Statistics of Polymer Chain Conformations in Solution

The conformation of polymer chains (in effect, their size) in solution is an important characteristic of a system in solution and at an interface. The detailed analysis of polymer conformations is a very complex process requiring powerful computer facilities. A simpUfied treatment based on random-flight (or random-walk) statistics allows for the estimation of chain dimensions to a degree adequate for most practical situations. 

FIGURE 14.1. By using known bond lengths and bond angles of monomer units, one can calculate (or at least make a good estimate of) the most probable configuration of a polymer chain in solution. 

This equation indicates that the average end-to-end length is proportional to the square root of the stretched chain length, which means that it will also be proportional to the molecular weight since each segment of the chain will have a segment molecular weight. 

The root-mean-square distance of a chain segment from the center of gravity of the coil will then be given by 

Other statistical data about a polymer chain can be determined using the same model but will not be discussed further here. 

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