Introduction ix
Chapter 1. Wettability of an Ideal Surface: Overview 1
1.1. Wetting angle 1
1.2. Adhesion effect 4
1.3. Surface tension and free surface energy 5
Chapter 2. Real Surfaces 9
2.1. Wenzel's model - topological defects 9
2.2. Cassie-Baxter model: chemical defects 11
2.3. Superhydrophilic surfaces 12
2.4. Superhydrophobic surfaces 16
2.5. Application 20
Chapter 3. Components of the Surface Energy 23
3.1. Overview 23
3.2. Molecular interactions and components of the energy 26
3.3. The hydrogen bond 28
3.4. Lewis acid-base interactions 28
3.5. The effective components of the interaction energy 31
3.6. Application 32
Chapter 4. The Acid-Base Component in the Work of Adhesion 37
4.1. Overview 37
4.2. Use of the acid-base component 38
4.3. The Owens-Wendt approximation 39
4.4. Van Oss-Good description 40
Chapter 5. Experimental Determination through Wettability Measurements 45
5.1. One liquid method 46
5.2. Two liquid method. Surfaces with high surface energy 48
5.3. Applications of the two liquid method 49
5.4. Comparison between Owens-Wendt and van Oss-Good methods 55
Chapter 6. Acid-Base Properties of Surfaces: Experimental Approaches 61
6.1. Overview 61
6.2. General methods 61
6.2.1. Wettability 61
6.2.2. Electrokinetic method 62
6.2.3. Scanning probe microscopies 68
6.2.4. Inverse gas chromatography at infinite dilution conditions 73
6.2.5. X-ray photoelectron spectroscopy (XPS) 78
6.2.6. Other methods 85
6.3. Local methods 86
6.3.1. Infrared spectroscopy 87
6.3.2. X-ray photoelectron spectroscopy (XPS) 91
6.3.3. Other methods 93
6.4. Application examples 94
6.4.1. Bonding ability of aluminum sheets 94
6.4.2. Mechanism of formation of the interphase in metal-polymer joints 96
6.4.3. Heterogeneous catalysis 98
Chapter 7. Oxide-Solution Interfaces: Surface Charges 99
7.1. Brønsted acidity and basicity 100
7.2. Point of zero charge (PZC) 101
7.3. The oxide-solution interface 103
7.4. Electrocapillarity in the oxide-solution interface 109
7.4.1. Evolution of the interfacial tension 110
Chapter 8. Electrocapillarity Applications 117
8.1. Study based on the pH of the oxide surfaces 117
8.2. Study of the stability of a liquid film on an oxide surface 123
8.2.1. Case of a flat surface 123
8.2.2. Case of a rough surface 125
8.3. Modification of the contact angle by an imposed potential (Electrowetting) 132
Conclusion 141
Bibliography 143
Index 153
2
Real Surfaces
The surfaces discussed in the previous chapter are ideal surfaces, meaning that they are atomically smooth and chemically homogeneous.
In practice, solid surfaces are both rough and chemically heterogeneous. These surface defects cause a dispersion of the contact angle around an average value which can be up to ten degrees or even higher. This dispersion, which corresponds to the hysteresis of the contact angle, shows that a single measurement of the angle is inadequate. A significant measurement of the contact angle corresponds to an average value taken from around 10 measurements at different points of the surface being studied, leading to a roughly Gaussian distribution.
There are two models which separately deal with the existence of topological or chemical defects. These models (Wenzel [WEN 49] and Cassie-Baxter [CAS 44]) are exhaustively examined by de Gennes in his 2002 book [DE 03]. We will address them briefly.
2.1. Wenzel's model - topological defects
Apparent contact angle and topological roughness.
The apparent contact angle ?* is observed on a chemically homogeneous surface with a low level of roughness r compared to the size of the droplet. The roughness r is defined by the ratio between the area of the real surface and that of the projected surface.
Figure 2.1. Equilibrium shift of the triple line of a liquid droplet in contact with a rough surface
The variation in the free energy dF associated with an equilibrium shift dx of the triple line is written per unit of length of the triple line:
since Young's equilibrium contact angle is given by the equation .
We obtain Wenzel's equation [2.1] connecting the apparent contact angle ?* and Young's angle ?E:
[2.1] In the case of a hydrophilic solid where ?E = 90° , the apparent contact angle is such that ?*= ?E.
Similarly, for a hydrophobic solid characterized by ?E = 90°, the apparent contact angle will be such that ?*=?E. The roughness of a surface accentuates its specific hydrophilic or hydrophobic nature.
This simple result is obtained for roughness values r clearly higher than 1 and with an upper limit around 1.8-2 as we will see in the following section.
For higher values, an air pocket regime is established leading to the trapping of air pockets by the wetting liquid at the bottom of the cavities.
2.2. Cassie-Baxter model: chemical defects
Apparent contact angle and chemical heterogeneity.
Here, the surface is considered as being atomically flat with supposedly small levels of chemical heterogeneity compared to the size of the liquid droplet.
Figure 2.2. Equilibrium shift of the triple line on a chemically heterogeneous surface
Let us assume two types of chemical defects with the fractions f1 and f2, characterized by Young's angles ?1 and ?2. The variation in the free energy corresponding to the equilibrium shift dx is written as follows:
Using Young's equation for each of the solids 1 and 2, we can obtain the Cassie-Baxter equation [2.2]:
[2.2] This equation shows that the cosine of the apparent contact angle ?* is given by an average of the cosines of Young's angles ?1 and ?2 characterizing phases 1 and 2.
This equation can be very useful for exploring situations corresponding to superhydrophobic and superhydrophilic surfaces.
2.3. Superhydrophilic surfaces
Superhydrophilic rough surface, development of a precursor film.
Definition of a critical angle between a Wenzel state and a Cassie-Baxter state with water pockets.
Let us consider a superhydrophilic porous surface (e.g. a mixture of oxides). The wetting liquid spontaneously fills the cavities of the surface. When equilibrium is reached, the droplet rests on a mixed solid/liquid surface with the respective proportions fS and 1-fS.
The application of the Cassie-Baxter equation leads to the following expression taking into account both Young's angles ?E and 0:
[2.3] Figure 2.3. Model of a superhydrophilic rough surface with the development of a precursor film
The total apparent wetting (?* = 0) can only be obtained with the condition ?E = 0.
The condition for this description to be valid is that a precursor film develops in front of the base of the droplet as indicated by de Gennes [DE 03] and Bormachenko [BOR 08].
In this zone, the vapor pressure of the gaseous phase is given by the equilibrium pressure of the liquid phase. For sufficiently-sized surface pores, the development of a horizontal liquid surface can be observed as indicated in Figure 2.3.
The variation in the free energy (per unit length for the triple line) corresponding to an equilibrium shift dx (Figure 2.3) is written by using r to represent the roughness associated with the solid surface simply modeled by regular cavities.
[2.4] The first term corresponds to the creation of a solid-liquid interface on the internal part of the surface, corrected by the fraction ?Sdx which corresponds to the external dry part of the surface.
The second part corresponds to the creation of a liquid-vapor interface.
Using Young's equation, the stability condition of the pre-wetting film (dF = 0) gives the following condition:
[2.5] The critical contact angle evolves between two limits for a perfectly flat surface (r=1) and which characterizes a completely porous solid with a high value of r.
Generally, when the Young's angle is between and p/2, the solid is dry in front of the base of the droplet and the wetting is described by Wenzel's equation. When , a pre-wetting film develops in form [2.3] of the Cassie-Baxter equation which describes the wetting of the liquid droplet resting on a liquid-solid composite.
Figure 2.4 shows this evolution.
Figure 2.4. Evolution of the apparent contact angle with Young's angle for a hydrophilic solid
COMMENT 2.1.- The simplified model of the surface which we have used in Figure 2.3 enables a simple calculation of the critical angle.
Figure 2.5. Simplified model of the roughness of the surface
Using the lengths indicated in Figure 2.5, the roughness coefficient r is written as:
, with a surface fraction .
[2.6] Table 2.1 provides an example of some values of critical angles.
COMMENT 2.2.- The presence of a pre-wetting film in front of the base of the droplet leads to a relatively flat liquid-vapor interface. It may develop withthe liquid-solid interface at the bottom of cavities long distance interactions, such as Van de Waals and electrostatic interactions denoted as GLD per unit area, which will be described in Chapter 8.
In these conditions, equation [2.5] must be corrected [JOU 13]:
The stability conditions for the pre-wetting film dF = 0 leads to a new condition:
[2.7] A new critical angle is thus defined as:
[2.8] 2h/L1
?crit deg 0.8 0.555 56 0.88 27 0.9 0.526 58 0.84 33 1 0.500 60 0.80 37 1.8 0.357 69 0.57 55 2h/L1
?crit deg 0.8 0.555 56 0.943 19 0.9 0.526 58 0.894 26 1 0.500 60 0.850 32 1.8 0.357 69 0.607 53
Table 2.1. Values of critical angles deduced from equations [2.6] and [2.8] for different geometries (Figure 2.5) set according to the GLD/?LV ratio
2h/L1
?crit deg 0.8 0.555 56 1.05? ? 0.9 0.526 58 0.999 2 1 0.500 60 0.95 18 1.8 0.357 69 0.68 47
The inclusion of long distance interactions GLD which are comparable in terms of magnitude with ?LV leads to a significant reduction...
