Biomedical Engineering Reference
In-Depth Information
Snapshot of the three-dimensional network structure produced from simulated aggregation of
particles with
ϕ
= 0.11,
ε
=4k
B
T, n
0
= 2. The pair interaction potential has a shorter finite attractive
range than the LJ potential. A coarse, phase separated structure is observed. Adapted from
Bijsterbosch and Bos (
1995
) with permission of the Royal Society of Chemistry.
Figure 2.22
attributed to a percolating network. This plateau is referred as an
'
equilibrium modulus
'
G
eq
, on intermediate time scales, even though there are no formal links.
G
eq
increases in time after the quench, and depends on the interaction potential. As
seen in
Figure 2.23
,with
= 0.2, a transition appears between temperatures T
*
=0.5
and 0.7, which suggests the formation of a network and determines the gel line in
Figure 2.19
.
Obviously, the de
ϕ
nition of the gel line from these simulations is somewhat impre-
cise because there is a lifetime associated with the persistence of the equilibrium
modulus. Gel-like behaviour was observed in the two-phase region of LJ potentials,
with comparatively large G
eq
values measured during relatively short lifetimes (of the
order of a
2
/D
0
). With the other potentials, the network is more diffuse (see
Figure 2.20c
). For the shortest-ranged (36:18) interaction, any potential phase separa-
tion was largely arrested on long length scales for a signi
cant part of the simulation
times. This system displayed the weakest of all rheological gel-like features.
A
finite equilibrium modulus G
eq
is associated with a gelation threshold, the formation
of a percolating network (
Chapter 3
) with distances between the particles close to the
minimum in the pair potential. In this situation the
tran-
sitions coincide. The value of G
eq
decreases with increasing temperature for the 12:6
potential. If temperature is maintained constant, G
eq
also increases with volume fraction.
'
structural
'
and
'
mechanical
'
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