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

Chapter 3.
Analytical Methods and Designs <strong>of</strong> Experiments
G
AB
SL
2(
1/ 2 1/ 2
S
.
L
) 2(
S
.
L
)
(3.27)
The expression used in this model is thus:
(1
cos
LW LW
) 2 . 2 ( )
(3.28)
L
S
L
S
LV
S
LV
By drawing L .(1+cos)/2 - ( S LW . L LW )]( L + ) 1/2 versus ( L − / L + ) 1/2 <strong>the</strong> slope will be ( S + ) 1/2 and <strong>the</strong>
origin intercept will be ( S - ) 1/2 . An example <strong>of</strong> application <strong>of</strong> <strong>the</strong> model is presented in Figure 3.26.
L (1+ cos )/2( S
LW . L
LW )]( L
+ )
1/2
8
6
4
2
0
0 1 2 3 4 5 6
_
( L L )1/2
Figure 3.26: Example <strong>of</strong> determining <strong>the</strong> surface energy components with Good-Van Oss’ method
for pure P L LA.
By depositing a drop <strong>of</strong> three different liquids, one can obtain <strong>the</strong> surface energy <strong>of</strong> <strong>the</strong> solid. This
method thus requires <strong>the</strong> use <strong>of</strong> 3 liquids <strong>of</strong> reference with given L LW (Lifshitz-van der Waals) and AB acidbase
components. The L LW component is generally approximated with <strong>the</strong> L nd component [Zenkiewicz,
2007a, 2007b; Wu, 2001; Van Oss et al., 1988; van Oss et al., 1987; Owens and Wendt, 1969; Neumann et
al., 1974].
7 Designs <strong>of</strong> Experiments
The aim <strong>of</strong> <strong>the</strong> experimental designs is to investigate <strong>the</strong> possible cause-and-effect relationship by
manipulating one independent variable to influence <strong>the</strong> o<strong>the</strong>r variable(s) in <strong>the</strong> experimental group, and by
controlling <strong>the</strong> o<strong>the</strong>r relevant variables, and measuring <strong>the</strong> effects <strong>of</strong> <strong>the</strong> manipulation by some statistical
means. By manipulating <strong>the</strong> independent variable, <strong>the</strong> researcher can see if <strong>the</strong> treatment makes a
significative difference on <strong>the</strong> factors.
7.1 Modelization Plans: Doehlert’s Design
Doehlert’s designs are quadratic plans with some interesting properties, i.e., <strong>the</strong>y can be built upon
and extended to o<strong>the</strong>r factor intervals. These designs allow <strong>the</strong> estimation <strong>of</strong> all main effects, all first-order
interactions and all quadratic effects without any confounding effects [Eriksson, 2008].
Geometrically, <strong>the</strong> Doehlert’ designs are polyhedrons based on hyper-triangles with a hexagonal
structure, in <strong>the</strong> simplest case (cf. geometry <strong>of</strong> <strong>the</strong> two factors presented in Figure 3.27). This means <strong>the</strong>y
have uniform space-filling properties with an equally spaced distribution <strong>of</strong> points lying on concentric
spherical shells. With <strong>the</strong> Doehlert’ plan <strong>of</strong> two variables; <strong>the</strong> model chosen a priori is <strong>the</strong> second degree. In
<strong>the</strong> case <strong>of</strong> two variables, <strong>the</strong> Y response depends on <strong>the</strong> reduced variables X 1 and X 2 according to <strong>the</strong>
equation:
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