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ACI Avances en Ciencias e Ingenierías

SECTION A: EXACT SCIENCES

Vol. 16 No. 1 (2024)

Inversion of two flux and four flux radiative transfer models for determining scattering and absorption coefficients for polymer dispersed liquid crystals

DOI
https://doi.org/10.18272/aci.v16i1.3165
Submitted
November 28, 2023
Published
2024-04-15

Abstract

Intrinsic and extrinsic scattering and absorption coefficients of eight non-absorbing light polymer dispersed liquid crystals samples, with two different sizes of the active area and with four different thicknesses of the internal active layer, at their translucent off and at their transparent on optical appearance states –without and with applied electrical voltage respectively– were successfully determined following the same procedure described in previous works with a suspended particle device −a light absorbing smart window sample− and with another commercial polymer dispersed liquid crystals smart window sample. This procedure, based on two-flux and four-flux radiative transfer models, considers the critical angle of total internal reflection for determining the internal diffuse interface reflectance, and uses the same previously proposed equation for average crossing parameter, based on diffuse and total intensities of forward and backward light beams, for solving the four-flux model in order to determine intrinsic coefficients. Simulated optical appearance resulted to be a milky white translucent off state and a colorless-transparent on state that becomes more transparent for polymer dispersed liquid crystals samples with thinner thicknesses, requiring higher applied voltage for the transparent on optical states of the thicker polymer dispersed liquid crystals samples characterized.

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References

  1. Lampert, C.M. (1994). Glazing Materials for Solar and Architectural Applications. International Energy Agency. https://www.iea-shc.org/Data/Sites/1/publications/Task%2010-Glazing-Materials-for-Solar-and-Architectural-Applications-Sept1994.pdf
  2. Lampert, C.M. (1995). Chromogenic switchable glazing: Towards the development of the smart window. Window innovations conference. https://www.osti.gov/servlets/purl/207602
  3. Lampert, C.M. (1998). Smart switchable glazing for solar energy and daylight control. Sol. Energy Mater. Sol. Cells, 52(3-4), 207-221. doi: https://doi.org/10.1016/S0927-0248(97)00279-1
  4. Barrios, D., Álvarez, C., Miguitama, J., Gallego, D., & Niklasson, G.A. (2019). Inversion of two-flux and four-flux radiative transfer models for determining scattering and absorption coefficients for a suspended particle device. Appl. Opt., 58(31), 8871-8881. doi: https://doi.org/10.1364/AO.58.008871
  5. Barrios, D., Álvarez, C., Miguitama, J., Gallego, D., Wang, J., & Niklasson, G.A. (2022). Light scattering parameters of polymer dispersed liquid crystals obtained by inversion of experimental data. Proceedings of the Bremen Zoom Workshop on Light Scattering. https://scattport.org/index.php/conferences-menu/715-bremen-zoom-workshopon-light-scattering-2022
  6. Maheu, B., Letoulouzan, J.N., & Gouesbet, G. (1984). Four-flux models to solve the scattering transfer equation in terms of Lorenz–Mie parameters. Appl. Opt., 23, 3353–3362. doi: https://doi.org/10.1364/AO.23.003353
  7. Kubelka, P. (1948). New contributions to the optics of intensely light-scattering materials: Part I. J. Opt. Soc. Am. 38, 448–457. doi: https://doi.org/10.1364/JOSA.38.000448
  8. Saunderson, J.L. (1942). Calculation of the color of pigmented plastics. J. Opt. Soc. Am., 32, 727–736. doi: https://doi.org/10.1364/JOSA.32.000727
  9. Kortüm, G. (1969). Reflectance Spectroscopy: Principles, Methods, Applications. Springer. doi: https://doi.org/10.1007/978-3-642-88071-1
  10. Kottler, F. (1960). Turbid Media with Plane-Parallel Surfaces. J. Opt. Soc. Am., 50(5), 483–490. doi: https://doi.org/10.1364/JOSA.50.000483
  11. Judd, D.B. (1942). Fresnel reflection of diffusely incident light. J. Research NBS, 29, 329-332. doi: https://doi.org/10.6028/jres.029.017
  12. Walsh, J.W.T. (1926). The reflection factor of a polished glass surface for diffused light. Department of Scientific and Industrial Research.
  13. Barrios, D., Vergaz, R., Sanchez-Pena, J.M., Granqvist, C.G., & Niklasson, G.A. (2013). Toward a quantitative model for suspended particle devices: optical scattering and absorption coefficients. Sol. Energy Mater. Sol. Cells, 111, 115–122. doi: https://doi.org/10.1016/j.solmat.2012.12.012
  14. Barrios, D., Vergaz, R., Sanchez-Pena, J.M., Granqvist, C.G., & Niklasson, G.A. (2015). Simulation of the thickness dependence of the optical properties of suspended particle devices. Sol. Energy Mater. Sol. Cells, 143, 613–622. doi: https://doi.org/10.1016/j.solmat.2015.05.044
  15. Levinson, R., Berdahl, P., & Akbari, H. (2005). Solar spectral optical properties of pigments– Part I: model for deriving scattering and absorption coefficients from transmittance and reflectance measurements. Sol. Energy Mater. Sol. Cells, 89, 319–349. doi: https://doi.org/10.1016/j.solmat.2004.11.012
  16. Vargas, W. E. (1999). Two-flux radiative transfer model under nonisotropic propagating diffuse radiation. Appl. Opt., 38, 1077-1085. doi: https://doi.org/10.1364/ao.38.001077
  17. Barrios, D., Torres, J.C., Marcos, C., Pinzón, P.J., Vergaz, R., Sánchez-Pena, J.M., & Viñuales, A. (2011). Dependence on the thickness and area of the parameters of equivalent electrical circuit model for devices in polymer dispersed liquid crystal on glass substrate. 7ª Reunión Española de Optoelectrónica.
  18. Yang, D.-K., & Wu, S.-T. (2006). Fundamentals of Liquid Crystal Devices. John Wiley and Sons, Ltd. doi: https://doi.org/10.1002/9781118751992
  19. Ramsey, R. A., Sharma, S. C., Henry, R. M., & Atman, J. B. (2003). Electro-optical Properties and Interfacial Charges in Polymer-Dispersed Liquid Crystal Devices. Mat. Res. Soc. Symp. Proc., 771, 339-344. doi: https://doi.org/10.1557/PROC-771-L10.18
  20. Barrios, D., Álvarez, C., & Miguitama, J. (2019). Visual appearance simulation of polymer dispersed liquid crystal smart windows. V Congreso Internacional de Ciencia, Tecnología e Innovación para la Sociedad. Universidad Politécnica Salesiana. https://abyayala.org.ec/producto/5to-congreso-internacional-de-ciencia-tecnologia-e-innovacion-parala-sociedad/
  21. Swanepoel, R. (1984). Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films. J. Phys. E: Sci. Instrum., 17(10), 896-903. doi: https://doi.org/10.1088/0022-3735/16/12/023
  22. Sagan, C., & Pollack, J.B. (1967). Anisotropic nonconservative scatttering and the clouds of Venus. J. Geophys. Res., 72(2): 469-477. doi: https://doi.org/10.1029/JZ072i002p00469
  23. Bohren, C.F., & Huffman, D.R. (1983). Absorption and scattering of light by small particles. New York: Wiley. doi: https://doi.org/10.1002/9783527618156
  24. Beasley, K., Atkins, J.T., & Billmeyer Jr, F.W. (1967). Scattering and absorption of light in turbid media. Gordon & Breach Science Publishers.
  25. Maheu, B., & Gouesbet, G. (1986). Four-flux models to solve the scattering transfer equation: special cases. Appl. Opt., 25, 1122–1128. doi: https://doi.org/10.1364/ao.25.001122
  26. Mie, G. (1908). Contributions to the Optics of Turbid Media, Particularly of Colloidal Metal solutions. Annalen der Physik, 25, 377-445. doi: https://doi.org/10.1002/andp.19083300302
  27. Wang, J., Nilsson, A.M., Barrios, D., Vargas, W.E., Wäckelgård, E., & Niklasson, G.A. (2020). Light scattering materials for energy-related applications: Determination of absorption and scattering coefficients. Materials Today: Proceedings, 33, 2474-2480. doi: https://doi.org/10.1016/j.matpr.2020.01.339
  28. Vargas, W.E., Wang, J., & Niklasson, G.A. (2020). Scattering and absorption cross sections of light diffusing materials retrieved from reflectance and transmittance spectra of collimated radiation. Journal of Modern Optics, 67(11), 974-991. doi: https://doi.org/10.1080/09500340.2020.1801872
  29. Vargas, W.E., Wang, J., & Niklasson, G.A. (2021). Effective backscattering and absorption coefficients of light diffusing materials retrieved from reflectance and transmittance spectra of diffuse radiation. Journal of Modern Optics, 68(12), 605-623. doi: https://doi.org/10.1080/09500340.2021.1936244
  30. Wang, J., & Niklasson, G.A. (2021). Extraction of light absorption and scattering coefficients of gold nanocomposites. Proceedings of the Bremen Zoom Workshop on Light Scattering. https://scattport.org/index.php/conferencesmenu/689-bremen-zoom-workshop-on-light-scattering-2021
  31. Vargas, W.E., Wang, J., & Niklasson, G.A. (2022). Inversion of light scattering experiments by using the four-flux theory. Proceedings of the Bremen Zoom Workshop on Light Scattering. https://scattport.org/index.php/conferencesmenu/715-bremen-zoom-workshop-on-light-scattering-2022
  32. Barrios, D. (2023). Forward scattering ratios, average crossing parameters and scattering and absorption coefficients new expressions using diffuse differential equations of four flux model. Proceedings of the Bremen Zoom Workshop on Light Scattering. https://scattport.org/index.php/programs-menu/multiple-particle-scattering-menu/739-scatteringworkshop-2023
  33. Barrios, D. (2023). Parameters of differential equations in four-flux models approximated for multilayers samples showing scattering and absorption. XX ELS Electromagnetic and Light Scattering Conference.
  34. Barrios, D. (2023). Parameters of differential equations in two-flux models approximated for multilayers samples showing scattering and absorption. XX ELS Electromagnetic and Light Scattering Conference.
  35. Barrios, D. (2023). Parameters of differential equations in four-flux and two-flux models approximated for scattering and absorption results on solar thermal collector black paints. XVIII Encuentro de Física. Escuela Politécnica Nacional.
  36. Barrios, D. (2023). Optical constants and thickness gradients for light intensities in glass substrate layers and for complex electric fields in indium tin oxide (ITO) transparent conductor thin film layer, using Bode and Nyquist wavelengthdependent diagrams. XVIII Encuentro Internacional de Física. Escuela Politécnica Nacional.
  37. Pfrommer, P., Lomas, K.J., Seale, C., & Kupke, C. (1995). The radiation transfer through coated and tinted glazing. Solar Energy, 54, 287-299. doi: https://doi.org/10.1016/0038-092X(94)00132-W
  38. Harbecke, B. (1986). Coherent and incoherent reflection and transmission of multi-layer structures. Appl. Phys. B, 39, 165-170. doi: https://doi.org/10.1007/BF00697414
  39. Barrios, D., Vergaz, R., Sanchez-Pena, J.M., Mihelcic, M., & Orel, B. (2012). Decoupling scattering and absorption coefficients of internal color active layers of an inorganic WO3 and NiO based electrochromic device at bleached and colored states. IME’10: International Meeting on Electrochromism.
  40. Barrios, D., & Álvarez, C. (2023). Spectral voltage contour plots of optical constants and interface parameters of the active layer of a multilayer structure suspended particle device smart window from clear on to dark off states. Orbital: Electron. J. Chem., 15(1), 8-20. doi: https://doi.org/10.17807/orbital.v15i1.16470