2. About polymer molecules

Repeat unit

Polymer molecules are long chains built from many small identical repeat units, also called monomers. For example polyvinylchloride (PVC) consists of many vinylchloride (-CH2-CHCl-) repeat units. And polyethylene (PE) consists of many ethylene (-CH2-CH2-) repeat units. The number of repeat units in a macromolecule can be very large: up to 10000 or more.

PVC macromolecule (www.shutterstock.com)
PVC macromolecule (www.shutterstock.com)
PE macromolecule (www.shutterstock.com)

The mutual direction between two neighbouring repeat units is not fixed but can change due to thermal movements. However, each repeat unit is hindered in its freedom by neighbouring repeat units. Their possibility to change their direction is limited.

Kuhn segment

It takes several repeat units in a row in order to be able to randomly take any direction. Such a group of repeat units is called a Kuhn segment. The number of repeat units in a Kuhn segment is a fixed number for each polymer. It is called the characteristic ratio Cโˆž. Some examples of this ratio for several polymers are shown in the table below.

Schematic representation of the macromolecule (coloured lines) and the Kuhn segments (black lines)
Characteristic ratio and Kuhn length for several polymers.
PBPPPEPVCPMMAPSPC
Cโˆž5.56.08.36.88.29.51.3
b (วบ)1011152615182.9

Let us assume that a polymer molecule contains N repeat units. Then the number of Kuhn elements in the macromolecule NK can be calculated from:

eq1

Size of macromolecule

Each Kuhn segment can randomly take any direction in space. The shape of the macromolecule in space therefor follows a random path.

Schematic view of a freely jointed chain.

We can now estimate the distance L between the start and the end of the macromolecule. If each Kuhn element has a length equal to b then the distance L covered by such a random path is:

eq2

Entanglements and blobs

The macromolecule is surrounded by many other macromolecules in the plastic. They will therefore all interfere with each other. Each macromolecule will be entangled with several other macromolecules. At each entanglement the possible movements of the Kuhn segments will be seriously limited.

Blobs and entanglements
Between neighbouring entanglements blobs are formed

In between two entanglements the Kuhn segments will follow a random path. This part of the macromolecule is called a blob. If there are on average Ne Kuhn segments in a blob then the average diameter of the blobs Dblob will be:

eq3

Our macromolecule contains NK/Ne blobs. Also the blobs will follow a random path in space. Therefore the start to end distance L of the macromolecule will be:

eq4

Summary

  • The smallest entity in a polymer molecule is the repeat unit. It has a limited possibility to change its direction.
  • It takes several repeat units in a row to be able to take a truely random direction. This is a Kuhn segment.
  • The number of repeat units in a Kuhn segment is the characteristic ratio Cโˆ.
  • The macromolecule is entangled by other macromolecules.
  • In between two entanglements a blob is formed.
  • The Kuhn segments in a blob follow a random path.

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