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

For a dilute solution, polarizability α may be written as:
where dn/dc is the differential refractive index and is an experimentally measurable quantity.
Substitution of the equation 2.12 into equation 2.10, and considering that
expressed as
number:
Defining the Rayleigh ratio and is often designed as R:
which is independents of r and . Simplifying:
Then the light scattering becomes:
where
2.12
can be
, where M is the molecular weight and NA is the Avogadro’s
.
As mentioned above, for very dilute solution of small particles (for example, nanoparticles or
polymer chains of size smaller than /20) the scattering intensity is independent of the
scattering angle, and the density fluctuation from the surrounding solvent can be substracted
by considering the excess Rayleigh ratio, R ( ; then, the scattering
intensity only depends on the scattering power of the dissolved particles (i.e., from their
molecular mass) and the osmotic pressure. For non ideal solutions, and after several
theoretical considerations (3), the scattering equation can be rewritten:
2.13
2.14
2.15
2.16
38