Abstract

We use light scattering to study spatial correlations in the pore space of Vycor glass upon draining a wetting fluid. We analyze the transmission spectrum of forward-scattered light on the basis of the theory of dielectric constant fluctuation, whereas conventional light scattering analyzes the scattered light at small angles of monochromatic incident light. Assuming that the drained pores, which are surrounded by filled pores, exhibit long-range correlations of a fractal dimension of 2.5, we analytically derive the corresponding turbidity. The slight deviation from the λ4 Rayleigh wavelength dependence directly provides the correlation length of the interconnected network of drained pores. The estimated length, ranging from 0.5 to 18 nm at most, is almost the same order as that indirectly estimated from our previous simple effective Rayleigh scatterer model.

© 2015 Optical Society of America

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  1. T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998).
    [Crossref]
  2. Y. Y. Maruo, “Measurement of ambient ozone using newly developed porous glass sensor,” Sens. Actuators B 126, 485–491 (2007).
    [Crossref]
  3. Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s regent,” Sens. Actuators B 129, 544–550 (2008).
    [Crossref]
  4. A. F. Novikov and V. I. Zemskii, “Glassy spectral gas sensors based on the immobilized indicators,” Proc. SPIE 2550, 119–129 (1995).
    [Crossref]
  5. J. H. Page, J. Liu, B. Abeles, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993).
    [Crossref]
  6. J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
    [Crossref]
  7. V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 114105 (2003).
    [Crossref]
  8. V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
    [Crossref]
  9. D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005).
    [Crossref]
  10. S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
    [Crossref]
  11. S. Ogawa, “1/λ4 scattering of light during the drying process in porous Vycor glass with nano-sized pores,” J. Opt. Soc. Am. A 30, 154–159 (2013).
    [Crossref]
  12. S. Ogawa and J. Nakamura, “Hysteretic characteristics of 1/λ4 scattering of light during adsorption and desorption of water in porous Vycor glass with nanopores,” J. Opt. Soc. Am. A 30, 2079–2089 (2013).
    [Crossref]
  13. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).
  14. P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
    [Crossref]
  15. P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid. II. The correlation function and its application,” J. Appl. Phys. 28, 679–683 (1957).
    [Crossref]
  16. J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
    [Crossref]
  17. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), p. 470.
  18. P. R. Wakeling, “What is Vycor glass?” Appl. Opt. 18, 3208–3210 (1979).

2013 (2)

2012 (1)

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

2008 (1)

Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s regent,” Sens. Actuators B 129, 544–550 (2008).
[Crossref]

2007 (1)

Y. Y. Maruo, “Measurement of ambient ozone using newly developed porous glass sensor,” Sens. Actuators B 126, 485–491 (2007).
[Crossref]

2005 (1)

D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005).
[Crossref]

2004 (1)

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
[Crossref]

2003 (1)

V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 114105 (2003).
[Crossref]

1998 (1)

T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998).
[Crossref]

1995 (2)

A. F. Novikov and V. I. Zemskii, “Glassy spectral gas sensors based on the immobilized indicators,” Proc. SPIE 2550, 119–129 (1995).
[Crossref]

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
[Crossref]

1994 (1)

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

1993 (1)

J. H. Page, J. Liu, B. Abeles, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993).
[Crossref]

1979 (1)

1957 (1)

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid. II. The correlation function and its application,” J. Appl. Phys. 28, 679–683 (1957).
[Crossref]

1949 (1)

P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
[Crossref]

Abeles, B.

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
[Crossref]

J. H. Page, J. Liu, B. Abeles, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993).
[Crossref]

Ackermann, R.

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
[Crossref]

Anderson, H. R.

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid. II. The correlation function and its application,” J. Appl. Phys. 28, 679–683 (1957).
[Crossref]

Brumberger, H.

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid. II. The correlation function and its application,” J. Appl. Phys. 28, 679–683 (1957).
[Crossref]

Bueche, A. M.

P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
[Crossref]

Debye, P.

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid. II. The correlation function and its application,” J. Appl. Phys. 28, 679–683 (1957).
[Crossref]

P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
[Crossref]

Deckman, H. W.

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
[Crossref]

J. H. Page, J. Liu, B. Abeles, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993).
[Crossref]

Egelhaaf, S. U.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

Fairclough, J. P. A.

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

Gruener, S.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

Hayashi, T.

T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998).
[Crossref]

Heenan, R.

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

Herbolzheimer, E.

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
[Crossref]

Hermes, H. E.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

Higuchi, M.

Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s regent,” Sens. Actuators B 129, 544–550 (2008).
[Crossref]

Howe, L. D.

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

Huber, P.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 114105 (2003).
[Crossref]

Ibel, K.

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

Izumi, K.

Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s regent,” Sens. Actuators B 129, 544–550 (2008).
[Crossref]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), p. 470.

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

Kityk, A. V.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
[Crossref]

Knorr, K.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 114105 (2003).
[Crossref]

Li, J. C.

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

Liu, J.

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
[Crossref]

J. H. Page, J. Liu, B. Abeles, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993).
[Crossref]

Maruo, Y. Y.

Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s regent,” Sens. Actuators B 129, 544–550 (2008).
[Crossref]

Y. Y. Maruo, “Measurement of ambient ozone using newly developed porous glass sensor,” Sens. Actuators B 126, 485–491 (2007).
[Crossref]

T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998).
[Crossref]

Nakamura, J.

S. Ogawa and J. Nakamura, “Hysteretic characteristics of 1/λ4 scattering of light during adsorption and desorption of water in porous Vycor glass with nanopores,” J. Opt. Soc. Am. A 30, 2079–2089 (2013).
[Crossref]

Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s regent,” Sens. Actuators B 129, 544–550 (2008).
[Crossref]

Novikov, A. F.

A. F. Novikov and V. I. Zemskii, “Glassy spectral gas sensors based on the immobilized indicators,” Proc. SPIE 2550, 119–129 (1995).
[Crossref]

Ogawa, S.

Ohyama, T.

T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998).
[Crossref]

Page, J. H.

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
[Crossref]

J. H. Page, J. Liu, B. Abeles, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993).
[Crossref]

Rieger, H.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

Ross, D. K.

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

Sadjadi, Z.

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

Soprunyuk, V. P.

D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 114105 (2003).
[Crossref]

Stefanopoulos, K. L.

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

Tanaka, T.

T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998).
[Crossref]

Uchiyama, M.

Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s regent,” Sens. Actuators B 129, 544–550 (2008).
[Crossref]

Wakeling, P. R.

Wallacher, D.

D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 114105 (2003).
[Crossref]

Weitz, D. A.

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
[Crossref]

J. H. Page, J. Liu, B. Abeles, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993).
[Crossref]

Zemskii, V. I.

A. F. Novikov and V. I. Zemskii, “Glassy spectral gas sensors based on the immobilized indicators,” Proc. SPIE 2550, 119–129 (1995).
[Crossref]

Appl. Opt. (1)

J. Appl. Phys. (2)

P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
[Crossref]

P. Debye, H. R. Anderson, and H. Brumberger, “Scattering by an inhomogeneous solid. II. The correlation function and its application,” J. Appl. Phys. 28, 679–683 (1957).
[Crossref]

J. Low Temp. Phys. (1)

V. P. Soprunyuk, D. Wallacher, P. Huber, R. Ackermann, K. Knorr, and A. V. Kityk, “Optical transmission measurements of phase transitions of O2 and CO in mesoporous glass,” J. Low Temp. Phys. 134, 1043–1053 (2004).
[Crossref]

J. Opt. Soc. Am. A (2)

Phys. Rev. B (3)

J. C. Li, D. K. Ross, L. D. Howe, K. L. Stefanopoulos, J. P. A. Fairclough, R. Heenan, and K. Ibel, “Small-angle neutron-scattering studies of the fractal-like network formed during desorption and adsorption of water in porous materials,” Phys. Rev. B 49, 5911–5917 (1994).
[Crossref]

D. Wallacher, V. P. Soprunyuk, A. V. Kityk, P. Huber, and K. Knorr, “Capillary sublimation of Ar in mesoporous glass,” Phys. Rev. B 71, 052101 (2005).
[Crossref]

V. P. Soprunyuk, D. Wallacher, P. Huber, and K. Knorr, “Freezing and melting of Ar in mesopores studied by optical transmission,” Phys. Rev. B 67, 114105 (2003).
[Crossref]

Phys. Rev. E (1)

J. H. Page, J. Liu, B. Abeles, E. Herbolzheimer, H. W. Deckman, and D. A. Weitz, “Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques,” Phys. Rev. E 52, 2763–2777 (1995).
[Crossref]

Phys. Rev. Lett. (1)

J. H. Page, J. Liu, B. Abeles, H. W. Deckman, and D. A. Weitz, “Pore-space correlations in capillary condensation in Vycor,” Phys. Rev. Lett. 71, 1216–1219 (1993).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proc. Natl. Acad. Sci. USA 109, 10245–10250 (2012).
[Crossref]

Proc. SPIE (1)

A. F. Novikov and V. I. Zemskii, “Glassy spectral gas sensors based on the immobilized indicators,” Proc. SPIE 2550, 119–129 (1995).
[Crossref]

Sens. Actuators B (3)

T. Tanaka, T. Ohyama, Y. Y. Maruo, and T. Hayashi, “Coloration reactions between NO2 and organic compounds in porous glass for cumulative gas sensor,” Sens. Actuators B 47, 65–69 (1998).
[Crossref]

Y. Y. Maruo, “Measurement of ambient ozone using newly developed porous glass sensor,” Sens. Actuators B 126, 485–491 (2007).
[Crossref]

Y. Y. Maruo, J. Nakamura, M. Uchiyama, M. Higuchi, and K. Izumi, “Development of formaldehyde sensing element using porous glass impregnated with Schiff’s regent,” Sens. Actuators B 129, 544–550 (2008).
[Crossref]

Other (2)

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), p. 470.

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

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Figures (2)

Fig. 1.
Fig. 1. (a) Change in UV–vis light transmission spectra of a porous Vycor glass chip relative to that in the dry state at 165 min, after drying for 0, 15, 30, 45, 60, 75, and 90 min immediately after removal from ultrapure water immersion for 2 h at room temperature. (b) Changes in the turbidity (estimated from the logarithm of the relative transmission) as a function of the inverse fourth power of wavelength in air (1/λ04). The slight deviation of the turbidity from the λ4 Rayleigh wavelength dependence is well fitted by the one-parameter theoretical curves based on the fractal scattering with fractal dimension of 2.5. In both (a) and (b), the previous results (Fig. 1 in Ref. [11]) are reexamined on the basis of the theory of dielectric constant fluctuation, and a comparison between the measured and fitted data is shown by dotted and solid lines, respectively.
Fig. 2.
Fig. 2. Correlation length ξ as a function of pore-filling fraction f, extracted from the peak absorbance at around 1900 nm, normalized by the initial maximum value measured immediately after removal from the immersion container [11]. The maximum correlation length reaches a value of about 18 nm at most at about f=0.6. The large error bar at f=0.97 is due to the deviation of measured curve 1 from the corresponding theoretical curve, as shown in Figs. 1(a) and 1(b). For comparison, the scatterer’s effective radius rsca, based on the previous Rayleigh scattering viewpoint [11,12], as a function of f is also included in the figure.

Equations (11)

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τ=η2AV·π2λ04·4πdΩ1+cos2θ2·ω(q),
ω(q)=04πr2γ(r)sin(qr)qrdr,
γ(r)=Aexp(r/ξ)r3D.
f5/2(q)=23[1+q2ξ21]1/2[1+q2ξ2+2]qξ[1+q2ξ2]3/2.
τ=η2AVk0416π2·ω0·Ω5/2,
Ω5/2=2π0πdθsinθ1+cos2θ2f5/2(2k0sinθ2)=22π3b3{h(1+4k02ξ2,b)h(1,b)}
h(z,b)=2z{z37z25z11z12b(z3+1+1z1)2b2z1}.
τ(λ0)=1dln(1Tr(λ0))Δη2AV·π2λ04·ω0·Ω5/2,
η2AV=(εpεs)2ϕ(1ϕ),
εp=(1f)·εair+f·εwater,
Δη2AV(εairεwater)2f(1f)·ϕ(1ϕ).

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