## 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.

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 element

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 element. The number of repeat units in a Kuhn element is a fixed number for each polymer. It is called the characteristic ratio Cโ. Some examples of this ratio for several polymers are shown in the table below.

 Characteristic ratio and Kuhn length for several polymers. PB PP PE PVC PMMA PS PC Cโ 5.5 6.0 8.3 6.8 8.2 9.5 1.3 b (วบ) 10 11 15 26 15 18 2.9

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:

## Size of macromolecule

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

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:

## 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 elements will be seriously limited.

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

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:

## 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 element.
• The number of repeat units in a Kuhn element is the characteristic ratio Cโ.
• The macromolecule is entangled by other macromolecules.
• In between two entanglements a blob is formed.
• The Kuhn elements in a blob follow a random path.