POLYMER-PEPTIDE CONJUGATE NETWORKS: FORMATION, SWELLING AND DEGRADATION - Biologically-Responsive Hybrid Biomaterials - page 64

multiarm polymer with only two chains linked to the network leads to an
increase in M c (Figure 5). Despite these complexities, analysis using relatively
simple combinatorics leads to excellent predictions.

Dangling ends

Dangling ends

Dangling ends

Fig. 5. Degradation of a network made from end-linked eight-arm PEG leads to the formation of
dangling ends and an increase in the average molecular weight between crosslinks. Circles
represent bonds, wavy lines represent the rest of the network. Dangling ends become numerous just
prior to dissolution of the gel. The eight-arm polymer in the lower right only has two arms joined to
the network, thus increasing the molecular weight between crosslinks.

Another scaling law is useful to relate the shear modulus to the swelling of
network:

−

3 ν

ν−

E ∝ Q [9]

1

s

Where E s is the modulus of the gel in the swollen state and here is not the
number of crosslinks but the universal exponent relating the Flory radius to the
size of the polymer chain [81]. In a good solvent, is 3/5, leading to

Q −

2.25

E ∝ . s

3

In a theta solvent or concentrated solution, is 1/2, leading to E Q∝ . A

power law plot of E s versus Q yielded a slope of -2.8 for photopolymerized PEG
hydrogels [82]. A slope close to -3 was found for end-linked hybrid PEG
hydrogels [32].

s

5. Conclusions

Characterization of hybrid hydrogels may be aided by the application of classic
statistical mechanical models of rubberlike elasticity and swelling. Although the