Anisotropic shift of surface plasmon resonance of gold nanoparticles doped in nematic liquid crystal Amit Choudhary3,4 and Guoqiang Li1,2,3,* 1
Department of Ophthalmology and Visual Science, The Ohio State University, ElectroScience Laboratory, 1330 Kinnear Road., Columbus, OH 43212, USA Department of Electrical and Computer Engineering, The Ohio State University, ElectroScience Laboratory, 1330 Kinnear Road., Columbus, OH 43212, USA 3 College of Optometry, University of Missouri, St. Louis, MO 63121, USA 4 Present Addresses: Physics Department, Deshbandhu College (University of Delhi, Delhi), Kalkaji, New Delhi110019, India * [email protected]
2
Abstract: Study of the liquid crystal (LC) director around nanoparticles has been an important topic of research very recently, since it allows design and fabrication of next-generation LC devices that are impossible in the past. In our experiment, alkanethiol-capped gold nanoparticles (GNPs) were dispersed in nematic LC. Analysis of the LC director around GNPs was performed by investigating the behavior of surface plasmon polariton (SPP) absorption peaks of the GNPs using spectrophotometry technique. It is found that the incident linearly polarized light orientated at 0°, 45°, and 90° angles with respect to the rubbing direction experiences varying interaction with the LC medium. The corresponding transmission of light reveals the anisotropic shift in wavelength of SPP peak. The anisotropic behavior of SPPs of the GNPs is in agreement with theoretical calculations. ©2014 Optical Society of America OCIS codes: (160.3710) Liquid crystals; (160.4236) Nanomaterials; (160.4670) Optical materials; (230.3720) Liquid-crystal devices; (230.2090) Electro-optical devices; (240.6680) Surface plasmons.
References and links 1.
K. Busch and S. John, “Liquid crystal photonic band gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83(5), 967–970 (1999). 2. P. G. de Gennes, The Physics of Liquid Crystal Research (Clarendon Press, 1974). 3. C. H. Jang, L. L. Cheng, C. W. Olsen, and N. L. Abbott, “Anchoring of nematic liquid crystals on viruses with different envelope structures,” Nano Lett. 6(5), 1053–1058 (2006). 4. O. V. Kuksenok, R. W. Ruhwandl, S. V. Shiyanovskii, and E. M. Terentjev, “Director structure around a colloid particle suspended in a nematic liquid crystal,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(5), 5198–5203 (1996). 5. J. Fukuda, M. Yoneya, and H. Yokoyama, “Defect structure of a nematic liquid crystal around a spherical particle: adaptive mesh refinement approach,” Phys. Rev. E. 65(4), 041709 (2002). 6. Y. Gu and N. L. Abbott, “Observation of Saturn-ring defects around solid microspheres in nematic liquid crystals,” Phys. Rev. Lett. 85(22), 4719–4722 (2000). 7. P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, “Novel colloidal interactions in anisotropic fluids,” Science 275(5307), 1770–1773 (1997). 8. R. Yamamoto, “Simulating particle dispersions in nematic liquid-crystal solvents,” Phys. Rev. Lett. 87(7), 075502 (2001). 9. J. Fukuda, M. Yoneya, and H. Yokoyama, “Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement,” Eur Phys J E Soft Matter 13(1), 87–98 (2004). 10. M. A. Bates, “Nanospheres in a nematic liquid crystal solvent: the influence of particle size,” Liq. Cryst. 32(1112), 1525–1529 (2005).
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24348
11. I. I. Smalyukh, O. D. Lavrentovich, A. N. Kuzmin, A. V. Kachynski, and P. N. Prasad, “Elasticity-mediated selforganization and colloidal interactions of solid spheres with tangential anchoring in a nematic liquid crystal,” Phys. Rev. Lett. 95(15), 157801 (2005). 12. V. M. Pergamenshchik and V. A. Uzunova, “Colloidal nematostatics,” Condens. Matter Phys. 13(3), 33602 (2010). 13. B. I. Lev, S. B. Chernyshuk, P. M. Tomchuk, and H. Yokoyama, “Symmetry breaking and interaction of colloidal particles in nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(2), 021709 (2002). 14. B. I. Lev and P. M. Tomchuk, “Interaction of foreign macrodroplets in a nematic liquid crystal and induced supermolecular structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(1), 591–602 (1999). 15. I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, “Two-Dimensional Nematic Colloidal Crystals Self-Assembled by Topological Defects,” Science 313(5789), 954–958 (2006). 16. V. Tomar, T. F. Roberts, N. L. Abbott, J. P. Hernández-Ortiz, and J. J. de Pablo, “Liquid Crystal Mediated Interactions Between Nanoparticles in a Nematic Phase,” Langmuir 28(14), 6124–6131 (2012). 17. F. Mondiot, R. Botet, P. Snabre, O. Mondain-Monval, and J.-C. Loudet, “Colloidal aggregation and dynamics in anisotropic fluids,” Proc. Natl. Acad. Sci. U.S.A. 111(16), 5831–5836 (2014). 18. S. Y. Park and D. Stroud, “Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle,” Phys. Rev. Lett. 94(21), 217401 (2005). 19. P. G. de Gennes, “An Analogy Between Superconductors And Smectic A,” Solid State Commun. 10(9), 753– 756 (1972). 20. P. G. de Gennes, “Some Remarks on the Polymorphism of Smectics,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 21(12), 49–76 (1973). 21. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters. (Springer, 1995). 22. L. H. Hsu, K. Y. Lo, S. A. Huang, C. Y. Huang, and C. S. Yang, “Irreversible redshift of transmission spectrum of gold nanoparticles doped in liquid crystals,” Appl. Phys. Lett. 92(18), 181112 (2008). 23. G. M. Koenig, Jr., M. V. Meli, J. S. Park, J. J. de Pablo, and N. L. Abbott, “Coupling of the Plasmon Resonances of Chemically Functionalized Gold Nanoparticles to Local Order in Thermotropic Liquid Crystals,” Chem. Mater. 19(5), 1053–1061 (2007). 24. H. Stark, “Director Field Configurations Around A Spherical Particle In A Nematic Liquid Crystal,” Eur. Phys. J. B 10(2), 311–321 (1999). 25. J. Fukuda, “Continuous Transformation Of A -1/2 Wedge Disclination Line To A +1/2 one,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(4), 040701 (2010). 26. M. Brust, M. Walker, D. Bethell, D. J. Schiffrin, and R. Whyman, “Synthesis of thiol derivatised gold nanoparticles in a two phase liquid/liquid system,” Chem. Commun. 7(7), 801–802 (1994). 27. I. C. Khoo, Liquid Crystal. (Wiley-Interscience, 2007). 28. J. Zhang, L. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D Appl. Phys. 45(11), 113001 (2012). 29. S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007). 30. S. Link and M. A. E. Sayed, “Size and temperature dependence of the plasmon absorption of colloidal gold nanoparticles,” J. Phys. Chem. B 103(21), 4212–4217 (1999). 31. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). 32. G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006). 33. G. Li, P. Valley, M. S. Giridhar, D. Mathine, G. Meredith, J. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode pattern,” Appl. Phys. Lett. 89(14), 141120 (2006). 34. G. Li, P. Valley, P. Äyräs, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007). 35. G. Li, “Adaptive lens,” Prog. Opt. 55, 199–283 (2010).
1. Introduction Recently, new perspectives of liquid crystals (LCs) have been shown in optics and photonics [1], display devices [2], virus detection by understanding its interaction with LC [3], and studying the interaction of LC with nanomaterials for enhanced applications [4–13]. Nanomaterials are emerging as a prototype to enrich the properties of LC materials. The active research in this direction has been focused on the analysis and control of the interaction between LC molecules and gold nanoparticles (GNP) at nanoscale dimension. Some mathematical models have been presented to understand the alignment of LC molecular
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24349
director around nanomaterials in the form of Saturn rings, hedgehogs, and boojams [4–17]. The inclusion of GNPs in nematic LC can create some stable defects with possible integral strength ± 1 or ± ½ depending on the interaction of LC with GNPs. The theoretical approach on the linearized director distortion in nematic LC formed by particles analyzes several properties like elastic charge density, multipole particles, mechanical torque balance on the basis of electrostatic interactions, and defect symmetry [12]. The anisotropic alignment of LC molecules is due to breaking of mirror symmetry and it leads to the dipolar interaction between colloidal particles in LC [13]. The long range interaction of inhomogeneous macrodroplet distribution within a liquid crystal sample shows the dependency on the spatial position and relative orientation of the droplets [14]. The gold nanoparticles are so sensitive to visible light that the incident light polarizes the GNP doped in the dielectric system due to the shifting of electron cloud which is influenced by electric component of incident light. This results in generation of surface plasmon polariton (SPP) waves at the interface of GNP and dielectric (LC in the present case). These SPP waves propagate along the interface of GNP and dielectric which end up in both media for some distance. The resulting behavior of SPP has shown that the boojam pair with planar configuration of LC director around GNP is more stable in comparison with Saturn ring and hedgehogs [7, 18]. In 1972, P. G. de Gennes proposed the phase separation at the interface of solid substrate and bulk nematic LC [19, 20]. The separate phase at the interface was the layer structured smectic A phase whereas the bulk phase was nematic in vertical alignment configuration of sample cell. The enhancement in the local ordering of 4-pentyl-4′-cyanobiphenyl (5CB) molecules has been observed at the interface of LC and thiol derivative functionalized GNP which is confirmed by observing the shift in wavelength of SPP peak. The redshift in wavelength of SPP peak has been reported in literature [21]. The controllable redshift is observed below threshold voltage before particle aggregation due to electrophoresis force whereas after threshold voltage, the magnitude of irreversible peak shift increases remarkably [22]. However, the surface chemistry has played a significant role in the SPP peak shifting due to the coupling of SPP with the 5CB nematic LC material [23]. The optical frequency response of GNPs strongly depends on the fundamental electronic configuration of the nanoparticles which can be influenced by the variation in the size of nanoparticles and its surrounding dielectric environment [21]. At the interface of metal and LC, the shift of SPP peak is found to be selective, i.e., the blue shift is caused by the low energetic SPP resonance, whereas the red shift is induced by the high energetic SPP resonance under the application of an external electric field. It has also been found that the SPP field can align the LC molecules due to the interaction of its electric component with dielectric anisotropy of the LC material. In vertical alignment of the sample cell, the point defect disclination is 1 while after conversion to planar it becomes either surface ring or a -½ disclination ring configuration [13, 24, 25]. Based on the previous theoretical observations, the alignment of LC molecular director in the close proximity of GNPs is not symmetric but it is anisotropic [4–15]. In this paper, the alignment of LC molecular director in the periphery of decanethiol decorated GNP has been observed experimentally in the vertical and bias induced planar alignment sample cells using electro-optical technique. In vertical alignment of the sample cell, the anchoring of director around the GNPs has been found symmetric whereas in planar alignment it is non-symmetric, i.e. anisotropic configuration around the GNPs. The SPP peak of the GNPs shows blue shift at 0° and 45° angles between the polarization state of the linearly polarized light and rubbing direction of the sample cell with the increase in external bias field. This has also been analyzed by theoretical calculations as well.
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24350
2. Experiments and analysis The nematic LC material, MLC 6608 which is used in the present study, has a negative dielectric anisotropy of ∆ε =ε − ε ⊥ =−4.2 (ε =3.6, ε ⊥ =7.7) at low frequency in dielectric spectroscopy, where ε|| and ε⊥ are the parallel and perpendicular components of the dielectric constant at low frequency with respect to long molecular axis of LC. The optical anisotropy of this material is Δn = ne - no = 0.083 with ne = 1.5586 and no = 1.4756 in optical frequency range. The nematic to isotropic phase transition temperature is 90° C. The decanethiol capped GNPs (~20 nm in size) dispersed in toluene were purchased from Sigma Aldrich, USA and used as it is. The decanethiol capped GNPs can be synthesized by the process discovered by Brust et al [26]. A two-phase (water-toluene) reduction of AuC14- by sodium borohydride in the presence of an decanethiol is carried out. The AuCl4- is transferred from aqueous solution to toluene by using tetraoctylammonium bromide as the phase-transfer reagent and sodium boronhydride acts as the reducing agent in the presence of decanethiol. After the reduction process, the color of the solution changes from orange to deep brown which confirms the formation of GNPs. The size of the particles can be controlled by the mole ratio of AuCl4- and thiol compound. The suspension of 5 wt. % of the decanethiol capped GNPs was prepared in MLC 6608 LC material using manual mixing in the first stage and the composites were sonicated for 30 mins at room temperature in the second stage. The sample cells were fabricated by using transparent and highly conductive indium tin oxide (ITO) coated glass substrates. In order to prepare the capacitive form of the sample cell, the ITO coated substrates were placed parallel to each other facing the ITO coating inside. The 20 µm spacer balls were used to maintain the uniform separation between the two substrates. Before assembling the cell, the ITO coated side of the two substrates was treated with the alignment layer of SE 1211 polymer and rubbed uniformly in a single direction. The SE 1211 polymer is used to induce vertical alignment of LC material in the sample cell. The 5 wt. % GNP doped MLC 6608 was sandwiched between the two substrates at 95° C temperature which is above its nematic to isotropic phase transition. The sample was kept at 95°C temperature for one hour and was allowed to cool down naturally to room temperature for better alignment. The optical transmission measurement was recorded by using a computer controlled digital fiber optic spectrometer in the dark room at room temperature in the wavelength ranging from 400 to 1100 nm. The schematic diagram of experimental set up for the measurement of the sample cell is shown in Fig. 1(a). The unpolarized light from the white light source is made linearly polarized by the polarizer and is incident on the sample cell. The requirement of the present experiment is the normal incidence of the linearly polarized light. The experimental observations are recorded at 0°, 45°, and 90° angles of the polarized light with respect to the rubbing direction of the sample cell. Figure 1(b) shows the schematic front-view of the pristine sample cell with the vertical alignment of LC molecules in the bulk nematic LC at 0V external bias field. However, the alignment of molecular director close to GNP is mediated by decanethiol molecules. This is shown partially vertical on the surface of GNP due to its interaction with LC molecules. Thus, the alignment close to GNP surface appears to be pretilted with respect to bulk alignment and constitutes the defect of the integral strength 1 [2,13]. Figure 1(c) shows the front-view of the planar alignment configuration of the bulk LC. This can be obtained by applying an external electric field on the sample cell because of the negative dielectric anisotropy of MLC 6608 at low frequencies. The planar alignment is along the rubbing direction of sample cell as shown in Fig. 1(c). In planar alignment, the LC director at the interface of the GNPs is assumed to be anchored in anisotropic manner with respect to the surface of the GNP and constitutes the defects of integral strength of -½. For small particles, the anchoring energy of GNP Wa2 (where W and a are the surface energy term
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24351
and the size of the particle respectively) is weaker than the elastic energy Ka of LC (where K is the elastic constant of LC), which dominates the bulk alignment in proximity of GNP and allows the LC alignment to constitute the Saturn-ring-type defect. The alignment configuration at the interface of GNP and LC is studied by observing the behavior of SPP of the GNPs doped in MLC 6608 LC material. For the absorption spectra measurement of GNP-doped LC, the polarized light is incident normally on the sample with the polarizing angle at 0°, 45°, and 90° to the rubbing direction in the absence and presence of
Fig. 1. (a) Schematic diagram of the experimental set up. (b) Front view of GNP-doped LC molecular alignment in vertical configuration. (c) Front view of GNP-doped LC in planar alignment configuration. The experimental observations recorded at 0°, 45°, and 90° angles between p-polarized light and the rubbing direction.
bias electric field. Application of the external bias electric field allows the orientation of bulk LC director to change from vertical to planar due to the interaction of electric field with negative dielectric anisotropy. The threshold voltage for alignment conversion from vertical K 33 , where Vth, K33, and εo are the to planar is related to dielectric anisotropy as Vth = π ε o ∆ε threshold voltage, the elastic constant of twist of the nematic LC and the permittivity of free space respectively, and Δε is the dielectric anisotropy of LC at lower frequencies. Figure 2 reveals the absorption spectra of MLC 6608 doped with 5 wt. % of GNP in the absence and presence of external electric field. At 0V, Fig. 2(a) reveals that there is a negligible shift in the absorption peak of SPP at various polarization angles of the incident polarized light with respect to the rubbing direction. This is due to the fact that the incident light experiences a uniform alignment of LC molecules on the surface of GNP as configured in Fig. 1(b). The same measurement is performed at 6V above threshold voltage of Fredericks transition. The alignment of the sample cell has been completely converted from vertical to planar. The absorption spectra are shown in Fig. 2(b). There is an obvious blue shift in the SPP peak at 0° and 45°. However, there is no shift in the SPP peak at 90°. The shift is due to the change in dielectric constant of LC molecules which has ne>no at optical frequencies i.e. the long molecular axis component is stronger than short axis at these optical frequencies. It is important to mention here that the applied DC field experiences the negative anisotropy (exists at low frequencies) whereas the incident light experiences the possible positive anisotropy (exists at optical frequencies).
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24352
Observation of the SPP peak wavelengths at various DC bias voltages from 0 to 10 V at 0°, 45°, and 90° angles is shown in Fig. 3. At 0V bias, there is negligible shift in the SPP peak value observed at angles 0°, 45°, and 90° as discussed above. This confirms our assumption that the incident light experiences the symmetric alignment at the interface of LC molecules and GNPs, as shown in Fig. 1(b). In this configuration, ε⊥ is experienced by incident polarized light. However, a negligible small shift in the SPP at 90° angle could be due to the pre-tilt nature of the LC director on the surface of GNP.
0.06
Absorbance
0.05
(a)
0V
0.04 0.03 0.02
0o 45o 90o
Absorbance
0.01 450 475 500 525 550 575 600 Wavelength (nm) 0.12 (b) 6V 0.11 0.10 0.09 0.08
Angle
0o 45o 90o
0.07 450 475 500 525 550 575 600 Wavelength (nm) Fig. 2. Absorption spectra of GNP-doped MLC 6608 LC material at 0°, 45°, and 90° between the polarizing angles of the incident light and rubbing direction of sample cell under the application of voltage (a) 0 V and (b) 6 V bias.
On the application of DC bias voltage, the bulk molecules would rotate from vertical to planer alignment. The rotation of bulk molecules is due to the fact that a torque is applied on the stronger component of dielectric constant. The stronger component is ε⊥ at low frequencies because the MLC 6608 material has negative dielectric anisotropy which means that the stronger electric dipoles are along the short molecular axis instead of long one. The applied DC field is also the special case of low frequencies (ω = 0). Hence, the transition of LC molecular director from vertical to planar is possible and is called Fredericks transition. In this transition, the effective change in the dielectric constant of the bulk LC medium will be in the rubbing direction (i.e. along 0° as shown in Figs. 1(b) and 1(c)). This change is also observed in the periphery of GNPs as well. The effective change in the dielectric constant in the periphery of GNP would be at angles 0° and 45° with respect to the rubbing direction, but not at 90° because ε⊥ will remain the same at this angle as shown in Figs. 1(b) and 1(c). The SPP is highly sensitive to the dielectric constant of the embedded medium. The SPP peak
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24353
shows the blue shift at 0° and 45° but not at 90° as shown in Fig. 3. This shows that the MLC 6608 is positively anisotropic at optical frequencies, i.e., ne > no and their respective dielectric components at these frequencies as well. Above the threshold voltage (~2V), the direction of molecular director has been found in the rubbing direction of sample cell. Now, there are two effective components of dielectric constant in the plane of substrate: one (ε||) is along the rubbing direction and another (ε⊥) is perpendicular to it as shown in Fig. 1(c). This leads to the increment in the dielectric constant value at 0° and 45° which results in the blue shift of the SPP peak from 0° to 90°. The effective dielectric constant at 90° angle is still ε⊥ and does not show any shift accordingly.
Fig. 3. Optical absorption peak wavelength against a wide range of external applied electric field at 0°, 45°, and 90° angles between the incident polarized light to the rubbing direction.
Further increase in DC bias leads to the reorientation of the director to be more planar near the surface of GNP. Hence, the maximum dielectric anisotropy is experienced by the polarized light at the interface of GNP and LC. This results in further small shift in the SPP peak at 0° and 45°, but not at 90°. Above the threshold voltage of ~2V, there has not been observed any reorientation of LC molecules and hence no further variation in the value of SPP peak. After the threshold voltage of Friedrich transition, the incident light experiences the configuration of integral strength of -½ as shown in Fig. 1(c). However, the behavior of SPP below threshold voltage at 0° and 45° (marked in Fig. 3 as dotted ellipse) shows irregularities in the SPP wavelength shifts. The reason could be that the plane of reorientation of Friedrich transition in nematic LC molecules could not be defined well [27], i.e., the plane of reorientation is random for individual molecule due to which there are irregularities in the peaks of SPP at the observed angles below threshold voltage. The continuously varying behavior of SPP peak at 0° from 0 to 5V bias in Fig. 3 has also been analyzed by theoretical calculations. The experimentally observed linear behavior of SPP at 0° from 0 to 5V bias has been estimated in the form of propagation constant of SPP waves as [28]
= k SPP ko ε mε LC / ( ε m + ε LC )
1/ 2
,
(1)
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24354
where ko = 2π n /λo (nm)−1, λo is the SPP wavelength of reference gold material, n is the refractive index of surrounding reference medium (toluene, n = 1.5) before adding gold nanoparticles in to LC. ε m and ε LC are the dielectric constants of the metal gold and LC medium respectively. The value of ε m 2 [29]. It does not change much in the visible range of light, so it has been kept constant, and ε LC varies from 2.1774 to 2.4292 in the surrounding of GNP at optical frequencies of incident light. Therefore, the whole range of dielectric constant at optical frequencies from 2.1774 to 2.4292 close to GNP at 0° has been divided into six equal parts. These values of ε LC are substituted in Eq. (1) and the corresponding results are plotted in Fig. 4. The results show linear behavior of k SPP for change in the dielectric constant of the surrounding medium of GNP as shown in Fig. 4.
0.022
Experimental Calculated
0.021
εII
|kSPP|(nm-1)
0.020 0.019
ε⊥
0.018 0.017 0.016 0.015 2.15
2.20
2.25
2.30
εLC
2.35
2.40
2.45
Fig. 4. Comparison of experimental and theoretical observations calculated from Eq. (1) of propagation constant of SPP wave as a function of dielectric constant (optical frequency dielectric constant) at 0° angle between the polarization state of incident light and the rubbing direction of the sample cell. The parameters used for calculations are λo = 520 nm (reference absorption of GNP in toluene), εm ≅ 2, ε⊥ = no2, ε|| = ne2 (optical frequency dielectric constant), and ns = 1.5 (toluene as a dispersing medium for GNP before adding in LC).
The experimental results of k SPP have been calculated in a simple way, i.e. by using the relation k SPP = 2π nLC / λSPP from the experimental data. nLC is the refractive index of LC in the close environment of GNP which varies from no = 1.4756 to ne = 1.5586 at wavelength 589.3 nm at 20°C on the application of 0 to 5 V. At 0 V bias, the GNP experiences the planar alignment at its surface i.e. ε ⊥ (optical frequency dielectric constant), shown schematically in Fig. 1(b), whereas at 5 V bias it becomes ε (optical frequency dielectric constant) as shown schematically in Fig. 1(c). In order to know the values of λSPP at corresponding six points, the respective value of λSPP at each point of bias voltage is used in the calculation. The experimental and calculated values from Eq. (1) are plotted in Fig. 4. The small variation in the experimental and theoretical results could be due to the fact that the LC molecules are not perfectly aligned in the periphery of GNPs.
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24355
The extinction of light is due to the scattering and absorption of light within the material. Therefore, the calculation of extinction cross-section of light within the GNP mixed LC material can highlight the interaction of GNP and LC molecules. Figure 5 reveals the extinction cross- section of the GNP in the anisotropic dielectric LC medium. The extinction cross-section of the GNP in nematic LC behaves as [30]
9V ε LC2 ωε 2 (ω ) 3
σ ext =
c ε1 (ω ) + 2ε LC + ε 2 (ω ) 2
2
(2)
,
where V is the volume of the nanoparticle, ω is angular frequency of incident electromagnetic
Extinction cross section (nm2)
350 300 Dielectric constant of MLC 6608
250
2.1756 ε⊥ 2.2248 2.274 2.3233 2.3725 2.4217 ε||
200 150 100 1.6
2.0
2.4
2.8
3.2
Energy (eV) Fig. 5. Calculated extinction cross section of the GNP doped in MLC 6608 LC material as a function of incident energy at various values of dielectric constant of LC material at optical frequencies, i.e., variation of ε LC from short molecular axis to long molecular axis component of dielectric constant.
radiation, ε1 and ε2 are the real and imaginary dielectric constants of GNP respectively [31], c is the speed of light in free space. As the alignment is converted from vertical to planar configuration, the behavior of the extinction cross-section of GNP doped in LC has also been influenced and is calculated from Eq. (2) at the same six points (as discussed above) of ε LC at optical frequency from ε ⊥ (2.1774) to ε (2.4292) of MLC 6608 from vertical to planer alignment. In the vertical alignment configuration, the GNP experiences the dielectric constant component ε⊥ of the LC at all angles, which is the weaker component at optical frequencies than the long molecular axis, ε of LC molecule. The same behavior is for refractive index as well which behaves in the same manner as dielectric constant. In planar alignment after the conversion, the dielectric constant component ε|| is experienced by the polarized light at the interface of GNP at 0° angle. Figure 5 reveals that when the dielectric constant varies from lower to higher value the extinction peak shifts towards longer wavelengths i.e. towards lower energies. In the present case also, there is a clear shift towards lower energy at 0° angle. This is in agreement with our assumption of anisotropic anchoring
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24356
of LC molecules around GNP which constitutes the predicted defect in the alignment of nematic LC. However, the redshift in the extinction and blue shift in the absorption data leaves the open question for further analysis on the interaction of thiol capped GNP with LC. This distinct behavior could be due to some factors such as the thiol derivate compound with LC and GNP, the resultant of applied electric field and electric component of optical radiations etc. 3. Conclusions In summary, the theoretically predicted LC molecular configuration around GNPs has been observed experimentally. The experimental results are in agreement with theoretical assumptions. This is accomplished by investigating the behavior of SPP absorption peaks of GNPs. Clearly, the variation in the dielectric constant around GNPs governs the behavior of SPP and has shown blue shift in SPP peak with the change in the alignment and associated dielectric properties of LC molecules. There has not been found any shift in the SPP when the polarization state of the incident light is at 90° angle to the rubbing direction of LC sample cell. This confirms that the dielectric properties of LC have not been changed much on the application of DC bias at 90° in comparison to other angles (0° and 45°). This is the clear visualization of anisotropic dynamics of LC molecules around GNPs. The future work on this topic involves the analysis of interaction of LC with the other nano-materials which would lead to the improved display applications. Moreover, the control of alignment of LC by using various sizes GNPs would allow the development of new non-display LC devices, including tunable lenses [32–35], optical sensors, lasers and other photonic devices. Acknowledgments G. Li would like to thank the support from National Institutes of Health National Eye Institute (through grant R01 EY020641), National Institute of Biomedical Imaging and Bioengineering (through grant R21 EB008857), National Institute of General Medical Sciences (through grant R21 RR026254/R21 GM103439), and Wallace H. Coulter Foundation Career Award (through grant WCF0086TN). G. Li also thanks Dr. David Stroud for reading the manuscript.
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24357
Department of Ophthalmology and Visual Science, The Ohio State University, ElectroScience Laboratory, 1330 Kinnear Road., Columbus, OH 43212, USA Department of Electrical and Computer Engineering, The Ohio State University, ElectroScience Laboratory, 1330 Kinnear Road., Columbus, OH 43212, USA 3 College of Optometry, University of Missouri, St. Louis, MO 63121, USA 4 Present Addresses: Physics Department, Deshbandhu College (University of Delhi, Delhi), Kalkaji, New Delhi110019, India * [email protected]
2
Abstract: Study of the liquid crystal (LC) director around nanoparticles has been an important topic of research very recently, since it allows design and fabrication of next-generation LC devices that are impossible in the past. In our experiment, alkanethiol-capped gold nanoparticles (GNPs) were dispersed in nematic LC. Analysis of the LC director around GNPs was performed by investigating the behavior of surface plasmon polariton (SPP) absorption peaks of the GNPs using spectrophotometry technique. It is found that the incident linearly polarized light orientated at 0°, 45°, and 90° angles with respect to the rubbing direction experiences varying interaction with the LC medium. The corresponding transmission of light reveals the anisotropic shift in wavelength of SPP peak. The anisotropic behavior of SPPs of the GNPs is in agreement with theoretical calculations. ©2014 Optical Society of America OCIS codes: (160.3710) Liquid crystals; (160.4236) Nanomaterials; (160.4670) Optical materials; (230.3720) Liquid-crystal devices; (230.2090) Electro-optical devices; (240.6680) Surface plasmons.
References and links 1.
K. Busch and S. John, “Liquid crystal photonic band gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83(5), 967–970 (1999). 2. P. G. de Gennes, The Physics of Liquid Crystal Research (Clarendon Press, 1974). 3. C. H. Jang, L. L. Cheng, C. W. Olsen, and N. L. Abbott, “Anchoring of nematic liquid crystals on viruses with different envelope structures,” Nano Lett. 6(5), 1053–1058 (2006). 4. O. V. Kuksenok, R. W. Ruhwandl, S. V. Shiyanovskii, and E. M. Terentjev, “Director structure around a colloid particle suspended in a nematic liquid crystal,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(5), 5198–5203 (1996). 5. J. Fukuda, M. Yoneya, and H. Yokoyama, “Defect structure of a nematic liquid crystal around a spherical particle: adaptive mesh refinement approach,” Phys. Rev. E. 65(4), 041709 (2002). 6. Y. Gu and N. L. Abbott, “Observation of Saturn-ring defects around solid microspheres in nematic liquid crystals,” Phys. Rev. Lett. 85(22), 4719–4722 (2000). 7. P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, “Novel colloidal interactions in anisotropic fluids,” Science 275(5307), 1770–1773 (1997). 8. R. Yamamoto, “Simulating particle dispersions in nematic liquid-crystal solvents,” Phys. Rev. Lett. 87(7), 075502 (2001). 9. J. Fukuda, M. Yoneya, and H. Yokoyama, “Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement,” Eur Phys J E Soft Matter 13(1), 87–98 (2004). 10. M. A. Bates, “Nanospheres in a nematic liquid crystal solvent: the influence of particle size,” Liq. Cryst. 32(1112), 1525–1529 (2005).
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24348
11. I. I. Smalyukh, O. D. Lavrentovich, A. N. Kuzmin, A. V. Kachynski, and P. N. Prasad, “Elasticity-mediated selforganization and colloidal interactions of solid spheres with tangential anchoring in a nematic liquid crystal,” Phys. Rev. Lett. 95(15), 157801 (2005). 12. V. M. Pergamenshchik and V. A. Uzunova, “Colloidal nematostatics,” Condens. Matter Phys. 13(3), 33602 (2010). 13. B. I. Lev, S. B. Chernyshuk, P. M. Tomchuk, and H. Yokoyama, “Symmetry breaking and interaction of colloidal particles in nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(2), 021709 (2002). 14. B. I. Lev and P. M. Tomchuk, “Interaction of foreign macrodroplets in a nematic liquid crystal and induced supermolecular structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(1), 591–602 (1999). 15. I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, “Two-Dimensional Nematic Colloidal Crystals Self-Assembled by Topological Defects,” Science 313(5789), 954–958 (2006). 16. V. Tomar, T. F. Roberts, N. L. Abbott, J. P. Hernández-Ortiz, and J. J. de Pablo, “Liquid Crystal Mediated Interactions Between Nanoparticles in a Nematic Phase,” Langmuir 28(14), 6124–6131 (2012). 17. F. Mondiot, R. Botet, P. Snabre, O. Mondain-Monval, and J.-C. Loudet, “Colloidal aggregation and dynamics in anisotropic fluids,” Proc. Natl. Acad. Sci. U.S.A. 111(16), 5831–5836 (2014). 18. S. Y. Park and D. Stroud, “Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle,” Phys. Rev. Lett. 94(21), 217401 (2005). 19. P. G. de Gennes, “An Analogy Between Superconductors And Smectic A,” Solid State Commun. 10(9), 753– 756 (1972). 20. P. G. de Gennes, “Some Remarks on the Polymorphism of Smectics,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 21(12), 49–76 (1973). 21. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters. (Springer, 1995). 22. L. H. Hsu, K. Y. Lo, S. A. Huang, C. Y. Huang, and C. S. Yang, “Irreversible redshift of transmission spectrum of gold nanoparticles doped in liquid crystals,” Appl. Phys. Lett. 92(18), 181112 (2008). 23. G. M. Koenig, Jr., M. V. Meli, J. S. Park, J. J. de Pablo, and N. L. Abbott, “Coupling of the Plasmon Resonances of Chemically Functionalized Gold Nanoparticles to Local Order in Thermotropic Liquid Crystals,” Chem. Mater. 19(5), 1053–1061 (2007). 24. H. Stark, “Director Field Configurations Around A Spherical Particle In A Nematic Liquid Crystal,” Eur. Phys. J. B 10(2), 311–321 (1999). 25. J. Fukuda, “Continuous Transformation Of A -1/2 Wedge Disclination Line To A +1/2 one,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(4), 040701 (2010). 26. M. Brust, M. Walker, D. Bethell, D. J. Schiffrin, and R. Whyman, “Synthesis of thiol derivatised gold nanoparticles in a two phase liquid/liquid system,” Chem. Commun. 7(7), 801–802 (1994). 27. I. C. Khoo, Liquid Crystal. (Wiley-Interscience, 2007). 28. J. Zhang, L. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D Appl. Phys. 45(11), 113001 (2012). 29. S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7(11), 3418–3423 (2007). 30. S. Link and M. A. E. Sayed, “Size and temperature dependence of the plasmon absorption of colloidal gold nanoparticles,” J. Phys. Chem. B 103(21), 4212–4217 (1999). 31. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). 32. G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006). 33. G. Li, P. Valley, M. S. Giridhar, D. Mathine, G. Meredith, J. Haddock, B. Kippelen, and N. Peyghambarian, “Large-aperture switchable thin diffractive lens with interleaved electrode pattern,” Appl. Phys. Lett. 89(14), 141120 (2006). 34. G. Li, P. Valley, P. Äyräs, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007). 35. G. Li, “Adaptive lens,” Prog. Opt. 55, 199–283 (2010).
1. Introduction Recently, new perspectives of liquid crystals (LCs) have been shown in optics and photonics [1], display devices [2], virus detection by understanding its interaction with LC [3], and studying the interaction of LC with nanomaterials for enhanced applications [4–13]. Nanomaterials are emerging as a prototype to enrich the properties of LC materials. The active research in this direction has been focused on the analysis and control of the interaction between LC molecules and gold nanoparticles (GNP) at nanoscale dimension. Some mathematical models have been presented to understand the alignment of LC molecular
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24349
director around nanomaterials in the form of Saturn rings, hedgehogs, and boojams [4–17]. The inclusion of GNPs in nematic LC can create some stable defects with possible integral strength ± 1 or ± ½ depending on the interaction of LC with GNPs. The theoretical approach on the linearized director distortion in nematic LC formed by particles analyzes several properties like elastic charge density, multipole particles, mechanical torque balance on the basis of electrostatic interactions, and defect symmetry [12]. The anisotropic alignment of LC molecules is due to breaking of mirror symmetry and it leads to the dipolar interaction between colloidal particles in LC [13]. The long range interaction of inhomogeneous macrodroplet distribution within a liquid crystal sample shows the dependency on the spatial position and relative orientation of the droplets [14]. The gold nanoparticles are so sensitive to visible light that the incident light polarizes the GNP doped in the dielectric system due to the shifting of electron cloud which is influenced by electric component of incident light. This results in generation of surface plasmon polariton (SPP) waves at the interface of GNP and dielectric (LC in the present case). These SPP waves propagate along the interface of GNP and dielectric which end up in both media for some distance. The resulting behavior of SPP has shown that the boojam pair with planar configuration of LC director around GNP is more stable in comparison with Saturn ring and hedgehogs [7, 18]. In 1972, P. G. de Gennes proposed the phase separation at the interface of solid substrate and bulk nematic LC [19, 20]. The separate phase at the interface was the layer structured smectic A phase whereas the bulk phase was nematic in vertical alignment configuration of sample cell. The enhancement in the local ordering of 4-pentyl-4′-cyanobiphenyl (5CB) molecules has been observed at the interface of LC and thiol derivative functionalized GNP which is confirmed by observing the shift in wavelength of SPP peak. The redshift in wavelength of SPP peak has been reported in literature [21]. The controllable redshift is observed below threshold voltage before particle aggregation due to electrophoresis force whereas after threshold voltage, the magnitude of irreversible peak shift increases remarkably [22]. However, the surface chemistry has played a significant role in the SPP peak shifting due to the coupling of SPP with the 5CB nematic LC material [23]. The optical frequency response of GNPs strongly depends on the fundamental electronic configuration of the nanoparticles which can be influenced by the variation in the size of nanoparticles and its surrounding dielectric environment [21]. At the interface of metal and LC, the shift of SPP peak is found to be selective, i.e., the blue shift is caused by the low energetic SPP resonance, whereas the red shift is induced by the high energetic SPP resonance under the application of an external electric field. It has also been found that the SPP field can align the LC molecules due to the interaction of its electric component with dielectric anisotropy of the LC material. In vertical alignment of the sample cell, the point defect disclination is 1 while after conversion to planar it becomes either surface ring or a -½ disclination ring configuration [13, 24, 25]. Based on the previous theoretical observations, the alignment of LC molecular director in the close proximity of GNPs is not symmetric but it is anisotropic [4–15]. In this paper, the alignment of LC molecular director in the periphery of decanethiol decorated GNP has been observed experimentally in the vertical and bias induced planar alignment sample cells using electro-optical technique. In vertical alignment of the sample cell, the anchoring of director around the GNPs has been found symmetric whereas in planar alignment it is non-symmetric, i.e. anisotropic configuration around the GNPs. The SPP peak of the GNPs shows blue shift at 0° and 45° angles between the polarization state of the linearly polarized light and rubbing direction of the sample cell with the increase in external bias field. This has also been analyzed by theoretical calculations as well.
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24350
2. Experiments and analysis The nematic LC material, MLC 6608 which is used in the present study, has a negative dielectric anisotropy of ∆ε =ε − ε ⊥ =−4.2 (ε =3.6, ε ⊥ =7.7) at low frequency in dielectric spectroscopy, where ε|| and ε⊥ are the parallel and perpendicular components of the dielectric constant at low frequency with respect to long molecular axis of LC. The optical anisotropy of this material is Δn = ne - no = 0.083 with ne = 1.5586 and no = 1.4756 in optical frequency range. The nematic to isotropic phase transition temperature is 90° C. The decanethiol capped GNPs (~20 nm in size) dispersed in toluene were purchased from Sigma Aldrich, USA and used as it is. The decanethiol capped GNPs can be synthesized by the process discovered by Brust et al [26]. A two-phase (water-toluene) reduction of AuC14- by sodium borohydride in the presence of an decanethiol is carried out. The AuCl4- is transferred from aqueous solution to toluene by using tetraoctylammonium bromide as the phase-transfer reagent and sodium boronhydride acts as the reducing agent in the presence of decanethiol. After the reduction process, the color of the solution changes from orange to deep brown which confirms the formation of GNPs. The size of the particles can be controlled by the mole ratio of AuCl4- and thiol compound. The suspension of 5 wt. % of the decanethiol capped GNPs was prepared in MLC 6608 LC material using manual mixing in the first stage and the composites were sonicated for 30 mins at room temperature in the second stage. The sample cells were fabricated by using transparent and highly conductive indium tin oxide (ITO) coated glass substrates. In order to prepare the capacitive form of the sample cell, the ITO coated substrates were placed parallel to each other facing the ITO coating inside. The 20 µm spacer balls were used to maintain the uniform separation between the two substrates. Before assembling the cell, the ITO coated side of the two substrates was treated with the alignment layer of SE 1211 polymer and rubbed uniformly in a single direction. The SE 1211 polymer is used to induce vertical alignment of LC material in the sample cell. The 5 wt. % GNP doped MLC 6608 was sandwiched between the two substrates at 95° C temperature which is above its nematic to isotropic phase transition. The sample was kept at 95°C temperature for one hour and was allowed to cool down naturally to room temperature for better alignment. The optical transmission measurement was recorded by using a computer controlled digital fiber optic spectrometer in the dark room at room temperature in the wavelength ranging from 400 to 1100 nm. The schematic diagram of experimental set up for the measurement of the sample cell is shown in Fig. 1(a). The unpolarized light from the white light source is made linearly polarized by the polarizer and is incident on the sample cell. The requirement of the present experiment is the normal incidence of the linearly polarized light. The experimental observations are recorded at 0°, 45°, and 90° angles of the polarized light with respect to the rubbing direction of the sample cell. Figure 1(b) shows the schematic front-view of the pristine sample cell with the vertical alignment of LC molecules in the bulk nematic LC at 0V external bias field. However, the alignment of molecular director close to GNP is mediated by decanethiol molecules. This is shown partially vertical on the surface of GNP due to its interaction with LC molecules. Thus, the alignment close to GNP surface appears to be pretilted with respect to bulk alignment and constitutes the defect of the integral strength 1 [2,13]. Figure 1(c) shows the front-view of the planar alignment configuration of the bulk LC. This can be obtained by applying an external electric field on the sample cell because of the negative dielectric anisotropy of MLC 6608 at low frequencies. The planar alignment is along the rubbing direction of sample cell as shown in Fig. 1(c). In planar alignment, the LC director at the interface of the GNPs is assumed to be anchored in anisotropic manner with respect to the surface of the GNP and constitutes the defects of integral strength of -½. For small particles, the anchoring energy of GNP Wa2 (where W and a are the surface energy term
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24351
and the size of the particle respectively) is weaker than the elastic energy Ka of LC (where K is the elastic constant of LC), which dominates the bulk alignment in proximity of GNP and allows the LC alignment to constitute the Saturn-ring-type defect. The alignment configuration at the interface of GNP and LC is studied by observing the behavior of SPP of the GNPs doped in MLC 6608 LC material. For the absorption spectra measurement of GNP-doped LC, the polarized light is incident normally on the sample with the polarizing angle at 0°, 45°, and 90° to the rubbing direction in the absence and presence of
Fig. 1. (a) Schematic diagram of the experimental set up. (b) Front view of GNP-doped LC molecular alignment in vertical configuration. (c) Front view of GNP-doped LC in planar alignment configuration. The experimental observations recorded at 0°, 45°, and 90° angles between p-polarized light and the rubbing direction.
bias electric field. Application of the external bias electric field allows the orientation of bulk LC director to change from vertical to planar due to the interaction of electric field with negative dielectric anisotropy. The threshold voltage for alignment conversion from vertical K 33 , where Vth, K33, and εo are the to planar is related to dielectric anisotropy as Vth = π ε o ∆ε threshold voltage, the elastic constant of twist of the nematic LC and the permittivity of free space respectively, and Δε is the dielectric anisotropy of LC at lower frequencies. Figure 2 reveals the absorption spectra of MLC 6608 doped with 5 wt. % of GNP in the absence and presence of external electric field. At 0V, Fig. 2(a) reveals that there is a negligible shift in the absorption peak of SPP at various polarization angles of the incident polarized light with respect to the rubbing direction. This is due to the fact that the incident light experiences a uniform alignment of LC molecules on the surface of GNP as configured in Fig. 1(b). The same measurement is performed at 6V above threshold voltage of Fredericks transition. The alignment of the sample cell has been completely converted from vertical to planar. The absorption spectra are shown in Fig. 2(b). There is an obvious blue shift in the SPP peak at 0° and 45°. However, there is no shift in the SPP peak at 90°. The shift is due to the change in dielectric constant of LC molecules which has ne>no at optical frequencies i.e. the long molecular axis component is stronger than short axis at these optical frequencies. It is important to mention here that the applied DC field experiences the negative anisotropy (exists at low frequencies) whereas the incident light experiences the possible positive anisotropy (exists at optical frequencies).
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24352
Observation of the SPP peak wavelengths at various DC bias voltages from 0 to 10 V at 0°, 45°, and 90° angles is shown in Fig. 3. At 0V bias, there is negligible shift in the SPP peak value observed at angles 0°, 45°, and 90° as discussed above. This confirms our assumption that the incident light experiences the symmetric alignment at the interface of LC molecules and GNPs, as shown in Fig. 1(b). In this configuration, ε⊥ is experienced by incident polarized light. However, a negligible small shift in the SPP at 90° angle could be due to the pre-tilt nature of the LC director on the surface of GNP.
0.06
Absorbance
0.05
(a)
0V
0.04 0.03 0.02
0o 45o 90o
Absorbance
0.01 450 475 500 525 550 575 600 Wavelength (nm) 0.12 (b) 6V 0.11 0.10 0.09 0.08
Angle
0o 45o 90o
0.07 450 475 500 525 550 575 600 Wavelength (nm) Fig. 2. Absorption spectra of GNP-doped MLC 6608 LC material at 0°, 45°, and 90° between the polarizing angles of the incident light and rubbing direction of sample cell under the application of voltage (a) 0 V and (b) 6 V bias.
On the application of DC bias voltage, the bulk molecules would rotate from vertical to planer alignment. The rotation of bulk molecules is due to the fact that a torque is applied on the stronger component of dielectric constant. The stronger component is ε⊥ at low frequencies because the MLC 6608 material has negative dielectric anisotropy which means that the stronger electric dipoles are along the short molecular axis instead of long one. The applied DC field is also the special case of low frequencies (ω = 0). Hence, the transition of LC molecular director from vertical to planar is possible and is called Fredericks transition. In this transition, the effective change in the dielectric constant of the bulk LC medium will be in the rubbing direction (i.e. along 0° as shown in Figs. 1(b) and 1(c)). This change is also observed in the periphery of GNPs as well. The effective change in the dielectric constant in the periphery of GNP would be at angles 0° and 45° with respect to the rubbing direction, but not at 90° because ε⊥ will remain the same at this angle as shown in Figs. 1(b) and 1(c). The SPP is highly sensitive to the dielectric constant of the embedded medium. The SPP peak
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24353
shows the blue shift at 0° and 45° but not at 90° as shown in Fig. 3. This shows that the MLC 6608 is positively anisotropic at optical frequencies, i.e., ne > no and their respective dielectric components at these frequencies as well. Above the threshold voltage (~2V), the direction of molecular director has been found in the rubbing direction of sample cell. Now, there are two effective components of dielectric constant in the plane of substrate: one (ε||) is along the rubbing direction and another (ε⊥) is perpendicular to it as shown in Fig. 1(c). This leads to the increment in the dielectric constant value at 0° and 45° which results in the blue shift of the SPP peak from 0° to 90°. The effective dielectric constant at 90° angle is still ε⊥ and does not show any shift accordingly.
Fig. 3. Optical absorption peak wavelength against a wide range of external applied electric field at 0°, 45°, and 90° angles between the incident polarized light to the rubbing direction.
Further increase in DC bias leads to the reorientation of the director to be more planar near the surface of GNP. Hence, the maximum dielectric anisotropy is experienced by the polarized light at the interface of GNP and LC. This results in further small shift in the SPP peak at 0° and 45°, but not at 90°. Above the threshold voltage of ~2V, there has not been observed any reorientation of LC molecules and hence no further variation in the value of SPP peak. After the threshold voltage of Friedrich transition, the incident light experiences the configuration of integral strength of -½ as shown in Fig. 1(c). However, the behavior of SPP below threshold voltage at 0° and 45° (marked in Fig. 3 as dotted ellipse) shows irregularities in the SPP wavelength shifts. The reason could be that the plane of reorientation of Friedrich transition in nematic LC molecules could not be defined well [27], i.e., the plane of reorientation is random for individual molecule due to which there are irregularities in the peaks of SPP at the observed angles below threshold voltage. The continuously varying behavior of SPP peak at 0° from 0 to 5V bias in Fig. 3 has also been analyzed by theoretical calculations. The experimentally observed linear behavior of SPP at 0° from 0 to 5V bias has been estimated in the form of propagation constant of SPP waves as [28]
= k SPP ko ε mε LC / ( ε m + ε LC )
1/ 2
,
(1)
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24354
where ko = 2π n /λo (nm)−1, λo is the SPP wavelength of reference gold material, n is the refractive index of surrounding reference medium (toluene, n = 1.5) before adding gold nanoparticles in to LC. ε m and ε LC are the dielectric constants of the metal gold and LC medium respectively. The value of ε m 2 [29]. It does not change much in the visible range of light, so it has been kept constant, and ε LC varies from 2.1774 to 2.4292 in the surrounding of GNP at optical frequencies of incident light. Therefore, the whole range of dielectric constant at optical frequencies from 2.1774 to 2.4292 close to GNP at 0° has been divided into six equal parts. These values of ε LC are substituted in Eq. (1) and the corresponding results are plotted in Fig. 4. The results show linear behavior of k SPP for change in the dielectric constant of the surrounding medium of GNP as shown in Fig. 4.
0.022
Experimental Calculated
0.021
εII
|kSPP|(nm-1)
0.020 0.019
ε⊥
0.018 0.017 0.016 0.015 2.15
2.20
2.25
2.30
εLC
2.35
2.40
2.45
Fig. 4. Comparison of experimental and theoretical observations calculated from Eq. (1) of propagation constant of SPP wave as a function of dielectric constant (optical frequency dielectric constant) at 0° angle between the polarization state of incident light and the rubbing direction of the sample cell. The parameters used for calculations are λo = 520 nm (reference absorption of GNP in toluene), εm ≅ 2, ε⊥ = no2, ε|| = ne2 (optical frequency dielectric constant), and ns = 1.5 (toluene as a dispersing medium for GNP before adding in LC).
The experimental results of k SPP have been calculated in a simple way, i.e. by using the relation k SPP = 2π nLC / λSPP from the experimental data. nLC is the refractive index of LC in the close environment of GNP which varies from no = 1.4756 to ne = 1.5586 at wavelength 589.3 nm at 20°C on the application of 0 to 5 V. At 0 V bias, the GNP experiences the planar alignment at its surface i.e. ε ⊥ (optical frequency dielectric constant), shown schematically in Fig. 1(b), whereas at 5 V bias it becomes ε (optical frequency dielectric constant) as shown schematically in Fig. 1(c). In order to know the values of λSPP at corresponding six points, the respective value of λSPP at each point of bias voltage is used in the calculation. The experimental and calculated values from Eq. (1) are plotted in Fig. 4. The small variation in the experimental and theoretical results could be due to the fact that the LC molecules are not perfectly aligned in the periphery of GNPs.
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24355
The extinction of light is due to the scattering and absorption of light within the material. Therefore, the calculation of extinction cross-section of light within the GNP mixed LC material can highlight the interaction of GNP and LC molecules. Figure 5 reveals the extinction cross- section of the GNP in the anisotropic dielectric LC medium. The extinction cross-section of the GNP in nematic LC behaves as [30]
9V ε LC2 ωε 2 (ω ) 3
σ ext =
c ε1 (ω ) + 2ε LC + ε 2 (ω ) 2
2
(2)
,
where V is the volume of the nanoparticle, ω is angular frequency of incident electromagnetic
Extinction cross section (nm2)
350 300 Dielectric constant of MLC 6608
250
2.1756 ε⊥ 2.2248 2.274 2.3233 2.3725 2.4217 ε||
200 150 100 1.6
2.0
2.4
2.8
3.2
Energy (eV) Fig. 5. Calculated extinction cross section of the GNP doped in MLC 6608 LC material as a function of incident energy at various values of dielectric constant of LC material at optical frequencies, i.e., variation of ε LC from short molecular axis to long molecular axis component of dielectric constant.
radiation, ε1 and ε2 are the real and imaginary dielectric constants of GNP respectively [31], c is the speed of light in free space. As the alignment is converted from vertical to planar configuration, the behavior of the extinction cross-section of GNP doped in LC has also been influenced and is calculated from Eq. (2) at the same six points (as discussed above) of ε LC at optical frequency from ε ⊥ (2.1774) to ε (2.4292) of MLC 6608 from vertical to planer alignment. In the vertical alignment configuration, the GNP experiences the dielectric constant component ε⊥ of the LC at all angles, which is the weaker component at optical frequencies than the long molecular axis, ε of LC molecule. The same behavior is for refractive index as well which behaves in the same manner as dielectric constant. In planar alignment after the conversion, the dielectric constant component ε|| is experienced by the polarized light at the interface of GNP at 0° angle. Figure 5 reveals that when the dielectric constant varies from lower to higher value the extinction peak shifts towards longer wavelengths i.e. towards lower energies. In the present case also, there is a clear shift towards lower energy at 0° angle. This is in agreement with our assumption of anisotropic anchoring
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24356
of LC molecules around GNP which constitutes the predicted defect in the alignment of nematic LC. However, the redshift in the extinction and blue shift in the absorption data leaves the open question for further analysis on the interaction of thiol capped GNP with LC. This distinct behavior could be due to some factors such as the thiol derivate compound with LC and GNP, the resultant of applied electric field and electric component of optical radiations etc. 3. Conclusions In summary, the theoretically predicted LC molecular configuration around GNPs has been observed experimentally. The experimental results are in agreement with theoretical assumptions. This is accomplished by investigating the behavior of SPP absorption peaks of GNPs. Clearly, the variation in the dielectric constant around GNPs governs the behavior of SPP and has shown blue shift in SPP peak with the change in the alignment and associated dielectric properties of LC molecules. There has not been found any shift in the SPP when the polarization state of the incident light is at 90° angle to the rubbing direction of LC sample cell. This confirms that the dielectric properties of LC have not been changed much on the application of DC bias at 90° in comparison to other angles (0° and 45°). This is the clear visualization of anisotropic dynamics of LC molecules around GNPs. The future work on this topic involves the analysis of interaction of LC with the other nano-materials which would lead to the improved display applications. Moreover, the control of alignment of LC by using various sizes GNPs would allow the development of new non-display LC devices, including tunable lenses [32–35], optical sensors, lasers and other photonic devices. Acknowledgments G. Li would like to thank the support from National Institutes of Health National Eye Institute (through grant R01 EY020641), National Institute of Biomedical Imaging and Bioengineering (through grant R21 EB008857), National Institute of General Medical Sciences (through grant R21 RR026254/R21 GM103439), and Wallace H. Coulter Foundation Career Award (through grant WCF0086TN). G. Li also thanks Dr. David Stroud for reading the manuscript.
#220155 - $15.00 USD Received 30 Jul 2014; revised 18 Sep 2014; accepted 19 Sep 2014; published 29 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024348 | OPTICS EXPRESS 24357
