# Polymer scattering and Relaxation time

In a polymer structure like plastic or gels the individual polymer chain are intertwined into a mesh with an overall structure with ordering such as a favored orientation relative to each other, but it is not a rigid and precise structure as found in crystals. This means that the polymer chains can move inside the material. These movements are due to thermal fluctuations in the material and there are a number of different kinds of movement they can undergo. Bond rotation round the carbon backbone as shown in the figure, translations where the polymers slide through the net, and stretching where the polymers are stretched. Since these movements originate from thermal fluctuations, the directions are random, and the speed is in some way governed by the temperature. How much they can move depends on a number of factors, including the packing of the polymers, their weight, how much they are entangled and if they are attracted to each other by polar interaction.

Describing the polymers movement with a single number is complicated, we describe it through the relaxation time. The relaxation time refers to the speed at which the polymers reach equilibrium after an external force has been applied. What that means is the speed at which a deformation in the polymer mesh is removed by the movement of the polymer to fill any gaps so the material is in equilibrium. This speed or relaxation time is material dependent, imagine blowing a hole in olive oil or syrup. The hole in the olive oil would disappear faster than in the syrup. So in the example, syrup has a smaller relaxation time than oil since it takes a longer time for it to reach equilibrium. These two examples are liquids but the principle are the same for plastic, glass, living tissue and any other solid structures composed of long molecule chains.

Any object that moves through a polymer mesh will be slowed by the mesh dependent on the relaxation time of the polymers, since this relates to how fast the polymers can be “pushed to the side” by the object. This could be other polymers themselves or molecules that are bound to a polymer from the mesh “hitching a ride” through the mesh.

The smaller the relaxation time, the larger the energy transfers (gain as well as loss) of the neutrons. This is generally seen in QENS experiments as a broadening of the peak. The relaxation time depends on the temperature of the material, in the data analysis of this simulation we have used the relation

(Iγ/π•(ΔE22))+background I per gamma divided by pi, multiplied by increase of E to the square, plus gamma to the square, plus background

where I is the intensity of the peak, ΔE is the energy change and γ increase of E is the energy change and gamma is 1/relaxation time.