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 />
where γ 12 is <str<strong>on</strong>g>the</str<strong>on</strong>g> surface energy <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>tact regi<strong>on</strong> between phase 1 and 2, γ 1 (γ 2 ) is <str<strong>on</strong>g>the</str<strong>on</strong>g> surface<br />
energy <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> phase 1 (phase 2) and <str<strong>on</strong>g>the</str<strong>on</strong>g> exp<strong>on</strong>ents γ d (γ p ) corresp<strong>on</strong>d to <str<strong>on</strong>g>the</str<strong>on</strong>g> dispersive fracti<strong>on</strong> and <str<strong>on</strong>g>the</str<strong>on</strong>g> polar<br />
fracti<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> surface energy.<br />
<strong>The</strong> force needed to extend <str<strong>on</strong>g>the</str<strong>on</strong>g> c<strong>on</strong>tact regi<strong>on</strong> between two immiscible phases relies <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> force<br />
needed to extend each phase separately minus <str<strong>on</strong>g>the</str<strong>on</strong>g> interacti<strong>on</strong> that <str<strong>on</strong>g>the</str<strong>on</strong>g>y have with each o<str<strong>on</strong>g>the</str<strong>on</strong>g>r.<br />
<strong>The</strong>rmodynamically this equati<strong>on</strong> can be interpretated as follows: each substance is seeking for <str<strong>on</strong>g>the</str<strong>on</strong>g> lowest<br />
energy possible. Since a surface has a higher energy state, each phase tries to reduce its surface area. When<br />
two immiscible liquids are combined, a c<strong>on</strong>tact regi<strong>on</strong> is formed between both. To extend this regi<strong>on</strong>, energy<br />
is needed. This energy depends <strong>on</strong> <str<strong>on</strong>g>the</str<strong>on</strong>g> energy needed to break <str<strong>on</strong>g>the</str<strong>on</strong>g> bindings <str<strong>on</strong>g>of</str<strong>on</strong>g> each phase separately minus<br />
<str<strong>on</strong>g>the</str<strong>on</strong>g> interacti<strong>on</strong>s <str<strong>on</strong>g>the</str<strong>on</strong>g>y have with each o<str<strong>on</strong>g>the</str<strong>on</strong>g>r. This negative sign is explained since, by creating two new<br />
surfaces, new interacti<strong>on</strong>s between <str<strong>on</strong>g>the</str<strong>on</strong>g> different phases will occur, causing a lower energy and <str<strong>on</strong>g>the</str<strong>on</strong>g>refore a<br />
more favourable state. C<strong>on</strong>sidering equati<strong>on</strong> 3.19, <str<strong>on</strong>g>the</str<strong>on</strong>g> following equati<strong>on</strong> can be set up in order to describe<br />
<str<strong>on</strong>g>the</str<strong>on</strong>g> interacti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a solid sample with a liquid:<br />
<br />
SL<br />
d d 1/<br />
2 p p 1/ 2<br />
SV LV 2[( <br />
SV<br />
. <br />
LV ) ( <br />
SV<br />
. <br />
LV ) ]<br />
(3.20)<br />
where γ SL = solid-liquid surface energy, γ SV = solid-vapour surface energy, γ LV = liquid-vapour<br />
surface tensi<strong>on</strong>, γ d = dispersive fracti<strong>on</strong> and γ P = polar fracti<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> surface energy.<br />
This equati<strong>on</strong> is, next to <str<strong>on</strong>g>the</str<strong>on</strong>g> Young-Dupré’ equati<strong>on</strong>, <str<strong>on</strong>g>the</str<strong>on</strong>g> sec<strong>on</strong>d equati<strong>on</strong> needed for calculating<br />
<str<strong>on</strong>g>the</str<strong>on</strong>g> surface free energy <str<strong>on</strong>g>of</str<strong>on</strong>g> a solid sample [Rudawska and Jacniacka, 2008; Owens and Wendt, 1969; Fowkes,<br />
1962]. By combining equati<strong>on</strong>s 3.20 and 3.17, a final ma<str<strong>on</strong>g>the</str<strong>on</strong>g>matical statement can be made in order to<br />
calculate <str<strong>on</strong>g>the</str<strong>on</strong>g> surface energy <str<strong>on</strong>g>of</str<strong>on</strong>g> a solid sample (γ SV ).[Rudawska and Jacniacka, 2008; Mykhaylyk et al.,<br />
2003]:<br />
<br />
<br />
SV<br />
SV<br />
SL LV Cos<br />
SV LV SL LV ( Cos<br />
1)<br />
(3.21)<br />
d d 1/<br />
2 p p 1/ 2<br />
LV <br />
SL 2[( <br />
SV<br />
. <br />
LV ) ( <br />
SV<br />
. <br />
LV ) ]<br />
(3.22)<br />
By substituting value from equati<strong>on</strong> 3.21 into equati<strong>on</strong> 3.22, we get:<br />
d d 1/<br />
2 p p 1/ 2<br />
LV ( Cos<br />
1) 2[( <br />
SV<br />
. <br />
LV ) ( <br />
SV<br />
. <br />
LV ) ]<br />
(3.23)<br />
where γ LV = liquid-vapour surface energy, θ = c<strong>on</strong>tact angle, γ SV = solid-vapour surface energy, γ d =<br />
dispersive fracti<strong>on</strong> and γ p = polar fracti<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> surface energy.<br />
By using a liquid that <strong>on</strong>ly interacts <strong>on</strong> a dispersive level (diiodomethane or -brom<strong>on</strong>aphtalene)<br />
with o<str<strong>on</strong>g>the</str<strong>on</strong>g>r phases, equati<strong>on</strong> 3.23 can be simplified by excluding <str<strong>on</strong>g>the</str<strong>on</strong>g> polar interacti<strong>on</strong>s. <strong>The</strong> liquid vapor<br />
surface energy and <str<strong>on</strong>g>the</str<strong>on</strong>g> c<strong>on</strong>tact angle can be directly measured. <strong>The</strong> dispersive tensi<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> liquid vapour<br />
surface energy (γ d LV) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> diiodomethane is equal to <str<strong>on</strong>g>the</str<strong>on</strong>g> total liquid vapour surface energy (γ LV ) since <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
polar interacti<strong>on</strong>s are null (cf. Table 3.1). C<strong>on</strong>sequently, <str<strong>on</strong>g>the</str<strong>on</strong>g> <strong>on</strong>ly unknown parameter (γ d SV) can be<br />
calculated.<br />
Extrapolating <str<strong>on</strong>g>the</str<strong>on</strong>g> γ d SV value and using a sec<strong>on</strong>d liquid having dispersive and polar interacti<strong>on</strong>s<br />
with <str<strong>on</strong>g>the</str<strong>on</strong>g> solid sample, <str<strong>on</strong>g>the</str<strong>on</strong>g> <strong>on</strong>ly unknown parameter (γ p SV) can be determined. <strong>The</strong> sum <str<strong>on</strong>g>of</str<strong>on</strong>g> both calculated<br />
fracti<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> solid material (γ p SV and γ d SV) gives <str<strong>on</strong>g>the</str<strong>on</strong>g> total surface free energy <str<strong>on</strong>g>of</str<strong>on</strong>g> a solid sample [Wu, 2001;<br />
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