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

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