Biomedical Engineering Reference
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where K depends on the average number of crosslink sites within the volume of a
single four-arm crosslink site. The 'constrained junction model' was derived
from the phantom model accounting for constriction of fluctuations due to
entanglements [65, 68, 69].
Total Precursor Concentration (wt%)
Fig. 3. The concentration of polymer during crosslinking affects subsequent swelling. The swelling
ratio predicted by the Flory-Rehner equation for a perfectly crosslinked gel is shown (---). Eight
arm PEG crosslinked with linear PEG (squares) approaches an asymptote in swelling at high
precursor concentration that is in good agreement with the Flory-Rehner equation. Four arm PEG
crosslinked with linear PEG (triangles) also reaches an asymptote in swelling, but this is not
predicted by the Flory-Rehner equation. Reprinted from Metters A. & Hubbell J. (2005). Network
formation and degradation behavior of hydrogels formed by Michael-type addition reactions.
Biomacromolecules 6(1): 290-301. Copyright 2005 American Chemical Society.
The formation of gels in solution also introduces complications. Flory
corrected for the effects of solvent present during crosslinking (equation 1), but
dilution in solvent also encourages loop formation, i.e. non-productive crosslinks
[50]. Accounting for loops is a challenge. For this reason, the model may
accurately predict the swelling of a gel as it approaches perfection, but may be
inaccurate under many crosslinking conditions, or as the gel degrades by
hydrolysis or enzymatic activity. Figure 3 illustrates that gel swelling is strongly
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