Abstract

The reflectance of a surface can be altered by controlling the concentration of dye ions in a region adjacent to an optically transparent and electrically conductive thin film. We present a method for nonmechanical light deflection achieved by altering the reflectance of a diffraction grating, an approach that creates new diffraction peaks that lie between those associated with the original grating spacing. We have demonstrated this effect by applying an electrical potential difference between interdigitated indium-tin oxide (ITO) electrodes and measuring the intensity of one of the new diffraction peaks. The measured diffraction peak intensities were found to reversibly deflect approximately 7% of the reflected light to previously nonexistent peaks. The diffraction grating was formed by patterning a thin film of planar, untreated ITO on a glass substrate using standard photolithography techniques. The size scale for this method of electrically controlled diffraction is limited only by the lithographic process; thus there is potential for the grating to deflect light to angles greater than those achievable using other methods. This approach could be used in applications such as telecommunications, where large deflection angles are required, or other applications where alternate beam-steering methods are cost prohibitive.

© 2013 Optical Society of America

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References

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2012

S. Roldan, M. Granda, R. Menendez, R. Santamaria, and C. Blanco, “Supercapacitor modified with methylene blue as redox active electrolyte,” Electrochim. Acta 83, 241–246 (2012).
[CrossRef]

2011

S. Valyukh, I. Valyukh, and V. Chigrinov, “Liquid-crystal based light steering optical elements,” Photon. Lett. Pol. 3, 88–90 (2011).
[CrossRef]

2009

P. Tafulo, R. Queiros, and G. Gonzalez-Aguilar, “On the ‘concentration-driven’ methylene blue dimerization,” Spectrochim. Acta Part A 73, 295–300 (2009).
[CrossRef]

2007

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007).
[CrossRef]

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

2006

E. Frackowiak, V. Khomenko, K. Jurewicz, K. Lota, and F. Beguin, “Supercapacitors based on conducting polymers/nanotubes composites,” J. Power Sources 153, 413–418 (2006).
[CrossRef]

2005

2004

P. Kurzweil and H. Fischle, “A new monitoring method for electrochemical aggregates by impedance spectroscopy,” J. Power Sources 127, 331–340 (2004).
[CrossRef]

2002

V. Kwong, M. Mossman, and L. Whitehead, “Electrical modulation of diffractive structures,” Appl. Opt. 41, 3343–3347 (2002).
[CrossRef]

P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002).
[CrossRef]

2001

V. Nikulin, M. Bouzoubaa, V. Skormin, and T. Busch, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40, 2208–2214 (2001).
[CrossRef]

1999

G. Keiser, “A review of WDM technology and applications,” Opt. Fiber Technol. 5, 3–39 (1999).
[CrossRef]

1996

1993

J. Younse, “Mirrors on a chip,” IEEE Spectrum 30, 27–31 (1993).
[CrossRef]

1991

B. Conway, “Transition from ‘supercapacitor’ to ‘battery’ behavior in electrochemical energy storage,” J. Electrochem. Soc. 138, 1539–1548 (1991).
[CrossRef]

1988

J. Cenens and R. Schoonheydt, “Visible spectroscopy of methylene blue on hectorite, laponite B, and barasym in aqueous suspension,” Clays Clay Miner. 36, 214–224 (1988).
[CrossRef]

1978

P. Murau, “The understanding and elimination of some suspension instabilities in an electrophoretic display,” J. Appl. Phys. 49, 4820–4829 (1978).
[CrossRef]

Bard, A.

A. Bard and L. Faulkner, “Introduction and overview of electrode processes,” in Electrochemical Methods: Fundamentals and Applications, D. Harris, E. Swain, C. Robey, and E. Aiello, eds. (Wiley, 2001), pp. 1–43.

Beguin, F.

E. Frackowiak, V. Khomenko, K. Jurewicz, K. Lota, and F. Beguin, “Supercapacitors based on conducting polymers/nanotubes composites,” J. Power Sources 153, 413–418 (2006).
[CrossRef]

Blanco, C.

S. Roldan, M. Granda, R. Menendez, R. Santamaria, and C. Blanco, “Supercapacitor modified with methylene blue as redox active electrolyte,” Electrochim. Acta 83, 241–246 (2012).
[CrossRef]

Born, M.

M. Born and E. Wolf, “Geometrical theory of optical imaging,” in Principles of Optics (Cambridge University, 1999), pp. 218–219.

Bouzoubaa, M.

V. Nikulin, M. Bouzoubaa, V. Skormin, and T. Busch, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40, 2208–2214 (2001).
[CrossRef]

Brett, M.

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007).
[CrossRef]

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

Busch, T.

V. Nikulin, M. Bouzoubaa, V. Skormin, and T. Busch, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40, 2208–2214 (2001).
[CrossRef]

Cenens, J.

J. Cenens and R. Schoonheydt, “Visible spectroscopy of methylene blue on hectorite, laponite B, and barasym in aqueous suspension,” Clays Clay Miner. 36, 214–224 (1988).
[CrossRef]

Chao, T.

T. Chao, J. Hanan, G. Reyes, and H. Zhou, “Holographic memory using beam steering,” U.S. Patent7251066 B2 (31July2007).

Chigrinov, V.

S. Valyukh, I. Valyukh, and V. Chigrinov, “Liquid-crystal based light steering optical elements,” Photon. Lett. Pol. 3, 88–90 (2011).
[CrossRef]

Clark, A.

A. Clark, “A variable spacing diffraction grating created with elastomeric surface waves,” M.Sc. thesis (University of British Columbia, 1997).

Conway, B.

B. Conway, “Transition from ‘supercapacitor’ to ‘battery’ behavior in electrochemical energy storage,” J. Electrochem. Soc. 138, 1539–1548 (1991).
[CrossRef]

Dorschner, T.

Dunbar, T.

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

Faulkner, L.

A. Bard and L. Faulkner, “Introduction and overview of electrode processes,” in Electrochemical Methods: Fundamentals and Applications, D. Harris, E. Swain, C. Robey, and E. Aiello, eds. (Wiley, 2001), pp. 1–43.

Fischle, H.

P. Kurzweil and H. Fischle, “A new monitoring method for electrochemical aggregates by impedance spectroscopy,” J. Power Sources 127, 331–340 (2004).
[CrossRef]

Frackowiak, E.

E. Frackowiak, V. Khomenko, K. Jurewicz, K. Lota, and F. Beguin, “Supercapacitors based on conducting polymers/nanotubes composites,” J. Power Sources 153, 413–418 (2006).
[CrossRef]

Friedman, L.

Gonzalez-Aguilar, G.

P. Tafulo, R. Queiros, and G. Gonzalez-Aguilar, “On the ‘concentration-driven’ methylene blue dimerization,” Spectrochim. Acta Part A 73, 295–300 (2009).
[CrossRef]

Granda, M.

S. Roldan, M. Granda, R. Menendez, R. Santamaria, and C. Blanco, “Supercapacitor modified with methylene blue as redox active electrolyte,” Electrochim. Acta 83, 241–246 (2012).
[CrossRef]

Hanan, J.

T. Chao, J. Hanan, G. Reyes, and H. Zhou, “Holographic memory using beam steering,” U.S. Patent7251066 B2 (31July2007).

Hecht, E.

E. Hecht, “Diffraction,” in Optics, 4th ed. (Addison Wesley, 2002), pp. 443–518.

Hobbs, D.

Hrudey, P.

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007).
[CrossRef]

Huizinga, J.

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007).
[CrossRef]

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

Jurewicz, K.

E. Frackowiak, V. Khomenko, K. Jurewicz, K. Lota, and F. Beguin, “Supercapacitors based on conducting polymers/nanotubes composites,” J. Power Sources 153, 413–418 (2006).
[CrossRef]

Keiser, G.

G. Keiser, “A review of WDM technology and applications,” Opt. Fiber Technol. 5, 3–39 (1999).
[CrossRef]

Khomenko, V.

E. Frackowiak, V. Khomenko, K. Jurewicz, K. Lota, and F. Beguin, “Supercapacitors based on conducting polymers/nanotubes composites,” J. Power Sources 153, 413–418 (2006).
[CrossRef]

Kurzweil, P.

P. Kurzweil and H. Fischle, “A new monitoring method for electrochemical aggregates by impedance spectroscopy,” J. Power Sources 127, 331–340 (2004).
[CrossRef]

Kwong, V.

Lin, K.

P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002).
[CrossRef]

Lota, K.

E. Frackowiak, V. Khomenko, K. Jurewicz, K. Lota, and F. Beguin, “Supercapacitors based on conducting polymers/nanotubes composites,” J. Power Sources 153, 413–418 (2006).
[CrossRef]

Lubensky, T.

P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002).
[CrossRef]

Mach, P.

P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002).
[CrossRef]

Martinuk, M.

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007).
[CrossRef]

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

Megens, M.

P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002).
[CrossRef]

Menendez, R.

S. Roldan, M. Granda, R. Menendez, R. Santamaria, and C. Blanco, “Supercapacitor modified with methylene blue as redox active electrolyte,” Electrochim. Acta 83, 241–246 (2012).
[CrossRef]

Mossman, M.

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007).
[CrossRef]

M. Mossman and L. Whitehead, “Controlled frustration of total internal reflection by electrophoresis of pigment particles,” Appl. Opt. 44, 1601–1609 (2005).
[CrossRef]

V. Kwong, M. Mossman, and L. Whitehead, “Electrical modulation of diffractive structures,” Appl. Opt. 41, 3343–3347 (2002).
[CrossRef]

Murau, P.

P. Murau, “The understanding and elimination of some suspension instabilities in an electrophoretic display,” J. Appl. Phys. 49, 4820–4829 (1978).
[CrossRef]

Nikulin, V.

V. Nikulin, M. Bouzoubaa, V. Skormin, and T. Busch, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40, 2208–2214 (2001).
[CrossRef]

Queiros, R.

P. Tafulo, R. Queiros, and G. Gonzalez-Aguilar, “On the ‘concentration-driven’ methylene blue dimerization,” Spectrochim. Acta Part A 73, 295–300 (2009).
[CrossRef]

Resler, D.

Reyes, G.

T. Chao, J. Hanan, G. Reyes, and H. Zhou, “Holographic memory using beam steering,” U.S. Patent7251066 B2 (31July2007).

Roldan, S.

S. Roldan, M. Granda, R. Menendez, R. Santamaria, and C. Blanco, “Supercapacitor modified with methylene blue as redox active electrolyte,” Electrochim. Acta 83, 241–246 (2012).
[CrossRef]

Santamaria, R.

S. Roldan, M. Granda, R. Menendez, R. Santamaria, and C. Blanco, “Supercapacitor modified with methylene blue as redox active electrolyte,” Electrochim. Acta 83, 241–246 (2012).
[CrossRef]

Schoonheydt, R.

J. Cenens and R. Schoonheydt, “Visible spectroscopy of methylene blue on hectorite, laponite B, and barasym in aqueous suspension,” Clays Clay Miner. 36, 214–224 (1988).
[CrossRef]

Sharp, R.

Skormin, V.

V. Nikulin, M. Bouzoubaa, V. Skormin, and T. Busch, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40, 2208–2214 (2001).
[CrossRef]

Tafulo, P.

P. Tafulo, R. Queiros, and G. Gonzalez-Aguilar, “On the ‘concentration-driven’ methylene blue dimerization,” Spectrochim. Acta Part A 73, 295–300 (2009).
[CrossRef]

Valyukh, I.

S. Valyukh, I. Valyukh, and V. Chigrinov, “Liquid-crystal based light steering optical elements,” Photon. Lett. Pol. 3, 88–90 (2011).
[CrossRef]

Valyukh, S.

S. Valyukh, I. Valyukh, and V. Chigrinov, “Liquid-crystal based light steering optical elements,” Photon. Lett. Pol. 3, 88–90 (2011).
[CrossRef]

van Popta, A.

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007).
[CrossRef]

Weitz, D.

P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002).
[CrossRef]

Whitehead, L.

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, J. Huizinga, and L. Whitehead, “Variable diffraction gratings using nanoporous electrodes and electrophoresis of dye ions,” Proc. SPIE 6645, 66450K (2007).
[CrossRef]

P. Hrudey, M. Martinuk, M. Mossman, A. van Popta, M. Brett, T. Dunbar, J. Huizinga, and L. Whitehead, “Application of transparent nanostructured electrodes for modulation of total internal reflection,” Proc. SPIE 6647, 66470A (2007).
[CrossRef]

M. Mossman and L. Whitehead, “Controlled frustration of total internal reflection by electrophoresis of pigment particles,” Appl. Opt. 44, 1601–1609 (2005).
[CrossRef]

V. Kwong, M. Mossman, and L. Whitehead, “Electrical modulation of diffractive structures,” Appl. Opt. 41, 3343–3347 (2002).
[CrossRef]

Wiltzius, P.

P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, “Geometrical theory of optical imaging,” in Principles of Optics (Cambridge University, 1999), pp. 218–219.

Wong, R.

R. Wong, “Sub-micron pitch variable diffraction grating using nanoporous electrodes and electrophoresis of dye ions,” M.A.Sc. thesis (University of British Columbia, 2009).

Yodh, A.

P. Mach, P. Wiltzius, M. Megens, D. Weitz, K. Lin, T. Lubensky, and A. Yodh, “Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,” Phys. Rev. E 65, 031720 (2002).
[CrossRef]

Younse, J.

J. Younse, “Mirrors on a chip,” IEEE Spectrum 30, 27–31 (1993).
[CrossRef]

Zhou, H.

T. Chao, J. Hanan, G. Reyes, and H. Zhou, “Holographic memory using beam steering,” U.S. Patent7251066 B2 (31July2007).

Appl. Opt.

Clays Clay Miner.

J. Cenens and R. Schoonheydt, “Visible spectroscopy of methylene blue on hectorite, laponite B, and barasym in aqueous suspension,” Clays Clay Miner. 36, 214–224 (1988).
[CrossRef]

Electrochim. Acta

S. Roldan, M. Granda, R. Menendez, R. Santamaria, and C. Blanco, “Supercapacitor modified with methylene blue as redox active electrolyte,” Electrochim. Acta 83, 241–246 (2012).
[CrossRef]

IEEE Spectrum

J. Younse, “Mirrors on a chip,” IEEE Spectrum 30, 27–31 (1993).
[CrossRef]

J. Appl. Phys.

P. Murau, “The understanding and elimination of some suspension instabilities in an electrophoretic display,” J. Appl. Phys. 49, 4820–4829 (1978).
[CrossRef]

J. Electrochem. Soc.

B. Conway, “Transition from ‘supercapacitor’ to ‘battery’ behavior in electrochemical energy storage,” J. Electrochem. Soc. 138, 1539–1548 (1991).
[CrossRef]

J. Power Sources

E. Frackowiak, V. Khomenko, K. Jurewicz, K. Lota, and F. Beguin, “Supercapacitors based on conducting polymers/nanotubes composites,” J. Power Sources 153, 413–418 (2006).
[CrossRef]

P. Kurzweil and H. Fischle, “A new monitoring method for electrochemical aggregates by impedance spectroscopy,” J. Power Sources 127, 331–340 (2004).
[CrossRef]

Opt. Eng.

V. Nikulin, M. Bouzoubaa, V. Skormin, and T. Busch, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40, 2208–2214 (2001).
[CrossRef]

Opt. Fiber Technol.

G. Keiser, “A review of WDM technology and applications,” Opt. Fiber Technol. 5, 3–39 (1999).
[CrossRef]

Opt. Lett.

Photon. Lett. Pol.

S. Valyukh, I. Valyukh, and V. Chigrinov, “Liquid-crystal based light steering optical elements,” Photon. Lett. Pol. 3, 88–90 (2011).
[CrossRef]

Phys. Rev. E

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Figures (12)

Fig. 1.
Fig. 1.

Schematic for two interdigitated electrodes, where conductive transparent film is shown in black.

Fig. 2.
Fig. 2.

Electrically controlled diffraction using controlled TIR. Light strikes the glass/liquid and electrode/liquid interfaces at the critical angle and undergoes TIR. In (a) the reflected light diffracts to angles associated with the spatial periodicity of the interdigitated electrodes. In (b) a potential is applied between the interdigitated electrodes, which changes the reflectance from the interdigitated electrodes, and new diffraction peaks are created that depend on twice the spatial periodicity of the interdigitated electrodes.

Fig. 3.
Fig. 3.

Top view of the pattern of interdigitated ITO electrodes (shown in black) made using lithography on glass. White space represents glass, i.e., places where ITO has been removed by a lithographic etch process.

Fig. 4.
Fig. 4.

Side view of the diffraction grating cell and prism. The ITO-coated glass with the interdigitated pattern is on top with the glass holding the large surface-area ITO electrode beneath it. The two different glass pieces are separated by spacer beads and edge-sealed with silicone adhesive.

Fig. 5.
Fig. 5.

Schematic representation of the system used to apply voltages (not to scale). Voltages applied to the two interdigitated electrodes, with respect to the grounded counter-electrode, were equal and opposite. The current to each electrode was monitored by measuring the voltage across the 900 Ω series resistors.

Fig. 6.
Fig. 6.

Voltage sequence applied to one of two interdigitated ITO electrodes. Each voltage level was applied for 0.5 s and was followed by an 80 s period during which all electrodes were electrically connected to allow the system to return to its original state.

Fig. 7.
Fig. 7.

Gray-scale digital photograph of the diffraction pattern from the diffraction grating cell.

Fig. 8.
Fig. 8.

Intensity of the new first order diffraction peak normalized to the total light striking the grating in response to the applied voltage sequence shown in Fig. 6. The intensity of the diffraction peak remains near zero at applied potentials below 0.6 V. The greatest intensity corresponds to 0.75% of the light incident on the grating, or equivalently 3.4% of the total light reflecting from the grating.

Fig. 9.
Fig. 9.

Equivalent circuit representation for an electrolytic capacitor. The series resistance primarily depends on the resistance of the electrolyte. The parallel resistance, sometimes referred to as the leakage resistance, depends on several factors such as chemical reaction rates and mass transfer rates.

Fig. 10.
Fig. 10.

Conceptual depiction of model used to calculate the diffraction peak intensities when the cell was filled with air. The width and thickness of the ITO comprising the interdigitated electrodes (labeled “ITO Width” and “ITO Thickness,” respectively) were set to match the experimentally observed diffraction pattern.

Fig. 11.
Fig. 11.

Conceptual depiction of setup used to calculate the diffraction peak intensities for the case where the cell was filled with a solution consisting of 1.317·1026molecules/m3 MB dissolved in water. The imaginary component of the solution (labeled κ1) was set to match the experimentally observed diffraction pattern.

Fig. 12.
Fig. 12.

Conceptual depiction of setup used to calculate the diffraction peak intensity with an electrode energized. In this case, the total diffraction grating spacing is 20 μm. The imaginary component of the solution surrounding one of the two interdigitated electrodes (labeled κ2) and the thickness of this layer were set to match the experimentally observed diffraction pattern.

Tables (3)

Tables Icon

Table 1. Charge Transfer through the Two-Electrode Electrolytic Cella

Tables Icon

Table 2. Measured Diffraction Peak Intensities versus Calculated Intensities and the Differences between These Values (Δ) for the Cell Filled with Aira

Tables Icon

Table 3. Measured Diffraction Peak Intensities versus Calculated Diffraction Peak Intensities and the Differences between These Values (Δ) for the Cell Filled with 1.317·1026molecules/m3 of MB Dissolved in Watera

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

λD=εoεrkBT2qe2I,
C=εoεrAλD,
θc=asin(n2n1),
Rs=|n1Cos(θi)n21(n1n2Sin(θi))2n1Cos(θi)+n21(n1n2Sin(θi))2|2,
κ=ρσλo4π,

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