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

where r is the distance of the dipole from the observer (from the scattered light sample to the
detector) and is the angle between the dipole axis and the line r. The division by the square
of the light velocity, c 2 , is a dimensional correction. Substituting
equation:
2.07
in the above
Comparing the intensity I of the scattered radiation to the intensity I0 of the incident radiation,
which is proportional to the square of its amplitude E0:
This equation is called the Rayleigth equation for plane polarized light. The scattering intensity
increases rapidly as the light wavelength decreases. The intensity also depends on the angle :
there is no radiation along the direction ( =0) in which the dipole vibrates.
Let us consider a system of volume V containing N independent identical scattering particles.
Then, the total intensity I of scattered light is:
Generally, the Rayleight scattering equation is directly applicable to gases, where molecules
move randonly. In liquids, there exists fluctuations in particle concentration inside a volume
element, which results in fluctuations of the polarizability α. Therefore, to apply the Rayleigh
scattering equation to the liquid state, it is necessary to account for these fluctuations by using
α. In this way, since the polarizability α depens on the dielectric permitittivity ε, and
correspondingly on the index of refraction n, then:
2.08
2.09
2.10
2.11
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