Abstract

Through the study of particulate-silica-filled cross-linked natural rubber, an optical characteristic phenomenon involving a transition from transparency to opacity and reentry to transparency with an increase of silica loading is reported and examined using ultraviolet/visible spectroscopy and haze and diffusion transmittance measurements. Additionally, three-dimensional transmission electron microscopy observation and volume resistivity measurements reveal that the silica is in a networklike structure in the rubbery matrix. Combining these experimental results with a few theoretical considerations, the characteristic phenomenon is estimated to originate from the optical multiple scattering due to isolated chains of silica, which are present in the networklike structure of silica, but one end of which is not connected to the networks even after the percolated silica network is formed.

© 2008 Optical Society of America

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2008

S. Kohjiya, A. Kato, and Y. Ikeda, “Visualization of nano-filler dispersion and morphology in rubbery matrix by 3D-TEM,” in Current Topics on Elastomers Research, 2008, A.K.Bhomick, ed. (CRC Press, 2008), Chap. 19.

M. Nakamura, H. Yoden, H. Yokogawa, T. Yamaki, K. Takahama, and N. Tanio, “Refractive index prediction of optical cross-linked polymer,” Polymer Preprints, Japan 57, 1348 (2008).

2007

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

Y. Ikeda, Y. Yasuda, S. Yamamoto, and Y. Morita, “Study on two-dimensional small-angle x-ray scattering of in situ silica filled nanocomposite elastomer during deformation,” J. Appl. Crystallogr. 40, s549-s552 (2007).
[CrossRef]

A. Kato, S. Kohjiya, and Y. Ikeda, “Nanostructure in traditional composites of natural rubber and reinforcing silica,” Rubber Chem. Technol. 80, 690-700 (2007).
[CrossRef]

S. Miyazaki, H. Endo, T. Karino, K. Haraguchi, and M. Shibayama, “Gelation mechanism of poly(N-isopropylacrylamide)-clay nanocomposite gels,” Macromolecules 40, 4287-4295 (2007).
[CrossRef]

2006

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

Y.-Q. Li, S.-Y. Fu, and Y.-W. Mai, “Preparation and characterization of transparent ZnO/epoxy nanocomposites with high-UV shielding efficiency,” Polymer 47, 2127-2133 (2006).
[CrossRef]

S. Kohjiya, A. Kato, T. Suda, J. Shimanuki, and Y. Ikeda, “Visualisation of carbon black networks in rubbery matrix by 3D-TEM image,” Polymer 47, 3298-3301 (2006).
[CrossRef]

A. Kato, J. Shimanuki, S. Kohjiya, and Y. Ikeda, “Three-dimensional morphology of carbon black in NR vulcanizates as revealed by 3D-TEM and dielectric measurements,” Rubber Chem. Technol. 79, 653-673 (2006).
[CrossRef]

V. P. Kandidov, V. O. Milisin, A. V. Bykov, and A. V. Priezzhev, “Application of corpuscular and wave Monte-Carlo method in optics of dipersive media,” Quantum Electron. 36, 1003-1008 (2006).
[CrossRef]

2005

S. Kohjiya, A. Kato, J. Shimanuki, and Y. Ikeda, “Three-dimensional nano-structure of in situ silica in natural rubber as revealed by 3D-TEM/electron tomography,” Polymer 46, 4440-4446 (2005).
[CrossRef]

S. Kohjiya, A. Kato, J. Shimanuki, T. Hasegawa, and Y. Ikeda, “Nano-structural observation of carbon black dispersion in natural rubber matrix by three-dimensional transmission electron microscopy,” J. Mater. Sci. Lett. 40, 2553-2555 (2005).

K. Haraguchi, H.-J. Li, K. Matsuda, T. Takehisa, and E. Elliot, “Mechanism of forming organic/inorganic network structures during in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels,” Macromolecules 38, 3482-3490 (2005).
[CrossRef]

S. Schelm and G. B. Smith, “Tuning the surface-plasmon resonance in nanoparticles for glazing application,” J. Appl. Phys. 97, 124314 (2005).
[CrossRef]

S. Poompradub, S. Kohjiya, and Y. Ikeda, “Natural rubber/in situ silica nanocomposite of a high silica content,” Chem. Lett. 34, 672-673 (2005).
[CrossRef]

2004

Y. Ikeda and Y. Kameda, “Preparation of 'green' composites by the sol-gel process: in situ silica filled natural rubber,” J. Sol-Gel Sci. Technol. 31, 137-142 (2004).
[CrossRef]

Y. Ikeda, A. Kato, J. Shimanuki, and S. Kohjiya, “Nano-structural observation of in situ silica in natural rubber matrix by three dimensional transmission electron microscopy,” Macromol. Rapid Commun. 25, 1186-1190 (2004).
[CrossRef]

G. Heinrich and M. Kluppel, “The role of polymer-filler-interphase in reinforcement of elastomers,” Kautsch. Gummi Kunstst. 57, 452-454 (2004).

N. He, S. Ge, G. Yan, C. Hu, and M. Gu, “Investigation on the mechanism of the photoluminescence of MCM-41,” Mater. Res. Bull. 39, 1931-1937 (2004).
[CrossRef]

R. Kaijou, M. Ito, and S. Ono, “Filler gel and rubber gel in silica-filled rubber systems,” J. Soc. Rubber Ind., Japan (in Japanese) 77, 375-381 (2004).
[CrossRef]

2003

M. Song, A. Ansarifar, R. Nijhawan, and T. Nanapoolsin, “Reinforcing effect of silica and silane fillers on the properties of some natural rubber vulcanizates,” Rubber Chem. Technol. 76, 1290-1310 (2003).

2002

R.P.Feynman, R.B.Leighton, and M.L.Sands, eds., Feynman Physics II, Light, Heat and Waves (translated by K. Tomiyama into Japanese, Iwanami Shoten, 2002).

2001

T. Akasaki and T. Fukunaga, “Characteristic and application of silica provided by gel method,” Tosoh. Res. Technol. Rev. 45, 65-69 (2001).

W. Zhang and A. I. Leonov, “IGC study of filler-filler and filler-rubber interaction in silica-filled compounds,” J. Appl. Polym. Sci. 81, 2517-2530 (2001).
[CrossRef]

2000

H.Tokumaru, ed., Our Interaction with Nature through Light and Electromagnetic Fields (Morikita Shuppan, 2000).

Y. Kagawa and H. Iba, “Optically transparent composites,” Mater. J. 39, 137-143 (2000).
[CrossRef]

Y. Ikeda and S. Kohjiya, “Reinforcement of general-purpose grade rubbers by silica generated in situ,” Rubber Chem. Technol. 73, 534-550 (2000).
[CrossRef]

1999

T. Naganuma, H. Iba, and Y. Kagawa, “Optothermal properties of glass particle-dispersed epoxy matrix composite,” J. Mater. Sci. Lett. 18, 1587-1589 (1999).
[CrossRef]

K. Ishii and T. Iwai, “Measurement of fine particle aggregates by using corpuscle the correlation function of time,” J. Electron. Research (in Japanese) 7, 1-3 (1999).

1993

J.-B.Donnet, R.-C.Bansal, and M.-J.Wang, eds., Carbon Black Science and Technology, Second Edition: Revised and Expanded (Marcel Dekker, 1993).

1992

S. Kohjiya and S. Yamashita, “Moisture cure and related processes of synthetic and natural rubber,” J. Appl. Polym. Sci. 50, 213-221 (1992).
[CrossRef]

K.Miyasaka, ed., Dictionary of Plastics (Asakura Shoten, 1992).

J.Frank ed., Electron Tomography: Three-Dimensional Imaging with the Transmission Electron Microscope (Plenum, 1992).

1990

S. Kohjiya, K. Maeda, S. Yamashita, and Y. Shibata, “Chemical modification of silicone elastomers for optics,” J. Mater. Sci. 25, 3368-3374 (1990).
[CrossRef]

1986

G.H.Meeten, ed., Optical Properties of Polymers (Elsevier, 1986).

1977

Department of Petrochemical Technology and Planning of JSR Co., ed., JSR Handbook (JSR Co., 1977).

1974

T. Nishi, “Effect of solvent and carbon black species on the rubber-carbon black interactions studied by pulsed NMR,” J. Polym. Sci., Polym. Phys. Ed. 12, 685-691 (1974).
[CrossRef]

1969

M. Kerker, The Scattering of Light and Other Electronmagnetic Radiation (Academic, 1969).

1957

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

1954

H.E.Rose, ed., The Measurement of Particle Size in Very Fine Powders (Constable & Co. Ltd., 1954).

Akasaki, T.

T. Akasaki and T. Fukunaga, “Characteristic and application of silica provided by gel method,” Tosoh. Res. Technol. Rev. 45, 65-69 (2001).

Ansarifar, A.

M. Song, A. Ansarifar, R. Nijhawan, and T. Nanapoolsin, “Reinforcing effect of silica and silane fillers on the properties of some natural rubber vulcanizates,” Rubber Chem. Technol. 76, 1290-1310 (2003).

Bykov, A. V.

V. P. Kandidov, V. O. Milisin, A. V. Bykov, and A. V. Priezzhev, “Application of corpuscular and wave Monte-Carlo method in optics of dipersive media,” Quantum Electron. 36, 1003-1008 (2006).
[CrossRef]

Den, F.

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

Elliot, E.

K. Haraguchi, H.-J. Li, K. Matsuda, T. Takehisa, and E. Elliot, “Mechanism of forming organic/inorganic network structures during in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels,” Macromolecules 38, 3482-3490 (2005).
[CrossRef]

Endo, H.

S. Miyazaki, H. Endo, T. Karino, K. Haraguchi, and M. Shibayama, “Gelation mechanism of poly(N-isopropylacrylamide)-clay nanocomposite gels,” Macromolecules 40, 4287-4295 (2007).
[CrossRef]

Fu, S.-Y.

Y.-Q. Li, S.-Y. Fu, and Y.-W. Mai, “Preparation and characterization of transparent ZnO/epoxy nanocomposites with high-UV shielding efficiency,” Polymer 47, 2127-2133 (2006).
[CrossRef]

Fukunaga, T.

T. Akasaki and T. Fukunaga, “Characteristic and application of silica provided by gel method,” Tosoh. Res. Technol. Rev. 45, 65-69 (2001).

Ge, S.

N. He, S. Ge, G. Yan, C. Hu, and M. Gu, “Investigation on the mechanism of the photoluminescence of MCM-41,” Mater. Res. Bull. 39, 1931-1937 (2004).
[CrossRef]

Gu, M.

N. He, S. Ge, G. Yan, C. Hu, and M. Gu, “Investigation on the mechanism of the photoluminescence of MCM-41,” Mater. Res. Bull. 39, 1931-1937 (2004).
[CrossRef]

Haraguchi, K.

S. Miyazaki, H. Endo, T. Karino, K. Haraguchi, and M. Shibayama, “Gelation mechanism of poly(N-isopropylacrylamide)-clay nanocomposite gels,” Macromolecules 40, 4287-4295 (2007).
[CrossRef]

K. Haraguchi, H.-J. Li, K. Matsuda, T. Takehisa, and E. Elliot, “Mechanism of forming organic/inorganic network structures during in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels,” Macromolecules 38, 3482-3490 (2005).
[CrossRef]

Hasegawa, T.

S. Kohjiya, A. Kato, J. Shimanuki, T. Hasegawa, and Y. Ikeda, “Nano-structural observation of carbon black dispersion in natural rubber matrix by three-dimensional transmission electron microscopy,” J. Mater. Sci. Lett. 40, 2553-2555 (2005).

He, H.

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

He, N.

N. He, S. Ge, G. Yan, C. Hu, and M. Gu, “Investigation on the mechanism of the photoluminescence of MCM-41,” Mater. Res. Bull. 39, 1931-1937 (2004).
[CrossRef]

Heinrich, G.

G. Heinrich and M. Kluppel, “The role of polymer-filler-interphase in reinforcement of elastomers,” Kautsch. Gummi Kunstst. 57, 452-454 (2004).

Hsiao, B. S.

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

Hu, C.

N. He, S. Ge, G. Yan, C. Hu, and M. Gu, “Investigation on the mechanism of the photoluminescence of MCM-41,” Mater. Res. Bull. 39, 1931-1937 (2004).
[CrossRef]

Iba, H.

Y. Kagawa and H. Iba, “Optically transparent composites,” Mater. J. 39, 137-143 (2000).
[CrossRef]

T. Naganuma, H. Iba, and Y. Kagawa, “Optothermal properties of glass particle-dispersed epoxy matrix composite,” J. Mater. Sci. Lett. 18, 1587-1589 (1999).
[CrossRef]

Ikeda, Y.

S. Kohjiya, A. Kato, and Y. Ikeda, “Visualization of nano-filler dispersion and morphology in rubbery matrix by 3D-TEM,” in Current Topics on Elastomers Research, 2008, A.K.Bhomick, ed. (CRC Press, 2008), Chap. 19.

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

A. Kato, S. Kohjiya, and Y. Ikeda, “Nanostructure in traditional composites of natural rubber and reinforcing silica,” Rubber Chem. Technol. 80, 690-700 (2007).
[CrossRef]

Y. Ikeda, Y. Yasuda, S. Yamamoto, and Y. Morita, “Study on two-dimensional small-angle x-ray scattering of in situ silica filled nanocomposite elastomer during deformation,” J. Appl. Crystallogr. 40, s549-s552 (2007).
[CrossRef]

S. Kohjiya, A. Kato, T. Suda, J. Shimanuki, and Y. Ikeda, “Visualisation of carbon black networks in rubbery matrix by 3D-TEM image,” Polymer 47, 3298-3301 (2006).
[CrossRef]

A. Kato, J. Shimanuki, S. Kohjiya, and Y. Ikeda, “Three-dimensional morphology of carbon black in NR vulcanizates as revealed by 3D-TEM and dielectric measurements,” Rubber Chem. Technol. 79, 653-673 (2006).
[CrossRef]

S. Kohjiya, A. Kato, J. Shimanuki, T. Hasegawa, and Y. Ikeda, “Nano-structural observation of carbon black dispersion in natural rubber matrix by three-dimensional transmission electron microscopy,” J. Mater. Sci. Lett. 40, 2553-2555 (2005).

S. Kohjiya, A. Kato, J. Shimanuki, and Y. Ikeda, “Three-dimensional nano-structure of in situ silica in natural rubber as revealed by 3D-TEM/electron tomography,” Polymer 46, 4440-4446 (2005).
[CrossRef]

S. Poompradub, S. Kohjiya, and Y. Ikeda, “Natural rubber/in situ silica nanocomposite of a high silica content,” Chem. Lett. 34, 672-673 (2005).
[CrossRef]

Y. Ikeda, A. Kato, J. Shimanuki, and S. Kohjiya, “Nano-structural observation of in situ silica in natural rubber matrix by three dimensional transmission electron microscopy,” Macromol. Rapid Commun. 25, 1186-1190 (2004).
[CrossRef]

Y. Ikeda and Y. Kameda, “Preparation of 'green' composites by the sol-gel process: in situ silica filled natural rubber,” J. Sol-Gel Sci. Technol. 31, 137-142 (2004).
[CrossRef]

Y. Ikeda and S. Kohjiya, “Reinforcement of general-purpose grade rubbers by silica generated in situ,” Rubber Chem. Technol. 73, 534-550 (2000).
[CrossRef]

Ishii, K.

K. Ishii and T. Iwai, “Measurement of fine particle aggregates by using corpuscle the correlation function of time,” J. Electron. Research (in Japanese) 7, 1-3 (1999).

Ito, M.

R. Kaijou, M. Ito, and S. Ono, “Filler gel and rubber gel in silica-filled rubber systems,” J. Soc. Rubber Ind., Japan (in Japanese) 77, 375-381 (2004).
[CrossRef]

Iwai, T.

K. Ishii and T. Iwai, “Measurement of fine particle aggregates by using corpuscle the correlation function of time,” J. Electron. Research (in Japanese) 7, 1-3 (1999).

Kagawa, Y.

Y. Kagawa and H. Iba, “Optically transparent composites,” Mater. J. 39, 137-143 (2000).
[CrossRef]

T. Naganuma, H. Iba, and Y. Kagawa, “Optothermal properties of glass particle-dispersed epoxy matrix composite,” J. Mater. Sci. Lett. 18, 1587-1589 (1999).
[CrossRef]

Kaijou, R.

R. Kaijou, M. Ito, and S. Ono, “Filler gel and rubber gel in silica-filled rubber systems,” J. Soc. Rubber Ind., Japan (in Japanese) 77, 375-381 (2004).
[CrossRef]

Kameda, Y.

Y. Ikeda and Y. Kameda, “Preparation of 'green' composites by the sol-gel process: in situ silica filled natural rubber,” J. Sol-Gel Sci. Technol. 31, 137-142 (2004).
[CrossRef]

Kandidov, V. P.

V. P. Kandidov, V. O. Milisin, A. V. Bykov, and A. V. Priezzhev, “Application of corpuscular and wave Monte-Carlo method in optics of dipersive media,” Quantum Electron. 36, 1003-1008 (2006).
[CrossRef]

Karino, T.

S. Miyazaki, H. Endo, T. Karino, K. Haraguchi, and M. Shibayama, “Gelation mechanism of poly(N-isopropylacrylamide)-clay nanocomposite gels,” Macromolecules 40, 4287-4295 (2007).
[CrossRef]

Kato, A.

S. Kohjiya, A. Kato, and Y. Ikeda, “Visualization of nano-filler dispersion and morphology in rubbery matrix by 3D-TEM,” in Current Topics on Elastomers Research, 2008, A.K.Bhomick, ed. (CRC Press, 2008), Chap. 19.

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

A. Kato, S. Kohjiya, and Y. Ikeda, “Nanostructure in traditional composites of natural rubber and reinforcing silica,” Rubber Chem. Technol. 80, 690-700 (2007).
[CrossRef]

S. Kohjiya, A. Kato, T. Suda, J. Shimanuki, and Y. Ikeda, “Visualisation of carbon black networks in rubbery matrix by 3D-TEM image,” Polymer 47, 3298-3301 (2006).
[CrossRef]

A. Kato, J. Shimanuki, S. Kohjiya, and Y. Ikeda, “Three-dimensional morphology of carbon black in NR vulcanizates as revealed by 3D-TEM and dielectric measurements,” Rubber Chem. Technol. 79, 653-673 (2006).
[CrossRef]

S. Kohjiya, A. Kato, J. Shimanuki, T. Hasegawa, and Y. Ikeda, “Nano-structural observation of carbon black dispersion in natural rubber matrix by three-dimensional transmission electron microscopy,” J. Mater. Sci. Lett. 40, 2553-2555 (2005).

S. Kohjiya, A. Kato, J. Shimanuki, and Y. Ikeda, “Three-dimensional nano-structure of in situ silica in natural rubber as revealed by 3D-TEM/electron tomography,” Polymer 46, 4440-4446 (2005).
[CrossRef]

Y. Ikeda, A. Kato, J. Shimanuki, and S. Kohjiya, “Nano-structural observation of in situ silica in natural rubber matrix by three dimensional transmission electron microscopy,” Macromol. Rapid Commun. 25, 1186-1190 (2004).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electronmagnetic Radiation (Academic, 1969).

Kluppel, M.

G. Heinrich and M. Kluppel, “The role of polymer-filler-interphase in reinforcement of elastomers,” Kautsch. Gummi Kunstst. 57, 452-454 (2004).

Kohjiya, S.

S. Kohjiya, A. Kato, and Y. Ikeda, “Visualization of nano-filler dispersion and morphology in rubbery matrix by 3D-TEM,” in Current Topics on Elastomers Research, 2008, A.K.Bhomick, ed. (CRC Press, 2008), Chap. 19.

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

A. Kato, S. Kohjiya, and Y. Ikeda, “Nanostructure in traditional composites of natural rubber and reinforcing silica,” Rubber Chem. Technol. 80, 690-700 (2007).
[CrossRef]

S. Kohjiya, A. Kato, T. Suda, J. Shimanuki, and Y. Ikeda, “Visualisation of carbon black networks in rubbery matrix by 3D-TEM image,” Polymer 47, 3298-3301 (2006).
[CrossRef]

A. Kato, J. Shimanuki, S. Kohjiya, and Y. Ikeda, “Three-dimensional morphology of carbon black in NR vulcanizates as revealed by 3D-TEM and dielectric measurements,” Rubber Chem. Technol. 79, 653-673 (2006).
[CrossRef]

S. Kohjiya, A. Kato, J. Shimanuki, T. Hasegawa, and Y. Ikeda, “Nano-structural observation of carbon black dispersion in natural rubber matrix by three-dimensional transmission electron microscopy,” J. Mater. Sci. Lett. 40, 2553-2555 (2005).

S. Kohjiya, A. Kato, J. Shimanuki, and Y. Ikeda, “Three-dimensional nano-structure of in situ silica in natural rubber as revealed by 3D-TEM/electron tomography,” Polymer 46, 4440-4446 (2005).
[CrossRef]

S. Poompradub, S. Kohjiya, and Y. Ikeda, “Natural rubber/in situ silica nanocomposite of a high silica content,” Chem. Lett. 34, 672-673 (2005).
[CrossRef]

Y. Ikeda, A. Kato, J. Shimanuki, and S. Kohjiya, “Nano-structural observation of in situ silica in natural rubber matrix by three dimensional transmission electron microscopy,” Macromol. Rapid Commun. 25, 1186-1190 (2004).
[CrossRef]

Y. Ikeda and S. Kohjiya, “Reinforcement of general-purpose grade rubbers by silica generated in situ,” Rubber Chem. Technol. 73, 534-550 (2000).
[CrossRef]

S. Kohjiya and S. Yamashita, “Moisture cure and related processes of synthetic and natural rubber,” J. Appl. Polym. Sci. 50, 213-221 (1992).
[CrossRef]

S. Kohjiya, K. Maeda, S. Yamashita, and Y. Shibata, “Chemical modification of silicone elastomers for optics,” J. Mater. Sci. 25, 3368-3374 (1990).
[CrossRef]

Leonov, A. I.

W. Zhang and A. I. Leonov, “IGC study of filler-filler and filler-rubber interaction in silica-filled compounds,” J. Appl. Polym. Sci. 81, 2517-2530 (2001).
[CrossRef]

Li, H.-J.

K. Haraguchi, H.-J. Li, K. Matsuda, T. Takehisa, and E. Elliot, “Mechanism of forming organic/inorganic network structures during in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels,” Macromolecules 38, 3482-3490 (2005).
[CrossRef]

Li, Y.-Q.

Y.-Q. Li, S.-Y. Fu, and Y.-W. Mai, “Preparation and characterization of transparent ZnO/epoxy nanocomposites with high-UV shielding efficiency,” Polymer 47, 2127-2133 (2006).
[CrossRef]

Lin, Z.

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

Maeda, K.

S. Kohjiya, K. Maeda, S. Yamashita, and Y. Shibata, “Chemical modification of silicone elastomers for optics,” J. Mater. Sci. 25, 3368-3374 (1990).
[CrossRef]

Mai, Y.-W.

Y.-Q. Li, S.-Y. Fu, and Y.-W. Mai, “Preparation and characterization of transparent ZnO/epoxy nanocomposites with high-UV shielding efficiency,” Polymer 47, 2127-2133 (2006).
[CrossRef]

Matsuda, K.

K. Haraguchi, H.-J. Li, K. Matsuda, T. Takehisa, and E. Elliot, “Mechanism of forming organic/inorganic network structures during in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels,” Macromolecules 38, 3482-3490 (2005).
[CrossRef]

Milisin, V. O.

V. P. Kandidov, V. O. Milisin, A. V. Bykov, and A. V. Priezzhev, “Application of corpuscular and wave Monte-Carlo method in optics of dipersive media,” Quantum Electron. 36, 1003-1008 (2006).
[CrossRef]

Miyazaki, S.

S. Miyazaki, H. Endo, T. Karino, K. Haraguchi, and M. Shibayama, “Gelation mechanism of poly(N-isopropylacrylamide)-clay nanocomposite gels,” Macromolecules 40, 4287-4295 (2007).
[CrossRef]

Morita, Y.

Y. Ikeda, Y. Yasuda, S. Yamamoto, and Y. Morita, “Study on two-dimensional small-angle x-ray scattering of in situ silica filled nanocomposite elastomer during deformation,” J. Appl. Crystallogr. 40, s549-s552 (2007).
[CrossRef]

Naganuma, T.

T. Naganuma, H. Iba, and Y. Kagawa, “Optothermal properties of glass particle-dispersed epoxy matrix composite,” J. Mater. Sci. Lett. 18, 1587-1589 (1999).
[CrossRef]

Nakamura, M.

M. Nakamura, H. Yoden, H. Yokogawa, T. Yamaki, K. Takahama, and N. Tanio, “Refractive index prediction of optical cross-linked polymer,” Polymer Preprints, Japan 57, 1348 (2008).

Nanapoolsin, T.

M. Song, A. Ansarifar, R. Nijhawan, and T. Nanapoolsin, “Reinforcing effect of silica and silane fillers on the properties of some natural rubber vulcanizates,” Rubber Chem. Technol. 76, 1290-1310 (2003).

Nijhawan, R.

M. Song, A. Ansarifar, R. Nijhawan, and T. Nanapoolsin, “Reinforcing effect of silica and silane fillers on the properties of some natural rubber vulcanizates,” Rubber Chem. Technol. 76, 1290-1310 (2003).

Nishi, T.

T. Nishi, “Effect of solvent and carbon black species on the rubber-carbon black interactions studied by pulsed NMR,” J. Polym. Sci., Polym. Phys. Ed. 12, 685-691 (1974).
[CrossRef]

Ono, S.

R. Kaijou, M. Ito, and S. Ono, “Filler gel and rubber gel in silica-filled rubber systems,” J. Soc. Rubber Ind., Japan (in Japanese) 77, 375-381 (2004).
[CrossRef]

Poompradub, S.

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

S. Poompradub, S. Kohjiya, and Y. Ikeda, “Natural rubber/in situ silica nanocomposite of a high silica content,” Chem. Lett. 34, 672-673 (2005).
[CrossRef]

Priezzhev, A. V.

V. P. Kandidov, V. O. Milisin, A. V. Bykov, and A. V. Priezzhev, “Application of corpuscular and wave Monte-Carlo method in optics of dipersive media,” Quantum Electron. 36, 1003-1008 (2006).
[CrossRef]

Schelm, S.

S. Schelm and G. B. Smith, “Tuning the surface-plasmon resonance in nanoparticles for glazing application,” J. Appl. Phys. 97, 124314 (2005).
[CrossRef]

Shibata, Y.

S. Kohjiya, K. Maeda, S. Yamashita, and Y. Shibata, “Chemical modification of silicone elastomers for optics,” J. Mater. Sci. 25, 3368-3374 (1990).
[CrossRef]

Shibayama, M.

S. Miyazaki, H. Endo, T. Karino, K. Haraguchi, and M. Shibayama, “Gelation mechanism of poly(N-isopropylacrylamide)-clay nanocomposite gels,” Macromolecules 40, 4287-4295 (2007).
[CrossRef]

Shimanuki, J.

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

A. Kato, J. Shimanuki, S. Kohjiya, and Y. Ikeda, “Three-dimensional morphology of carbon black in NR vulcanizates as revealed by 3D-TEM and dielectric measurements,” Rubber Chem. Technol. 79, 653-673 (2006).
[CrossRef]

S. Kohjiya, A. Kato, T. Suda, J. Shimanuki, and Y. Ikeda, “Visualisation of carbon black networks in rubbery matrix by 3D-TEM image,” Polymer 47, 3298-3301 (2006).
[CrossRef]

S. Kohjiya, A. Kato, J. Shimanuki, T. Hasegawa, and Y. Ikeda, “Nano-structural observation of carbon black dispersion in natural rubber matrix by three-dimensional transmission electron microscopy,” J. Mater. Sci. Lett. 40, 2553-2555 (2005).

S. Kohjiya, A. Kato, J. Shimanuki, and Y. Ikeda, “Three-dimensional nano-structure of in situ silica in natural rubber as revealed by 3D-TEM/electron tomography,” Polymer 46, 4440-4446 (2005).
[CrossRef]

Y. Ikeda, A. Kato, J. Shimanuki, and S. Kohjiya, “Nano-structural observation of in situ silica in natural rubber matrix by three dimensional transmission electron microscopy,” Macromol. Rapid Commun. 25, 1186-1190 (2004).
[CrossRef]

Smith, G. B.

S. Schelm and G. B. Smith, “Tuning the surface-plasmon resonance in nanoparticles for glazing application,” J. Appl. Phys. 97, 124314 (2005).
[CrossRef]

Song, M.

M. Song, A. Ansarifar, R. Nijhawan, and T. Nanapoolsin, “Reinforcing effect of silica and silane fillers on the properties of some natural rubber vulcanizates,” Rubber Chem. Technol. 76, 1290-1310 (2003).

Suda, T.

S. Kohjiya, A. Kato, T. Suda, J. Shimanuki, and Y. Ikeda, “Visualisation of carbon black networks in rubbery matrix by 3D-TEM image,” Polymer 47, 3298-3301 (2006).
[CrossRef]

Takahama, K.

M. Nakamura, H. Yoden, H. Yokogawa, T. Yamaki, K. Takahama, and N. Tanio, “Refractive index prediction of optical cross-linked polymer,” Polymer Preprints, Japan 57, 1348 (2008).

Takehisa, T.

K. Haraguchi, H.-J. Li, K. Matsuda, T. Takehisa, and E. Elliot, “Mechanism of forming organic/inorganic network structures during in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels,” Macromolecules 38, 3482-3490 (2005).
[CrossRef]

Tanio, N.

M. Nakamura, H. Yoden, H. Yokogawa, T. Yamaki, K. Takahama, and N. Tanio, “Refractive index prediction of optical cross-linked polymer,” Polymer Preprints, Japan 57, 1348 (2008).

Toki, S.

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

Tosaka, M.

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Wang, L.

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

Wen, X.

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

Yamaki, T.

M. Nakamura, H. Yoden, H. Yokogawa, T. Yamaki, K. Takahama, and N. Tanio, “Refractive index prediction of optical cross-linked polymer,” Polymer Preprints, Japan 57, 1348 (2008).

Yamamoto, S.

Y. Ikeda, Y. Yasuda, S. Yamamoto, and Y. Morita, “Study on two-dimensional small-angle x-ray scattering of in situ silica filled nanocomposite elastomer during deformation,” J. Appl. Crystallogr. 40, s549-s552 (2007).
[CrossRef]

Yamashita, S.

S. Kohjiya and S. Yamashita, “Moisture cure and related processes of synthetic and natural rubber,” J. Appl. Polym. Sci. 50, 213-221 (1992).
[CrossRef]

S. Kohjiya, K. Maeda, S. Yamashita, and Y. Shibata, “Chemical modification of silicone elastomers for optics,” J. Mater. Sci. 25, 3368-3374 (1990).
[CrossRef]

Yan, G.

N. He, S. Ge, G. Yan, C. Hu, and M. Gu, “Investigation on the mechanism of the photoluminescence of MCM-41,” Mater. Res. Bull. 39, 1931-1937 (2004).
[CrossRef]

Yang, D.

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

Yasuda, Y.

Y. Ikeda, Y. Yasuda, S. Yamamoto, and Y. Morita, “Study on two-dimensional small-angle x-ray scattering of in situ silica filled nanocomposite elastomer during deformation,” J. Appl. Crystallogr. 40, s549-s552 (2007).
[CrossRef]

Yoden, H.

M. Nakamura, H. Yoden, H. Yokogawa, T. Yamaki, K. Takahama, and N. Tanio, “Refractive index prediction of optical cross-linked polymer,” Polymer Preprints, Japan 57, 1348 (2008).

Yokogawa, H.

M. Nakamura, H. Yoden, H. Yokogawa, T. Yamaki, K. Takahama, and N. Tanio, “Refractive index prediction of optical cross-linked polymer,” Polymer Preprints, Japan 57, 1348 (2008).

Yuan, P.

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

Zhang, W.

W. Zhang and A. I. Leonov, “IGC study of filler-filler and filler-rubber interaction in silica-filled compounds,” J. Appl. Polym. Sci. 81, 2517-2530 (2001).
[CrossRef]

Chem. Lett.

S. Poompradub, S. Kohjiya, and Y. Ikeda, “Natural rubber/in situ silica nanocomposite of a high silica content,” Chem. Lett. 34, 672-673 (2005).
[CrossRef]

J. Appl. Crystallogr.

Y. Ikeda, Y. Yasuda, S. Yamamoto, and Y. Morita, “Study on two-dimensional small-angle x-ray scattering of in situ silica filled nanocomposite elastomer during deformation,” J. Appl. Crystallogr. 40, s549-s552 (2007).
[CrossRef]

J. Appl. Phys.

S. Schelm and G. B. Smith, “Tuning the surface-plasmon resonance in nanoparticles for glazing application,” J. Appl. Phys. 97, 124314 (2005).
[CrossRef]

J. Appl. Polym. Sci.

S. Kohjiya and S. Yamashita, “Moisture cure and related processes of synthetic and natural rubber,” J. Appl. Polym. Sci. 50, 213-221 (1992).
[CrossRef]

W. Zhang and A. I. Leonov, “IGC study of filler-filler and filler-rubber interaction in silica-filled compounds,” J. Appl. Polym. Sci. 81, 2517-2530 (2001).
[CrossRef]

J. Electron. Research (in Japanese)

K. Ishii and T. Iwai, “Measurement of fine particle aggregates by using corpuscle the correlation function of time,” J. Electron. Research (in Japanese) 7, 1-3 (1999).

J. Mater. Sci.

S. Kohjiya, K. Maeda, S. Yamashita, and Y. Shibata, “Chemical modification of silicone elastomers for optics,” J. Mater. Sci. 25, 3368-3374 (1990).
[CrossRef]

J. Mater. Sci. Lett.

T. Naganuma, H. Iba, and Y. Kagawa, “Optothermal properties of glass particle-dispersed epoxy matrix composite,” J. Mater. Sci. Lett. 18, 1587-1589 (1999).
[CrossRef]

S. Kohjiya, A. Kato, J. Shimanuki, T. Hasegawa, and Y. Ikeda, “Nano-structural observation of carbon black dispersion in natural rubber matrix by three-dimensional transmission electron microscopy,” J. Mater. Sci. Lett. 40, 2553-2555 (2005).

J. Non-Cryst. Solids

P. Yuan, D. Yang, Z. Lin, H. He, X. Wen, L. Wang, and F. Den, “Influences of pretreatment temperature on the surface silylation of diatomaceous amorphous silica with trimethylchlorosilane,” J. Non-Cryst. Solids 352, 3762-3771 (2006).
[CrossRef]

J. Polym. Sci., Polym. Phys. Ed.

T. Nishi, “Effect of solvent and carbon black species on the rubber-carbon black interactions studied by pulsed NMR,” J. Polym. Sci., Polym. Phys. Ed. 12, 685-691 (1974).
[CrossRef]

J. Soc. Rubber Ind., Japan (in Japanese)

R. Kaijou, M. Ito, and S. Ono, “Filler gel and rubber gel in silica-filled rubber systems,” J. Soc. Rubber Ind., Japan (in Japanese) 77, 375-381 (2004).
[CrossRef]

J. Sol-Gel Sci. Technol.

Y. Ikeda and Y. Kameda, “Preparation of 'green' composites by the sol-gel process: in situ silica filled natural rubber,” J. Sol-Gel Sci. Technol. 31, 137-142 (2004).
[CrossRef]

Kautsch. Gummi Kunstst.

G. Heinrich and M. Kluppel, “The role of polymer-filler-interphase in reinforcement of elastomers,” Kautsch. Gummi Kunstst. 57, 452-454 (2004).

Macromol. Rapid Commun.

Y. Ikeda, A. Kato, J. Shimanuki, and S. Kohjiya, “Nano-structural observation of in situ silica in natural rubber matrix by three dimensional transmission electron microscopy,” Macromol. Rapid Commun. 25, 1186-1190 (2004).
[CrossRef]

Macromolecules

K. Haraguchi, H.-J. Li, K. Matsuda, T. Takehisa, and E. Elliot, “Mechanism of forming organic/inorganic network structures during in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels,” Macromolecules 38, 3482-3490 (2005).
[CrossRef]

S. Miyazaki, H. Endo, T. Karino, K. Haraguchi, and M. Shibayama, “Gelation mechanism of poly(N-isopropylacrylamide)-clay nanocomposite gels,” Macromolecules 40, 4287-4295 (2007).
[CrossRef]

Mater. J.

Y. Kagawa and H. Iba, “Optically transparent composites,” Mater. J. 39, 137-143 (2000).
[CrossRef]

Mater. Res. Bull.

N. He, S. Ge, G. Yan, C. Hu, and M. Gu, “Investigation on the mechanism of the photoluminescence of MCM-41,” Mater. Res. Bull. 39, 1931-1937 (2004).
[CrossRef]

Polymer

S. Kohjiya, A. Kato, T. Suda, J. Shimanuki, and Y. Ikeda, “Visualisation of carbon black networks in rubbery matrix by 3D-TEM image,” Polymer 47, 3298-3301 (2006).
[CrossRef]

Y.-Q. Li, S.-Y. Fu, and Y.-W. Mai, “Preparation and characterization of transparent ZnO/epoxy nanocomposites with high-UV shielding efficiency,” Polymer 47, 2127-2133 (2006).
[CrossRef]

S. Kohjiya, A. Kato, J. Shimanuki, and Y. Ikeda, “Three-dimensional nano-structure of in situ silica in natural rubber as revealed by 3D-TEM/electron tomography,” Polymer 46, 4440-4446 (2005).
[CrossRef]

Polymer Preprints, Japan

M. Nakamura, H. Yoden, H. Yokogawa, T. Yamaki, K. Takahama, and N. Tanio, “Refractive index prediction of optical cross-linked polymer,” Polymer Preprints, Japan 57, 1348 (2008).

Quantum Electron.

V. P. Kandidov, V. O. Milisin, A. V. Bykov, and A. V. Priezzhev, “Application of corpuscular and wave Monte-Carlo method in optics of dipersive media,” Quantum Electron. 36, 1003-1008 (2006).
[CrossRef]

Rubber Chem. Technol.

A. Kato, J. Shimanuki, S. Kohjiya, and Y. Ikeda, “Three-dimensional morphology of carbon black in NR vulcanizates as revealed by 3D-TEM and dielectric measurements,” Rubber Chem. Technol. 79, 653-673 (2006).
[CrossRef]

Y. Ikeda, A. Kato, J. Shimanuki, S. Kohjiya, M. Tosaka, S. Poompradub, S. Toki, and B. S. Hsiao, “Nano-structural elucidation in carbon black loaded NR vulcanizate by 3D-TEM and in situ WAXD measurements,” Rubber Chem. Technol. 80, 251-264 (2007).
[CrossRef]

M. Song, A. Ansarifar, R. Nijhawan, and T. Nanapoolsin, “Reinforcing effect of silica and silane fillers on the properties of some natural rubber vulcanizates,” Rubber Chem. Technol. 76, 1290-1310 (2003).

A. Kato, S. Kohjiya, and Y. Ikeda, “Nanostructure in traditional composites of natural rubber and reinforcing silica,” Rubber Chem. Technol. 80, 690-700 (2007).
[CrossRef]

Y. Ikeda and S. Kohjiya, “Reinforcement of general-purpose grade rubbers by silica generated in situ,” Rubber Chem. Technol. 73, 534-550 (2000).
[CrossRef]

Tosoh. Res. Technol. Rev.

T. Akasaki and T. Fukunaga, “Characteristic and application of silica provided by gel method,” Tosoh. Res. Technol. Rev. 45, 65-69 (2001).

Other

J.Frank ed., Electron Tomography: Three-Dimensional Imaging with the Transmission Electron Microscope (Plenum, 1992).

R.P.Feynman, R.B.Leighton, and M.L.Sands, eds., Feynman Physics II, Light, Heat and Waves (translated by K. Tomiyama into Japanese, Iwanami Shoten, 2002).

H.Tokumaru, ed., Our Interaction with Nature through Light and Electromagnetic Fields (Morikita Shuppan, 2000).

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

M. Kerker, The Scattering of Light and Other Electronmagnetic Radiation (Academic, 1969).

G.H.Meeten, ed., Optical Properties of Polymers (Elsevier, 1986).

The Boulder Laboratory for 3-Dimensional Electron Microscopy of Cells and Regents of the University of Colorado, “The IMOD Home Page,” http://bio3d.colorado.edu/imod/.

Mercury Visualization Sciences, “Visualization Software,” http://www.tgs.com/.

J.-B.Donnet, R.-C.Bansal, and M.-J.Wang, eds., Carbon Black Science and Technology, Second Edition: Revised and Expanded (Marcel Dekker, 1993).

S. Kohjiya, A. Kato, and Y. Ikeda, “Visualization of nano-filler dispersion and morphology in rubbery matrix by 3D-TEM,” in Current Topics on Elastomers Research, 2008, A.K.Bhomick, ed. (CRC Press, 2008), Chap. 19.

K.Miyasaka, ed., Dictionary of Plastics (Asakura Shoten, 1992).

H.E.Rose, ed., The Measurement of Particle Size in Very Fine Powders (Constable & Co. Ltd., 1954).

Department of Petrochemical Technology and Planning of JSR Co., ed., JSR Handbook (JSR Co., 1977).

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Figures (17)

Fig. 1
Fig. 1

Diffusion transmittance and haze.

Fig. 2
Fig. 2

Influence of particle size distribution of silica aggregates on light transmission. (a) Case 1, narrow size distribution of silica aggregates. (b) Case 2, wide size distribution of silica aggregates.

Fig. 3
Fig. 3

Definition of the closest distance ( d p ) of two neighboring aggregates and the closest distance ( d g ) between the center of gravity of two neighboring aggregates as 3D parameters.

Fig. 4
Fig. 4

Silica aggregate network structure.

Fig. 5
Fig. 5

Optical transparency of NR-P-10, NR-P-30, NR-P-40, and NR-P-80 films.

Fig. 6
Fig. 6

UV/Vis spectra of silica-filled NR in air at room temperature for different silica loading (TR stands for transmittance).

Fig. 7
Fig. 7

Relationship between total transmittance ( TR total ) and silica loading of silica-filled cross-linked NR.

Fig. 8
Fig. 8

Dependence of total transmittance ( T t ) , shield effect ( T shield ) , diffuse transmittance ( T d ) , and haze (H) on silica loading.

Fig. 9
Fig. 9

3D-TEM images of NR-P-10 (Media 1), NR-P-30 ( Media 2), NR-P-40 ( Media 3 ), and NR-P-80 ( Media 4).

Fig. 10
Fig. 10

3D image processing results of NR-P-10, NR-P-30, NR-P-40, and NR-P-80 for easy recognition of aggregation.

Fig. 11
Fig. 11

Dependence of T shield ( = 1 T t ) on n D r n 2 .

Fig. 12
Fig. 12

Silica-loading dependence on (a) the closest distance ( d p ) between two neighboring silica aggregates and (b) volume resistivity ( ρ v ) at room temp.

Fig. 13
Fig. 13

Visualization of network structures of silica and of isolated chain structure of silica in a NR matrix.

Fig. 14
Fig. 14

(a) Dependence of ( Chain density ) × ( Length of the chain ) 2 of three types of network chains on silica loading. (b) Dependence of ( Chain density ) × ( Length of the chain ) 2 of isolated chains on silica loading.

Fig. 15
Fig. 15

Dependence of diffusion transmittance ( T d ) and haze ( H ) on ( Chain density ) × ( Length of the chain ) 2 of cross-linked chains.

Fig. 16
Fig. 16

Dependence of diffusion transmittance ( T d ) and haze ( H ) on ( Chain density ) × ( Length of the chain ) 2 of branched chains.

Fig. 17
Fig. 17

Dependence of diffusion transmittance ( T d ) and haze ( H ) on ( Chain density ) × ( Length of the chain ) 2 of isolated chains

Tables (1)

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Table 1 Recipes of Silica-Filled Cross-Linked Natural Rubber (NR) a

Equations (24)

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TR = 100 ( I 0 I ) .
TR total = 100 WL = 400 WL = 800 TRd ( WL ) WL = 400 WL = 800 100 d ( WL ) = WL = 400 WL = 800 TRd ( WL ) WL = 400 WL = 800 d ( WL ) ,
T shield = 1 T t ,
T d = T t T p ,
H = T d T t ,
log ( I 0 I ) = log ( 1 T t ) = log T t 1 T t .
log ( I 0 I ) = k n L R i = 1 i n i r i 2 ,
log ( I 0 I ) = k L R i = 1 i n i r i 2 .
log ( I 0 I ) = k L R n 1 r 1 2 .
μ s = a 0 = π K p n r 2 ,
Number of particles per unit volume ( n ) = i = 1 i n i ,
Number - average radius of particles ( r n ) = i 1 i n i r i i = 1 i n i ,
Weighted - average particle radius ( r w ) = i = 1 i n i r i 2 i = 1 i n i r i ,
Coefficient of particle dispersion ( D ) = r w r n .
log ( I 0 I ) = k L R ( i = 1 i n i ) ( i = 1 i n i r i 2 i = 1 i n i r i ) ( i = 1 i n i r i i = 1 i n i ) .
1 T t A n r w r n = A n D r n 2 ,
T shield = 1 T t A n D r n 2 .
T shield = A n D r n 2 + T surf ,
T shield ( mono ) = A n r n 2 + T surf .
T shield T shield ( mono ) = A n r n 2 ( D 1 ) 0 ,
T shield T shield ( mono ) > 0 .
T d ( or H ) μ s = π K p n r 2 = ( π K p 4 ) n ( 2 r ) 2 .
T d = C × ( Chain density ) × ( Length of the chain ) 2 + T d ( NR ) ,
H = C × ( Chain density ) × ( Length of the chain ) 2 H ( NR ) .

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