Autocorrelation function Gaussian chain

If the PPy-DBSA micelle-like structure were constructed by the aggregation of the multiple PPy-DBSA molecules, the obtained autocorrelation functions should be fitted by Gaussian decays as the a regate of PANi does [72,73]. Therefore, it is expected that the micelle-like structure of PPy-DBSA is composed of a single chain of PPy-DBSA surrounded by many extra DBSA molecules. 

The density autocorrelation function for two segments on the Gaussian chain is given as... 

Figure 2.41. Probability distribution for the distance r of other segments from a given segment in a Gaussian chain. The segment density autocorrelation function p(r)p(0))/p multi-phed by is plotted as a function of r/Rg. Short-distance and long-distance asymptotes are indicated.

The segment density autocorrelation function the Gaussian chain is calculated as follows. 

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