Page 33 - Nanotechnology an introduction

3.3. Capillary Force
It follows from the previous considerations that an attractive interaction between a liquid (of density ρ) and a solid will cause that liquid to rise to a
height h within a vertical tube of diameter r made from the solid, emerging from a reservoir of the liquid until the gravitational pull on the liquid
column equals the interfacial attraction:

(3.23)
where g is the acceleration due to gravity. For a small diameter tube, the rising of the liquid can be appreciable and easily visible to the naked eye.
This is the classical manifestation of the capillary force. Since water is both a strong hydrogen bond donor and a strong hydrogen bond acceptor, it
is able to interact attractively with a great many different substances, especially minerals, which tend to be oxidized.
Consequences for Nano-Objects
It is part of everyday experience that a human emerging from a bath carries with them a film of water—depending on the hydrophobicity of their skin
—that may be of the order of 100 μm thick, hence weighing a few hundred grams—negligible compared with the weight of its bearer. A wet small
furry creature like a mouse has to carry about its own weight in water. A wet fly would have a surplus weight many times its own, which is
presumably why most insects use a long proboscis to drink; bringing their bodies into contact with a sheet of water usually spells disaster. The
inadvertent introduction of water (e.g., by condensation) into microsystems may completely degrade their performance (cf. Figure 3.1);
nanosystems are even more vulnerable.
The Force Environment of Nano-Objects and Nanodevices
Apart from the capillary force referred to above, we should also consider objects wholly immersed in a liquid. In this environment viscosity, rather
than inertia, dominates. In contrast to the Newtonian mechanics appropriate to describing the solar system, the movement of a bacterium
swimming in water is governed by a Langevin equation comprising frictional force and random fluctuations (Brownian motion). This also
encompasses the realm of soft matter, a good definition of which is matter whose behavior is dominated by Brownian motion (fluctuations).
3.4. Heterogeneous Surfaces
The expressions given in the preceding sections have assumed that the surfaces are perfectly flat and chemically homogeneous. Most
manufactured surfaces are, however, rough and may be chemically inhomogeneous, either because of impurities present from the beginning, or
because impurities acquired from the environment have segregated due to roughness (Figure 3.5).

3.4.1. Wetting on Rough and Chemically Inhomogeneous Surfaces

If the roughness is in the nanorange—a few nanometers to a micrometer—the (subnanometer-sized) molecules of the liquid interact locally with
planar segments of the surface, while still yielding a unique contact angle, denoted by θ*, supposed different from the contact angle θ of the same
liquid with a perfectly smooth planar surface. Now suppose that the liquid drop on the rough surface is perturbed by a small horizontal displacement
by a distance dx in the plane of the surface. Because of the roughness, characterized by the ratio of actual to apparent surface areas, the real
distance is dx, . According to Young's law (3.20), the work done is

(3.24)
The drop should then find an equilibrium state at which dW/dx = 0, yielding

(3.25)
Comparison with (3.20) yields Wentzel's law:

(3.26)
In other words, since , roughness will always make a hydrophobic surface more hydrophobic and a hydrophilic surface more hydrophilic. This
is the basis of technologies to manufacture superhydrophobic and superhydrophilic surfaces. Typically, natural superhydrophobic materials such as
the leaves of the lupin (Figure 3.7) have roughnesses at multiple length scales.