Linear polymers as freely jointed chains

This gave the coil the following properties root mean separation of ends 

From mechanics, the radius of gyration, i g, is the average value of the first moment of all segments of the chain with respect to the centre of mass of the chain. If the chain is fully extended with no constraints regarding bond angles, i.e. a fully jointed chain as defined by Kuhn, then the maximum value of i nns becomes 

The ratio (i ms/- max) is a measure of the stiffness of the chain and is termed the Kuhn length. Thus, if there is a hypothetical freely jointed polyethylene that has 1000 carbon atoms separated by 1.54 A then i max= 1540 A, R s = 49 A and i g = 20A 

The limitations of the random-flight model when applied to real polymer chains arise from 

When all of these effects are taken into account, a characteristic ratio C may be introduced as a measure of the expansion of the actual end-to-end distance of the polymer chain, i o, Ifom that calculated from a Kuhn model  

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