Quasi-elastic Light Scattering

QELS allows one to study the dyamics of a system in real time
[see, *e.g.*, Berne and Pecora, **Dynamic Light Scattering**,
John Wiley & Sons, 1978]. In this method one sits at a particular
scattering angle and measures the temporal autocorrelation function
for that particular scattering vector. For example, in a binary
mixture of two fluids, *under proper conditions* the two fluids
will phase separate (each phase having a different composition from
the original) in a continuous phase transition. Near the transition
temperature _{c}_{c}**Q**_{scatter}**Q**_{final} - **Q**_{incident}*magnitudes* of both the incident and final momenta
**Q**_{i,f}|**Q**_{i,f}|

For smaller scattering angles and therefore smaller
**Q**_{scatter}|

Another very common application of QELS is particle sizing. As
particles translationally diffuse, the scattered light intensity
fluctuates. [see Berne and Pecora]. One can think of this problem
as follows: imagine a large number of statistically independent
scatterers. At a given point in time one measures a scattering
intensity I(t). At this time they can be thought of as one very
powerful superscatterer located at the origin, such that the spatial
Fourier components of this delta function all have the same amplitude.
A short time later the particles have all translationally diffused in
different directions, and their scattering fields will interfere to
produce a different intensity. Statistically, this is equivalent to
the one intense scatterer spreading out in accordance with the
diffusion equation. Thus, instead of a delta function, at this later
time the superparticle is washed out a bit in space, and now each
spatial Fourier component has a different amplitude. At an even later
time the particles will have diffused even more, and the super
scatterer will be even more washed out in space. It turns out that
the larger **Q**_{scatter}**Q**_{scatter}**Q**_{scatter}^{2})-1

In a liquid crystal experiment, the situation is complicated by the
fact that the nematic and smectic phases are either uniaxial or
biaxial, meaning that the incident and final momenta are determined
by the direction of propagation and the polarization of the light.
Judicious choice of scattering geometry may facilitate different
sorts of measurements on the same system. A classical example is the
study of "director fluctuations" in the nematic phase, corresponding
to collective orientational modes of the molecular axis. For an
appropriate incident momentum and polarization of light, the scattered
light may be "depolarized," *i.e.*, the polarization vector may
change. Thus, detecting the light with a crossed polarizer would
permit only this depolarized component of light to pass, and all other
scattering (from both the liquid crystal and artifacts in the oven)
would be blocked from the detector. A study of the time evolution of
the scattered light then tells us information about the dynamics of the
collective modes.