Self-Assembly of Synthetic and Biological Polymeric Systems of ...

As commented above, Figure 2.10a illustrates how the intensity (I) varies with time (t). I(t)
fluctuates around its mean value, . It may appear completely random and, therefore,
meaningless, but it is not. Motions of particles (i.e. polymer molecules) and solvent molecules
contribute to the change of I(t) with time. This apparently noisy signal carries the information
about particles motions.
Figure 2.10. a) Light scattering intensity I(t) fluctuates around its mean value . b)
Autocorrelation function is obtained as the long-time average of
for various delay times . The aurocorrelation function decays from to over time. The
amplitude of the decaying component is .
The autocorrelator calculates the product average of two scattering intensities I(t) and I(t+)
measured at two different times separated by , the delay time. The average product
is a function of and is called the correlation function of I(t), or the intensity-
intensity correlation function. The correlator converts I(t) into . Hence, the
intensity-intensity correlation function is the average of over a long period T.
Hence, assuming that the long time average is equal to the ensemble average, we can write:
Note that, if the system is at equilibrium, the ensemble average does not change with time
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