JAIC 1997, Volume 36, Number 3, Article 3 (pp. 207 to 230)
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Journal of the American Institute for Conservation
JAIC 1997, Volume 36, Number 3, Article 3 (pp. 207 to 230)






In developing the general kinetic law for the fading of a transparent glaze, we adopt the approach of Malac (1989), in which the rate of total colorant loss is determined by the total amount of photochemically active light absorbed. This model rests on a number of simplifying assumptions, and later we discuss the extension of these kinetics to more general systems. We begin by assuming:

  1. The glaze is purely absorbing, that is, there is no optical scattering.
  2. The light incident upon the glaze is collimated and monochromatic.
  3. The fading reaction creates nonabsorbing, nonscattering products.
  4. The photochemical reaction rate depends on the amount of light absorbed.

The loss of colorant per unit time is equal to the light flux (in moles of photons per unit time) incident on the colorant, multiplied by the probability that the light is absorbed by the glaze, multiplied by the probability that an absorbed photon causes conversion of the colorant to colorless product. In symbolic notation, this is written as:

Fig. .
where m is the number of moles of colorant, ΔLt is the photon flux, α is the probability of absorbing a photon (or the fraction of incident light absorbed by the film), and φ is the probability of reaction from the light absorption. The quantity φ is also known as the quantum yield for the reaction. The reciprocity principle is implicit in the assumption that the rate of colorant loss is linearly dependent on the light flux. An equivalent form of this relation expresses the colorant loss in more convenient terms by dividing by the film volume:
Fig. .
where A is the surface area of the film and X its thickness. But the term (Δm/A X) is just ΔC, the change in the colorant concentration (in weight per film volume), and (ΔL/A Δt) is the light intensity I0, so the general kinetic law reduces to:
Fig. .
for all glazes.

This expression indicates that the loss of colorant concentration will generally be proportional to the fraction of incident light absorbed by the film (represented by α). This relationship suggests two results: The concentration loss rate in very highly absorbing glazes will be constant as long as the absorption strength does not change during the fading; and the loss rate will become progressively smaller as the fading proceeds and the light absorption by the glaze decreases. A more explicit analysis of these cases reveals the relationship between the fading for these extreme cases.

For transparent glazes illuminated with collimated light making a single pass through the film, the absorbed fraction of light can be expressed using Beer's law: α = 1 − eKCX where K is the molar absorption coefficient. So the kinetic relation (3) becomes:

Fig. .

For very highly absorbing glazes (optically thick), all of the incident light is absorbed by the glaze (α = 1, or alternatively KCX is very large and e−KCX = 0), and a small concentration loss does not appreciably alter the amount of light that is absorbed. The kinetic expression for the overall concentration loss becomes:

Fig. .
Note that the rate of colorant loss depends only on the photon density (the light intensity per film thickness) and on the reaction probability, and not on any absorption properties of the colorant (as long as all of the light is absorbed). As the three quantities on the right side of equation 5a are constants, this relation describes a so-called “zero-order” reaction in which the loss of colorant concentration is constant with time:
Fig. .
where C0 is the initial colorant concentration and C is the concentration at time t.

In these glazes, the upper layers of colorant completely absorb the photochemically active wavelengths and fade while effectively protecting the underlying strata. This process has been observed in dye fading in films and textiles and has been dubbed the “layer effect” or the “filter effect.” Giles has reviewed the major observations and descriptions of this phenomenon in dye studies (Giles and Forrester 1980), and this same behavior has been alluded to in the analysis of the fading of very highly absorbing glazes by Johnston-Feller (1986).

For glazes that absorb only a fraction of the photochemically active wavelengths of incident light, the exponential term in equation 4 can be approximated eKCX ≅ 1−KCX), and the kinetic relation becomes:

Fig. .
assuming that the light passes through the glaze asingle time.

This approximation for the exponential term is reasonable for KCX < 0.3, that is, for glazes having transmittances above about 75%.

Equation 6a describes a rate of colorant loss that is proportional to colorant concentration: each increment of fading will cause the glaze to absorb slightly less light, causing the subsequent reaction to occur more slowly. This is an example of a so-called “first-order” reaction, and for such a process the concentration decreases exponentially with time:

Fig. .
Note that in this case the rate of the reaction depends on the molar absorption coefficient of the colorant, K: this quantity determines how much less light absorption results from a given concentration loss, and thus how rapidly the reaction rate decreases during the fading. The product (φI0K) is called the first-order rate constant for this reaction, denoted as k. This rate constant for the reaction of colorant in very thin glazes is also the rate constant for the local photochemical reaction of individual molecules.

It is valuable to examine the relationship between the zero-order rate constant of the “thick” glaze fading and the first-order rate constant of the “thin” glaze fading. One can see that the zero-order rate constant (i.e., the slope of the linear fading of the thick glaze) is equal to the first-order reaction rate constant divided by K X (the product of absorption coefficient and film thickness). Thus one can recast the general kinetic expression of equation 3 in terms of this first-order reaction rate constant:

Fig. .
This relation is especially useful because it expresses the fading reaction in terms of the first-order reaction rate constant k, which also represents the intrinsic rate constant for the reaction of an individual colorant molecule. This property is the intrinsic light fading tendency that is constant for the colorant in all of the different formulations of the glaze. Determination of this rate constant and of the absorption strength for a given colorant should allow reasonable prediction of the fading of any glaze formulated from it.

At this point, it is appropriate to examine the validity of the original simplifying assumptions that were the basis for this description. The most obvious restriction of the model is its presumption of monochromatic illumination that allows the use of absorption coefficients and quantum yields of reaction for a single wavelength. Strictly speaking, the model can be extended to describe fading due to polychromatic illumination (far more typical of gallery lighting) by summing the effects of each wavelength (that is, the appropriate absorption coefficients and quantum yields) across the spectrum. This approach is similar to that used by Krochmann (1988) and necessitates the measurement of reaction rates due to absorptions at different wavelengths. It seems likely, however, that this fineness of detail may be unnecessary for describing fading due to absorption in a single broad spectral peak, which probably can be adequately described according to an average quantum yield for reaction due to absorption in that peak. As long as the description is thus restricted to illumination with a visible light source, so that the fading due to visible and ultraviolet wavelengths need not be summed, the above treatment should be adequate if the average values of absorption and reaction probabilities are used. Another assumption in this model is that the absorbed wavelengths are also the photochemically active ones. Recent studies have tended to support the notion that, provided that only a single absorption band is present, the absorption spectrum for the colorant coincides with the action spectrum of wavelengths that produce most of the photochemical reaction (McLaren 1956; Saunders and Kirby 1994).

The assumption of collimated light incident on the glaze film is also an inaccurate representation of the combination of diffuse and oblique collimated light often used to illuminate objects. Similarly, glazes are usually viewed over a reflective and optically scattering substrate, and the light fluxes within the film are expected to more closely approximate diffuse fluxes than collimated ones. It has been pointed out by many authors that the absorption coefficient of diffuse light is about twice that of collimated fluxes, probably by virtue of the greater absorption path length for the light traveling at oblique angles in the film (Beasley et al. 1967). As a result, the kinetic behavior for fading of glazes illuminated by diffuse light should be the same as for collimated light, with the absorption coefficients doubled. Also, since the model assumes that the light intensity distribution has no effect on the rate for the total colorant loss, the model should adequately describe fading of a glaze on a reflective substrate. For these reasons, the simple model that has been described is expected to allow at least qualitative predictions of the course of fading of a glaze under any given illumination and also to allow semiquantitative comparison of different glaze formulations when exposed to the same illumination.


Glazes of known pigment loadings were prepared by first ball milling for 3.5 days dry Pigment Red 66 (Colour Index No. 18000:1, a barium salt of an azo dye) in a xylene/toluene solution of poly(vinyl acetate) (PVA). The proportions of pigment, resin, xylene and toluene in this base paint were 2.83:37.04:47.10:13.00 by weight. This pigment dispersion was mixed in varying proportions with a 44% by weight solution of PVA in xylene in order to produce transparent paints of the desired pigment concentrations. Two paints were prepared: one, used to make glaze 5 and the thin glazes in figure 5, produced dry films at a pigment volume concentration (PVC) of 1.14% (2.24% pigment by weight of dry film), and the other, used for glazes 1-4, produced films having 0.68% PVC (1.34% pigment by weight). These transparent red paints were applied to 2.5 7.6 cm glass microscopes slides that had been precoated with layers of titanium white paint (in PVA) at complete hiding. The red paints were drawn down using a doctor blade on the white substrates at varying thicknesses to achieve the desired depth of shade for the glazes.

The glazes were exposed in a commercial fading apparatus that employs a xenon light source, filtered to eliminate infrared and short ultraviolet wavelengths, and a parabolic reflector. Collimated light was directed onto a water-cooled sample tray held at 20C with a recirculating water chiller. An additional filter consisting of a 3.2 mm thick sheet of ultraviolet-absorbing Plexiglas (UF-3) was placed just above the samples so that only visible wavelengths were incident upon them. Visible light intensity during the exposures was 12,600 footcandles (1.36 105 lux), and ultraviolet light intensity (between 300–400 nm wavelength) was 1.56 10−4 watts/cm2, as measured at the sample position with a radiometer.

Reflectance spectra of the glazes were measured periodically during the exposures using a spectrophotometer. Measurements at 20 nm wavelength intervals were made both with the specular reflection included (for chemical kinetic analysis) and excluded (for color analysis). From these experimental data and from the model reflectance spectra of ideal red glazes, tristimulus values (X,Y,Z) were calculated for CIE standard illuminant C using the standard formulas and tables. These values were in turn used to calculate Munsell notations (hue, value, chroma), chromaticity coordinates (x, y), and color differences ΔE (CIE 1976 L∗a∗b∗ equation) using either commercial color-analysis software or a Microsoft Excel spreadsheet. Photochemical reaction kinetics were studied by calculating the absorbances (proportional to the pigment concentrations) using Beer's law, Abs = −0.5 ln (Rinternal), where ln represents the natural logarithm. In this relation Rinternal is the so-called internal reflectance, which is calculated from the total reflectance (specular reflection included) using the appropriate equation (Johnston-Feller and Bailie 1982).


This work was performed at the Research Center on the Materials of the Artist and Conservator at Carnegie Mellon University and was supported by a grant from the Andrew W. Mellon Foundation. The authors also thank R. Roberts of Sandoz Chemicals Corp. (now Clariant Corp.) for kindly supplying the Pigment Red 66 and Hugh Davidson of Davidson Colleagues for the color-analysis computer software.


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Color-analysis computer software

Davidson Colleagues, P. O. Box 490, Tatamy, Pa. 18085

Graphtol Red 1630–1 (Pigment Red 66, Colour Index No. 18000:1)

Sandoz Chemicals Corp. (now Clariant Corp.), 4000 Monroe Rd., Charlotte, N.C. 28205

Light exposure apparatus (Suntest CPS)

Atlas Electric Devices Co., 4114 North Ravenswood Ave., Chicago, Ill. 60613

Poly(vinyl acetate) (Vinac B-7)

Air Products and Chemicals, Inc., 7201 Hamilton Blvd., Allentown, Pa. 18195

Radiometer (IL1700)

International Light, 17 Graf Rd., Newburyport, Mass. 01950

Recirculating water chiller (Coolflow-75)

Neslab Instruments, Inc., P. O. Box 1178, Portsmouth, NH 03802

Spectrophotometer (Color Eye Model 1500)

Macbeth Division, Kollmorgen Instruments Corp., 405 Little Britain Rd., New Windsor, N.Y. 12553

Titanium white (Ti-Pure R-960)

Du Pont Co., White Pigment and Mineral Products, 1007 Market St., Wilmington, Del. 19898

UF-3 Plexiglas

TALAS, 213 W. 35th St., New York, N.Y. 10001


PAUL WHITMORE received a Ph.D. in physical chemistry from the University of California at Berkeley. Following an appointment at the Environmental Quality Laboratory at Caltech studying the effects of photochemical smog on works of art, he joined the staff at the Center for Conservation and Technical Studies at the Harvard University Art Museums. Since 1988 he has been director of the Research Center on the Materials of the Artist and Conservator at Carnegie Mellon Research Institute, where his research has been directed toward the study of the permanence of modern art and library materials. Address: Carnegie Mellon University, 4400 Fifth Ave., Pittsburgh, Pa. 15213.

CATHERINE BAILIE has an A.B. in chemistry from Bryn Mawr College. Since 1977 she has been at the Research Center on the Materials of the Artist and Conservator, where she is now an associate staff scientist. Address as for Whitmore.

Copyright 1997 American Institute for Conservation of Historic and Artistic Works