Transcript Power Law Decay of Phosphorescent Materials

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
Shannon 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
linear 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.