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Transparent and superhydrophobic Ta2O5 nanostructured thin films |
Optical Materials Express, Vol. 2, Issue 2, pp. 214-221 (2012)
http://dx.doi.org/10.1364/OME.2.000214
Acrobat PDF (1162 KB)
Abstract
Transparent Ta2O5 nanostructured thin films have been fabricated using a multi-step anodization process. Obtained by a combination of the nanostructured surface and the deposition of the hydrophobic CFx coating, the transparent films can be made highly water repellent or superhydrophobic useful for self-cleaning and anti-fogging optical coatings. Contact angle measurements and optical transmittance curves of the nanostructured films are in good agreement with theoretical calculations.
© 2012 OSA
1. Introduction
W. Barthlott and C. Neinhuis, “Purity of the sacred lotus, or escape from contamination in biological surfaces,” Planta 202(1), 1–8 (1997). [CrossRef]
L. Mishchenko, B. Hatton, V. Bahadur, J. A. Taylor, T. Krupenkin, and J. Aizenberg, “Design of ice-free nanostructured surfaces based on repulsion of impacting water droplets,” ACS Nano 4(12), 7699–7707 (2010). [CrossRef] [PubMed]
K. Tadanaga, N. Katata, and T. Minami, “Formation process of super-water-repellent Al2O3 coating films with high transparency by the sol-gel method,” J. Am. Ceram. Soc. 80(12), 3213–3216 (1997). [CrossRef]
M. Im, H. Im, J. H. Lee, J. B. Yoon, and Y. K. Choi, “A robust superhydrophobic and superoleophobic surface with inverse-trapezoidal microstructures on a large transparent flexible substrate,” Soft Matter 6(7), 1401–1404 (2010). [CrossRef]
S. J. Ingrey, W. D. Westwood, Y. C. Cheng, and J. Wei, “Variable refractive index and birefringent waveguides by sputtering tantalum in O2-N2 mixtures,” Appl. Opt. 14(9), 2194–2198 (1975). [CrossRef] [PubMed]
K. Schmitt, K. Oehse, G. Sulz, and C. Hoffmann, “Evanescent field sensors based on tantalum pentoxide waveguides–a review,” Sensors (Basel Switzerland) 8(2), 711–738 (2008). [CrossRef]
D. Husted, L. Gruss, and T. Mackus, “Electrical properties of anodic oxide films of Ta, Nb, Zr, Ti, W, and V formed by the ion‐cathode method,” J. Electrochem. Soc. 118(12), 1989–1992 (1971). [CrossRef]
L. Young, “The determination of the thickness, dielectric constant, and other properties of anodic oxide films on tantalum from the interference colours,” Proc. R. Soc. A 244(1236), 41–53 (1958). [CrossRef]
C. Chaneliere, J. L. Autran, R. A. B. Devine, and B. Balland, “Tantalum pentoxide (Ta2O5) thin films for advanced dielectric applications,” Mater. Sci. Eng. Rep. 22(6), 269–322 (1998). [CrossRef]
2. Experimental section
A. Mozalev, M. Sakairi, I. Saeki, and H. Takahashi, “Nucleation and growth of the nanostructured anodic oxides on tantalum and niobium under the porous alumina film,” Electrochim. Acta 48(20-22), 3155–3170 (2003). [CrossRef]
A. Mozalev, A. J. Smith, S. Borodin, A. Plihauka, A. W. Hassel, M. Sakairi, and H. Takahashi, “Growth of multioxide planar film with the nanoscale inner structure via anodizing Al/Ta layers on Si,” Electrochim. Acta 54(3), 935–945 (2009). [CrossRef]
3. Results and discussion
T. N. Krupenkin, J. A. Taylor, T. M. Schneider, and S. Yang, “From rolling ball to complete wetting: the dynamic tuning of liquids on nanostructured surfaces,” Langmuir 20(10), 3824–3827 (2004). [CrossRef] [PubMed]
G. McHale, N. J. Shirtcliffe, and M. I. Newton, “Contact-angle hysteresis on super-hydrophobic surfaces,” Langmuir 20(23), 10146–10149 (2004). [CrossRef] [PubMed]
A. B. D. Cassie and S. Baxter, “Wettability of porous surfaces,” Trans. Faraday Soc. 40, 546–551 (1944). [CrossRef]
D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935). [CrossRef]
D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935). [CrossRef]
4. Conclusion
Acknowledgments
References and links
W. Barthlott and C. Neinhuis, “Purity of the sacred lotus, or escape from contamination in biological surfaces,” Planta 202(1), 1–8 (1997). [CrossRef] | |
L. Mishchenko, B. Hatton, V. Bahadur, J. A. Taylor, T. Krupenkin, and J. Aizenberg, “Design of ice-free nanostructured surfaces based on repulsion of impacting water droplets,” ACS Nano 4(12), 7699–7707 (2010). [CrossRef] [PubMed] | |
K. Tadanaga, N. Katata, and T. Minami, “Formation process of super-water-repellent Al2O3 coating films with high transparency by the sol-gel method,” J. Am. Ceram. Soc. 80(12), 3213–3216 (1997). [CrossRef] | |
A. Nakajima, A. Fujishima, K. Hashimoto, and T. Watanabe, “Preparation of transparent superhydrophobic boehmite and silica films by sublimation of aluminum acetylacetonate,” Adv. Mater. (Deerfield Beach Fla.) 11(16), 1365–1368 (1999). [CrossRef] | |
M. Miwa, A. Nakajima, A. Fujishima, K. Hashimoto, and T. Watanabe, “Effects of the surface roughness on sliding angles of water droplets on superhydrophobic surfaces,” Langmuir 16(13), 5754–5760 (2000). [CrossRef] | |
A. Nakajima, K. Hashimoto, T. Watanabe, K. Takai, G. Yamauchi, and A. Fujishima, “Transparent superhydrophobic thin films with self-cleaning properties,” Langmuir 16(17), 7044–7047 (2000). [CrossRef] | |
K. Tadanaga, J. Morinaga, A. Matsuda, and T. Minami, “Superhydrophobic-superhydrophilic micropatterning on flowerlike alumina coating film by the sol-gel method,” Chem. Mater. 12(3), 590–592 (2000). [CrossRef] | |
H. M. Shang, Y. Wang, S. J. Limmer, T. P. Chou, K. Takahashi, and G. Z. Cao, “Optically transparent superhydrophobic silica-based films,” Thin Solid Films 472(1-2), 37–43 (2005). [CrossRef] | |
H. Yabu and M. Shimomura, “Single-step fabrication of transparent superhydrophobic porous polymer films,” Chem. Mater. 17(21), 5231–5234 (2005). [CrossRef] | |
J. Fresnais, J. P. Chapel, and F. Poncin-Epaillard, “Synthesis of transparent superhydrophobic polyethylene surfaces,” Surf. Coat. Tech. 200(18-19), 5296–5305 (2006). [CrossRef] | |
M. Kemell, E. Färm, M. Leskelä, and M. Ritala, “Transparent superhydrophobic surfaces by self‐assembly of hydrophobic monolayers on nanostructured surfaces,” Phys. Status Solidi A 203(6), 1453–1458 (2006). [CrossRef] | |
C. Su, J. Li, H. Geng, Q. Wang, and Q. Chen, “Fabrication of an optically transparent super-hydrophobic surface via embedding nano-silica,” Appl. Surf. Sci. 253(5), 2633–2636 (2006). [CrossRef] | |
J. Bravo, L. Zhai, Z. Wu, R. E. Cohen, and M. F. Rubner, “Transparent superhydrophobic films based on silica nanoparticles,” Langmuir 23(13), 7293–7298 (2007). [CrossRef] [PubMed] | |
N. Vourdas, A. Tserepi, and E. Gogolides, “Nanotextured super-hydrophobic transparent poly (methyl methacrylate) surfaces using high-density plasma processing,” Nanotechnology 18(12), 125304 (2007). [CrossRef] | |
X. Zhang, H. Kono, Z. Liu, S. Nishimoto, D. A. Tryk, T. Murakami, H. Sakai, M. Abe, and A. Fujishima, “A transparent and photo-patternable superhydrophobic film,” Chem. Commun. (Camb.) (46): 4949–4951 (2007). [CrossRef] [PubMed] | |
K. C. Chang, Y. K. Chen, and H. Chen, “Fabrication of highly transparent and superhydrophobic silica-based surface by TEOS/PPG hybrid with adjustment of the pH value,” Surf. Coat. Tech. 202(16), 3822–3831 (2008). [CrossRef] | |
J. T. Han, S. Y. Kim, J. S. Woo, and G. W. Lee, “Transparent, conductive, and superhydrophobic films from stabilized carbon nanotube/silane sol mixture solution,” Adv. Mater. (Deerfield Beach Fla.) 20(19), 3724–3727 (2008). [CrossRef] | |
Q. F. Xu, J. N. Wang, I. H. Smith, and K. D. Sanderson, “Superhydrophobic and transparent coatings based on removable polymeric spheres,” J. Mater. Chem. 19(5), 655–660 (2009). [CrossRef] | |
Y. Li, F. Liu, and J. Sun, “A facile layer-by-layer deposition process for the fabrication of highly transparent superhydrophobic coatings,” Chem. Commun. (Camb.) (19): 2730–2732 (2009). [CrossRef] [PubMed] | |
X. Y. Ling, I. Y. Phang, G. J. Vancso, J. Huskens, and D. N. Reinhoudt, “Stable and transparent superhydrophobic nanoparticle films,” Langmuir 25(5), 3260–3263 (2009). [CrossRef] [PubMed] | |
A. Venkateswara Rao, S. S. Latthe, D. Y. Nadargi, H. Hirashima, and V. Ganesan, “Preparation of MTMS based transparent superhydrophobic silica films by sol-gel method,” J. Colloid Interface Sci. 332(2), 484–490 (2009). [CrossRef] [PubMed] | |
J. Yang, Z. Zhang, X. Men, and X. Xu, “Fabrication of stable, transparent and superhydrophobic nanocomposite films with polystyrene functionalized carbon nanotubes,” Appl. Surf. Sci. 255(22), 9244–9247 (2009). [CrossRef] | |
M. Im, H. Im, J. H. Lee, J. B. Yoon, and Y. K. Choi, “A robust superhydrophobic and superoleophobic surface with inverse-trapezoidal microstructures on a large transparent flexible substrate,” Soft Matter 6(7), 1401–1404 (2010). [CrossRef] | |
S. J. Ingrey, W. D. Westwood, Y. C. Cheng, and J. Wei, “Variable refractive index and birefringent waveguides by sputtering tantalum in O2-N2 mixtures,” Appl. Opt. 14(9), 2194–2198 (1975). [CrossRef] [PubMed] | |
F. Z. Tepehan, F. E. Ghodsi, N. Ozer, and G. G. Tepehan, “Optical properties of sol–gel dip-coated Ta2O5 films for electrochromic applications,” Sol. Energy Mater. Sol. Cells 59(3), 265–275 (1999). [CrossRef] | |
W. Cheng, S. Chi, and A. Chu, “Effect of thermal stresses on temperature dependence of refractive index for Ta2O5 dielectric films,” Thin Solid Films 347(1-2), 233–237 (1999). [CrossRef] | |
K. Schmitt, K. Oehse, G. Sulz, and C. Hoffmann, “Evanescent field sensors based on tantalum pentoxide waveguides–a review,” Sensors (Basel Switzerland) 8(2), 711–738 (2008). [CrossRef] | |
P. Patnaik, Handbook of Inorganic Chemicals (McGraw-Hill, 2003). | |
W. Martienssen and H. Warlimont, Springer Handbook of Condensed Matter and Materials Data (Springer, 2005). | |
D. Husted, L. Gruss, and T. Mackus, “Electrical properties of anodic oxide films of Ta, Nb, Zr, Ti, W, and V formed by the ion‐cathode method,” J. Electrochem. Soc. 118(12), 1989–1992 (1971). [CrossRef] | |
L. Young, “The determination of the thickness, dielectric constant, and other properties of anodic oxide films on tantalum from the interference colours,” Proc. R. Soc. A 244(1236), 41–53 (1958). [CrossRef] | |
C. Chaneliere, J. L. Autran, R. A. B. Devine, and B. Balland, “Tantalum pentoxide (Ta2O5) thin films for advanced dielectric applications,” Mater. Sci. Eng. Rep. 22(6), 269–322 (1998). [CrossRef] | |
A. Mozalev, M. Sakairi, I. Saeki, and H. Takahashi, “Nucleation and growth of the nanostructured anodic oxides on tantalum and niobium under the porous alumina film,” Electrochim. Acta 48(20-22), 3155–3170 (2003). [CrossRef] | |
C. Wu, F. Ko, and H. Hwang, “Self-aligned tantalum oxide nanodot arrays through anodic alumina template,” Microelectron. Eng. 83(4-9), 1567–1570 (2006). [CrossRef] | |
A. Mozalev, A. J. Smith, S. Borodin, A. Plihauka, A. W. Hassel, M. Sakairi, and H. Takahashi, “Growth of multioxide planar film with the nanoscale inner structure via anodizing Al/Ta layers on Si,” Electrochim. Acta 54(3), 935–945 (2009). [CrossRef] | |
T. N. Krupenkin, J. A. Taylor, T. M. Schneider, and S. Yang, “From rolling ball to complete wetting: the dynamic tuning of liquids on nanostructured surfaces,” Langmuir 20(10), 3824–3827 (2004). [CrossRef] [PubMed] | |
G. McHale, N. J. Shirtcliffe, and M. I. Newton, “Contact-angle hysteresis on super-hydrophobic surfaces,” Langmuir 20(23), 10146–10149 (2004). [CrossRef] [PubMed] | |
A. B. D. Cassie and S. Baxter, “Wettability of porous surfaces,” Trans. Faraday Soc. 40, 546–551 (1944). [CrossRef] | |
D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. 416(7), 636–664 (1935). [CrossRef] |
OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(310.0310) Thin films : Thin films
(220.4241) Optical design and fabrication : Nanostructure fabrication
ToC Category:
Nanomaterials
History
Original Manuscript: December 12, 2011
Revised Manuscript: January 19, 2012
Manuscript Accepted: January 23, 2012
Published: January 25, 2012
Citation
Supone Manakasettharn, Tsung-Hsing Hsu, Graham Myhre, Stanley Pau, J. Ashley Taylor, and Tom Krupenkin, "Transparent and superhydrophobic Ta2O5 nanostructured thin films," Opt. Mater. Express 2, 214-221 (2012)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-2-2-214
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References
- W. Barthlott and C. Neinhuis, “Purity of the sacred lotus, or escape from contamination in biological surfaces,” Planta202(1), 1–8 (1997). [CrossRef]
- L. Mishchenko, B. Hatton, V. Bahadur, J. A. Taylor, T. Krupenkin, and J. Aizenberg, “Design of ice-free nanostructured surfaces based on repulsion of impacting water droplets,” ACS Nano4(12), 7699–7707 (2010). [CrossRef] [PubMed]
- K. Tadanaga, N. Katata, and T. Minami, “Formation process of super-water-repellent Al2O3 coating films with high transparency by the sol-gel method,” J. Am. Ceram. Soc.80(12), 3213–3216 (1997). [CrossRef]
- A. Nakajima, A. Fujishima, K. Hashimoto, and T. Watanabe, “Preparation of transparent superhydrophobic boehmite and silica films by sublimation of aluminum acetylacetonate,” Adv. Mater. (Deerfield Beach Fla.)11(16), 1365–1368 (1999). [CrossRef]
- M. Miwa, A. Nakajima, A. Fujishima, K. Hashimoto, and T. Watanabe, “Effects of the surface roughness on sliding angles of water droplets on superhydrophobic surfaces,” Langmuir16(13), 5754–5760 (2000). [CrossRef]
- A. Nakajima, K. Hashimoto, T. Watanabe, K. Takai, G. Yamauchi, and A. Fujishima, “Transparent superhydrophobic thin films with self-cleaning properties,” Langmuir16(17), 7044–7047 (2000). [CrossRef]
- K. Tadanaga, J. Morinaga, A. Matsuda, and T. Minami, “Superhydrophobic-superhydrophilic micropatterning on flowerlike alumina coating film by the sol-gel method,” Chem. Mater.12(3), 590–592 (2000). [CrossRef]
- H. M. Shang, Y. Wang, S. J. Limmer, T. P. Chou, K. Takahashi, and G. Z. Cao, “Optically transparent superhydrophobic silica-based films,” Thin Solid Films472(1-2), 37–43 (2005). [CrossRef]
- H. Yabu and M. Shimomura, “Single-step fabrication of transparent superhydrophobic porous polymer films,” Chem. Mater.17(21), 5231–5234 (2005). [CrossRef]
- J. Fresnais, J. P. Chapel, and F. Poncin-Epaillard, “Synthesis of transparent superhydrophobic polyethylene surfaces,” Surf. Coat. Tech.200(18-19), 5296–5305 (2006). [CrossRef]
- M. Kemell, E. Färm, M. Leskelä, and M. Ritala, “Transparent superhydrophobic surfaces by self‐assembly of hydrophobic monolayers on nanostructured surfaces,” Phys. Status Solidi A203(6), 1453–1458 (2006). [CrossRef]
- C. Su, J. Li, H. Geng, Q. Wang, and Q. Chen, “Fabrication of an optically transparent super-hydrophobic surface via embedding nano-silica,” Appl. Surf. Sci.253(5), 2633–2636 (2006). [CrossRef]
- J. Bravo, L. Zhai, Z. Wu, R. E. Cohen, and M. F. Rubner, “Transparent superhydrophobic films based on silica nanoparticles,” Langmuir23(13), 7293–7298 (2007). [CrossRef] [PubMed]
- N. Vourdas, A. Tserepi, and E. Gogolides, “Nanotextured super-hydrophobic transparent poly (methyl methacrylate) surfaces using high-density plasma processing,” Nanotechnology18(12), 125304 (2007). [CrossRef]
- X. Zhang, H. Kono, Z. Liu, S. Nishimoto, D. A. Tryk, T. Murakami, H. Sakai, M. Abe, and A. Fujishima, “A transparent and photo-patternable superhydrophobic film,” Chem. Commun. (Camb.) (46): 4949–4951 (2007). [CrossRef] [PubMed]
- K. C. Chang, Y. K. Chen, and H. Chen, “Fabrication of highly transparent and superhydrophobic silica-based surface by TEOS/PPG hybrid with adjustment of the pH value,” Surf. Coat. Tech.202(16), 3822–3831 (2008). [CrossRef]
- J. T. Han, S. Y. Kim, J. S. Woo, and G. W. Lee, “Transparent, conductive, and superhydrophobic films from stabilized carbon nanotube/silane sol mixture solution,” Adv. Mater. (Deerfield Beach Fla.)20(19), 3724–3727 (2008). [CrossRef]
- Q. F. Xu, J. N. Wang, I. H. Smith, and K. D. Sanderson, “Superhydrophobic and transparent coatings based on removable polymeric spheres,” J. Mater. Chem.19(5), 655–660 (2009). [CrossRef]
- Y. Li, F. Liu, and J. Sun, “A facile layer-by-layer deposition process for the fabrication of highly transparent superhydrophobic coatings,” Chem. Commun. (Camb.) (19): 2730–2732 (2009). [CrossRef] [PubMed]
- X. Y. Ling, I. Y. Phang, G. J. Vancso, J. Huskens, and D. N. Reinhoudt, “Stable and transparent superhydrophobic nanoparticle films,” Langmuir25(5), 3260–3263 (2009). [CrossRef] [PubMed]
- A. Venkateswara Rao, S. S. Latthe, D. Y. Nadargi, H. Hirashima, and V. Ganesan, “Preparation of MTMS based transparent superhydrophobic silica films by sol-gel method,” J. Colloid Interface Sci.332(2), 484–490 (2009). [CrossRef] [PubMed]
- J. Yang, Z. Zhang, X. Men, and X. Xu, “Fabrication of stable, transparent and superhydrophobic nanocomposite films with polystyrene functionalized carbon nanotubes,” Appl. Surf. Sci.255(22), 9244–9247 (2009). [CrossRef]
- M. Im, H. Im, J. H. Lee, J. B. Yoon, and Y. K. Choi, “A robust superhydrophobic and superoleophobic surface with inverse-trapezoidal microstructures on a large transparent flexible substrate,” Soft Matter6(7), 1401–1404 (2010). [CrossRef]
- S. J. Ingrey, W. D. Westwood, Y. C. Cheng, and J. Wei, “Variable refractive index and birefringent waveguides by sputtering tantalum in O2-N2 mixtures,” Appl. Opt.14(9), 2194–2198 (1975). [CrossRef] [PubMed]
- F. Z. Tepehan, F. E. Ghodsi, N. Ozer, and G. G. Tepehan, “Optical properties of sol–gel dip-coated Ta2O5 films for electrochromic applications,” Sol. Energy Mater. Sol. Cells59(3), 265–275 (1999). [CrossRef]
- W. Cheng, S. Chi, and A. Chu, “Effect of thermal stresses on temperature dependence of refractive index for Ta2O5 dielectric films,” Thin Solid Films347(1-2), 233–237 (1999). [CrossRef]
- K. Schmitt, K. Oehse, G. Sulz, and C. Hoffmann, “Evanescent field sensors based on tantalum pentoxide waveguides–a review,” Sensors (Basel Switzerland)8(2), 711–738 (2008). [CrossRef]
- P. Patnaik, Handbook of Inorganic Chemicals (McGraw-Hill, 2003).
- W. Martienssen and H. Warlimont, Springer Handbook of Condensed Matter and Materials Data (Springer, 2005).
- D. Husted, L. Gruss, and T. Mackus, “Electrical properties of anodic oxide films of Ta, Nb, Zr, Ti, W, and V formed by the ion‐cathode method,” J. Electrochem. Soc.118(12), 1989–1992 (1971). [CrossRef]
- L. Young, “The determination of the thickness, dielectric constant, and other properties of anodic oxide films on tantalum from the interference colours,” Proc. R. Soc. A244(1236), 41–53 (1958). [CrossRef]
- C. Chaneliere, J. L. Autran, R. A. B. Devine, and B. Balland, “Tantalum pentoxide (Ta2O5) thin films for advanced dielectric applications,” Mater. Sci. Eng. Rep.22(6), 269–322 (1998). [CrossRef]
- A. Mozalev, M. Sakairi, I. Saeki, and H. Takahashi, “Nucleation and growth of the nanostructured anodic oxides on tantalum and niobium under the porous alumina film,” Electrochim. Acta48(20-22), 3155–3170 (2003). [CrossRef]
- C. Wu, F. Ko, and H. Hwang, “Self-aligned tantalum oxide nanodot arrays through anodic alumina template,” Microelectron. Eng.83(4-9), 1567–1570 (2006). [CrossRef]
- A. Mozalev, A. J. Smith, S. Borodin, A. Plihauka, A. W. Hassel, M. Sakairi, and H. Takahashi, “Growth of multioxide planar film with the nanoscale inner structure via anodizing Al/Ta layers on Si,” Electrochim. Acta54(3), 935–945 (2009). [CrossRef]
- T. N. Krupenkin, J. A. Taylor, T. M. Schneider, and S. Yang, “From rolling ball to complete wetting: the dynamic tuning of liquids on nanostructured surfaces,” Langmuir20(10), 3824–3827 (2004). [CrossRef] [PubMed]
- G. McHale, N. J. Shirtcliffe, and M. I. Newton, “Contact-angle hysteresis on super-hydrophobic surfaces,” Langmuir20(23), 10146–10149 (2004). [CrossRef] [PubMed]
- A. B. D. Cassie and S. Baxter, “Wettability of porous surfaces,” Trans. Faraday Soc.40, 546–551 (1944). [CrossRef]
- H. Anders, ThinFilms in Optics (Focal Press, 1967).
- D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys.416(7), 636–664 (1935). [CrossRef]
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