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This work focuses on experimentally demonstrating the modification in diffusion kinetics, formation of holographic polymer dispersed liquid crystal gratings and an improvement in its electro optic response by doping them with multi-walled carbon nanotubes. Results indicate a faster rise and fall times which is attributed to the reduction in size of the liquid crystal droplets formed and a reduction in switching voltage due to change in dielectric properties of the medium as manifested by a rise in capacitance. Real time diffraction efficiency measurements reveal a time delay in the appearance of the diffracted order due to non-participation of the nanotube in the polymerization induced phase separation process. An analysis of this effect is presented based on the Stoke- Einstein’s diffusion equation incorporating shape anisotropy of the nanotubes.
©2010 Optical Society of America
1. Introduction
Holographic polymer dispersed liquid crystals (H-PDLC) are electro-optic thin films devices which, on application of an electric field, can be switched between a diffracting and a transmissive state. Based on the holographic recording geometry either diffraction H-PDLC gratings or reflection H-PDLC gratings can be formed. Exposure of an interference pattern, generated by a laser beam, on a homogenous mixture of photo-polymerizable monomer and liquid crystal (LC) results in a photo polymerization induced phase separation where in the monomers polymerize in the bright regions causing counter diffusion of LC’s into the dark region of the interference pattern where they coalesce to form nanometer size LC droplets with shape anisotropy. Such a phenomenon results in a periodic refractive index variation in the thin film where the alternating polymer and LC droplet rich planes form a Bragg grating. The grating pitch is determined by the angle of the recording beams [1]. Application of an electric field across such film reorients the LC droplet directors causing a reduction in the refractive index modulation and hence reduction in reflected Bragg wavelength and random scattering.
The kinetics of formation of these gratings and the real time evolution of the diffracted order has been studied by Bowley using a phenomenological diffusion model [2] and by Sutherland incorporating photo-physics and reaction-diffusion kinetics [3]. The grating structure formation upon exposure and subsequent evolution of the diffracted order has been characterized into in three distinct processes: a short induction period, rapid polymerization accompanied by photo bleaching and a plateau region [4]. The short induction period is observed due to the time needed for the dissolved oxygen or polymerization inhibitors to be consumed before the onset of rapid polymerization. The extension of this induction period, however, has also been observed by addition of dyes and nanoparticles to the prepolymer mixture which subsequently affects the dynamics of formation of H-PDLC, its electro-optic properties and its morphology. Woo observed the introduction of a long induction period, otherwise absent, in the evolution of the diffracted order by addition of azo dye and attributed it to the absorption of the incident light by dye molecules hence leading to slow polymerization and phase separation [5]. On addition of TiO2 nanoparticles in the H-PDLC prepolymer mixture Shim observed longer induction, slower polymerization and decreased polymer - liquid crystal phase separation due to increased viscosity of the polymer matrix [6].
Reflection based HPDLC’s seem attractive for applications such as spectrometers, optical switches [7], photonic crystals [8], reflective displays [9] and numerous other electro-optic applications. Although HPDLC’s exhibit high switching speeds and polarization insensitivity they suffer from low diffraction efficiency (DE) and high switching voltages. Various methods have been shown to improve the DE such as application of an electric field and shear stress [10] to the sample during fabrication. Attempts to reduce the switching voltages include addition of surfactant molecules [11], conductive polymers [12], dielectric anisotropic compounds [13] and so on. An anomalous dependence of transmission on control voltage in PDLC films with multiwalled carbon nanotubes was previously reported [14]
In this work we experimentally demonstrate a reduction in switching voltage and further improvement in switching speed of reflection based HPDLC’s by doping them with oxidized multiwalled carbon nanotubes (MWNT). These HPDLC’s are doped with various concentrations of MWNT’s and their effect on the electro-optic response and reflection efficiency is characterized and compared to regular HPDLC’s with no MWNT content. The results are attributed to a reduction in LC droplet size and a change in the dielectric properies of the medium. In order to quantify these changes diffraction gratings with MWNT are fabricated and the physical role of MWNT in the formation of the diffraction grating is studied. Experimentally, a longer induction period during the photo polymerization induced phase separation in diffraction H-PLDC doped with MWNT is seen. Real time diffracted order measurements indicate a lengthened induction period with increasing concentration of MWNT when compared to ones with no MWNT. An analysis based on diffusion constants of participating monomers, LC and MWNT, incorporating the shape anisotropy is presented, which reveals that the MWNT acts as a physical barrier for the counter diffusing liquid crystals hence slowing phase separation and eventually reducing liquid crystal droplet size. An optimal MWNT doping range is arrived at based on the observed experimental observations.
2. Material set, fabrication and characterization
The prepolymer, used in this work, comprises of a thiolene based homogeneous blend of NOA65 (Norland Optical Adheives,Inc.), LC BL038 (Merck& Co.Inc) and a photoinitiator to sensitize the blend to visible wavelengths. The photoinitaitor comprises of Rhodamine 6G (Acros organics) and benzoyl peroxide (Aldrich). The percent weights of the components used are 68% NOA65, 25% BL038, 0.4% Rhodamine 6G, 3% benzoyl peroxide and 3.6% N-Vinyl Pyrrolidone. In addition oxidized conductive multiwalled carbon nanotubes were added to the HPDLC mixture in various proportions measured per gram of LC. The process of oxidation and dispersion of MWNT in Dimethylformamide (DMF) to obtain a stable suspension is discussed elsewhere [15,16]. The as received MWNT from Arkema had undergone prior purification steps and did not contain large amount of amorphous carbon and metal impurities if any were removed after further purification [16]. The process of oxidation adds carboxylic groups on the MWNT surface which leads to better adhesion of the MWNT on such an epoxy based polymer matrix due to strong interfacial adhesion and the effects on its electrical conductivity has been very well studied in past [17]. The following quantities (measured per gram of LC) of oxidized MWNT suspended in DMF were added to the LC: 0.01mg, 0.025mg, 0.05mg, 0.1mg, 0.25mg, and 0.5mg. The DMF was eventually evaporated and the LC-MWNT suspension was ultrasonicated to obtain a stable suspension. The LC-MWNT suspension was stable for upto 24 hours after evaporation of DMF and subsequent ultrasonication (for 1 hour) of the suspension. In our experiments all the suspensions were used within 3 hours of ultrasonication. This stable suspension of LC and MWNT was then introduced in to the prepolymer blend and results were compared to an HPDLC with no MWNT. The MWNT’s used had a poly-dispersity of 5µm to a maximum length of 10µm and an outer diameter of 20nm. The sizes of the MWNT’s were chosen such that its diffusion constant lied well below that of the diffusing polymer and counter diffusing LC components as calculated in section 3. The conductivity (σMWNT) of MWMT’s used were 103 S/cm [15].
The prepolymer mixture was sandwiched between ITO coated glass slides spaced 20 µm apart using glass spacers, to form a cell, and were exposed to an interference pattern, for 60 seconds, generated using a Coherent Verdi 532 nm laser radiating at 200mW/cm2. The prism method, as shown in Fig. 1a was used to record the interference pattern in to the cell to form a reflection Bragg grating. All samples were recorded at the same Bragg angle and the reflection notch was at about 685nm. The designed reflection grating pitch was about 221nm. A two-beam interference method, as shown in Fig. 1b, was used to record the interference pattern in to the cell to form a Bragg diffraction grating. All samples were recorded at the same Bragg angle and the grating pitch (Λ) was approximately 600nm. A 633nm He-Ne laser was used as a probe beam in order to capture the real time evolution of the diffracted order using labview. The fabricated cells were cured under a UV lamp for five minutes to polymerize any remnant monomers.
Fig. 1 a) Recording geometry of the H-PDLC reflection grating. b) Recording geometry of the H-PDLC diffraction grating with setup for recording real time evolution of diffracted order.
The fabricated cells, both reflection and diffraction gratings, were imaged under a polarized optical microscope (Leica Microsystems) to see the effect of addition of MWNT’s on the diffusion of LC’s into the cross-section of the cell and identify influence on LC orientation in presence of MWNT’s. Change in resistivity and capacitance of the fabricated cells with different concentration of MWNT were recorded using an LCR meter in order to tap the change in dielectric properties of the medium.
The reflection H-PDLC gratings samples were illuminated with an unpolarised halogen white light source with the angle of incidence of light perpendicular to the cell and the transmission spectra was recorded using a spectrometer (Ocean Optics) to observe any changes in reflection efficiency in samples doped with various concentrations of MWNT’s. Electro-optic data for each sample was generated by applying a square wave of 50% duty cycle at various Peak-Peak voltage levels to determine reduction in switching voltage. A monochromator (Oriel, Newport Corporation) was used to generate the reflected Bragg wavelength of 685nm and the rise and fall time were recorded using a photodiode and oscilloscope. All the samples were switched at the same voltage of 137 V peak to peak in order to determine the influence of MWNT on switching speed and subsequently verify reduction in LC droplet size.
The diffraction gratings were illuminated with 633nm He-Ne source with the angle of incidence of light at the recorded Bragg angle to the cell and electro-optic data for each sample was recorded by applying a square wave, 1kHz, of 50% duty cycle and at a constant peak-peak voltage level to determine any changes in rise and fall times. Switching times were recorded using a photodiode and oscilloscope. These samples were switched at 120V peak-peak in order to determine the influence of MWNT on switching speed and subsequently verify reduction in LC droplet size.
The samples were freeze fractured in liquid nitrogen to obtain the thin films. LC was washed out in methanol before imaging using a scanning electron microscope (Zeiss Supra 50VP). All samples were imaged under high vacuum in order to visualize the effect of MWNT on LC droplet formation.
3. Experimental results and discussion
Figure 2 shows the Polarized Optical Microscopy Images (POM) of the reflection HPDLC cells doped with various concentrations of oxidized MWNT. A dark field is observed for the images labeled a, b, c, d and e which corresponds to a MWNT doping level of 0mg, 0.01mg, 0.025mg, 0.05mg, and 0.1 mg respectively. However on increasing the concentration of MWNT to 0.25mg the birefringence of the liquid crystal begins to appear (Fig. 2f) indicating an incomplete phase separation of the LC’s which were unable to counter diffuse into the cross section to from droplets due to the high MWNT concentration and at 0.5mg a bright total birefringent field is seen (Fig. 2g). This is the first indication of MWNT’s acting physical barriers to the counter diffusing LC’s hence inhibiting grating formation at high MWNT doping levels causing the LC’s to remain trapped near the surface of the substrates.
Fig. 2 POM images of HPDLC reflection gratings doped with various MWNT concentrations a) 0mg b) 0.01mg c) 0.025mg d) 0.05mg e) 0.1mg f) 0.25mg g) 1mg.
The measurement of the transmission spectra using a spectrometer and a while light source indicates a decrease in the reflection efficiency on increasing the MWNT doping concentration as shown in Fig. 3 . However a close examination reveals that at relatively lower levels of MWNT doping such as 0.01mg and 0.025mg the reflection efficiency of the HPDLC remains close to the one with no MWNT’s hence suggesting that trace amount of MWNT’s do not affect the counter diffusion of LC’s on an average during the photo polymerization induced phase separation process. The reflection efficiency starts to drop beyond 0.05mg MWNT and weak gratings are formed beyond 0.1mg of MWNT with reduced transmission baselines indicating an increase in overall scattering. The lower baseline transmission is also indicative of aggregation of MWNT’s and hence reducing the overall transparency. At 0.5mg MWNT concentration no grating is formed as most of the LC’s fail to diffuse into the cross section (as shown in Fig. 2g) due the presence of large amount of MWNT across the diffusion length.
Fig. 3 Transmission spectra of HPDLC reflection gratings doped with various concentrations of MWNT. The inset plot shows a decrease in reflection efficiency with increasing MWNT concentration.
A change in the capacitance and resistivity of the cells were observed on increasing the doping levels of MWNT as shown in Fig. 4 . Increase in capacitance of the cells is seen upto 0.1mg of MWNT and then a decrease in the capacitance values is recorded at 0.25mg MWNT and beyond. High amount of randomly aligned MWNT’s increase the probability of forming a short between the ITO coated electrodes. A continuous drop in resistivity of the cells is observed with increasing amounts of MWNT’s as shown in Fig. 4. A change in capacitance and resistivity is indicative of a change in dielectric properties of the HPDLC medium and hence for a given applied voltage a stronger electric field is experienced by the LC droplet in the HPDLC cell when compared to the ones with no MWNT.
Fig. 4 Change in capacitance and resistivity of the HPDLC reflection gratings doped with MWNT at a driving frequency of 1kHz. The inset plot shows the range of MWNT concentration in which no shorting of the ITO electrodes is observed. The circles represent capacitance and the triangles represent resistivity.
Electro-optic switching measurements show a clear improvement in the switching characteristics. The theoretical estimate of reorientation field for a liquid crystal droplet trapped in a polymer matrix is given by Eq. (1) [18]
where d0, l, a, σlc and σp are the sample thickness, shape anisotropy of the LC droplet, radius of the LC droplet, conductivity of the LC and conductivity of the polymer. σp ≈10−6 S/cm [19] and σlc/ σp ≈25 [18]. K and Δε are the LC constants and dielectric anisotropy respectively. Since, during photo-polymerization the viscosity of the medium increases the MWNT’s remain trapped in the polymer matrix instead of diffusing along with the LC’s. This increases the conductivity of the polymer matrix. In such a case the local field acting on the LC droplet is given by Eq. (2) [18]where is now the composite conductivity of the polymer matrix doped with MWNT. Hence a lower electric field is required to reorient the liquid crystal droplets as shown in Fig. 5 . The switching voltage was reduced from 153V at 0mg MWNT to 129V at 0.05mg MWNT. However an increase in switching voltage was recorded at 0.1mg MWNT and slight shorting between the electrodes were observed, reducing the overall local electric field strength experienced by the LC droplets. Anomalous behavior and heavy shorting was observed in all samples doped with 0.25mg MWNT and 0.5mgMWNT. Although Vc is inversely proportional to the radius, a, of the droplet which would suggests an increased Vc for decreasing droplet radius; the reduction in Vc stems from the fact that the ratio σlc/ σp is reduced and Elc is increased due to addition of MWNT’s which increases polymer conductivity and as shown in Eq. (3) is responsible for enhancing the local E-field seen by the LC droplet.Fig. 5 Transmission vs applied voltage plots for various concentrations of MWNT. The inset plot shows a reduction in switching voltage with increasing amount of MWNT.
A reduction in switching time is also observed as shown in Fig. 6 . In HPDLC systems the rise time is proportional to the applied electric field and LC droplet size [18]. All the cells were switched at 137V in order to quantify the effect of MWNT on formation of LC droplet size. The fall time on the other hand is dependent on the droplet size and the visco-elastic coefficient of the LC. A reduction in both rise and fall time is indicative of formation of LC droplets with a smaller diameter and hence a reduction in relaxation time. A decrease in both these parameters occurs upto a doping level of 0.1mg but beyond this the rise and fall time dramatically increases at concentration of 0.25mg and 0.5mg MWNT indicating switching times due to the bulk LC, since most of the LC’s fail to diffuse into the cross section as show in Fig. 2f and g. The error bars in Fig. 6 indicate 5% error in each data point.
Fig. 6 Rise and fall time measurements of HPDLC reflection gratings doped with various concentrations of MWNT. The inset plots show the rise and fall time readings up to 0.1mg MWNT.
Now, in order to quantify the above improvements it was necessary to understand the role that MWNT plays during the formation of the H-PDLC. A reduction in LC droplet size can occur due to rapid polymerization [20]. Since MWNT’s cannot influence the polymerization rate of the photopolymers we believe that in this case the MWNT’s act as physical barriers to the counter diffusing LC’s due to its sheer size compared to the participating photopolymer and LC molecules. To prove this H-PDLC diffraction gratings were fabricated. They tend to have a higher grating pitch compared to reflection gratings and in essence will also magnify the effect on LC droplet size due to the larger LC diffusion length. Figure 7a shows the real time measurement of diffracted order for various samples doped with MWNT. They reveal a typical rise in the diffracted order, as expected, and then reach a plateau value. The stable diffraction efficiency is slightly reduced at the lower MWNT concentrations of 0.01mg and 0.05 mg compared to the ones without MWNT and a dramatic reduction is seen at higher concentrations of 0.1 and 0.25 mg MWNT. However zooming into the first five seconds of the evolution reveals that after initial fluorescence from the Rhodamine dye, there exits an induction period for all the samples doped with MWNT and the induction period grows longer with increasing MWNT concentration as seen in Fig. 7b. Figure 7c shows a plot of rise in induction time with increasing concentration of MWNT where beyond 0.1 mg of MWNT an anomalous behavior in the rise of the diffracted order is seen with very low efficiency.
Fig. 7 a) Real time evolution of diffracted order for various concentrations of MWNT, b) Time delay in rise of diffracted order observed in the first 5 seconds during exposure c) Increase in induction period with increasing concentration of MWNT.
The polymerization and phase separation are largely influenced by the physical and chemical properties of the LC’s and the prepolymers used, specifically, the solubility parameters and diffusion coefficients. Mutual diffusion and counter diffusion is possible when the diffusion constants of the participating elements are within a comparable range. The diffusion constant of photo-polymerizable monomers lies in the range of 10−9 to 10−7 cm2/s [21] and that of the LC is of the order of 10−7cm2/s [2] suggesting that mutual diffusion is possible. In order for the MWNT to participate in mutual diffusion and counter diffusion, its diffusion constant in such a viscous media should lie within that range. It is possible to compute the diffusion constant for a nanoparticle based on the Stoke- Einstein’s diffusion equation in viscous media. However, it is valid only for spherical particles and MWNT has large shape anisotropy. In order to incorporate such a shape anisotropy to compute the diffusion constant we use the Eq. (3) [22] which computes the translational diffusion constant of MWNT considering it as a rigid rod:
where, k is the Boltzmann’s constant, η is the viscosity of the monomer, r = l/d is the aspect ratio (l and d are the major and minor axes of the rod respectively). Taking into account the shape anisotropy of MWNT and the viscosity of the monomer which is about 1200cps the translational diffusion constant of MWNT in such a viscous media is about 10−15 cm2/s. Such a low diffusion constant reveals that the MWNT used does not participate in the phase separation process. This is also complicated by the fact that during photo polymerization the viscosity of the medium is constantly evolving and is given by Eq. (4) [2]:where, Di0 is the diffusion constant of the pure monomer, αi is the decay constant and is the polymer concentration. This equation describes the inhibition of diffusion through the increasingly dense polymer network. Hence, as the polymerization begins the MWNT’s get trapped in the polymer matrix and act as physical barriers for the counter diffusing LC’s. As a result a delay is seen in the growth of the diffracted order. This delay increases with increase in the MWNT concentration as seen in Fig. 7.Since the rise and fall times of H-PDLC are dependent on the morphology of the gratings formed, especially the size of the LC droplets we measured these times in order to observe any changes in the ones with MWNT when compared to the ones with no MWNT. In HPDLC systems the rise time is proportional to the applied electric field and LC droplet size. The fall time on the other hand is dependent on the droplet size and the visco- elastic coefficient of the LC. A reduction in both rise and fall time is indicative of formation of LC droplets with a smaller diameter and hence a reduction in relaxation time. The rise and fall times are given by Eq. (5) [18]:
where, where γ1 is the viscosity coefficient of the LC, K is the LC constant, a is the droplet diameter and l being the droplet shape anisotropy. All diffraction H-PDLC’s were switched at the same voltage of 120V peak to peak with a 1kHz square wave with 50% duty cycle. As seen in Fig. 8 the rise and fall times decrease up to a concentration of 0.1mg MWNT, beyond which a rise in switching times is seen which is due to the presence of bulk liquid crystals on the surface which were unable to diffuse into the polymer matrix and form droplets. Since the switching voltage was consistent in all the samples it can be concluded that the size of the LC droplets formed have changed with increasing concentrations of MWNT and in particular have decreased. The error bars in Fig. 8 indicate 5% error in each data point.Fig. 8 Rise and fall time measurements of HPDLC diffraction gratings doped with various concentrations of MWNT. The inset plots show the rise and fall time readings upto 0.1mg MWNT.
In order to verify the reduction in the size of the LC droplets formed in the LC rich regions of the polymer matrix, all samples were imaged under a scanning electron microscope. The samples were prepared as detailed in section 2. It is seen that on an average the LC droplet size decreases with increasing concentration of MWNT as shown in Fig. 9 . With no MWNT the size of the LC droplets were measured to be on an average of 147nm. With 0.01mg MWNT the average droplet size reduced to 122nm and with 0.05mg MWNT the LC droplet size reduced to 90nm. However, with 0.1mg MWNT although the average LC droplet size reduced to 61nm, smaller sized droplets are seen trapped in the polymer rich regions as well, indicating that not all droplets managed to phase separate into the LC rich region and hence possibly lowering the diffraction efficiency. At 0.25 mg no LC droplets are seen since such a high concentration of MWNT hindered the phase separation of LC.
Fig. 9 Scanning electron microscopy images of H-PDLC diffraction gratings with various concentrations of MWNT: a) 0mg, b) 0.01mg, c) 0.05mg) 0.1mg) and 0.25mg).
4. Conclusion
Incorporating multiwalled carbon nanotubes in holographic polymer dispersed liquid crystals improves its electro-optic response. It modifies the dielectric properties of the medium as manifested by an increase in conductance of the polymer resulting in lowering of the switching voltages. In reflection H-PDLC’s the switching voltage reduced from 153V with no MWNT to 129 V with 0.05mg MWNT. An improvement in switching was seen where in the rise time reduced from 3ms to 1ms. The fall time reduced from 5ms to 2ms. Real time diffraction efficiency measurements from diffraction H-PDLC’s reveal an increased induction period with increasing concentration of MWNT. Based on the derived diffusion constants, using the Stoke-Einstein’s diffusion equation incorporating shape anisotropy, it was seen that the MWNT’s do not participate in the phase separation process and remain trapped in the polymer matrix hence acing a physical barriers to the counter diffusing LC’s due to its sheer size. This results in a reduction of LC droplet size from 147nm with no MWNT to 61nm at 0.1mg MWNT.
Acknowledgements
The authors would like to acknowledge Dr. Yury Gogotsi for providing the carbon nanotubes, the Drexel Centralized research Facility for the scanning electron microscopy, undergraduate student C. William Hicks IV for the Labview setup and the Department of Energy for the STTR Phase I and phase II (grant number: DE-FG02-08ER86355).
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