Biomedical Engineering Reference
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Therefore, if either of these two conditions occurs independently or simultane-
ously the system evolves to form a vitreous state known as a repulsive glass. The
distinction between the glass and liquid transitions observed in different regions of the
phase diagram was made on the basis of the height and width of the S(Q) peaks. The
structure factors of the glass phase, which appear like an “enlarged” FCC structure,
displayed a measured peak width (FWHM) ranging between 0.06 nm
-1
and 0.073 nm
-1
for the first peak of S
eff
(Q) for lipid A-diphosphate
.
The width of liquid phase peak
was greater than 0.013 nm
-1
with the glass phase showing a structure-factor peak well
above Hansen and Verlet (1969) criteria for the volume-fraction range 1.5 × 10
-4
≤ f
≤ 3.5 × 10
-4
and 1.0-10.0 µM HCl. The dynamic-light scattering and shear-viscosity
results also agreed well with the calculated values obtained from the mode coupling
theory
(Bosse et al., 1978). A dramatic reduction in the low shear viscosity occurred
for this sample if the surface charges were neutralized or protonated. Also observed
for this system was a substantial decrease in stress at the onset of shear thickening.
After weeks or months crystallization took place in the system if a polydisper-
sity of 5.5% existed in the charge or the sphere radii. At high-volume fractions and a
polydispersity of ~7.5%, a glass phase formed. For a system like lipid A-diphosphate,
which contained a single species interacting with a spherical symmetric potential, a
glass phase will normally form if quenched at a sufficiently rapid rate. Such a system
was heavily dependent on deionization time, requiring several days (or weeks) to form
a solid phase from a liquid-stock solution. The fundamental time steps in the crystal-
lization of atomic materials were the inverse of the phonon frequency @ 10
-13
s. For a
system of lipid A-diphosphate with a polyball morphology, an interparticle spacing of
55 nm, a Stokes-Einstein diffusion coefficient D
0
= 4.0 × 10
-8
cm
2
s
-1
and in an aqueous
solution at 20°C, the value calculated for
a
2
/D
0
@ 1.0-1.5 s. The deionization process
on a time scale of between 3 and 4 days would be equivalent to a 10
-4
s quench from
the liquid to the solid phase. It was much easier to attain the crystalline state when
the liquid-phase boundary was approached through an increase in the volume fraction
and/or by slowly changing the ionic strength. Phonon frequencies in colloidal systems
are small because of the large particle mass and long spacing distances (0.05-1.5 µm).
The Phonon frequencies scale with
m-0.5
×
a
-1
and are 10
5
times smaller for colloidal
crystals than for normal solids. The links of the onset of melting to the thermally
driven rms displacements, dr, of particles about their mean positions roughly approach
0.15×
a
when the crystal
melts (Lindemann criterion): This results in a movement of
~6.5 nm, a distance considerably less than the spacing between the surfaces of the
colloidal spheres and less than the screening length. Therefore, if either of these two
conditions occurred independently or simultaneously the system would evolve to form
a vitreous state known as a repulsive glass. Constructing a phase diagram for for ex-
ample lipid A-diphosphate, for behavior at a low, moderate and high volume frac-
tions (f) in the pH range 5.6-7.0, revealed additional phases. The disclosed phases
which formed in an acidic pH were; another cubic structure and two glassy forms.
In the experiments, the bare lipid A-diphosphate charge was not constant when the
particle number density,
n
, changed, because of the formation of distinct cubic struc-
tures (FCC, BCC, and S.C.). Three main effects could be responsible for the obser-
vation: (i) counter ion condensation, (ii) self screening and (iii) many-body effects
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