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 3.<br />
Analytical Methods and Designs <str<strong>on</strong>g>of</str<strong>on</strong>g> Experiments<br />
In our analyses, <str<strong>on</strong>g>the</str<strong>on</strong>g> diameter and thickness <str<strong>on</strong>g>of</str<strong>on</strong>g> pellets and foams have been measured using a<br />
standard engineering caliber. <strong>The</strong> volume <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> polymers is evaluated by v = πr 2 h, where r is <str<strong>on</strong>g>the</str<strong>on</strong>g> radius and<br />
h is <str<strong>on</strong>g>the</str<strong>on</strong>g> thickness <str<strong>on</strong>g>of</str<strong>on</strong>g> pellets and scaffolds. <strong>The</strong> P(%) porosity is calculated by:<br />
foamed<br />
P(%) (1 ) 100<br />
unfoamed<br />
(3.11)<br />
where unfoamed and foamed are <str<strong>on</strong>g>the</str<strong>on</strong>g> density <str<strong>on</strong>g>of</str<strong>on</strong>g> pellets and foams respectively.<br />
5.1.2 Mercury Porosimetry<br />
<strong>The</strong> number <str<strong>on</strong>g>of</str<strong>on</strong>g> pores that exist in a typical porous sample is usually <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> order <str<strong>on</strong>g>of</str<strong>on</strong>g> milli<strong>on</strong>s,<br />
billi<strong>on</strong>s or even trilli<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g>m per unit mass <str<strong>on</strong>g>of</str<strong>on</strong>g> solid. <strong>The</strong>se pores are generally interc<strong>on</strong>nected to each<br />
o<str<strong>on</strong>g>the</str<strong>on</strong>g>r by way <str<strong>on</strong>g>of</str<strong>on</strong>g> a sinuous 3-D pathway. In lattice models Mayagoitia et al., [1994], <str<strong>on</strong>g>the</str<strong>on</strong>g> porous space is<br />
distributed between two types <str<strong>on</strong>g>of</str<strong>on</strong>g> elements: <str<strong>on</strong>g>the</str<strong>on</strong>g> sites (cavities) and <str<strong>on</strong>g>the</str<strong>on</strong>g> b<strong>on</strong>ds (necks).<br />
<strong>The</strong> technique involves <str<strong>on</strong>g>the</str<strong>on</strong>g> intrusi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a n<strong>on</strong>-wetting liquid (mercury) at high pressure into a<br />
material through <str<strong>on</strong>g>the</str<strong>on</strong>g> use <str<strong>on</strong>g>of</str<strong>on</strong>g> a porosimeter (cf. Figure 3.12-A). Hg porosimetry experiments comprise two<br />
stages. <strong>The</strong> first stage (intrusi<strong>on</strong>) starts with <str<strong>on</strong>g>the</str<strong>on</strong>g> immersi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a porous sample in Hg. As <str<strong>on</strong>g>the</str<strong>on</strong>g> pressure <str<strong>on</strong>g>of</str<strong>on</strong>g> Hg<br />
is increased, <str<strong>on</strong>g>the</str<strong>on</strong>g> pore entities are penetrated sequentially, i.e. from <str<strong>on</strong>g>the</str<strong>on</strong>g> largest to <str<strong>on</strong>g>the</str<strong>on</strong>g> smaller <strong>on</strong>es according<br />
to <str<strong>on</strong>g>the</str<strong>on</strong>g> current value <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> external pressure. <strong>The</strong> sec<strong>on</strong>d stage (retracti<strong>on</strong>) c<strong>on</strong>sists in <str<strong>on</strong>g>the</str<strong>on</strong>g> withdrawal <str<strong>on</strong>g>of</str<strong>on</strong>g> Hg<br />
from <str<strong>on</strong>g>the</str<strong>on</strong>g> pores. Since this last process involves <str<strong>on</strong>g>the</str<strong>on</strong>g> gradual decrease <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> external pressure, <str<strong>on</strong>g>the</str<strong>on</strong>g> successi<strong>on</strong><br />
by which pores are emptied goes from <str<strong>on</strong>g>the</str<strong>on</strong>g> smallest to <str<strong>on</strong>g>the</str<strong>on</strong>g> largest <strong>on</strong>es.<br />
(A)<br />
(B)<br />
Figure 3.12: (A): Hg porosimeter apparatus and (B): Pore size distributi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> P L LA samples.<br />
[Ho et al., 2004]<br />
<strong>The</strong> pore size can be determined based <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> external pressure needed to force <str<strong>on</strong>g>the</str<strong>on</strong>g> liquid into a<br />
pore against <str<strong>on</strong>g>the</str<strong>on</strong>g> opposing force <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> liquid’s surface tensi<strong>on</strong>. A force balance equati<strong>on</strong> known as<br />
Washburn’s relati<strong>on</strong>ship (equati<strong>on</strong> 3.12), for <str<strong>on</strong>g>the</str<strong>on</strong>g> above material having cylindrical pores is given as:<br />
4..Cos<br />
PL - PG<br />
(3.12)<br />
D P<br />
where P L = pressure <str<strong>on</strong>g>of</str<strong>on</strong>g> liquid, P G = pressure <str<strong>on</strong>g>of</str<strong>on</strong>g> gas, σ = surface tensi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> liquid, θ = c<strong>on</strong>tact angle<br />
<str<strong>on</strong>g>of</str<strong>on</strong>g> intrusi<strong>on</strong> liquid (i.e. mercury) and D P = pore diameter.<br />
As pressure increases, so does <str<strong>on</strong>g>the</str<strong>on</strong>g> cummulative pore volume. From <str<strong>on</strong>g>the</str<strong>on</strong>g> cummulative pore volume,<br />
<strong>on</strong>e can find <str<strong>on</strong>g>the</str<strong>on</strong>g> pressure and <str<strong>on</strong>g>the</str<strong>on</strong>g> pore diameter where 50% <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> total volume has been added to give <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
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