Abstract

The recent discovery of brilliant whiteness in ultrathin beetle scales indicated the availability of significant whiteness, brightness, and opacity from limited sample thickness. This is achieved in the beetle through optimization of the packing density of scattering centers in its elytral scales. Here, we directly test and apply this idea to whiteness and brightness in the production and appearance of mineral coatings on paper by varying the scattering center parameters that underpin its optical properties. Through biomimetic design principles, we find that desirably high optical scattering from mineral coatings can be achieved. Commercially, by using appropriately designed coating formulations, this leads to the prospect of equal optical performance using less scattering material.

© 2009 Optical Society of America

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References

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  1. P. Vukusic, B. Hallam, and J. Noyes, “Brilliant whiteness in ultrathin beetle scales,” Science 315, 348-348 (2007).
    [CrossRef] [PubMed]
  2. G. Pring, C. Nutbeem, and B. Lindqvist, “New solutions for optical performance in coated papers,” presented at the 19th PTS Coating Symposium, Munich, 14-17 September 1999.
  3. C. Nutbeem, J. C. Husband, and J. S. Preston, “The role of pigments in controlling coating structure,” in PITA Coating Conference, Bradford, Proceedings (PITA, 2005), pp. 97-102.
  4. B. Hallam, C. Nutbeem, and T. Asano, “Optimisation of steep carbonate coating formulations with ultra fine platy kaolin,” presented at the TAPPI Coating and Graphic Arts Conference, Miami, Florida, 22-25 April 2007.
  5. J. C. Husband and C. Nutbeem, “A practical approach to the use of engineered pigments,” Paper Technol. 42, 57-66 (2001).
  6. P. Burri, C. Naydowski, D. Spielmann, and E. Swanson, “Using classical theory to design a pigment with improved optical properties,” Tappi J. 80, 193-199 (1997).
  7. D. W. Donigian, J. N. Ishley, and K. J. Wise, “Coating pore structure and offset printed gloss,” Tappi J. 80, 163-172(1997).
  8. F. B. Stieg, “Opaque white coatings,” in ACS Symposium Series 285: Applied Polymer Science, 2nd ed., R.W.Tess and G.W.Poehlein, eds. (American Chemical Society, 1985).
  9. R. J. Bruehlman, L. W. Thomas, and E. Gonick, “Effect of particle size and pigment volume concentration on hiding power of titanium dioxide,” Off.l Dig. 33, 252-267(1961).
  10. W. K. Asbeck and M. Van Loo, “Critical pigment-volume relationships,” Ind. Eng. Chem. 41, 1470-1475 (1949).
    [CrossRef]
  11. P. Lepoutre and A. Rezanowich, “Optical properties and structure of clay-latex coatings,” Tappi J. 60, 86-91(1977).
  12. L. F. Gate, “Light scattering in microporous materials using a photon diffusion model,” J. Phys. D 5, 837-846 (1972).
    [CrossRef]
  13. P. Lepoutre and B. Alince, “Effect of post-treatment on the optical properties of plastic pigment coatings,” Tappi J. 64, 67 (1981).
  14. P. Lepoutre, “The structure of paper coatings: an update,” Prog. Org. Coatings 17, 89-106 (1989).
    [CrossRef]
  15. L. Abrams, C. W. Favorite, P. J. Capano, and R. W. Johnson, “Using mercury porosimetry to characterise coating pore structure and its relation to coating optical performance,” in Proceedings of the 1996 TAPPI Coating Conference (TAPPI, 1996), pp. 185-192.
  16. L. E. McNeil and R. H. French, “Multiple scattering from rutile TiO2 particles,” Acta Mater. 48, 4571-4576 (2000).
    [CrossRef]
  17. F. B. Steig, “Ending the 'crowding/spacing theory' debate,” J. Coatings Technol. 59, 96-97 (1987).
  18. J. H. Braun, “Crowding and spacing of titanium dioxide pigments,” J. Coatings Technol. 60, 67-71 (1988).
  19. J. Kettle, “Investigation and computer modeling of the pore structure of paper and of consolidated coatings,” Ph.D. dissertation (University of Plymouth, 1996).
  20. P. Kulbelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).
  21. N. Pauler, Paper Optics (Lorentzen & Wettre, 2000).
  22. G. Mie, “Contributions to the optics of turbid media, particularly of colloidal metal solutions,” Ann. Physik 330, 377-445 (1908).
    [CrossRef]
  23. For example, the Mie Theory calculator by Ivan Charamisinau or the Mie Plot v3.4.10s by Philip Laven
  24. A. Penttilä, K. Lumme, and L. Kuutti, “Light-scattering efficiency of starch acetate pigments as a function of size and packing density,” Appl. Opt. 45, 3501-3509 (2006).
    [CrossRef] [PubMed]
  25. N. A. Climpson and J. H. Taylor, “Pore size distributions and optical scattering coefficients of clay structures,” Tappi J. 59, 89-92 (1976).
  26. R. W. Wygant, R. R. Iyer, J. P. E. Jones, and D. O. Cummings, “Glossing properties of engineered kaolins,” in Proceedings of the 1998 TAPPI Coating Conference (TAPPI, 1998), p. 837.
  27. J. Borch and P. Lepoutre, “Light reflectance of spherical pigments in paper coatings: a comparison with theory,” Tappi J. 61 (2), 45 (1978).

2007 (1)

P. Vukusic, B. Hallam, and J. Noyes, “Brilliant whiteness in ultrathin beetle scales,” Science 315, 348-348 (2007).
[CrossRef] [PubMed]

2006 (1)

2001 (1)

J. C. Husband and C. Nutbeem, “A practical approach to the use of engineered pigments,” Paper Technol. 42, 57-66 (2001).

2000 (1)

L. E. McNeil and R. H. French, “Multiple scattering from rutile TiO2 particles,” Acta Mater. 48, 4571-4576 (2000).
[CrossRef]

1997 (2)

P. Burri, C. Naydowski, D. Spielmann, and E. Swanson, “Using classical theory to design a pigment with improved optical properties,” Tappi J. 80, 193-199 (1997).

D. W. Donigian, J. N. Ishley, and K. J. Wise, “Coating pore structure and offset printed gloss,” Tappi J. 80, 163-172(1997).

1989 (1)

P. Lepoutre, “The structure of paper coatings: an update,” Prog. Org. Coatings 17, 89-106 (1989).
[CrossRef]

1988 (1)

J. H. Braun, “Crowding and spacing of titanium dioxide pigments,” J. Coatings Technol. 60, 67-71 (1988).

1987 (1)

F. B. Steig, “Ending the 'crowding/spacing theory' debate,” J. Coatings Technol. 59, 96-97 (1987).

1981 (1)

P. Lepoutre and B. Alince, “Effect of post-treatment on the optical properties of plastic pigment coatings,” Tappi J. 64, 67 (1981).

1978 (1)

J. Borch and P. Lepoutre, “Light reflectance of spherical pigments in paper coatings: a comparison with theory,” Tappi J. 61 (2), 45 (1978).

1977 (1)

P. Lepoutre and A. Rezanowich, “Optical properties and structure of clay-latex coatings,” Tappi J. 60, 86-91(1977).

1976 (1)

N. A. Climpson and J. H. Taylor, “Pore size distributions and optical scattering coefficients of clay structures,” Tappi J. 59, 89-92 (1976).

1972 (1)

L. F. Gate, “Light scattering in microporous materials using a photon diffusion model,” J. Phys. D 5, 837-846 (1972).
[CrossRef]

1961 (1)

R. J. Bruehlman, L. W. Thomas, and E. Gonick, “Effect of particle size and pigment volume concentration on hiding power of titanium dioxide,” Off.l Dig. 33, 252-267(1961).

1949 (1)

W. K. Asbeck and M. Van Loo, “Critical pigment-volume relationships,” Ind. Eng. Chem. 41, 1470-1475 (1949).
[CrossRef]

1931 (1)

P. Kulbelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).

1908 (1)

G. Mie, “Contributions to the optics of turbid media, particularly of colloidal metal solutions,” Ann. Physik 330, 377-445 (1908).
[CrossRef]

Abrams, L.

L. Abrams, C. W. Favorite, P. J. Capano, and R. W. Johnson, “Using mercury porosimetry to characterise coating pore structure and its relation to coating optical performance,” in Proceedings of the 1996 TAPPI Coating Conference (TAPPI, 1996), pp. 185-192.

Alince, B.

P. Lepoutre and B. Alince, “Effect of post-treatment on the optical properties of plastic pigment coatings,” Tappi J. 64, 67 (1981).

Asano, T.

B. Hallam, C. Nutbeem, and T. Asano, “Optimisation of steep carbonate coating formulations with ultra fine platy kaolin,” presented at the TAPPI Coating and Graphic Arts Conference, Miami, Florida, 22-25 April 2007.

Asbeck, W. K.

W. K. Asbeck and M. Van Loo, “Critical pigment-volume relationships,” Ind. Eng. Chem. 41, 1470-1475 (1949).
[CrossRef]

Borch, J.

J. Borch and P. Lepoutre, “Light reflectance of spherical pigments in paper coatings: a comparison with theory,” Tappi J. 61 (2), 45 (1978).

Braun, J. H.

J. H. Braun, “Crowding and spacing of titanium dioxide pigments,” J. Coatings Technol. 60, 67-71 (1988).

Bruehlman, R. J.

R. J. Bruehlman, L. W. Thomas, and E. Gonick, “Effect of particle size and pigment volume concentration on hiding power of titanium dioxide,” Off.l Dig. 33, 252-267(1961).

Burri, P.

P. Burri, C. Naydowski, D. Spielmann, and E. Swanson, “Using classical theory to design a pigment with improved optical properties,” Tappi J. 80, 193-199 (1997).

Capano, P. J.

L. Abrams, C. W. Favorite, P. J. Capano, and R. W. Johnson, “Using mercury porosimetry to characterise coating pore structure and its relation to coating optical performance,” in Proceedings of the 1996 TAPPI Coating Conference (TAPPI, 1996), pp. 185-192.

Climpson, N. A.

N. A. Climpson and J. H. Taylor, “Pore size distributions and optical scattering coefficients of clay structures,” Tappi J. 59, 89-92 (1976).

Cummings, D. O.

R. W. Wygant, R. R. Iyer, J. P. E. Jones, and D. O. Cummings, “Glossing properties of engineered kaolins,” in Proceedings of the 1998 TAPPI Coating Conference (TAPPI, 1998), p. 837.

Donigian, D. W.

D. W. Donigian, J. N. Ishley, and K. J. Wise, “Coating pore structure and offset printed gloss,” Tappi J. 80, 163-172(1997).

Favorite, C. W.

L. Abrams, C. W. Favorite, P. J. Capano, and R. W. Johnson, “Using mercury porosimetry to characterise coating pore structure and its relation to coating optical performance,” in Proceedings of the 1996 TAPPI Coating Conference (TAPPI, 1996), pp. 185-192.

French, R. H.

L. E. McNeil and R. H. French, “Multiple scattering from rutile TiO2 particles,” Acta Mater. 48, 4571-4576 (2000).
[CrossRef]

Gate, L. F.

L. F. Gate, “Light scattering in microporous materials using a photon diffusion model,” J. Phys. D 5, 837-846 (1972).
[CrossRef]

Gonick, E.

R. J. Bruehlman, L. W. Thomas, and E. Gonick, “Effect of particle size and pigment volume concentration on hiding power of titanium dioxide,” Off.l Dig. 33, 252-267(1961).

Hallam, B.

P. Vukusic, B. Hallam, and J. Noyes, “Brilliant whiteness in ultrathin beetle scales,” Science 315, 348-348 (2007).
[CrossRef] [PubMed]

B. Hallam, C. Nutbeem, and T. Asano, “Optimisation of steep carbonate coating formulations with ultra fine platy kaolin,” presented at the TAPPI Coating and Graphic Arts Conference, Miami, Florida, 22-25 April 2007.

Husband, J. C.

J. C. Husband and C. Nutbeem, “A practical approach to the use of engineered pigments,” Paper Technol. 42, 57-66 (2001).

C. Nutbeem, J. C. Husband, and J. S. Preston, “The role of pigments in controlling coating structure,” in PITA Coating Conference, Bradford, Proceedings (PITA, 2005), pp. 97-102.

Ishley, J. N.

D. W. Donigian, J. N. Ishley, and K. J. Wise, “Coating pore structure and offset printed gloss,” Tappi J. 80, 163-172(1997).

Iyer, R. R.

R. W. Wygant, R. R. Iyer, J. P. E. Jones, and D. O. Cummings, “Glossing properties of engineered kaolins,” in Proceedings of the 1998 TAPPI Coating Conference (TAPPI, 1998), p. 837.

Johnson, R. W.

L. Abrams, C. W. Favorite, P. J. Capano, and R. W. Johnson, “Using mercury porosimetry to characterise coating pore structure and its relation to coating optical performance,” in Proceedings of the 1996 TAPPI Coating Conference (TAPPI, 1996), pp. 185-192.

Jones, J. P. E.

R. W. Wygant, R. R. Iyer, J. P. E. Jones, and D. O. Cummings, “Glossing properties of engineered kaolins,” in Proceedings of the 1998 TAPPI Coating Conference (TAPPI, 1998), p. 837.

Kettle, J.

J. Kettle, “Investigation and computer modeling of the pore structure of paper and of consolidated coatings,” Ph.D. dissertation (University of Plymouth, 1996).

Kulbelka, P.

P. Kulbelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).

Kuutti, L.

Lepoutre, P.

P. Lepoutre, “The structure of paper coatings: an update,” Prog. Org. Coatings 17, 89-106 (1989).
[CrossRef]

P. Lepoutre and B. Alince, “Effect of post-treatment on the optical properties of plastic pigment coatings,” Tappi J. 64, 67 (1981).

J. Borch and P. Lepoutre, “Light reflectance of spherical pigments in paper coatings: a comparison with theory,” Tappi J. 61 (2), 45 (1978).

P. Lepoutre and A. Rezanowich, “Optical properties and structure of clay-latex coatings,” Tappi J. 60, 86-91(1977).

Lindqvist, B.

G. Pring, C. Nutbeem, and B. Lindqvist, “New solutions for optical performance in coated papers,” presented at the 19th PTS Coating Symposium, Munich, 14-17 September 1999.

Lumme, K.

McNeil, L. E.

L. E. McNeil and R. H. French, “Multiple scattering from rutile TiO2 particles,” Acta Mater. 48, 4571-4576 (2000).
[CrossRef]

Mie, G.

G. Mie, “Contributions to the optics of turbid media, particularly of colloidal metal solutions,” Ann. Physik 330, 377-445 (1908).
[CrossRef]

Munk, F.

P. Kulbelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).

Naydowski, C.

P. Burri, C. Naydowski, D. Spielmann, and E. Swanson, “Using classical theory to design a pigment with improved optical properties,” Tappi J. 80, 193-199 (1997).

Noyes, J.

P. Vukusic, B. Hallam, and J. Noyes, “Brilliant whiteness in ultrathin beetle scales,” Science 315, 348-348 (2007).
[CrossRef] [PubMed]

Nutbeem, C.

J. C. Husband and C. Nutbeem, “A practical approach to the use of engineered pigments,” Paper Technol. 42, 57-66 (2001).

B. Hallam, C. Nutbeem, and T. Asano, “Optimisation of steep carbonate coating formulations with ultra fine platy kaolin,” presented at the TAPPI Coating and Graphic Arts Conference, Miami, Florida, 22-25 April 2007.

C. Nutbeem, J. C. Husband, and J. S. Preston, “The role of pigments in controlling coating structure,” in PITA Coating Conference, Bradford, Proceedings (PITA, 2005), pp. 97-102.

G. Pring, C. Nutbeem, and B. Lindqvist, “New solutions for optical performance in coated papers,” presented at the 19th PTS Coating Symposium, Munich, 14-17 September 1999.

Pauler, N.

N. Pauler, Paper Optics (Lorentzen & Wettre, 2000).

Penttilä, A.

Preston, J. S.

C. Nutbeem, J. C. Husband, and J. S. Preston, “The role of pigments in controlling coating structure,” in PITA Coating Conference, Bradford, Proceedings (PITA, 2005), pp. 97-102.

Pring, G.

G. Pring, C. Nutbeem, and B. Lindqvist, “New solutions for optical performance in coated papers,” presented at the 19th PTS Coating Symposium, Munich, 14-17 September 1999.

Rezanowich, A.

P. Lepoutre and A. Rezanowich, “Optical properties and structure of clay-latex coatings,” Tappi J. 60, 86-91(1977).

Spielmann, D.

P. Burri, C. Naydowski, D. Spielmann, and E. Swanson, “Using classical theory to design a pigment with improved optical properties,” Tappi J. 80, 193-199 (1997).

Steig, F. B.

F. B. Steig, “Ending the 'crowding/spacing theory' debate,” J. Coatings Technol. 59, 96-97 (1987).

Stieg, F. B.

F. B. Stieg, “Opaque white coatings,” in ACS Symposium Series 285: Applied Polymer Science, 2nd ed., R.W.Tess and G.W.Poehlein, eds. (American Chemical Society, 1985).

Swanson, E.

P. Burri, C. Naydowski, D. Spielmann, and E. Swanson, “Using classical theory to design a pigment with improved optical properties,” Tappi J. 80, 193-199 (1997).

Taylor, J. H.

N. A. Climpson and J. H. Taylor, “Pore size distributions and optical scattering coefficients of clay structures,” Tappi J. 59, 89-92 (1976).

Thomas, L. W.

R. J. Bruehlman, L. W. Thomas, and E. Gonick, “Effect of particle size and pigment volume concentration on hiding power of titanium dioxide,” Off.l Dig. 33, 252-267(1961).

Van Loo, M.

W. K. Asbeck and M. Van Loo, “Critical pigment-volume relationships,” Ind. Eng. Chem. 41, 1470-1475 (1949).
[CrossRef]

Vukusic, P.

P. Vukusic, B. Hallam, and J. Noyes, “Brilliant whiteness in ultrathin beetle scales,” Science 315, 348-348 (2007).
[CrossRef] [PubMed]

Wise, K. J.

D. W. Donigian, J. N. Ishley, and K. J. Wise, “Coating pore structure and offset printed gloss,” Tappi J. 80, 163-172(1997).

Wygant, R. W.

R. W. Wygant, R. R. Iyer, J. P. E. Jones, and D. O. Cummings, “Glossing properties of engineered kaolins,” in Proceedings of the 1998 TAPPI Coating Conference (TAPPI, 1998), p. 837.

Acta Mater. (1)

L. E. McNeil and R. H. French, “Multiple scattering from rutile TiO2 particles,” Acta Mater. 48, 4571-4576 (2000).
[CrossRef]

Ann. Physik (1)

G. Mie, “Contributions to the optics of turbid media, particularly of colloidal metal solutions,” Ann. Physik 330, 377-445 (1908).
[CrossRef]

Appl. Opt. (1)

Ind. Eng. Chem. (1)

W. K. Asbeck and M. Van Loo, “Critical pigment-volume relationships,” Ind. Eng. Chem. 41, 1470-1475 (1949).
[CrossRef]

J. Coatings Technol. (2)

F. B. Steig, “Ending the 'crowding/spacing theory' debate,” J. Coatings Technol. 59, 96-97 (1987).

J. H. Braun, “Crowding and spacing of titanium dioxide pigments,” J. Coatings Technol. 60, 67-71 (1988).

J. Phys. D (1)

L. F. Gate, “Light scattering in microporous materials using a photon diffusion model,” J. Phys. D 5, 837-846 (1972).
[CrossRef]

Off.l Dig. (1)

R. J. Bruehlman, L. W. Thomas, and E. Gonick, “Effect of particle size and pigment volume concentration on hiding power of titanium dioxide,” Off.l Dig. 33, 252-267(1961).

Paper Technol. (1)

J. C. Husband and C. Nutbeem, “A practical approach to the use of engineered pigments,” Paper Technol. 42, 57-66 (2001).

Prog. Org. Coatings (1)

P. Lepoutre, “The structure of paper coatings: an update,” Prog. Org. Coatings 17, 89-106 (1989).
[CrossRef]

Science (1)

P. Vukusic, B. Hallam, and J. Noyes, “Brilliant whiteness in ultrathin beetle scales,” Science 315, 348-348 (2007).
[CrossRef] [PubMed]

Tappi J. (6)

P. Burri, C. Naydowski, D. Spielmann, and E. Swanson, “Using classical theory to design a pigment with improved optical properties,” Tappi J. 80, 193-199 (1997).

D. W. Donigian, J. N. Ishley, and K. J. Wise, “Coating pore structure and offset printed gloss,” Tappi J. 80, 163-172(1997).

P. Lepoutre and B. Alince, “Effect of post-treatment on the optical properties of plastic pigment coatings,” Tappi J. 64, 67 (1981).

P. Lepoutre and A. Rezanowich, “Optical properties and structure of clay-latex coatings,” Tappi J. 60, 86-91(1977).

N. A. Climpson and J. H. Taylor, “Pore size distributions and optical scattering coefficients of clay structures,” Tappi J. 59, 89-92 (1976).

J. Borch and P. Lepoutre, “Light reflectance of spherical pigments in paper coatings: a comparison with theory,” Tappi J. 61 (2), 45 (1978).

Z. Tech. Phys. (Leipzig) (1)

P. Kulbelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 11a, 593-601 (1931).

Other (9)

N. Pauler, Paper Optics (Lorentzen & Wettre, 2000).

L. Abrams, C. W. Favorite, P. J. Capano, and R. W. Johnson, “Using mercury porosimetry to characterise coating pore structure and its relation to coating optical performance,” in Proceedings of the 1996 TAPPI Coating Conference (TAPPI, 1996), pp. 185-192.

R. W. Wygant, R. R. Iyer, J. P. E. Jones, and D. O. Cummings, “Glossing properties of engineered kaolins,” in Proceedings of the 1998 TAPPI Coating Conference (TAPPI, 1998), p. 837.

For example, the Mie Theory calculator by Ivan Charamisinau or the Mie Plot v3.4.10s by Philip Laven

J. Kettle, “Investigation and computer modeling of the pore structure of paper and of consolidated coatings,” Ph.D. dissertation (University of Plymouth, 1996).

F. B. Stieg, “Opaque white coatings,” in ACS Symposium Series 285: Applied Polymer Science, 2nd ed., R.W.Tess and G.W.Poehlein, eds. (American Chemical Society, 1985).

G. Pring, C. Nutbeem, and B. Lindqvist, “New solutions for optical performance in coated papers,” presented at the 19th PTS Coating Symposium, Munich, 14-17 September 1999.

C. Nutbeem, J. C. Husband, and J. S. Preston, “The role of pigments in controlling coating structure,” in PITA Coating Conference, Bradford, Proceedings (PITA, 2005), pp. 97-102.

B. Hallam, C. Nutbeem, and T. Asano, “Optimisation of steep carbonate coating formulations with ultra fine platy kaolin,” presented at the TAPPI Coating and Graphic Arts Conference, Miami, Florida, 22-25 April 2007.

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Figures (7)

Fig. 1
Fig. 1

(a) Head, legs, and body of the Cyphochilus beetle are covered with flattened scales, the interiors of which comprise a random network of interconnected filaments shown here in (b) scanning electron microscopy (SEM) and (c) transmission electron microscopy (TEM) images [Scale bars: (a)  5 mm ; (b) and (c)  1 μm ].

Fig. 2
Fig. 2

(a) Matrix of pigments coated in the study, allowing the effect on coating structure of changes of D50 and PSD steepness ( D 30 / D 70 * 100 ) to be studied independently; (b)  blending broad (black) and narrow (gray) distribution pigments with matched D50 enabled the matrix of coating minerals to be controlled.

Fig. 3
Fig. 3

Light-scatter contribution per air void; data points show experimental data [ D 50 = 0.3 μm (black square with white cross), D 50 = 0.4 μm (triangle), D 50 = 0.6 μm (square), D 50 = 1.0 μm (circle), D 50 = 1.4 μm (diamond)], solid black line is included as a guide to the eye, dotted gray line is the predicted response according to Mie Theory (scattered intensity, arb. units).

Fig. 4
Fig. 4

Number density of scattering sites as a function of average scatter site diameter. Data points show experimental data [ D 50 = 0.3 μm (black square with white cross), D 50 = 0.4 μm (triangle), D 50 = 0.6 μm (square), D 50 = 1.0 μm (circle), D 50 = 1.4 μm (diamond)], solid line is a guide to the eye.

Fig. 5
Fig. 5

Average pore separation as a function of typical mineral parameters.

Fig. 6
Fig. 6

Light-scatter contribution from individual Ti O 2 particles as a function of average particle separation for red light at 650 nm (black), green light at 550 nm (medium gray) and blue light at 450 nm light (light gray).

Fig. 7
Fig. 7

Calendered sheet light scattering (at 460 nm ) as a function of typical mineral parameters.

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