Power Law Decay of Phosphorescent Materials

Jill Chen, John Noé, Harold Metcalf
Laser Teaching Center, Department of Physics and Astronomy,
Stony Brook University

Phosphorescence is the emission of light from "glow-in-the dark" materials seconds, minutes, hours, or even days after they have been activated by a light source. Phosphorescence has many valuable applications, such as safety signs that don't require electricity, and also has a complex and interesting underlying physics and chemistry related to "triplet states" in solids.

My research involved measuring the delayed light emission from a 7 * 6 cm sample of commercial phosphorescent film (type B-901) provided by Shannon Luminous Materials, Inc. in Santa Ana, California; it was said to contain "mixed oxides of Al, B, Sr, Eu, and possibly, Hf." After activating the sample with various light sources the greenish-yellow afterglow light was observed over a period of hours with a photodetector and voltmeter interfaced to a computer. The several thousand readings obtained were analyzed and plotted in a spreadsheet program. In these measurements the photodetector was placed directly on top of the sample to get the most sensitivity. In a separate set of measurements I also studied the light intensity as a function of distance from a simulated sample of nearly the same size with constant light output (an electroluminescent nightlight) in order to create an intensity calibration curve.

During the analysis of my initial data, it was discovered that the light emission after about the first minute following activation obeys a power law of the form L(t) = 1 / t^n, where the exponent n is very close to 1. The graph of such a relationship is a straight line when plotted on a log-log scale. Power laws are known to describe many diverse phenomena in science, from statistics (the Pareto curve) to physics (1/f noise), but the underlying reason a power law applies in this case isn't as yet understood.

More recently I have collected a decay curve over a much longer period of time (18 hours versus 2 hours) for the same sample after activation in sunlight instead of incandescent light. Readings were still taken at one second intervals, but after the first 10 seconds they were averaged in the spreadsheet over periods of 10, 100, or 1000 seconds before plotting. A computer program is being written to do this averaging automatically during the data taking. Both the light versus distance and light versus time plots level off at small distance or small time in a similar way, and both can be well described by "modified hyperbolic curves" of the form 1/(a+x^n) with n = 2 or about 1, respectively.

Future plans include observing the decay with the sample held at a different temperature, to see if this changes the exponent n in the power law.