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

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Chapter 3. Analytical Methods and Designs <strong>of</strong> Experiments where γ 12 is <strong>the</strong> surface energy <strong>of</strong> contact region between phase 1 and 2, γ 1 (γ 2 ) is <strong>the</strong> surface energy <strong>of</strong> <strong>the</strong> phase 1 (phase 2) and <strong>the</strong> exponents γ d (γ p ) correspond to <strong>the</strong> dispersive fraction and <strong>the</strong> polar fraction <strong>of</strong> <strong>the</strong> surface energy. The force needed to extend <strong>the</strong> contact region between two immiscible phases relies on <strong>the</strong> force needed to extend each phase separately minus <strong>the</strong> interaction that <strong>the</strong>y have with each o<strong>the</strong>r. Thermodynamically this equation can be interpretated as follows: each substance is seeking for <strong>the</strong> lowest energy possible. Since a surface has a higher energy state, each phase tries to reduce its surface area. When two immiscible liquids are combined, a contact region is formed between both. To extend this region, energy is needed. This energy depends on <strong>the</strong> energy needed to break <strong>the</strong> bindings <strong>of</strong> each phase separately minus <strong>the</strong> interactions <strong>the</strong>y have with each o<strong>the</strong>r. This negative sign is explained since, by creating two new surfaces, new interactions between <strong>the</strong> different phases will occur, causing a lower energy and <strong>the</strong>refore a more favourable state. Considering equation 3.19, <strong>the</strong> following equation can be set up in order to describe <strong>the</strong> interaction <strong>of</strong> a solid sample with a liquid: SL d d 1/ 2 p p 1/ 2 SV LV 2[( SV . LV ) ( SV . LV ) ] (3.20) where γ SL = solid-liquid surface energy, γ SV = solid-vapour surface energy, γ LV = liquid-vapour surface tension, γ d = dispersive fraction and γ P = polar fraction <strong>of</strong> <strong>the</strong> surface energy. This equation is, next to <strong>the</strong> Young-Dupré’ equation, <strong>the</strong> second equation needed for calculating <strong>the</strong> surface free energy <strong>of</strong> a solid sample [Rudawska and Jacniacka, 2008; Owens and Wendt, 1969; Fowkes, 1962]. By combining equations 3.20 and 3.17, a final ma<strong>the</strong>matical statement can be made in order to calculate <strong>the</strong> surface energy <strong>of</strong> a solid sample (γ SV ).[Rudawska and Jacniacka, 2008; Mykhaylyk et al., 2003]: SV SV SL LV Cos SV LV SL LV ( Cos 1) (3.21) d d 1/ 2 p p 1/ 2 LV SL 2[( SV . LV ) ( SV . LV ) ] (3.22) By substituting value from equation 3.21 into equation 3.22, we get: d d 1/ 2 p p 1/ 2 LV ( Cos 1) 2[( SV . LV ) ( SV . LV ) ] (3.23) where γ LV = liquid-vapour surface energy, θ = contact angle, γ SV = solid-vapour surface energy, γ d = dispersive fraction and γ p = polar fraction <strong>of</strong> <strong>the</strong> surface energy. By using a liquid that only interacts on a dispersive level (diiodomethane or -bromonaphtalene) with o<strong>the</strong>r phases, equation 3.23 can be simplified by excluding <strong>the</strong> polar interactions. The liquid vapor surface energy and <strong>the</strong> contact angle can be directly measured. The dispersive tension <strong>of</strong> <strong>the</strong> liquid vapour surface energy (γ d LV) <strong>of</strong> <strong>the</strong> diiodomethane is equal to <strong>the</strong> total liquid vapour surface energy (γ LV ) since <strong>the</strong> polar interactions are null (cf. Table 3.1). Consequently, <strong>the</strong> only unknown parameter (γ d SV) can be calculated. Extrapolating <strong>the</strong> γ d SV value and using a second liquid having dispersive and polar interactions with <strong>the</strong> solid sample, <strong>the</strong> only unknown parameter (γ p SV) can be determined. The sum <strong>of</strong> both calculated fractions <strong>of</strong> <strong>the</strong> solid material (γ p SV and γ d SV) gives <strong>the</strong> total surface free energy <strong>of</strong> a solid sample [Wu, 2001; - 82 -
Chapter 3. Analytical Methods and Designs <strong>of</strong> Experiments Andrade, 1985]. The Liquid-Vapour tension and <strong>the</strong> Solid-Vapour energy are generally approximated by <strong>the</strong> liquid tension and <strong>the</strong> surface energy. Selected liquids need to have suitable properties in order to interact in <strong>the</strong> best possible way to determine <strong>the</strong> surface energy. Firstly, <strong>the</strong> liquids have to carry a wide range <strong>of</strong> intermolecular interactions from polar to apolar. In addition, <strong>the</strong> liquid surface tension has to be higher than <strong>the</strong> solid surface energy: <strong>the</strong> working forces on <strong>the</strong> surface <strong>of</strong> <strong>the</strong> solid sample are superior to <strong>the</strong> forces needed to create <strong>the</strong> drop, resulting in a high wettability. The latter makes it impossible to determine a contact angle [Mykhaylyk et al., 2003]. By drawing L (1+ cos)/( L d ) 1/2 versus ( L nd ) 1/2 /( L d ) 1/2 , <strong>the</strong> slope will be ( S nd ) 1/2 and <strong>the</strong> origin intercept will be ( S d ) 1/2 (cf. Figure 3.25). L (1+cos)/2.( L d ) 1/2 12 11 10 9 8 7 6 y = 3.0332 x + 5.8084 R 2 = 0.8369 Water Ethylene Glycol romonaphtalene 5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 ( nd / d ) 1/2 L L Figure 3.25: Example <strong>of</strong> determination <strong>of</strong> surface energy components <strong>of</strong> a blend PLGA + 5 % HA with <strong>the</strong> Owens-Wendt’ method. In this model, <strong>the</strong> measure <strong>of</strong> contact angle between two different liquids and <strong>the</strong> solid is necessary to calculate <strong>the</strong> surface energy. However, it is an approximation to consider that <strong>the</strong> solid surface energy is <strong>the</strong> simple geometrical mean <strong>of</strong> p S and d S (equation 3.15). This approximation can not predict <strong>the</strong> behaviour <strong>of</strong> polar polymer in aqueous environment. 6.2.2.3 Model <strong>of</strong> Good-Van Oss : Three Components Theory In <strong>the</strong> model <strong>of</strong> Good-Van Oss [Owens and Wendt, 1969], surface energy is written: d S S 2 ( S . S ) (3.24) where γ S d is <strong>the</strong> dispersive component and γ S + and γ S - are <strong>the</strong> acid-base components respectively. Van Oss et al. [1988] proposed <strong>the</strong> so-called Lifshitz–Van der Waals approach in which <strong>the</strong> total surface tension is divided in Lifshitz–Van der Waals ( LW ) and acid-base ( AB ) components. The last one is decomposed in acid ( + ) and basic ( - ) components. Young-Dupré equation can be expressed as: ( 1 cos ) G G (3.25) L LW SL AB SL where LW LW LW 1 / 2 G SL 2 ( S . L ) (3.26) We may define <strong>the</strong> AcidBase free energy <strong>of</strong> interaction between two substances in <strong>the</strong> condensed state [van Oss et al., 1987]. - 83 -
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