Detecting Phase Boundaries in Hard-Sphere Suspensions
- Tuesday, 01 December 2009
Liquid and solid phases are distinguished through differences in motions of spheres.
A special image-data-processing technique has been developed for use in experiments that involve observation, via optical microscopes equipped with electronic cameras, of moving boundaries between the colloidal-solid and colloidal-liquid phases of colloidal suspensions of monodisperse hard spheres. Such suspensions are used as physical models of thermodynamic phase transitions and of precursors to photonic-band-gap materials. During an experiment, it is necessary to adjust the position of a microscope to keep the phase boundary within view. A boundary typically moves at a speed of the order of microns per hour. Because an experiment can last days or even weeks, it is impractical to require human intervention to keep the phase boundary in view. The present imagedata- processing technique yields results within a computation time short enough to enable generation of automated- microscope-positioning commands to track the moving phase boundary.
The experiments that prompted the
development of the present technique
include a colloidal equivalent of directional
solidification. The interactions
between the spheres in these suspensions
closely approximate an ideal hardsphere
potential, so that the phase
behavior becomes, to a close approximation,
solely a function of volume fraction
(ϕ) of spheres. When ϕ of a given
suspension sample is less than a threshold
value (ϕf = 0.494) denoted the freezing
volume fraction, the suspension is in
the colloidal-liquid phase, in which the
spheres are disordered and free to diffuse
throughout the entire volume of
the sample. When ϕ exceeds another
threshold value (ϕm = 0.545) denoted
the melting volume fraction, the suspension
is in the colloidal-solid phase,
in which the sample is crystalline in the
sense that each sphere is “caged” by its
neighbors and thus restricted to small
movement about a lattice point.
Between ϕf and ϕm is a regime of coexisting
colloidal liquid and colloidal
At the beginning of an experiment, a
suspension is prepared at ϕ well below ϕf
and placed in a cell. Then through slow
evaporation or gravitational sedimentation,
the spheres become concentrated
toward one end of the cell, where crystallization
starts when ϕf is reached.
When the sphere size falls within a range
accessible to optical microscopy, the disordered
(liquid) phase and the ordered
(solid) phase (and, hence, the boundary
between them) are visible to, and clearly
distinguishable by, a human observer.
However, prior image-data-processing
techniques do not enable automated distinction
between regions of order and
disorder in images of closely packed
In the present technique, automated
distinction (see figure) is made possible
by differences between the motions of
the spheres in the liquid and solid
regions. In particular, the technique
exploits the fact that in the solid phase,
the spheres are restricted to their small
“cages,” whereas in the liquid phase,
the spheres are free to move.
Consequently, when images are averaged
over successive frame periods, the
liquid region tends to become blurred
or gray while the solid region retains a
higher degree of contrast, showing the
spheres as individual particles. Each
frame-averaged image is subjected to a
brightness-slicing, a cleaning (noisesuppression),
and a particle-finding
operation. These operations utilize the
brightness and contrast differences
between the solid and liquid regions.
Then the image region showing particles
is deemed to be the solid region
and the phase boundary is located
This work was done by Mark McDowell and
Richard B. Rogers of Glenn Research Center
and Elizabeth Gray of Scientific Consulting,
Inc. For more information, download the
Technical Support Package (free white
paper) at www.techbriefs.com/tsp under the
Physical Sciences category.
Inquiries concerning rights for the commercial use of this invention should be addressed to NASA Glenn Research Center, Innovative Partnerships Office, Attn: Steve Fedor, Mail Stop 4–8, 21000 Brookpark Road, Cleveland, Ohio 44135. Refer to LEW-18157-1.
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