Biomedical Engineering Reference
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A = Triple point
B = Tricritical point
B
Liquid binodal
Vapour
Vapour binodal
Liquid
Solid
A
Liquid spinodal
Gel line
Vapour spinodal
ρ
Figure 2.19
Typical phase diagram for a colloidal system of attractive particles. The position of the transient
gel line is somewhat imprecise because there is a lifetime associated with persistence of the
equilibrium modulus G
eq
. Therefore, the exact location of the gel line will depend on the value
given to this lifetime (Lodge and Heyes,
1999b
). Reproduced by permission of the PCCP Owner
Societies.
ratio of temperature T to interaction potential well depth
ε
, is the key parameter that
determines phase separation.
Shortly after the temperature quench, the development of local structure can be seen in
instantaneous (snapshot) con
gurations (Lodge and Heyes,
1997
). The snapshots shown
in
Figure 2.20
represent colloidal suspensions after quenching at a time t =82a²/D
0
,a
long elapsed time in the simulation, for each of three interaction potentials, at the same
reduced temperature T
*
= 0.3 and the same volume fraction of particles
ϕ
= 0.1:
¼
6
3
V
:
σ
N
ð
2
:
36
Þ
Here N is the total number of particles and V is the volume of the cubic simulation
box. In
Figure 2.20
the spheres represent 1
and are drawn to scale relative to the
simulation box (Lodge and Heyes,
1999a
). At this low temperature, all of the systems
displayed phase separation, eventually forming dense aggregates that spanned the
simulation box.
With the LJ 12:6 potential, the particles start clustering soon after the quench and, at a
later stage as shown in
Figure 2.20a
, they have collapsed into dense structures. As the
attractive part of the potential becomes more short-range (24:12 potential,
Figure 2.20b
)
the aggregates adopt a more diffuse morphology. The particles still cluster, but they no
longer collapse into a dense mass. For the system with the 36:18 potential (
Figure 2.20c
)
σ
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