Page 29 - Nanotechnology an introduction

3.2. Intermolecular Interactions
The forces described in this section are responsible for the relatively weak interactions between two objects, typically in the presence of an
intervening medium. They are all electrostatic in origin. As Pilley has pointed out in his book on electricity, it is pervasive in bulk matter but not
directly perceptible in everyday life. On the other hand, it is quite likely to be manifested at surfaces. When they carry electrostatic charges (they are
sometimes called electrified interfaces)—for example, created by rubbing in air, or by ionization in solution—they will manifest Coulombic
interaction. Even neutral surfaces will, however, interact via the Lifshitz–van der Waals family of forces. Finally there are the Lewis acid/base
interactions, involving some electron exchange between the partners (e.g., the hydrogen bond), which might be considered as a weak covalent
interaction.

3.2.1. The Concept of Surface Tension

Surface tension γ is formally defined as the free energy G required to create and extend an interface of area A:

(3.1)
where the practically encountered constant temperature and pressure makes the Gibbs free energy the appropriate choice for G. In the Système
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International, the units of γ are N/m, which is the same as an energy per unit area (J/m ). It is customary to refer to γ as a surface tension if the
increase of area is reversible, and as a surface energy if it is not.
Generally speaking, work needs to be done to create an interface; it has a higher free energy than the bulk. The work of cohesion of a solid is

(3.2)
(see Figure 3.2). On the other hand, the work of adhesion (needed to separate two dissimilar substances 1 and 2) is given by (see Figure 3.2)

(3.3)
a formalism introduced in the 19th century by Dupré. γ and γ account for the old interfaces lost, and γ accounts for the new interface gained.
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Most of the subsequent difficulties experienced by the field of interfacial interactions have concerned the theoretical calculation (i.e., prediction) of
terms involving two (or more) substances such as γ . The nanoscopic viewpoint is that the “microscopic” surface tension (or energy) γ depends
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on specific chemical interactions between the surfaces of the two substances 1 and 2.

Figure 3.2 Cohesion and adhesion of substances 1 (white) and 2 (gray) (see text).
Fowkes, Girifalco and Good introduced the reasonable assumption that the tension at the interface of substance 1 against substance 2 is lowered
by the presence of 2 by an amount equal to the geometric mean of the tensions of the two substances individually, hence equal to , and
similarly the tension at the interface of substance 2 against substance 1 is . Summing these two terms, we have

(3.4)
called the Girifalco–Good–Fowkes equation. This is equivalent to the work of adhesion being the geometric mean of the works of cohesion, i.e.
. The Dupréequation (3.3) then becomes

(3.5)
Fowkes and van Oss developed the idea that the total interfacial energy is linearly separable into the dispersive (London–van der Waals), dipole-
induced dipole (Debye), dipole–dipole (Keesom) and electron donor–acceptor terms, and Lifshitz has pointed out that the London–van der Waals,
Debye and Keesom interactions are all of the same type (cf. the Hellman–Feynman theorem), with the same dependence of magnitude on
separation between the two interacting substances, and hence

(3.6)
where LW denotes Lifshitz–van der Waals and ab denotes (Lewis) acid/base, and a fortiori

(3.7)
Whereas the Lifshitz–van der Waals interaction is always attractive, the sign of the Lewis acid/base interaction depends on the relative proportions