Sunday, October 23, 2011

Birefringence, Photoelasticity, Anisotropic Materials, Iridescence and the Rainbow Effect - Part 1

One question that we are often asked about Polycarbonate is what causes the rainbow like patterns on coated sheet and how can they be eliminated.
The answer is not simple and we will need to answer the question over two or three posts. There is also a lot of confusion in the industry about what causes the effect. Often people try to explain the effect using the wrong terms.

Birefringence and anisotropic materials
The first term that we will discuss is Birefringence or the double refraction of light when it passes through an Anisotropic material. At this stage, don't worry too much about these terms, we will explain them as we go. Birefringence is often the term that is incorrectly used to explain the rainbow patterns seen on the surface of some coated Polycarbonate sheet. As we will explain, Birefringence can allow us to see stresses in the sheet using polarizing filters - they allow us to see the stresses which will appear as rainbow like effects. However, birefringence is not the cause of the rainbow like effect which can be seen with the eye on the surface of hard coated Polycarbonate sheet.

To explain birefringence and anisotropic materials we will start with a discussion about the structure of Polycarbonate. Polycarbonate is a long molecule containing Carbon, Hydrogen and Oxygen atoms. A simple web search can give details of the chemical formula. When Polycarbonate is heated and allowed to cool without being subject to any stresses, these molecules will be arranged randomly.
During the production of extruded sheet, the Polycarbonate is melted and then extruded through a wide die into a sheet format. The sheet is then pulled out of the die by some pull rollers through some chrome polishing rolls to create a smooth surface on the sheet. The pull rolls create some stress in the sheet in the direction of extrusion, but not in the direction perpendicular to the extrusion. The sheet is cooled and allowed to "set" while still being pulled by these rolls. This difference in stress in the sheet between the extrusion direction and the direction perpendicular to extrusion is commonly referred to as shrinkage. We have discussed shrinkage in more detail in previous blog posts; shrinkage is able to be controlled below 1%, although often it is possible to find sheet with high levels of shrinkage of 10% or more.

The stresses in the Polycarbonate can be eliminate by annealing the sheet - heating it above its glass transition temperature and then allowing it to cool. Also stresses can often be added to the sheet by some fabrication methods.

The more shrinkage that the Polycarbonate sheet has, the more stress it has in the extrusion direction and the more the Polycarbonate molecules are aligned in the extrusion direction. This alignment of the Polycarbonate molecule chains causes the Refractive Index of the Polycarbonate in the direction of the extrusion to be different than the Refractive Index in the direction perpendicular to the extrusion. As explained in previous blog posts, the refractive index is a measure of how fast light travels in a material. The difference of refractive index in the two directions causes extruded Polycarbonate to become what is known as an Anisotropic Material - where the speed of light traveling through the material is dependent upon the direction of the material.
If a Polycarbonate sheet is produced without any stress or 0% shrinkage, it would not be Anisotropic.

The difference in the Refractive Index between the two directions can be calculated using the Stress Optics Law:

(RI1 - RI2) = C x (Stress1 - Stress2)
RI1 = Refractive Index in extrusion direction
RI2 = Refractive Index in direction perpendicular to extrusion
C = Stress Optic Constant
Stress1 = Stress in extrusion direction
Stress2 = Stress in direction perpendicular to extrusion.

If the Refractive Index in one direction is different than the Refractive Index in the other direction, the components of the waves of light moving through the Polycarbonate in one direction will travel at a different speed than the light in another direction. The more Polycarbonate that the waves travel through, the more the one wave will lag behind the other. This effect is known as Retardation of the wave.
The retardation of the wave can be calculated using the following formula:

Retardation = C x thickness of Polycarbonate x (Stress1 - Stress2)

The amount of retardation of the wave is therefore proportional to both the thickness of the sheet and the differences in the stresses in the two directions. The retardation will be much lower on thin sheet with low shrinkage.

When the components of the light in the two directions emerge from the sheet they will recombine. However, how they recombine will be a function of the phase difference caused by the retardation of the light. There could be constructive or destructive recombining of the waves at different wavelengths.

In the next post on this subject we will look at how these waves combine. We will also look at how we can use a polarizer to look at the stresses in the sheet using an experimental method known as Photoelasticity.