BIOMATERIALS FOR BIOPRINTING - 3D Bioprinting and Nanotechnology in Tissue Engineering and Regenerative Medicine - page 128

v
V

−++

ln(1 v ) v xv

2
2,

)

2, s 2, s 1 s

1 1

1

=−

MM

1
3

c N

v
v

v
v

2, s 2, s

v [ − ]

2, r

2

2, r 2, r

Here, the term v 2. r and v 2. s show the volume fraction of the polymer in the relaxed and swollen
state. The relaxed state refers to the cross-linked polymer without the occurrence of swelling. Thus, in
the absence of a solvent, the volume fraction of the relaxed state is 1, simplifying the equation back
to the Flory-Rhener equation.
For ionic gels, two separate but equivalent expressions were derived for anionic and cationic gels
( Brannon-Peppas and Peppas, 1991 ). These equations for average molecular weight between cross-
links require ionic strength I and dissociation constants K a and K b .

2

2
2,

V v

v

K

s

1 a

− pH

4 I 10 − K

a

1
3

=−++ +

V
vM

2 M

M

v
v

−

v
v

2, s 2, s

2
2,

1 c

[ln(1 v ) v xv ] 1 − v [ ]

2, s 2, s 1 s 2, r

2

c N 2, r 2, r

2

2
2,

V v K

s

1 a

pH − 14

4 I v 10 − K

a

1
3

=−++ +

V
vM

2 M

M

v
v

−

v
v

2, s 2, s

2
2,

1 c

[ln(1 v ) v xv ] 1 − v [ ]

2, s 2, s 1 s 2, r

2

c 2, r 2, r

N

6.2.6 ELASTICITY
When pressure is applied on the hydrogel, it displays a variety of responses, from rapid recovery to
slow time-dependent approach. This characteristic is dependent on the hydrogel's glass transition state
(Tg). At temperatures below Tg, the rearrangement of the polymer segments is slowed down. Thus,
the gel becomes more viscoelastic. During this system, the mechanical properties of the gel, such as
creep, stress relaxation, and dynamic loading, are most important. However, during tissue culturing, the
hydrogel is usually water swollen to allow cell to proliferate. The excess water and solutes entering
the hydrogel plasticize it and induce a reduction in the polymer glass transition due to the swelling.
This decreases the Tg to below 37 o C and subsequently causes the hydrogel to move toward a rubbery
elastic region.

6.2.7 SOLUTE TRANSPORTATION
Another important aspect of designing hydrogel for tissue engineering is the development of an effec-
tive solute transport. This determines how cellular products, nutrients, and waste are exchanged within