Biomedical Engineering Reference
In-Depth Information
of crosslinking is supported by small angle neutron scattering studies with PEG-
dimethacrylate [64]. Crosslinking without vinyl pyrrolidone is possible and thus
the hydrogels are formed with 100% crosslinker [62]. The crosslinked network
might be best described by a model that treats each polyacrylate backbone as a
high functionality point crosslink. Perhaps an even better model might
incorporate the bimodal nature of M
c
, using the number average of the smaller
M
c
along the polyacrylate backbone and a larger M
c
equal to the molecular
weight of PEG. Polysiloxane gels with bimodal distributions of M
c
are tougher
than gels with a unimodal distribution [65], which may have some impact on the
mechanical properties of PEG-DA hydrogels.
Considering that the Flory-Rehner model was developed with four-arm
polymers in mind, application of the model to gels formed by end-linking
multiarm PEG may be more straightforward, but some limitations still remain.
Flory imagined that each four arm polymer filled its own tetrahedron and the
crosslinks occurred with the nearest neighbor. However, most crosslinking
reactions occur at relatively high concentrations of PEG. The concentration at
which overlap of chains becomes significant is called c* [66]. The c*
concentration depends on the molecular weight of the PEG and may be
determined by viscometry, e.g. c* for four arm PEG 10,000 in water is about
6%(w/v) [23]. Typical PEG concentrations used for end-crosslinking are 10-
20%(w/v) PEG [25, 35]. Thus, multiarm polymer chains may form crosslinks
well beyond their nearest neighbors, producing an interdigitated, entangled
structure (Figure 2).
The presence of entanglements is intimately linked with the relative success
of the Flory-Rehner equation. The equation assumes an affine network, in which
the crosslink sites expand relative to one other to the same degree as the
expansion of the macroscopic network. An alternative possibility is a phantom
network, in which the crosslink sites may fluctuate within the network. The
position of the crosslink sites in a phantom network deforms affinely, but the
fluctuations about the mean are invariant [67]. The phantom model is more
relevant than the former for highly swollen networks, while real networks
typically lie somewhere in between the two models [53]. Entanglements increase
the stress in a swollen network by restricting fluctuations in the crosslink sites,
enhancing agreement with the affine model [67]. Flory later proposed a model of
the following form:
1
+
K
(
)
2
2
1
−
Ç
ln(1
−
v
)
+
v
+ χ
(v
)
×
=
[6]
(v
) (v
)
É
Ù
3
3
2,s
2,s
12
2,s
2,0
2,s
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