Macroscopic bodies

Generally speaking, intermolecular forces act over a short range. Were this not the case, the specific energy of a portion of matter would depend on its size quantities such as molar enthalpies of formation would be extensive variables On the other hand, the cumulative effects of these forces between macroscopic bodies extend over a rather long range and the discussion of such situations constitutes the chief subject of this chapter. 

This chapter and the two that follow are introduced at this time to illustrate some of the many extensive areas in which there are important applications of surface chemistry. Friction and lubrication as topics properly deserve mention in a textbook on surface chemistiy, partly because these subjects do involve surfaces directly and partly because many aspects of lubrication depend on the properties of surface films. The subject of adhesion is treated briefly in this chapter mainly because it, too, depends greatly on the behavior of surface films at a solid interface and also because friction and adhesion have some interrelations. Studies of the interaction between two solid surfaces, with or without an intervening liquid phase, have been stimulated in recent years by the development of equipment capable of the direct measurement of the forces between macroscopic bodies. 

In continuum boundary conditions the protein or other macromolecule is treated as a macroscopic body surrounded by a featureless continuum representing the solvent. The internal forces of the protein are described by using the standard force field including the Coulombic interactions in Eq. (6), whereas the forces due to the presence of the continuum solvent are described by solvation tenns derived from macroscopic electrostatics and fluid dynamics. 

Once it is recognized that particles adhere to a substrate so strongly that cohesive fracture often results upon application of a detachment force and that the contact region is better describable as an interphase [ 18J rather than a sharp demarcation or interface, the concept of treating a particle as an entity that is totally distinct from the substrate vanishes. Rather, one begins to see the substrate-particle structure somewhat as a composite material. To paraphrase this concept, one could, in many instances, treat surface roughness (a.k.a. asperities) as particles appended to the surface of a substrate. These asperities control the adhesion between two macroscopic bodies. 

At this point a Danish physicist, Niels Bohr, decided to take a fresh start. In effect, he faced the fact that an explanation is a search for likenesses between a system under study and a well-understood model system. An explanation is not good unless the likenesses are strong. Niels Bohr suggested that the mechanical and electrical behavior of macroscopic bodies is not a completely suitable model for the hydrogen atom. He pro-... 

Fig. 8—(a) Position of the macroscopic body, and (b) the acting force, plotted as a function of supporter position, Xq. 

The term molecular crystal refers to crystals consisting of neutral atomic particles. Thus they include the rare gases He, Ne, Ar, Kr, Xe, and Rn. However, most of them consist of molecules with up to about 100 atoms bound internally by covalent bonds. The dipole interactions that bond them is discussed briefly in Chapter 3, and at length in books such as Parsegian (2006). This book also discusses the Lifshitz-Casimir effect which causes macroscopic solids to attract one another weakly as a result of fluctuating atomic dipoles. Since dipole-dipole forces are almost always positive (unlike monopole forces) they add up to create measurable attractions between macroscopic bodies. However, they decrease rapidly as any two molecules are separated. A detailed history of intermolecular forces is given by Rowlinson (2002). 

To achieve such properties and to maintain them under practical service conditions it is essential that all phases are synthesized to high qualitative homogeneity and that the structural arrangement shown in Fig. 9.1 prevails homogeneously throughout the macroscopic body of the part. Synthesis is thus a critical step since not only chemical precision but also macroscopic homogeneity are critical properties requiring carefully controlled and automated unit operations. 

Hamaker (1932) and de Boer (1936) calculated van der Waals forces between macroscopic bodies using the summation method. 

Lifshitz (1955-60) developed a complete quantum electrodynamic (continuum) theory for the van der Waals interaction between macroscopic bodies. 

Before we move on to consider the interaction between macroscopic bodies, let us look briefly at the phenomenon of retardation . The electric field emitted by an instantaneously polarized neutral molecule takes a finite time to travel to another, neighbouring molecule. If the molecules are not too far apart the field produced by the induced dipole will reach the first molecule before it has time to disappear, or perhaps form a dipole in the opposite direction. The latter effect does, however, occur at larger separations (>5 nm) and effectively strengthens the rate of decay with distance, producing a dependence of 1/R instead of 1/R . 

In colloid and surface science we are interested in calculating the van der Waals interaction between macroscopic bodies, such as spherical particles and planar surfaces. If the dispersion interaction, for example, were additive we could sum the total interaction between every molecule in a body with that in another. Thus, if the separation distance between any two molecules i and f in a system is... 

Examination of Table 7.2 reveals some interesting features, such as the effect of the medium in between two macroscopic bodies, which clearly... 

Once we have established reasonable values for the Hamaker constants we shonld be able to calculate, for example, adhesion and surface energies, as well as the interaction between macroscopic bodies and colloidal particles. Clearly, this is possible if the only forces involved are van der Waals forces. That this is the case for non-polar liquids such as hydrocarbons can be illustrated by calculating the surface energy of these liqnids, which can be directly measured. When we separate a liquid in air we mnst do work Wc (per unit area) to create new surface, thus ... 

The minus sign signifies an attractive interaction.) For macroscopic (this includes microscopic and nanoscopic) bodies, this interaction is much less short-range, and the distance dependence varies both with the geometry of the interacting bodies and with the distance of separation. For macroscopic bodies, it is usually assumed... 

The van der Waals forces at the atomic level as well as those between macroscopic bodies (Chapter 10)... 

Our objectives in this chapter are to look into the origin of van der Waals forces, see how they affect macroscopic behavior and properties of materials, and establish relations for scaling up the molecular-level forces to forces between macroscopic bodies. 

Phenomena such as the ones described above are usually (and conveniently) described in terms of macroscopic properties such as surface tension, contact angle, and so on. This is what was done in Chapters 6 and 7. In the present chapter, we probe the molecular origin of van der Waals forces, go into some of the details of how they scale up in the case of macroscopic bodies, and illustrate their importance in molecular as well as macroscopic phenomena. 

The van der Waals forces are always attractive (although, as we see in Section 10.8b, the London forces between two macroscopic bodies immersed in a medium can be repulsive, depending on the material properties). 

Colloid stability serves as a convenient example to illustrate the importance of the strength and range of van der Waals attraction between macroscopic bodies in a practical context and to introduce the idea of potential energy curves. 

We have already seen from Example 10.1 that van der Waals forces play a major role in the heat of vaporization of liquids, and it is not surprising, in view of our discussion in Section 10.2 about colloid stability, that they also play a significant part in (or at least influence) a number of macroscopic phenomena such as adhesion, cohesion, self-assembly of surfactants, conformation of biological macromolecules, and formation of biological cells. We see below in this chapter (Section 10.7) some additional examples of the relation between van der Waals forces and macroscopic properties of materials and investigate how, as a consequence, measurements of macroscopic properties could be used to determine the Hamaker constant, a material property that represents the strength of van der Waals attraction (or repulsion see Section 10.8b) between macroscopic bodies. In this section, we present one illustration of the macroscopic implications of van der Waals forces in thermodynamics, namely, the relation between the interaction forces discussed in the previous section and the van der Waals equation of state. In particular, our objective is to relate the molecular van der Waals parameter (e.g., 0n in Equation (33)) to the parameter a that appears in the van der Waals equation of state ... 

This is the one entry in Table 10.1 that has not yet been discussed. Direct measurement of the force of attraction between macroscopic bodies reveals a crossover from an inverse sixth-power to an inverse seventh-power law at separations in the range 10 to 100 nm. 

CALCULATING VAN DER WAALS FORCES BETWEEN MACROSCOPIC BODIES... 

The strategy for scaling up the van der Waals attraction to macroscopic bodies requires that all pairwise combinations of intermolecular attraction between the two bodies be summed. This has been done for several different geometries by Hamaker. We consider only one example of the calculations involved, namely, the case of blocks of material with planar surfaces. This example serves to illustrate the method and also provides a foundation for connecting van der Waals forces with surface tension, the subject of the next section. 

The primary objective of the present discussion is to show the intrinsic connection between surface tension and the van der Waals energy of attraction between macroscopic bodies. The connection not only provides computational options but also —and more importantly — unites two apparently separate phenomena and strengthens our confidence in the correctness of our understanding. 

It is extremely difficult to measure the Hamaker constant directly, although this has been the object of considerable research efforts. Direct evaluation, however, is complicated either by experimental difficulties or by uncertainties in the values of other variables that affect the observations. The direct measurement of van der Waals forces has been undertaken by literally measuring the force between macroscopic bodies as a function of their separation. The distances, of course, must be very small, so optical interference methods may be used to evaluate the separation. The force has been measured from the displacement of a sensitive spring (or from capacitance-type measurements). 

Until now we have considered the interaction between isolated molecules or macroscopic bodies when the particles are separated by a vacuum. Interactions in a vacuum is reasonable for molecules in the gas phase. However, for dispersions of one phase in another, the effect of the medium must be taken into account. Accounting for the effects of the medium leads to some useful combining relations for the Hamaker constant AIJk, which is the Hamaker constant for interaction between / and k in medium j. In addition, situations may arise in which AlJk is negative, that is, the interaction is repulsive. We review these in this section. 

The larger the Hamaker constant, the larger is the attraction between macroscopic bodies. 

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