Influence of the Processes Parameters on the Properties of The ...

Chapter 2.
<strong>Processes</strong> to Manufacture Foams and to Functionalize <strong>the</strong> Surface
where C is <strong>the</strong> concentration <strong>of</strong> <strong>the</strong> dissolved fluid inside <strong>the</strong> polymer matrix (number <strong>of</strong> molecules per
volume), k is <strong>the</strong> Boltzmann constant, T is <strong>the</strong> temperature and f 0 <strong>the</strong> frequency factor for <strong>the</strong> gas molecules,
which describes <strong>the</strong> rate at which nuclei with critical radius are transformed into stable bubbles.
Frequency factor f 0 can be expressed as a function <strong>of</strong> <strong>the</strong> critical radius [Goel and Beckman, 1994a]:
f
2
0
4 c
ZR imp
r
(2.22)
where Z is <strong>the</strong> Zeldovich factor and R imp is <strong>the</strong> impingement rate <strong>of</strong> <strong>the</strong> gas molecules per unit area. ZR imp
can be used as a one time fitter parameter within <strong>the</strong> calculations.
Since foaming is an unsteady state process, we have to take into consideration time as a variable
and integrate <strong>the</strong> nucleation rate in order to calculate total number <strong>of</strong> nuclei generated within <strong>the</strong> nucleation
time:
N
total
t,
vitr
0
P,
vitr
dP
N
0
dt N
0
(2.23)
dP dt
P,
sat
where sat and vitr denotes <strong>the</strong> saturation and vitrification respectively.
It is in our knowledge that <strong>the</strong> foaming <strong>of</strong> polymers occurs while <strong>the</strong> CO 2 is desorbs. Hence, one
can say that <strong>the</strong> dissolved amount <strong>of</strong> fluid in <strong>the</strong> polymer matrix is not constant within <strong>the</strong> foaming time and
it decreases. Also, while foaming occurs, polymer swells as <strong>the</strong> CO 2 changes its state from supercritical to
gas (<strong>the</strong> volume <strong>of</strong> CO 2 increases). So, one can say that in <strong>the</strong> presence <strong>of</strong> <strong>the</strong>se two effects <strong>the</strong> concentration
<strong>of</strong> CO 2 in <strong>the</strong> matrix decreases. This concentration dependency must be placed in <strong>the</strong> nucleation rate
equation and nucleation rate must be integrated with time. One can model <strong>the</strong> decrease <strong>of</strong> mass within <strong>the</strong>
foaming time by using equation 2.3 and fitting it to <strong>the</strong> desorption data. The change within <strong>the</strong> volume can
be expressed with a linear relationship between initial and final volumes. One can assume that <strong>the</strong>re is no
volume change after vitrification. The variation <strong>of</strong> CO 2 concentration is not considered in <strong>the</strong> existing
model.
4.4 Distribution <strong>of</strong> Pores
Scaffolds must meet certain fundamental characteristics such as high porosity, appropriate pore
size, biocompatibility, biodegradability and proper degradation rate [Ma and Choi, 2001]. Scaffolds for
tissues require specific properties such as an interconnected porosity higher than 75% to provide a high void
volume for nutrient diffusion [Temen<strong>of</strong>f et al., 2000]. Fur<strong>the</strong>rmore an optimal pore size necessary to promote
cell adhesion must be in <strong>the</strong> range <strong>of</strong> 100−300 μm [Boyan et al., 1996]. Finally, mechanical properties
should approximate those <strong>of</strong> native cartilage bone, in order to support body load and avoid excessive micromotions
at <strong>the</strong> scaffold/bone interface [Büchler et al., 2003; Temen<strong>of</strong>f et al., 2000].
Ideally a scaffold should possess <strong>the</strong> following characteristics containing <strong>the</strong> desired biologic
response [Hutmacher, 2001]:
three-dimensional and highly porous with an interconnected pore network for cell/tissue growth and
flow transport <strong>of</strong> nutrients and metabolic waste,
biodegradable or bioresorbable with a controllable degradation and resorption rate to match
cell/tissue growth in vitro and/or in vivo,
suitable surface chemistry for cell attachment, proliferation and differentiation,
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