Free-standing smectic films : diffusion
Collaboration with Patrick Oswald, John Bechhoefer and Lydéric Bocquet.
Introduction
Stable, free-standing smectic-liquid-crystal films can be made from two to hundreds of molecular layers thick and uniform over cm2. They are model systems for studying the crossover between two- and three-dimensional phenomena. We performed the first direct study of the diffusion of a tracer molecule in free-standing films of various thicknesses. We measured how the value of the vertically averaged, in-plane diffusion constant evolves in very thin films.
Experimental method
Our measurement method for the diffusion constant is an adaptation of the technique known as fluorescence after photobleaching (FRAP). The general principle is that an intense laser beam is used to photobleach (destroy) the fluorescence of tracer molecules in a small region. A much weaker beam then monitors the recovery of the signal as unbleached molecules diffuse into the bleached area, leading to recovery of the fluorescence signal (Fig.1).
Fig.1:
Image of
the film
after
bleaching
and
concentration
profile of
the
bleached
molecules.
A
fluorescent
dye is
introduced
in the
liquid
crystal.
An intense
laser beam
makes
possible
to bleach
a small
region of
the
sample.
The
diffusion
coefficient
is deduced
from the
evolution
of the
concentration
profile
after
bleaching
(The black
dots
correspond
to the
experimental
concentration
profile
along the
dashed
line, the
black line
to the
Gaussian
interpolation).
Results
Our measurements show that the diffusion coefficient significantly increases when the film thickness is decreased (Fig.2). The results can be accounted by a model which brings into play the hydrodynamical interactions between the diffusing molecules and the free surfaces of the films. Amazingly, the hydrodynamics seems to provide reliable results even when the film thickness is reduced to a few molecular layers.
Fig.2: Diffusion coefficient vs. film thickness (molecular layers).
Related publications
Experiments on
tracer diffusion in thin free-standing liquid-crystal films,
Bechhoefer J., Geminard J.-C., Bocquet L. and Oswald P., Phys.
Rev. Lett. 79 (1997) 4922.