Abstract

The experimentally determined chromaticities and reflectance spectra of films consisting of uniform ellipsoidal or spherical colloidal hematite particles are compared with calculated values and are found to be in good agreement. The theoretical treatment of the light-scattering problem involves the Mie theory for the spheres and the T-matrix method for the ellipsoids. The reflectance spectra for the pigment films are calculated through the use of the Kubelka–Munk analysis.

© 1994 Optical Society of America

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References

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  1. G. Mie, “Contributions on the optics of turbid media, especially colloidal metal sols,” Ann. Phys. (Leipzig) 25, 377–380 (1908).
  2. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–54, 93–96.
  3. M. Kerker, P. Scheiner, D. D. Cooke, J. P. Kratohvil, “Absorption index and color of colloidal hematite,” J. Colloid Interface Sci. 71, 176–187 (1979).
    [CrossRef]
  4. W. P. Hsu, E. Matijević, “Optical properties of monodispersed hematite hydrosols,” Appl. Opt. 24, 1623–1630 (1985).
    [CrossRef] [PubMed]
  5. E. Matijević, P. Scheiner, “Ferris hydrous oxide sols. III. Preparation of uniform particles,” J. Colloid Interface Sci. 63, 509–524 (1978).
    [CrossRef]
  6. M. Ozaki, S. Kratohvil, E. Matijević, “Formation of monodispersed spindle-type hematite particles,” J. Colloid Interface Sci. 102, 146–151 (1984).
    [CrossRef]
  7. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 130–158.
  8. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Teaneck, N.J., 1990), Chap. 3, p. 79.
    [CrossRef]
  9. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farban-striche,” Z. Tech. Phys. 12, 593–595 (1931).
  10. D. B. Judd, Color in Business, Science, and Industry (Wiley, New York, 1952), pp. 314–317.
  11. F. W. Billmeyer, M. Saltzman, Principles of Color Technology (Interscience, New York, 1966), Chap. 2, p. 25.

1985

1984

M. Ozaki, S. Kratohvil, E. Matijević, “Formation of monodispersed spindle-type hematite particles,” J. Colloid Interface Sci. 102, 146–151 (1984).
[CrossRef]

1979

M. Kerker, P. Scheiner, D. D. Cooke, J. P. Kratohvil, “Absorption index and color of colloidal hematite,” J. Colloid Interface Sci. 71, 176–187 (1979).
[CrossRef]

1978

E. Matijević, P. Scheiner, “Ferris hydrous oxide sols. III. Preparation of uniform particles,” J. Colloid Interface Sci. 63, 509–524 (1978).
[CrossRef]

1931

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farban-striche,” Z. Tech. Phys. 12, 593–595 (1931).

1908

G. Mie, “Contributions on the optics of turbid media, especially colloidal metal sols,” Ann. Phys. (Leipzig) 25, 377–380 (1908).

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Teaneck, N.J., 1990), Chap. 3, p. 79.
[CrossRef]

Billmeyer, F. W.

F. W. Billmeyer, M. Saltzman, Principles of Color Technology (Interscience, New York, 1966), Chap. 2, p. 25.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 130–158.

Cooke, D. D.

M. Kerker, P. Scheiner, D. D. Cooke, J. P. Kratohvil, “Absorption index and color of colloidal hematite,” J. Colloid Interface Sci. 71, 176–187 (1979).
[CrossRef]

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Teaneck, N.J., 1990), Chap. 3, p. 79.
[CrossRef]

Hsu, W. P.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 130–158.

Judd, D. B.

D. B. Judd, Color in Business, Science, and Industry (Wiley, New York, 1952), pp. 314–317.

Kerker, M.

M. Kerker, P. Scheiner, D. D. Cooke, J. P. Kratohvil, “Absorption index and color of colloidal hematite,” J. Colloid Interface Sci. 71, 176–187 (1979).
[CrossRef]

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–54, 93–96.

Kratohvil, J. P.

M. Kerker, P. Scheiner, D. D. Cooke, J. P. Kratohvil, “Absorption index and color of colloidal hematite,” J. Colloid Interface Sci. 71, 176–187 (1979).
[CrossRef]

Kratohvil, S.

M. Ozaki, S. Kratohvil, E. Matijević, “Formation of monodispersed spindle-type hematite particles,” J. Colloid Interface Sci. 102, 146–151 (1984).
[CrossRef]

Kubelka, P.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farban-striche,” Z. Tech. Phys. 12, 593–595 (1931).

Matijevic, E.

W. P. Hsu, E. Matijević, “Optical properties of monodispersed hematite hydrosols,” Appl. Opt. 24, 1623–1630 (1985).
[CrossRef] [PubMed]

M. Ozaki, S. Kratohvil, E. Matijević, “Formation of monodispersed spindle-type hematite particles,” J. Colloid Interface Sci. 102, 146–151 (1984).
[CrossRef]

E. Matijević, P. Scheiner, “Ferris hydrous oxide sols. III. Preparation of uniform particles,” J. Colloid Interface Sci. 63, 509–524 (1978).
[CrossRef]

Mie, G.

G. Mie, “Contributions on the optics of turbid media, especially colloidal metal sols,” Ann. Phys. (Leipzig) 25, 377–380 (1908).

Munk, F.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farban-striche,” Z. Tech. Phys. 12, 593–595 (1931).

Ozaki, M.

M. Ozaki, S. Kratohvil, E. Matijević, “Formation of monodispersed spindle-type hematite particles,” J. Colloid Interface Sci. 102, 146–151 (1984).
[CrossRef]

Saltzman, M.

F. W. Billmeyer, M. Saltzman, Principles of Color Technology (Interscience, New York, 1966), Chap. 2, p. 25.

Scheiner, P.

M. Kerker, P. Scheiner, D. D. Cooke, J. P. Kratohvil, “Absorption index and color of colloidal hematite,” J. Colloid Interface Sci. 71, 176–187 (1979).
[CrossRef]

E. Matijević, P. Scheiner, “Ferris hydrous oxide sols. III. Preparation of uniform particles,” J. Colloid Interface Sci. 63, 509–524 (1978).
[CrossRef]

Ann. Phys. (Leipzig)

G. Mie, “Contributions on the optics of turbid media, especially colloidal metal sols,” Ann. Phys. (Leipzig) 25, 377–380 (1908).

Appl. Opt.

J. Colloid Interface Sci.

E. Matijević, P. Scheiner, “Ferris hydrous oxide sols. III. Preparation of uniform particles,” J. Colloid Interface Sci. 63, 509–524 (1978).
[CrossRef]

M. Ozaki, S. Kratohvil, E. Matijević, “Formation of monodispersed spindle-type hematite particles,” J. Colloid Interface Sci. 102, 146–151 (1984).
[CrossRef]

M. Kerker, P. Scheiner, D. D. Cooke, J. P. Kratohvil, “Absorption index and color of colloidal hematite,” J. Colloid Interface Sci. 71, 176–187 (1979).
[CrossRef]

Z. Tech. Phys.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farban-striche,” Z. Tech. Phys. 12, 593–595 (1931).

Other

D. B. Judd, Color in Business, Science, and Industry (Wiley, New York, 1952), pp. 314–317.

F. W. Billmeyer, M. Saltzman, Principles of Color Technology (Interscience, New York, 1966), Chap. 2, p. 25.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–54, 93–96.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 130–158.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Teaneck, N.J., 1990), Chap. 3, p. 79.
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Scanning electron micrographs of hematite samples (a) B and (b) D, prepared under conditions given in Table 1.

Fig. 2
Fig. 2

Complex refractive index for hematite in air.3,4

Fig. 3
Fig. 3

Calculated scattering and absorbance cross sections for single particles having refractive index of hematite of types A and B (Table 1). Cross sections for λ > 570 nm are also shown for sample C.

Fig. 4
Fig. 4

Calculated scattering and absorbance cross sections for single spherical particles E–G having refractive index of hematite (Table 1).

Fig. 5
Fig. 5

Experimental and calculated reflectance spectra for pigment films of hematite particles, described in Table 1. The amounts of solids in milligrams per inverse square centimeters in respective films: A, 2.0; B, 3.3; C, 2.6; D, 0.90; E, 0.90; F, 0.47; G, 0.67.

Fig. 6
Fig. 6

Reflectance spectra of films of ellipsoidal hematite particle A (Table 1), calculated for different layer thicknesses d. Experimentally measured values are for films made up with 2.0 (○), 1.0 (□), 0.67 (△), and 0.16 mg cm−2 (⋄) of solids.

Fig. 7
Fig. 7

Same plots as in Fig. 6 for films of spherical hematite particles E. Experimentally measured values are for films made up with 0.90 (○) and 0.71 mg cm−2 (□) of solids.

Fig. 8
Fig. 8

Extinction efficiency Q ext = C ext/r 2π as a function of diameter and wavelength, calculated according to the Mie theory for spheres having refractive index of hematite.

Fig. 9
Fig. 9

Chromaticity diagrams for films of ellipsoidal particles A–D. Circles represent experimental points. The dominant wavelength is given by the intersection with the boundary of the line connecting the neutral and experimental points. The calculated chromaticities are for system A (○) and for system B (□), respectively.

Fig. 10
Fig. 10

Same plot as in Fig. 9, except for spherical particles E–G.

Fig. 11
Fig. 11

Chromaticity diagram for hematite particles in films of different thicknesses as given in Figs. 6 and 7. Circles and squares refer to measured quantities for ellipsoidal and spherical particles, respectively. The solid curve is calculated for ellipsoids of the same size but increasing film thickness, whereas the dashed curve is for spheres of the same diameter as E. The end of both curves nearest to the boundary refers to an infinitely thick layer.

Tables (2)

Tables Icon

Table 1 Description of Preparation Conditions and Size Characteristics of Hematite Particles

Tables Icon

Table 2 Dominant Wavelengths and Purities for Experimental and Calculated Chromaticities as Shown in Fig. 5

Equations (12)

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C ext = C sca + C abs ,
C sca = π k 2 0 π [ i 1 ( θ ) + i 2 ( θ ) ] sin θ d θ ,
i u = ( i 1 + i 2 ) / 2.
R = 1 + K S - ( K 2 S 2 + 2 K S ) 1 / 2 .
R = ( R g - R ) / R - R ( R g - 1 / R ) exp [ S d ( 1 / R - R ) ] R g - R - ( R g - 1 / R ) exp [ S d ( 1 / R - R ) ] ,
K = 3 C abs 2 π r 3 ,
K = 3 C abs 2 π a b 2 ,
S = 9 C sca ( 1 - cos θ ¯ ) 16 π r 3 ,
S = 9 C sca ( 1 - cos θ ¯ ) 16 π a b 2 ,
cos θ ¯ = π k 2 0 π [ i 1 ( θ ) + i 2 ( θ ) ] cos θ sin θ d θ π k 2 0 π [ i 1 ( θ ) + i 2 ( θ ) ] sin θ d θ .
X = λ R ( λ ) E ( λ ) x ¯ ( λ ) d λ , Y = λ R ( λ ) E ( λ ) y ¯ ( λ ) d λ , Z = λ R ( λ ) E ( λ ) z ¯ ( λ ) d λ .
x = X X + Y + Z , y = Y X + Y + Z .

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