Influence of the Processes Parameters on the Properties of The ...
Influence of the Processes Parameters on the Properties of The ...
Influence of the Processes Parameters on the Properties of The ...
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Chapter 2.<br />
<str<strong>on</strong>g>Processes</str<strong>on</strong>g> to Manufacture Foams and to Functi<strong>on</strong>alize <str<strong>on</strong>g>the</str<strong>on</strong>g> Surface<br />
where C is <str<strong>on</strong>g>the</str<strong>on</strong>g> c<strong>on</strong>centrati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> dissolved fluid inside <str<strong>on</strong>g>the</str<strong>on</strong>g> polymer matrix (number <str<strong>on</strong>g>of</str<strong>on</strong>g> molecules per<br />
volume), k is <str<strong>on</strong>g>the</str<strong>on</strong>g> Boltzmann c<strong>on</strong>stant, T is <str<strong>on</strong>g>the</str<strong>on</strong>g> temperature and f 0 <str<strong>on</strong>g>the</str<strong>on</strong>g> frequency factor for <str<strong>on</strong>g>the</str<strong>on</strong>g> gas molecules,<br />
which describes <str<strong>on</strong>g>the</str<strong>on</strong>g> rate at which nuclei with critical radius are transformed into stable bubbles.<br />
Frequency factor f 0 can be expressed as a functi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> critical radius [Goel and Beckman, 1994a]:<br />
f<br />
2<br />
0<br />
4 c<br />
<br />
<br />
ZR imp<br />
r<br />
(2.22)<br />
where Z is <str<strong>on</strong>g>the</str<strong>on</strong>g> Zeldovich factor and R imp is <str<strong>on</strong>g>the</str<strong>on</strong>g> impingement rate <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> gas molecules per unit area. ZR imp<br />
can be used as a <strong>on</strong>e time fitter parameter within <str<strong>on</strong>g>the</str<strong>on</strong>g> calculati<strong>on</strong>s.<br />
Since foaming is an unsteady state process, we have to take into c<strong>on</strong>siderati<strong>on</strong> time as a variable<br />
and integrate <str<strong>on</strong>g>the</str<strong>on</strong>g> nucleati<strong>on</strong> rate in order to calculate total number <str<strong>on</strong>g>of</str<strong>on</strong>g> nuclei generated within <str<strong>on</strong>g>the</str<strong>on</strong>g> nucleati<strong>on</strong><br />
time:<br />
N<br />
total<br />
<br />
t,<br />
vitr<br />
<br />
0<br />
P,<br />
vitr<br />
dP<br />
N<br />
0<br />
dt N<br />
0<br />
(2.23)<br />
dP dt<br />
P,<br />
sat<br />
where sat and vitr denotes <str<strong>on</strong>g>the</str<strong>on</strong>g> saturati<strong>on</strong> and vitrificati<strong>on</strong> respectively.<br />
It is in our knowledge that <str<strong>on</strong>g>the</str<strong>on</strong>g> foaming <str<strong>on</strong>g>of</str<strong>on</strong>g> polymers occurs while <str<strong>on</strong>g>the</str<strong>on</strong>g> CO 2 is desorbs. Hence, <strong>on</strong>e<br />
can say that <str<strong>on</strong>g>the</str<strong>on</strong>g> dissolved amount <str<strong>on</strong>g>of</str<strong>on</strong>g> fluid in <str<strong>on</strong>g>the</str<strong>on</strong>g> polymer matrix is not c<strong>on</strong>stant within <str<strong>on</strong>g>the</str<strong>on</strong>g> foaming time and<br />
it decreases. Also, while foaming occurs, polymer swells as <str<strong>on</strong>g>the</str<strong>on</strong>g> CO 2 changes its state from supercritical to<br />
gas (<str<strong>on</strong>g>the</str<strong>on</strong>g> volume <str<strong>on</strong>g>of</str<strong>on</strong>g> CO 2 increases). So, <strong>on</strong>e can say that in <str<strong>on</strong>g>the</str<strong>on</strong>g> presence <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g>se two effects <str<strong>on</strong>g>the</str<strong>on</strong>g> c<strong>on</strong>centrati<strong>on</strong><br />
<str<strong>on</strong>g>of</str<strong>on</strong>g> CO 2 in <str<strong>on</strong>g>the</str<strong>on</strong>g> matrix decreases. This c<strong>on</strong>centrati<strong>on</strong> dependency must be placed in <str<strong>on</strong>g>the</str<strong>on</strong>g> nucleati<strong>on</strong> rate<br />
equati<strong>on</strong> and nucleati<strong>on</strong> rate must be integrated with time. One can model <str<strong>on</strong>g>the</str<strong>on</strong>g> decrease <str<strong>on</strong>g>of</str<strong>on</strong>g> mass within <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
foaming time by using equati<strong>on</strong> 2.3 and fitting it to <str<strong>on</strong>g>the</str<strong>on</strong>g> desorpti<strong>on</strong> data. <strong>The</strong> change within <str<strong>on</strong>g>the</str<strong>on</strong>g> volume can<br />
be expressed with a linear relati<strong>on</strong>ship between initial and final volumes. One can assume that <str<strong>on</strong>g>the</str<strong>on</strong>g>re is no<br />
volume change after vitrificati<strong>on</strong>. <strong>The</strong> variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> CO 2 c<strong>on</strong>centrati<strong>on</strong> is not c<strong>on</strong>sidered in <str<strong>on</strong>g>the</str<strong>on</strong>g> existing<br />
model.<br />
4.4 Distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> Pores<br />
Scaffolds must meet certain fundamental characteristics such as high porosity, appropriate pore<br />
size, biocompatibility, biodegradability and proper degradati<strong>on</strong> rate [Ma and Choi, 2001]. Scaffolds for<br />
tissues require specific properties such as an interc<strong>on</strong>nected porosity higher than 75% to provide a high void<br />
volume for nutrient diffusi<strong>on</strong> [Temen<str<strong>on</strong>g>of</str<strong>on</strong>g>f et al., 2000]. Fur<str<strong>on</strong>g>the</str<strong>on</strong>g>rmore an optimal pore size necessary to promote<br />
cell adhesi<strong>on</strong> must be in <str<strong>on</strong>g>the</str<strong>on</strong>g> range <str<strong>on</strong>g>of</str<strong>on</strong>g> 100−300 μm [Boyan et al., 1996]. Finally, mechanical properties<br />
should approximate those <str<strong>on</strong>g>of</str<strong>on</strong>g> native cartilage b<strong>on</strong>e, in order to support body load and avoid excessive micromoti<strong>on</strong>s<br />
at <str<strong>on</strong>g>the</str<strong>on</strong>g> scaffold/b<strong>on</strong>e interface [Büchler et al., 2003; Temen<str<strong>on</strong>g>of</str<strong>on</strong>g>f et al., 2000].<br />
Ideally a scaffold should possess <str<strong>on</strong>g>the</str<strong>on</strong>g> following characteristics c<strong>on</strong>taining <str<strong>on</strong>g>the</str<strong>on</strong>g> desired biologic<br />
resp<strong>on</strong>se [Hutmacher, 2001]:<br />
<br />
<br />
<br />
three-dimensi<strong>on</strong>al and highly porous with an interc<strong>on</strong>nected pore network for cell/tissue growth and<br />
flow transport <str<strong>on</strong>g>of</str<strong>on</strong>g> nutrients and metabolic waste,<br />
biodegradable or bioresorbable with a c<strong>on</strong>trollable degradati<strong>on</strong> and resorpti<strong>on</strong> rate to match<br />
cell/tissue growth in vitro and/or in vivo,<br />
suitable surface chemistry for cell attachment, proliferati<strong>on</strong> and differentiati<strong>on</strong>,<br />
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