers cast onto the substrate [36] for thickness control in the past studies, our method can control the thickness of the CNC film accurately and is more efficient. The optical performance of CNC waveplates is investigated by Mueller matrix analysis and examined by measuring the transmission spectra of the waveplates between two polarizers, where experimental results are in agreement with the theoretical analysis. Optical extinction and birefringence of CNCs are extracted from the measured spectra as well. These fabricated waveplates are flexible and can be tailored into any desirable shapes conveniently.

2. Experiment

CNC nematic LCs were prepared by hydrolysis reaction and further pH control according to the established protocols [33]. 6.5 g of degreasing cotton was dispersed in 70 mL of 65wt % sulfuric acid and stirred at 46°C in a water bath for 1 hour to ensure the hydrolysis of cellulose into CNCs completely. 70 mL of deionized water was added to the resulting dispersion to quench the hydrolysis process. The CNC suspension was purified by centrifugation at 9000 rpm for 10 min several times and the resulting residual was under dialysis (MWCO 12000) for several days until the pH value reached 7. The CNC suspension was centrifugated at 12500 rpm for 40 min to remove impurities and the redundant solvent. The obtained sample with 13wt % of CNCs showed a chiral nematic liquid crystal phase while adjusting the pH value to ∼1.5 by adding 2 µL of 65wt % sulfuric acid to 200 µL of the sample led to the nematic phase. The pH value of the CNC dispersion was measured by a pH meter (PH5S) with 0.01 resolution. The liquid crystal phases were identified by polarizing optical microscope (POM, Olympus BX53M). Shape and size of the obtained CNCs were also characterized. The cellulose suspension was diluted to 0.003wt % and dropped on a copper grid and negatively stained with uranyl acetate. The specimen was then observed by transmission electron microscopy (TEM, JEM-1200). The size distribution of CNCs was measured by dynamic laser scattering meter (Zano ZS).

Uniform CNC nematic films were made by aligning CNCs by shearing forces on patterned PDMS substrates produced from photoresist molds (Fig. 1). This aligned CNC nematmic films could be served as optical waveplates. First photoresist SU-8 (GM1050, Gersteltec Sarl) was spin-coated on glass substrates with controlled thickness d and a pattern of gratings with a period of 800 µm was produced on this substrate by UV-lithography (SUSS MA6). PDMS prepolymer mixed with a curing agent (Sylgard 184, Dow Corning Corporation) with a weight ratio of 10:1 was added onto the surface of the SU-8 mold and cured at 80°C for 2 h. Then a flexible PDMS film was formed and detached from the SU-8 mold. For different waveplates, the thickness d, which also corresponded to the height of the grating ridges of the PDMS substrate, was controlled as 2.1 µm and 4.2 µm for 1/4 λ and 1/2 λ waveplate ($\lambda = 530\;\textrm{nm}$) respectively and further confirmed by a step profiler (Veeco Dektak 150). The surface of the PDMS substrates was modified by plasma treatment (Plasma Cleaner PDC-002) for 5 min to increase the hydrophilicity. CNC nematic LCs mixed with 10wt % PEG (number-average molecular weight 400, Sigma-Aldrich) were dropped on the PDMS substrate and sheared by a piece of glass sliding along the ridges of the gratings at an appropriate speed to produce high-quality alignment. Excess CNC suspension on the ridges was removed and confirmed by the interference color at the ridges of the gratings under an optical microscope. Two identical films with CNC LCs were aligned face-to-face with half-period displacement and bonded firmly to form the waveplate after the CNC LCs completely dried at room temperature. The optical performance of the CNC waveplates was characterized by measuring their transmitted spectra recorded by a spectrometer (Ocean Optics, USB2000+, USA).

Fig. 1. The fabrication process of the CNC waveplate.

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3. Results and discussion

The TEM image of the CNCs shown in Fig. 2(a) demonstrates that the CNC rods are hundreds of nanometers long and 5∼20 nm wide. Dynamic laser scattering further characterizes the general size distribution of the CNCs (Fig. 2(b)). This distribution is mostly related to the length of the CNCs. Although the CNCs form chiral nematic phase under most conditions [22,23], they form nematic phase at extreme pH [34]. Under a fixed concentration (e.g. 13wt %) chiral nematic phase is obtained with high pH value (typically larger than 2), while the nematic phase is formed with low pH value (typically smaller than 1.5). Figure 2(c) presents POM images of the two different phases. Fingerprint texture, a typical feature of chiral nematic phase only appears in the high pH sample, while the low pH sample exhibits Schlieren texture of the nematic phase. In the low pH region, the Debye length is short (<2 nm) and the electrostatic twist is weakened leading to the formation of the nematic phase. Nematic order is preserved when the CNC nematic LCs dry at room temperature. The POM images of the resultant films (Figs. 2(d) and 2(e)) show typical nematic defects, when LCs are not deliberately aligned.

Fig. 2. (a) TEM image of the CNCs. (b) Size distribution of the CNCs measured by dynamic laser scattering meter. (c) POM images of the CNC LCs which exhibit nematic phase (left) with low pH ∼ 1.5 and chiral nematic phase (middle and right) with high pH ∼ 2 and 3 under a fixed concentration of CNCs (13wt %). (d) POM image of the film produced by drying unaligned CNC nematic LCs. (e) POM image of the same film with a phase compensator (530 nm λ-plate). P and A indicate the polarization direction of the polarizer and the analyzer; γ indicates the slow axis of the λ-plate.

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Producing well-aligned CNC LCs is challenging work, especially for chiral nematic LCs. However, for nematic LCs large-scale alignment can be achieved by shearing LCs on patterned substrates. Figures 3(a)–3(f) demonstrate the POM images of the aligned CNC nematic films, where Figs. 3(a)–3(c) correspond to one slice of CNC film on PDMS substrate and Figs. 3(d)–3(f) correspond to the waveplate with two slices bonded together. The orientation of the LC director n is parallel to the shearing direction k and this is confirmed by the POM images. When k is perpendicular to the polarization P of the polarizer, areas corresponding to the LC film are dark; when k is at 45° with P, the areas become bright. Inserting a 530 nm λ-plate with its slow axis γ at 45° with P will exclusive determine the orientation of the liquid crystal director. The λ-plate results in a yellow interference color when ${\textbf k} \,\bot \,{\textbf P}$, indicating n is parallel to k as the CNCs have a positive birefringence. Grating ridges not covered with CNC films (Figs. 3(a)–3(c)) are optically isotropic, since PDMS has a negligible birefringence. Defects have been dramatically eliminated in the CNC LC films and nematic LCs can be effectively aligned on large scale, such as in a 1.5 cm×1.5 cm waveplate (see insets of Figs. 3(d)–3(f)). The produced CNC waveplates are flexible and can be bent easily (Fig. 3(g)). CNC films are usually crisp, whereas adding PEG can effectively enhance the mechanical strength of the encapsulated CNC film, which will then be able to endure the mechanical deformations. The CNC waveplates can also be tailored into any arbitrary shapes conveniently as well. Figure 3(h) demonstrates the CNC waveplate cut into square, parallelogram and triangle shapes by scissors.

Fig. 3. (a), (b) POM images of one slice of the CNC film on patterned PDMS substrate. (c) POM image of the same film with a phase compensator (530 nm λ-plate). (d), (e) POM images of the CNC waveplate with two slices of CNC films bonded together. (f) POM image of the same CNC waveplate with a phase compensator (530 nm λ-plate). k indicates the shearing direction, P and A indicate the polarization directions of the polarizer and the analyzer; γ indicates the slow axis of the λ-plate. (g) The flexible CNC waveplate can be bent easily. (h) The CNC waveplates can be tailored into square, parallelogram and triangle shapes conveniently.

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The optical performance of the CNC waveplates is examined by measuring the transmission spectra of the waveplates between two polarizers (Figs. 4(a) and 4(b)) and investigated by Mueller matrix analysis. The unpolarized incident light from a lamp first travels through a polarizer whose polarization is along x axis and denoted by P and becomes linearly polarized with the intensity ${I_0}$. Then the light is focused by a condenser on the sample and collected by an objective and further travels through an analyzer whose polarization is denoted by A. Finally the transmitted light was recorded by a spectrometer. The Stokes vector ${\textbf S}$ of the light travelling through the first polarizer is

(1)$${\textbf S} = {I_0}\left[ {\begin{array}{{c}} 1\\ 1\\ 0\\ 0 \end{array}} \right].$$

The Mueller matrix ${\textbf M}$ for an optical waveplate is

(2)$${\textbf M} (\delta ,\theta ) = (1 - \textrm{R)}{\textrm{e}^{ - \alpha d}}\left[ {\begin{array}{{cccc}} 1&0&0&0\\ 0&{{{\cos }^2}2\theta + \cos \delta {{\sin }^2}2\theta }&{(1 - \cos \delta )\sin 2\theta \cos 2\theta }&{ - \sin \delta \sin 2\theta }\\ 0&{(1 - \cos \delta )\sin 2\theta \cos 2\theta }&{{{\sin }^2}2\theta + \cos \delta {{\cos }^2}2\theta }&{\sin \delta \cos 2\theta }\\ 0&{\sin \delta \sin 2\theta }&{ - \sin \delta \cos 2\theta }&{\cos \delta } \end{array}} \right],$$

where $\theta $ is the angle between the fast axis of the waveplate and x axis; $\delta = 2\pi \Delta nd/\lambda $ is the phase retardation of the waveplate, $\Delta n$ is the birefringence of the CNC film, $d$ is the thickness of the waveplate, $\lambda $ is the wavelength; the reflectance R and the extinction $\alpha $ of the waveplate are measured to be polarization insensitive, and the depolarization is neglected. The Mueller matrix ${{\textbf M}_\textrm{A}}$ for the analyzer is

(3)$${{\textbf M}_\textrm{A}} (\beta ) = \frac{1}{2}\left[ {\begin{array}{{cccc}} 1&{\cos 2\beta }&{\sin 2\beta }&0\\ {\cos 2\beta }&{{{\cos }^2}2\beta }&{\sin 2\beta \cos 2\beta }&0\\ {\sin 2\beta }&{\sin 2\beta \cos 2\beta }&{{{\sin }^2}2\beta }&0\\ 0&0&0&0 \end{array}} \right],$$

where $\beta $ is the angle between A and x axis. The Stokes vector ${\textbf S}^{\prime}$ of the light collected by the spectrometer is

(4)$$\begin{array}{l} {\textbf S}^{\prime} = {{\textbf M}_\textrm{A}}(\beta ) \cdot {\textbf M}(\delta ,\theta ) \cdot {\textbf S}\\ = \frac{{{I_0}(1 - R)\mathop e\nolimits^{ - \alpha d} }}{2}\{ 1 + \cos 2\beta ({\cos ^2}2\theta + \cos \delta {\sin ^2}2\theta ) + \sin 2\beta [(1 - \cos \delta )\sin 2\theta \cos 2\theta ]\} \left[ {\begin{array}{{c}} 1\\ {\cos 2\beta }\\ {\sin 2\beta }\\ 0 \end{array}} \right]. \end{array}$$

When the fast axis of the CNC waveplate is at 45° with P ($\theta = 45^\circ $), the intensity $I$ of the light collected by the spectrometer satisfies:

(5)$$I(\beta ,\delta ) = \frac{{{I_0}(1 - R){e^{ - \alpha d}}}}{2}(1 + \cos 2\beta \cos \delta ),$$

or equivalently

(6)$$I(\beta ,\lambda ) = \frac{{{I_0}(1 - R){e^{ - \alpha d}}}}{2}(1 + \cos 2\beta \cos \frac{{2\pi \Delta nd}}{\lambda }).$$

Therefore, the phase retardation $\delta $ of the waveplate can be calculated as

(7)$$\delta = {\cos ^{ - 1}}[\frac{{I(0^\circ ,\delta ) - I(90^\circ ,\delta )}}{{I(0^\circ ,\delta ) + I(90^\circ ,\delta )}}].$$

To fabricate the 1/4 λ waveplate for 530 nm, we set $d = 2.1$ µm. The measured spectra ${I_{\textrm{1/4 }\lambda ,\;\textrm{exp}}}(\beta ,\lambda )$ are shown in Fig. 4(c). The phase retardation ${\delta _{1/4 \lambda }}(\lambda )$ can be calculated by Eq. (7) and is shown in Fig. 4(d). For the working wavelength $\lambda = 530\;\textrm{nm}$, the phase retardation is $\delta _{1/4} \lambda ,\;\textrm{exp}(530\;\textrm{nm} = 1.58 \approx \pi /2$. Furthermore the measured light intensity ${I_{1/4 \lambda ,\textrm{exp}}}(\beta ,530\;\textrm{nm})$ at $\lambda = 530\;\textrm{nm}$ (red dots) is in good agreement with the theoretical intensity ${I_{1/4 \lambda ,\textrm{theo}}}(\beta ,530\;\textrm{nm)} = \frac{{{I_0}(1 - R){e^{ - \alpha d}}}}{2} = \textrm{const}$ (black dots) (Fig. 4(e)), confirming that the phase retardation of the waveplate produced at $\lambda = 530\;\textrm{nm}$ is close to $\pi /2$. Similarly, we set $d = 4.2$ µm to fabricate the 1/2 λ waveplate for 530 nm. The measured spectra ${I_{1/2 \lambda ,\textrm{exp}}}(\beta ,\lambda )$ are shown in Fig. 4(f). The phase retardation ${\delta _{1/2 \lambda }}(\lambda )$ calculated by Eq. (7) is shown in Fig. 4(g). At the working wavelength $\lambda = 530\;\textrm{nm}$, the phase retardation is $\delta _{1/2} \lambda , \textrm{exp}(530\;\textrm{nm} = 3.11 \approx \pi $. Moreover the measured light intensity ${I_{1/2 \lambda ,\textrm{exp}}}(\beta ,530\;\textrm{nm})$ at $\lambda = 530\;\textrm{nm}$ (red dots) is in good agreement with the theoretical intensity ${I_{1/2 \lambda ,\textrm{theo}}}(\beta ,530\;\textrm{nm)} = \frac{{{I_0}(1 - R){e^{ - \alpha d}}}}{2}(1 - \cos 2\beta )$ (black dots) (Fig. 4(h)), also justifying that the phase retardation of the waveplate produced at $\lambda = 530\;\textrm{nm}$ is close to $\pi $.

Fig. 4. (a) The experimental setup for measuring the transmission spectra of the CNC waveplates. (b) Schematics for the theoretical analysis. (c) Measured ${I_{1/4 \lambda ,\textrm{exp}}}(\lambda )/{I_0}(\lambda )$ for the 1/4 λ CNC waveplate with different $\beta $. (d) Phase retardation ${\delta _{1/4 \lambda }}(\lambda )$ calculated for the 1/4 λ CNC waveplate. (e) Theoretical (black squares) and measured (red dots) ${I_{1/4 \lambda ,\textrm{exp}}}(\beta )/{I_0}(\beta )$ for the 1/4 λ CNC waveplates with $\lambda = 530\;\textrm{nm}$. (f) Measured ${I_{1/2 \lambda ,\textrm{exp}}}(\lambda )/{I_0}(\lambda )$ for the 1/2 λ CNC waveplate with different $\beta $. (g) Phase retardation ${\delta _{1/2 \lambda }}(\lambda )$ calculated for the 1/2 λ CNC waveplate. (h) Theoretical (black squares) and measured (red dots) ${I_{1/2 \lambda ,\textrm{exp}}}(\beta )/{I_0}(\beta )$ for the 1/2 λ CNC waveplate with $\lambda = 530\;\textrm{nm}$.

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The produced waveplates also allow us to measure the optical extinction and birefringence of CNC films, which are important parameters for the application of CNC-based optical devices. Transmittance T and reflectance $R$ of the waveplates for unpolarized light (with no polarizers) are measured and shown in Figs. 5(a) and 5(b) respectively. And thus the extinction $\alpha $ of CNC films can be calculated as $\alpha = \frac{{ - \ln (T/(1 - R))}}{d} \sim 0.03$ µm⁻¹ for the whole visible spectrum (Fig. 5(c)). The birefringence of CNC films can be deduced from Eq. (6) as $\Delta n(\lambda ) = \frac{\lambda }{{2\pi d}}{\cos ^{ - 1}}\left[ {(\frac{{2I(\lambda )}}{{(1 - R){e^{ - \alpha d}}{I_0}(\lambda )}} - 1)/\cos 2\beta } \right]$. Figure 5(d) demonstrates the $\Delta n(\lambda )$ calculated by using the spectrum of the 1/4 λ CNC waveplates (Fig. 4(c)) with $\beta = 0^\circ $. $\Delta n(\lambda )$ of the nematic film made from cotton CNCs is found ∼0.06 when $\lambda $ is in the range of 500 ∼ 620 nm and decreasing quickly when $\lambda > 620\;\textrm{nm}$. The measured birefringence of the CNC films is consistent with the previous report [28,33].

Fig. 5. Measured transmittance $T$ (a) and reflectance $R$ (b) of the 1/4 λ and the 1/2 λ CNC waveplates for unpolarized light. (c) Extinction $\alpha $ of CNC films deduced from the measured $T$ and $R$ of the CNC waveplates. (d) Birefringence $\Delta n(\lambda )$ of CNC films extracted from the spectrum ${I_{1/4 \lambda ,\textrm{exp}}}(\lambda )/{I_0}(\lambda )$ of the 1/4 λ CNC waveplate with $\beta = 0^\circ $.

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4. Conclusions

We have produced well-aligned CNC nematic films which can serve as optical waveplates. PEG-doped CNC nematic LCs are utilized and aligned without defects on large scale by shearing force on patterned PDMS substrates. A 1/4 λ and a 1/2 λ waveplates have been made as a demonstration of the viability. Their optical properties have been examined and the measured results fit well with the theoretical analysis. Optical extinction and birefringence of CNC films have also been deduced based on the spectra of our CNC waveplates. The present CNC waveplates are thin, flexible, have good mechanical strength and can be tailored easily. Besides, the method may allow the production of a useful CNC-based “rolling tape”, which can be cut and tailored into any desirable shapes and coated on optical components conveniently serving as effective optical waveplates.

Funding

National Natural Science Foundation of China (11621101, 61550110246, 61850410525, 91833303); National Key Research and Development Program of China (2017YFA0205700).

Acknowledgments

We gratefully thank Hua Wang and Hehe Qian for their useful help during the experiment.

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Preparation of optical waveplates from cellulose nanocrystal nematics on patterned polydimethylsiloxane substrates

Abstract

1. Introduction

2. Experiment

3. Results and discussion

4. Conclusions

Funding

Acknowledgments

References

Cited By

Figures (5)

Equations (7)

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