Biomedical Engineering Reference
In-Depth Information
2.2
Light scattering
All media - solids, liquids and gases - scatter light. Scattering from homo-
geneous media is due to density fl uctuations. If a polymer is present in a
solvent, then there is an excess scattering that can be analyzed to determine
the characteristics of the polymer. We will consider both elastic scattering,
which occurs without a change in the frequency of the scattered light, and
inelastic scattering, in which the frequency changes. In elastic light scattering
(also called static light scattering) measurements, time averaged intensity is
measured as a function of the scattering angle. In inelastic light scattering
(also called dynamic light scattering), the diffusion of the molecules is mon-
itored, and these data are used to determine the size of the molecules. Light
scattering data are used to determine the molecular weight and size of the
polymer without resorting to any reference standards. These methods are
extensively discussed in many text books and monographs.
1,2
Light scattering technique is an important tool not only for the determi-
nation of molecular weight and thermodynamic interaction parameters, but
also for estimating the heterogeneity of the polymer. It has been used to
measure molecular weights from 15 000 to 1 500 000. In a typical light scat-
tering experiment, a high intensity monochromatic light is used to illumi-
nate a solution containing macromolecules (Fig. 2.2). Scattered intensity is
measured at one or several angles. A laser source is often used. Laser can be
focused to a diameter much smaller than 1 mm for microbeam studies, but is
sometimes expanded to minimize speckling so that a statistically signifi cant
number of structures is sampled.
2.2.1 Small particles
Elastic scattering from particles in a solution is called Rayleigh scattering
when the particles are small compared to the wavelength of light, and when
the solution is dilute enough for the particles to be considered as indepen-
dent scatterers. The ratio of the scattered light from a single particle (
i
s
) to
that of the incident light (
I
o
) is given by the following equation fi rst derived
by Lord Rayleigh:
16
4
sin
2
i
θ
πα
4
s
o
=
[2.1]
2
1
42
r
λ
4
I
r
In this equation,
α
is the polarizability of the particle,
θ
1
is the angle between
the incident beam and the direction observation,
λ
is the wavelength (
in
vacuo
) and
r
is the distance from the sample to the detector. The most sig-
nifi cant feature of this equation is that it shows that the intensity falls off as
the 4th power of the wavelength of light.
