2 ARRHENIUS TESTING

For this paper it is useful to review the method for Arrhenius testing (Eastman Kodak Company 1988). At room conditions (approximately 24�C [75�F] and 40% RH), significant changes occur in color materials only after a long period of time. For this reason, it is difficult to obtain timely information on the stability of a product by evaluation at the actual keeping conditions. We can, however, predict the long-term density changes expected to occur in color materials by performing short-term tests at a series of high temperatures. In practice, samples of a given product are exposed and processed according to current recommendations to provide dye patches (see section 3) at densities of 1.0. These samples are stored in the dark at 40% RH for various lengths of time at temperatures ranging from 52�C to 93�C (126�F to 199�F). Samples are removed at appropriate time intervals to make density measurements.

The method of predicting dark-keeping changes can be understood by examining the graph in figure 1. The relationship between keeping temperature and the time required to produce various degrees of fading is shown. The solid curved lines illustrate the blue density of the associated yellow dye at various temperatures during the Arrhenius test. The time (log scale) to obtain a specific density change for each of the temperature curves is replotted against the reciprocal of the absolute temperature. Dotted lines with downward arrows illustrate the method for replotting the data from the 0.90 dye density level (a 0.10 dye density loss). Similar replotting can be done from other density levels. After data points are derived from fading curves, they can be fitted with a straight, solid line. Theoretically, such straight lines can then be extended to predict the keeping time expected to produce a specific loss for any of the dyes. This prediction is made by extrapolation, which is shown by dashes. The intersection of these extended straight-line plots with the 24�C (75�F), or lower temperature lines, provides an estimate of the dark-keeping stability at that temperature. The times associated with specific dye losses are used to make a predicted dye-loss plot versus time at temperatures lower than those used in the actual test (see dotted lines with upward arrows, between the time temperature plots and the density plots). The curve shows a 0.3 blue density loss for the yellow dye after 100 years of storage at room temperature 24�C (75�F). Using the same methods, predictions for other density losses, dyes, and temperatures can be made.

Fig. 1. Illustration of prediction method (blue density change for 1.0 yellow dye)

The full value of Arrhenius testing, however, cannot be determined at this time because we do not know how accurate the predictions are. Figures 2 and 3 show Arrhenius data for KODAK VERICOLOR III Professional Film, type S. Figure 2 shows waterfall plots of the fading of the yellow dye across the series of temperatures shown at the bottom of the plots. The points appear to fall well on the lines, and the various temperatures show even spreads from one another and are smooth and similar in shape. In figure 3, the plots of the time for a 10% loss at the various temperatures form a well-behaved line with a 95%-confidence interval represented by the dotted lines, which are tight. We use a 10% change as an analytical tool only; losses would have to be larger for the photographic image to be considered unacceptable. Data like these (for the limiting dye of KODAK VERICOLOR Professional Film 6006) indicate that the Arrhenius model is working. Although there are scientific reasons to expect that our predictions are meaningful from such statistical and theoretical examination of many data, the only certain way to determine accuracy is by making direct comparisons with actual aging effects. Such comparisons are not easy to come by because of the scarcity of accurate measurements under moderate conditions for long periods of time. Furthermore, Arrhenius data are not available for older products, since the Arrhenius method has been applied to photographic products only in recent years. For the earliest products, we have data only from single accelerated tests. It is true that users have judged the stability of products by noting their behavior over many years of actual use, but almost always at conditions that were uncontrolled and often unknown.

Fig. 2. Fading plots. Arrhenius data for KODAK VERICOLOR III Professional Film, type S. Density yellow/40%RH..−.10 prediction is 34 years. b=93�C, c=89�C, d=85�C, e=81�C, f=77�C, g=72�C, h=68�C, m=60�G, o=52�C

Fig. 3. Arrhenius prediction line for KODAK VERICOLOR III Professional Film, type S. Density yellow/40%RH. −.10 prediction is 34 years.

Eastman Kodak Company has been conducting long-range or natural-aging tests for more than 20 years using carefully controlled conditions that simulate average use and storage. The Image Stability Technical Center, the repository for samples in this important study, contains a wide variety of film and paper products of various ages, both black-and-white and color. In this continuous study we monitor densitometry changes on products over time in controlled dark-keeping conditions. The conditions include a control at −23�C in addition to 24�C/40% RH and 26�C/60%RH.

Fortunately, these conditions, which were selected many years ago for natural aging, are in good agreement with recent studies carried out to estimate actual conditions of use. In a Kodak study conducted in 1981 (Anderson and Larson 1987), we collected data on temperature and humidity continuously for the full year in two homes in Rochester, New York. The yearly averages were 50% RH and 21�C (70�F). Our test humidities (40% RH and 60% RH) bracket the 50% RH level, while the test temperatures (24�C and 26�C) are a few degrees higher than what we found in the homes. We do not know how these test conditions were chosen. However, it is fortunate that they appear to be more stringent than the average conditions found in homes, thereby ensuring that we will not miss any changes that might occur in actual use. The fluctuations in temperature and humidity are, however, not taken into account. More work is needed to determine if fluctuations are a factor.