4. Mobility of polymer molecules

Polymer molecules have two ways to change their shape or change their position: rotation of the Kuhn segments and reptation of the entire molecule.

Rotation of Kuhn segments

Due to the thermal vibrations of the atoms the Kuhn segments in a polymer molecule can rotate in any direction. This allows the molecule to change its shape locally within a blob and, if applicable, to change its entire shape under load. The rotations of the Kuhn segments make a polymer flexible.

Deformation of molecules

Rotation of the Kuhn segments make the molecule flexible

The time needed for these rotations, the rotation time, is strongly temperature dependent. At low temperatures the rotation time is long and at high temperatures the rotation time is short. At a sufficiently high temperature the Kuhn segments have a rotation time of, for example, 0.001 second. Now the polymer molecules easily change their shape under a force. The polymer is flexible now. On the other hand, at low temperature the rotation time can be as high as 1 million seconds. The polymer behaves as a rigid (stiff) solid now.

We humans experience the polymer as flexible when the rotation time is less than 1 second. The polymer feels as a rubbery substance. We experience the polymer as stiff when the rotation frequency is much higher than 1 second. The polymer now feels as a rigid glassy substance. The temperature at which the rotation time is 1 second is the glass transition temperature.

Rotation of the Kuhn segments allow for large deformations in the polymer molecule. However, the position of each molecule relative to others does not change. Due to this, a polymer deformed by a force will regain its original shape when heated close to the glass transition temperature.

Recoverable deformation
A deformed polymer remembers its original shape

Reptation

Due to the wriggling motions of all the rotation Kuhn segments the entire polymer molecule may shift its position a little bit. The surrounding molecules will limit this shift to a displacement along the axis of the molecule. Other displacements are not possible. The polymer molecule moves as a snake along its axis through the other molecules. This way of motion is called reptation.

Reptation is caused by the random rotations of the Kuhn elements

The reptation of the polymer molecules can be visualized by means of a pile of worms that move through each other:

Compared to rotation reptation is a relatively slow process. Due to the random nature of the rotations that counteract each other a single shift over the length of one Kuhn segment may take very many rotations.

After some time, the polymer molecule will have reptated over its entire length. It has moved into an entirely new position compared to the surrounding molecules. The time that this process takes is called the reptation time. At times longer than the reptation time the polymer behaves as a fluid because the position of the molecules changes continuously. Contrary to the rotation of the Kuhn segments the reptation makes the polymer to forget its original shape.

We humans experience a polymer as a fluid when the reptation time is less than 1 second. In case that the reptation time is higher than 1 second then we experience the polymer as a rubber. The temperature at which the reptation time is 1 second is the rubber-melt transition temperature.

Summary

  • A polymer molecule has two ways to change its shape or position: rotation and reptation.
  • The rotation time of the Kuhn segments reduces strongly with temperature.
  • The polymer feels stiff when the rotation time is much more than 1 second.
  • The polymer feels flexible when the rotation time is much shorter than 1 second.
  • The glass transition is the temperature at which the rotation time of the Kuhn segments is 1 second.
  • Reptation is the displacement of the entire molecule along its own axis.
  • Reptation is driven by the random rotations of the Kuhn elements. It is a very slow process.
  • The reptation time is the time that is needed to displace the molecule over its entire length.
  • At times longer than the reptation time the polymer behaves like a fluid.
  • At times shorter than the reptation time the polymer behaves like a rubber.

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