Page 28 - Nanotechnology an introduction

Chapter Contents

3.1 The Casimir Force 36
3.2 Intermolecular Interactions 37
3.2.1 The Concept of Surface Tension 37
3.2.2 Critique of the Surface Tension Formalism 41
3.2.3 Experimental Determination of Single-Substance Surface Tensions 42
3.2.4 Wetting and Dewetting 43
3.2.5 Length Scales for Defining Surface Tension 44
3.2.6 The Wetting Transition 44
3.3 Capillary Force 45
3.4 Heterogeneous Surfaces 45
3.4.1 Wetting on Rough and Chemically Inhomogeneous Surfaces 46
3.4.2 Three-Body Interactions 47
3.5 Weak Competing Interactions 48
3.6 Cooperativity 48
3.7 Percolation 49
3.8 The Structure of Water 51
3.9 Summary 51
3.10 Further Reading 52
The large ratio of surface to volume characteristic of nanoscale objects and devices places interfacial forces in a prominent position in governing their behavior. Although subject to criticism, the surface-tension formalism allows the
magnitudes of these forces between objects made from different materials in the presence of different liquids to be quickly estimated from tables of experimentally-derived “single substance surface tensions”. In aqueous systems, Lewis
acid/base interactions, most notably hydrogen bonding, typically dominate the interfacial forces. Real, that is morphologically and chemically heterogeneous, surfaces require some modification to the basic theory. In some cases a simple
mean-field correction may be adequate; in others nanostructure must explicitly be taken into account. This is especially strikingly shown in protein interactions, which are actually three-body in nature and depend on the subtle interplay of
solvation and desolvation. Multiple forces of different strength and range may be operating simultaneously. This provides the basis for programmability. The assembly of objects into constructions of definite size and shape is only possible
if programmability is incorporated, and in the nanoscale this can typically only be achieved by judicious design at the level of the constituent atoms and groups of atoms of the objects.
Keywords: Casimir force, intermolecular interactions, surface tension, wetting, capillarity, competing interactions, cooperativity, percolation, water structure
We have established in the previous chapter that the smallness (of nano-objects) implies preponderance of surfaces over bulk. This implies that
interfacial forces are particularly important in the nanorealm, governing the behavior of nano-objects and determining the performance of
nanostructured materials and nanodevices. Of particular importance are the interfacial forces that are electrostatic in origin: Section 3.2 is mostly
about them. The so-called local van der Waals or Casimir force is of unique relevance to the nanoscale—it is described first, in Section 3.1. As for
the other fundamental forces, the gravitational force is so weak at the nanoscale—distance or mass—that it can be neglected. Conversely, the
range of the strong nuclear force is much smaller than the nanoscale, and hence can also be neglected. The capillary force, which in the past has
sometimes been considered as a “fundamental” force, is of course simply a manifestation of the wetting phenomena originating in the interfacial
forces discussed in Section 3.2.

Familiar monolithic substances rely on strong metallic, ionic or covalent bonds to hold their constituent atoms together. These three categories
correspond to the “elements” of mercury, sodium chloride and sulfur that Paracelsus added to the classical Greek ones of earth (solid—but
possibly also encompassing granular matter), air (gas), fire (plasma) and water (liquid). Presumably mankind first encountered complex
multicomponent materials (i.e., composites) in nature—wood is perhaps the best example. While the components individually (in the case of wood,
cellulose and lignin) are covalently bonded, bonding at the cellulose–lignin interface depends on the relatively weak forces discussed in Section
3.2. Thus, knowledge of these interfacial forces are essential for understanding nanocomposites (Section 6.5). They also enable the self-assembly
of nano-objects to take place (see Section 8.2.1).
3.1. The Casimir Force
A cavity consisting of two mirrors facing each other disturbs the pervasive zero-point electromagnetic field, because only certain wavelengths of the
field vibrations can fit exactly into the space between the mirrors. This lowers the zero-point energy density in the region between the mirrors,
−4
resulting in an attractive Casimir force between them [28]. The force falls off rapidly (as z ) with the distance z between the mirrors, and hence is
5
negligible at the microscale and above, but at a separation of 10 nm it is comparable with atmospheric pressure (10 N/m), and therefore can be
expected to affect the operation of nanoscale mechanical devices (Figure 3.1) and nanoscale assembly.

Figure 3.1 An illustration of the practical problems that may arise when micro or nano components approach each other to within nanoscale distances. (a) Stuck finger on a comb drive; (b) cantilever after release etch, adhering to the
substrate. These effects are often collectively categorized as manifestations of stiction (“sticking friction”). Condensation of water and the resulting capillary force also contributes as well as the Casimir force. Reproduced with permission
from [28].