Statistics of the random coil

A transparent model can be derived from the backbone bond description given above to illustrate the properties of the random coil. The backbone of n bonds is divided into m equal groups, where n/m exceeds the degree of polymerization required to achieve the asymptotic characteristic ratio. Each subgroup is characterized by its own end-to-end vector,, where  

Another important measure of the statistics of the random coil is the probability distribution for the end-to-end vector,. In the long-chain limit, this function is  

A macromolecule that can be described by these statistics is called a Gaussian chain. 

The existence of an analytic form for the probability distribution means that any function of the end-to-end vector can be averaged over the conformations of a random coil chain  

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