Birefringence of Stressed Polystyrene Reinforced With Clay

Rohit Gupta, Harold Metcalf, John No
Laser Teaching Center, Department of Physics & Astronomy 

and 

Miriam Rafailovich
Department of Materials Science and Engineering, 

Stony Brook University 


ABSTRACT:

This was a study of whether blending clay into polystyrene will reduce
the material's response to stress, as observed by the intensity and form
of birefringence patterns. This type of material modification is a
relatively new field of study with important engineering implications. 
The hypothesis was that blending clay into polystyrene would deflect the
stress to the edges and lessen the intensity of the stress.

Birefringence is the optical phenomenon that occurs when an object that
has different indices of refraction in different directions is placed
between two crossed polarizers; these different indices can be inherent
in the object or induced by means of applied stress. Thus birefringence
literally allows one to "see" the stress produced on an object because
of the colored fringes induced. 

The clay additive used was cloisite 20A at a concentration of 5% clay. 
Polystyrene samples with clay and samples without clay were molded into
the same rectangular shapes (2x12 cm with a thickness of 2 mm). 
Differing levels of stress were chosen, and the samples with clay and
the samples without clay were subjected to these levels of stress.

Adjustable stresses were applied to the samples in a Stress Opticon, and
pictures of the stress fringes were recorded with a camera. The shape,
form, and intensity of the fringes were qualitatively described.

This research was supported by the Simons Foundation.


INTRODUCTION:

Birefringence is the optical phenomenon that occurs when an object that
has different indices of refraction in different directions is placed
between two crossed polarizers; these different indices can be inherent
in the object or induced by means of applied stress. It is the result of
a phase difference of the light hitting the object.  The phase
difference results because of the different directions' of the object
(ie length, width) having different indices of refraction.  The phase
difference equals the thickness of the sample (ie the distance the light
will go through the sample) divided by the wavelength of the light, all
multiplied by the difference in the indices of refraction of the two
other directions (the first direction being the thickness of the
sample).  Birefringence literally allows one to "see" the stress
produced on an object because of the colored fringes.  The fringes
follow the stress field (the path of stress), and that is why they are
curved and not straight.

This project involved blending clay into polystyrene and detecting how
this blending affected the material's response to stress, as observed by
the intensity and form of birefringence patterns.  This type of material
modification is a relatively new field of study with important
engineering implications.  Clay blending is very important in the
Materials Science arena, and many modern experiments are underway to
determine what all the effects of the blending are.  A specific concern
of experiments involving clay blending is whether or not the clay will
increase the mechanical strength of the substance.  The hypothesis of
this research project was that adding clay to polystyrene would make the
material more strong.


MATERIALS:

Cloisite 20A (clay)

Polystyrene

Stress Opticon, made by Vishay Measurements Corp.

Brabender machine for blending

Machine for molding samples

Camera

Molding plate that fits dimensions 2 cm x 12 cm x 2 mm


METHODS:

        The first step is making the samples.  The molding plate, which is a
disc with a cutout of the shape of the samples to be made, must be a
appropriate for the size of the Stress Opticon. (The Stress Opticon,
made by Vishay Measurements Corp., is a device for inducing stress on
and seeing birefringence in photoelastic materials.  In a shop, the
right-sized molding plate must be made out of aluminum/steel (2 cm x 12
cm x 2 mm).  Then, in the Brabender machine for blending, the clay is
mixed with the polystyrene.  To prepare a sample with 5% clay, 47.5 g of
polystyrene and 2.5 g of cloisite 20A clay are put in.  Then, the pure
polystyrene and the polystyrene mixed with clay are taken to the machine
for molding.  Here, the polystyrene is placed in the slit of the molding
plate's, and the samples are made.  Samples are made of the polystyrene
mixed with clay, also.

        The next step is to place the samples in the Stress Opticon and put
stress on them.  The Stress Opticon is as such: a sample is held by
screws which not only hold the sample in place but provide stress in
adjustable positions.  The sample is, of course, placed between two
crossed polarizers, which are attached to the device (they come attached
to the device readymade).  The screws will not be able to hold the
sample unless the sample is flat or extremely close to flat.  If the
samples are not flat, their edges must be sanded.

Then, the pure polystyrene samples and the mixed clay-polystyrene
samples are subjected to the same amounts of stress.  One way of
measuring the stress is simply by the number of turns of the screws.  A
torque wrench can also be used for more accurate values.  The torque
wrench is attached to the screw, and measurements are read off the
wrench.  The stress can be raised or lowered by tightening or loosening
the screws, respectively, and the same values of stress must be used for
the pure polystyrene samples and polystyrene-clay samples The shape and
form of the fringes are now noted, and the intensities, if possible, are
measured.

There were some problems with the methods behind this experiment.  For
one, it was extremely difficult to produce samples which were
homogenous, if not impossible.  For this reason, the materials showed
birefringence in the imperfect parts of the sample.  This added
birefringence could not be ignored because at these imperfect parts, the
stress is amplified.  For example, if I were to produce uniform stress
on the entire object (at every point), the stress at the imperfect parts
would be higher than we would expect, since already-stressed parts are
more vulnerable to stress than ``perfect,'' homogeneous parts.

Additionally, there was the problem of data collection.  Since the data
were not single measurements but an image of birefringence over an
entire sample, it was difficult to take data.  This fact led to the
partial solution of making qualitative observations and taking pictures
of the birefringence present in the sample under stress.  Quantitative
results were impossible unless there were some constant relation between
the birefringence at every point in the stressed pure polystyrene and
the corresponding point in the stressed clay-polystyrene sample.


RESULTS:

     Some preliminary pictures are as follows, showing birefringence in
stressed pure polystyrene.  These pictures demonstrate the kind of data
this investigation seeks to find.  What must be done is the taking of
pictures of samples under stress and the comparing of the birefringence
of the samples with clay to those without clay.  

                Fig 1

       Fig 2 

      Fig 3 

      Fig 4 


As shown, when the stress was gradually increased from Fig 1 to Fig 4,
the birefringence increased.  The screws were tightened, and the
corollary increase in the fringes present was apparent.  The stress
applied can be measured a number of ways; one way was by number of turns
of the screw.  The most difficult data of this project to measure were
the results of the birefringence.  This problem should be the most
important issue for anyone in the future who wants to undertake this
project.

The samples with clay were slightly too cloudy to show much
birefringence.  The birefringence was extremely faint and small, and
additionally the clay samples were not uniform enough to show good
birefringence in the Stress Opticon.

 
RECOMMENDATIONS:

One of the recommendations for such future experiments is that a more
appropriate apparatus than the Stress Opticon should be used.  The
possibilities of this experiment were severely limited because of the
device.  The size of the samples, the number of places for stress to be
induced, and the size of the area of the sample under stress are
limited.  Also, the Stress Opticon's screws, which apply stress and hold
the object, have a tendency to be unstable, and it is difficult to get
any samples but the most flat to stay aloft.  Additionally, the sample
must not be too thin, which limits the project again.  Instead of such
an apparatus, a sample could be simply placed between two crossed
polarizers that can be found in any optics lab.  An interesting setup
that Dr. Metcalf showed me is one in which an overhead projector is
used.  An object is placed between two crossed polarizers on the
projector.  In this way, we not only produced the birefringence, but
also reflected the image of it on the screen/wall.  We can then take
pictures of the enlarged image showing excellent birefringence.  Some
setup that is similar would be better than the Stress Opticon for this
study.

Another problem was the cloudiness in the sample which results from clay
being added.  When the sample becomes opaque, no birefringence can be
measured because only transparent and translucent materials are
photoelastic.  Other methods of stress measurement other than
birefringence should be used if the concentration of clay is too high to
produce a transparent or translucent sample.  The 5% clay concentration
used in this experiment was slightly high; the samples were not optimal
for photoelastic observation.  In the future, concentrations should be
explored to determine the optimal concentration for photoelastic study,
the concentration not being too low as well because an extremely low
concentration of clay will have very little effect on the stress fields.