Abstract

An equation is derived from which the fluorescence obtained from a fluorescent whitener on a given substrate can be calculated from several reflectivity measurements. By use of this equation, one can explain theoretically and quantitatively such effects as the shape of the fluorescence vs concentration curve, the effect of the color of the substrate on fluorescence, the effect of the thickness or opacity of the substrate on fluorescence, and the effect of concentration of whitener on the shape of the emission curve.

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  1. P. Kubelka and F. Munk, Z. Tech. Physik 11, 593–601 (1931).
  2. P. Kubelka, J. Opt. Soc. Am. 38, 448–457 (1948).
  3. T. H. Morton, J. Soc. Dyers Colourists 79, 238–242 (1963).
  4. See Ref. 2, Eqs. (19) and (20).
  5. See Ref. 2, Eq. (22).
  6. See Ref. 2, Eq. (28).
  7. D. B. Judd, J. Res. Natl. Bur. Std. 19, 287–317 (1937); Paper Trade J. 106, 39–46 (1938).
  8. The ratio α can be calculated from a transmittance curve of the dye in a clear substrate which is chemically similar to the substrate used for dyeing. An example is given in a subsequent paragraph. Alternatively, it may be determined from measurements on the dyed sample by a method to be described in a subsequent publication.
  9. A convenient table for the conversion of R to ρ and back, with a spacing of 0.001 in R, is given by D. B. Judd, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1952), pp. 358–362.
  10. P. Kubelka, Ref. 2, Eq. (25a).
  11. In the case of paper, for example, owing to inhomogeneity in the sheet, the measured thickness is not the same as the true effective thickness.
  12. E. Allen, Am. Dyestuff Reptr. 48, 27–29 (1959).
  13. S. N. Glarum and S. E. Penner, Am. Dyestuff Reptr. 43, P310–P314 (1954).
  14. Other examples are given in Ref. 12.
  15. Papermaker's brightness is defined by TAPPI as the reflectance through a specifically defined filter in a carefully defined instrument. Often the reflectance at 459 mµ is used as an approximation. The reflectance at 440 mµ, used in this study, is probably slightly lower than the true "brightness" value, but is reliable as a relative indication of "brightness."
  16. E. Allen, J. Opt. Soc. Am. 47, 933–943 (1957); Am. Dyestuff Reptr. 46, 425–432 (1957).

Allen, E.

E. Allen, J. Opt. Soc. Am. 47, 933–943 (1957); Am. Dyestuff Reptr. 46, 425–432 (1957).

E. Allen, Am. Dyestuff Reptr. 48, 27–29 (1959).

Glarum, S. N.

S. N. Glarum and S. E. Penner, Am. Dyestuff Reptr. 43, P310–P314 (1954).

Judd, D. B.

A convenient table for the conversion of R to ρ and back, with a spacing of 0.001 in R, is given by D. B. Judd, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1952), pp. 358–362.

D. B. Judd, J. Res. Natl. Bur. Std. 19, 287–317 (1937); Paper Trade J. 106, 39–46 (1938).

Kubelka, P.

P. Kubelka, Ref. 2, Eq. (25a).

P. Kubelka and F. Munk, Z. Tech. Physik 11, 593–601 (1931).

P. Kubelka, J. Opt. Soc. Am. 38, 448–457 (1948).

Morton, T. H.

T. H. Morton, J. Soc. Dyers Colourists 79, 238–242 (1963).

Munk, F.

P. Kubelka and F. Munk, Z. Tech. Physik 11, 593–601 (1931).

Penner, S. E.

S. N. Glarum and S. E. Penner, Am. Dyestuff Reptr. 43, P310–P314 (1954).

Other

P. Kubelka and F. Munk, Z. Tech. Physik 11, 593–601 (1931).

P. Kubelka, J. Opt. Soc. Am. 38, 448–457 (1948).

T. H. Morton, J. Soc. Dyers Colourists 79, 238–242 (1963).

See Ref. 2, Eqs. (19) and (20).

See Ref. 2, Eq. (22).

See Ref. 2, Eq. (28).

D. B. Judd, J. Res. Natl. Bur. Std. 19, 287–317 (1937); Paper Trade J. 106, 39–46 (1938).

The ratio α can be calculated from a transmittance curve of the dye in a clear substrate which is chemically similar to the substrate used for dyeing. An example is given in a subsequent paragraph. Alternatively, it may be determined from measurements on the dyed sample by a method to be described in a subsequent publication.

A convenient table for the conversion of R to ρ and back, with a spacing of 0.001 in R, is given by D. B. Judd, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1952), pp. 358–362.

P. Kubelka, Ref. 2, Eq. (25a).

In the case of paper, for example, owing to inhomogeneity in the sheet, the measured thickness is not the same as the true effective thickness.

E. Allen, Am. Dyestuff Reptr. 48, 27–29 (1959).

S. N. Glarum and S. E. Penner, Am. Dyestuff Reptr. 43, P310–P314 (1954).

Other examples are given in Ref. 12.

Papermaker's brightness is defined by TAPPI as the reflectance through a specifically defined filter in a carefully defined instrument. Often the reflectance at 459 mµ is used as an approximation. The reflectance at 440 mµ, used in this study, is probably slightly lower than the true "brightness" value, but is reliable as a relative indication of "brightness."

E. Allen, J. Opt. Soc. Am. 47, 933–943 (1957); Am. Dyestuff Reptr. 46, 425–432 (1957).

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