BIOMATERIALS FOR BIOPRINTING - 3D Bioprinting and Nanotechnology in Tissue Engineering and Regenerative Medicine - page 127

6.2.5 SWELLING BEHAVIOR
Swelling and contraction of the bioprinted construct have to be considered and accounted for during
the design of the tissue construct. Differences in the swelling properties among different hydrogels will
cause complications, such as restricted grafting of the layers and overall uneven deformation of the
construct ( Murphy et al., 2013 ). Swelling behavior is also strongly dependent on the local environment,
such as pH, ionic strength, and solvent conditions. Swelling rates also affect the surface properties of
the gel, the solute diffusion coefficient through hydrogels, and the optical properties. The dynamic
swelling and equilibrium in solutions of hydrogel governs the mechanical integrity of hydrogels. As
described earlier, most water molecules within hydrogel are bound by either hydrophilic or hydropho-
bic groups. Most solutes can only diffuse into and through hydrogel from within the unbound regions
of the macropores and voids. Solutes that are chaotropic can diffuse through hydrogel by disturbing the
interaction of the bound water layers around the polymer chain.
The swelling behavior of hydrogel can be thermodynamically described by the Flory-Huggins
theory ( Flory and Rehner, 1943 ). However, this theory does not account for the imperfections of the
network or the finite volume of network chains and cross-links in the gel. In this model, the equilibrium
of cross-linked polymer network swelling was described by the elastic forces of the polymer chains
and the thermodynamic compatibility of the hydrogel polymer and the solvent, as shown in the Gibbs
Free energy equation shown here. Swelling rates can be controlled by copolymerizing monomers of
varying hydrophobicity.

∆= ∆ G G + ∆ G

total elastic mixing

However, for ionic gels, the total free energy contribution by hydrogel would require the involve-
ment of the ionic properties of the network.

∆= ∆ G G + ∆ G + ∆ G

total elastic mixing ionic

At equilibrium potential, the net chemical potential between the solvent and the surrounding solu-
tion is zero. This zero net chemical potential balances the elastic and mixing potential. The Flory-
Rhener theory evolves the expression that the hydrogel prepared in the absence of solvent should
contain the following relationship:

v
V

2
2

ln(1 −++ vvxv ) )

2 2, s 1

1 1

1

=−

1
3
2

MM v

c N

v −

2

2

where v is the specific volume of the hydrophilic polymer, M N is the primary molecular mass, M c is the
average molecular mass between the cross-links, v 2 is the volume fraction of the polymer in the swollen
mass, and V 1 is the molar volume of the solvent. The mixing term ∆G mixing depends on the compat-
ibility of the hydrophilic polymer and the solvent, and is expressed as the polymer-solvent interaction
parameter, χ 1.
The equation is then modified by Peppas and Merrill for gels prepared in the presence of a solvent
by including the changes in the elastic potential due to the solvent ( Peppas and Merrill, 1977 ).