Page 32 - Nanotechnology an introduction

contaminated in a highly nonuniform fashion. Figure 3.5 shows how surface roughness can be the origin of this nonuniformity. Adsorbed impurity
molecules will experience different interfacial energies at different locations on the surface due to the different curvatures.

Figure 3.5 Cross-section of a possible real machined surface. Note the two distinct length scales of roughness. A and B are adsorbed impurity molecules. After Bikerman [20].

3.2.4. Wetting and Dewetting

Wetting means the spreading of a liquid over a solid surface; dewetting is its converse, the withdrawal of liquid from a surface (the term “wetting” is
used regardless of the nature of the liquid—hence “dry” in this context means not that water is absent, but that all liquid is absent). They are basic
processes in countless natural and industrial processes. Although pioneering work in characterizing the interfacial tensions upon which wetting
depends was reported 200 years ago by Young, the processes are still relatively poorly understood. Wetting is mostly considered from a
mesoscopic viewpoint and therefore fits well into the framework of nanotechnology. Few experimental techniques are available for investigating the
important solid/liquid interfaces: the contact angle method is simple and probably still the most important, but only a handful of laboratories in the
world have shown themselves capable of usefully exploiting it. The history of dewetting, a phenomenon of no less industrial importance than wetting,
is much more recent: quantitative experimental work dates from the early 1990s.
It is essentially intuitive to expect that the spreading of a liquid on a solid surrounded by vapor depends on γ (S = solid, V = vapor, L = liquid). The
SV
quantitative relationship was given by Young in 1805 (cf. equation 3.19):

(3.20)
The degree of wetting is inversely proportional to the contact angle θ; θ = 0 corresponds to complete wetting. Young's equation (3.20) can be easily
derived by noting that the surface tension can be written as a force per unit distance. The interfacial forces acting on the triple line T, where three
phases S, L, V (solid, liquid, vapor) meet must sum to zero in a given direction (x, parallel to the interface) (Figure 3.6). More formally, it follows
from the condition that (at equilibrium) the energies must be invariant with respect to small shifts dx of the position of T. The structure of T may be
very complex. For example, for water containing dissolved electrolyte, the local ion composition may differ from that in the bulk; soft solids may be
deformed in the vicinity of T. Although Young's equation ignores these details it provides a remarkably accurate description of contact angles.

Figure 3.6 A drop of a liquid (substance 2) on a solid (substance 1). The vapor is neglected here (i.e., γ 1 ≡ γ SV , etc.).

3.2.5. Length Scales for Defining Surface Tension

The region in which deviations from “far field” quantities occur is known as the core, with radius r ~ 10 nm. Hence for typical drops (with a radius R
C
~ 1 mm) used in the contact angle determinations from which surface tension can be calculated, the curvature of T may be neglected; atomic scale
heterogeneity on the subnanometer scale may also be neglected.

3.2.6. The Wetting Transition

Complete wetting is characterized by θ = 0, which implies (from equation 3.20)

(3.21)
at equilibrium (out of equilibrium, this relation may not hold). The Cooper–Nuttall spreading coefficient S is

(3.22)
where is the interfacial tension of a dry solid. Three regimes can thus be defined:

1 . S > 0. This corresponds to , i.e. the wetted surface has a lower energy than the unwetted one. Hence wetting takes place
2
spontaneously. The thickness h of the film is greater than monomolecular if . The difference can be as much as 300 mJ/m for
water on metal oxides. Such systems therefore show enormous hysteresis between advancing and receding contact angles. Other sources of
hysteresis include chemical and morphological inhomogeneity (contamination and roughness).

2. S = 0. Occurs if practically equals γ , as is typically the case for organic liquids on molecular solids.
SV
3. S < 0. Partial wetting. Films thinner than a certain critical value, usually ~ 1 mm, break up spontaneously into droplets (cf. Section 8.1.2).