Power Law Decay of Phosphorescent Materials

Chungchi Chen, John Noe, Harold Metcalf

Laser Teaching Center

SUNY - Stony Brook University

What is phosphorescence?• Phosphorescence is the emission of light over seconds, minutes, hours or even days after activated by light source.

• It's the effect in "Glow in the Dark" materials.

• Applications of Phosphorescent Materials:

1."Glow in the Dark" safety signs. 2.“Glow in the Dark” toys and decorative materials.

Pictures of Application

Safety sign under Daylight

Safety sign in the dark

Properties of Phosphorescent Materials

1. Emits light after activated by a light source.

2. Traps light for a longer period of time than flourescent light.

3. Phosphor goes from a “singlet state” to a “triplet state” after it’s activated.

4. Never stops glowing!

Setup of the Experiments – Commercial phosphorescent films - provided by Shann

on Luminous Materials. Inc.

– Radio Shack multimeter with PC interface.

– Light detector with different resistors.

– A dark box with black cloth covered on top.

– Various light sources: incandescent light, sunlight, ultravoilet light, etc.

Setup of Experiments (Con’d)

• For heating the sample

– A heating element (cup warmer).

– A thermometer.

– A variable power supply.

Pictures of samples

Picture of Setup

Initial Experiment

Initial purpose: To find out how long the phosphorescent film glows after it's been activated by light.

– Sample was activated by incandescent light for about 1 minute.

– 1 mega ohm resistor was used.

– Two hours of decay data was obtained and plotted on a log-log scale.

Intensity of Phosphorescent Material v.s. Time

Discovery!

• After about 2 minutes(120 seconds) of data, the graph appears to be a straight line of the equation 1/t^n, where n ~ 1.

• Question to find out:– Does the graph on log-log scale always follow

this function?– Is the exponent n at the denominator always

close to 1?

What’s a Power Law?

• Definition:– A Power Law is a function that describes a line

ar relationship of some kind of data on a log-log scale.

• Formula:P = CX^n

n is fixed, C is constant.

Examples of Power Law

• Zipf’s Law: when the exponent n = -1.– It’s mostly used in statistics.

More on Power Law

• It can be the function to describe either a rare or a very common event.

• Example:– A count of the top 50 words in 423 TIME magazine

articles (total 245,412 occurrences of words), with "the" as the number one (occurring 15861 times), "of" as the second (occurring 7239 times), "to" as the third (6331 times), etc.

– When the number of occurrences is plotted as the function of the rank (1, 2, 3, etc.), the functional form is a power-law function with exponent close to 1.

Decay observed for 20 hours

Significance of the Graph• Resistance is 10 mega-ohm.• The sample was activated under sunlight for about 5

minutes.• After the first 10 seconds of data, data was averaged

according to time interval:– For 10 to 100 seconds, data was averaged every 10

seconds.– For 101 to 1000 seconds, data was averaged every 100

seconds.– For 1001 and beyond, data was averaged every 1000

seconds.• The data follows a Power Law after 1 ~ 2 minutes.• Data was taken for about 20 hours.

Intensity of Phosphorescent Material VS. Time in Different Temperature

Pictures on Setup of Higher Temperature experiment

Significances of This Experiment• The sample is kept at 45 degree Celsius.

• The data was taken over 20 hours.

– After 15 minutes, data was taken every 10 seconds for 2 hours.

– After 2 hours the data was taken every 60 seconds for more than 20 hours.

Conclusion:• In the light versus time graphs, Power Law explains the ongoing straight line after the first 1 or 2 minutes.• After waiting ten times longer the light is ten times weaker, and so on.• The relationship of time and light intensity of the afterglow of the phosphorescent material is found to be described in a form of Power Law function.• Both sunlight-activated-sample measurement, and the incandescent-light-activated-sample measurements obey Power Law after about the first 100 seconds.• The underlying reason why a Power Law applies to this case is not yet understood.

Future Work

• To carefully study and examine the light decay of the (same) sample at a different temperature, after the sample is activated by a light source.

• To see if the exponent n on the denominator of the function 1/t^n is always close to 1.

Special Thanks

• Dr. John Noe for guiding me on doing this research project.

• Professor Harold Metcalf for inviting me to come.