The van der Waals force between macroscopic solids

We now move from the interaction between two molecules to the interaction between two macroscopic solids. There are two approaches to calculate the van der Waals force between extended solids the microscopic and the macroscopic [114], 

We move from the interaction between two molecules to the interaction between two macroscopic solids. It was recognized soon after London had published his explanation of the dispersion forces that dispersion interaction could be responsible for the attractive forces acting between macroscopic objects. This idea led to the development of a theoretical description of van der Waals forces between macroscopic bodies based on the pairwise summation of the forces between all molecules in the objects. This concept was developed by Hamaker [9] based on earlier work by Bradley [10] and de Boer [11]. This microscopic approach of Hamaker of pairwise summation of the dipole interactions makes the simplifying assumption that the 

6) Hugo Christiaan Hamaker, 1905-1993, Dutch scientist at the Philips Laboratories and professor in Eindhoven. 

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The Van der Waals Force Between Macroscopic Solids 17 The force per unit area is equal to the negative derivative of versus distance ... 

In the microscopic calculation pairwise additivity was assumed. We ignored the influence of neighboring molecules on the interaction between any pair of molecules. In reality the van der Waals force between two molecules is changed by the presence of a third molecule. For example, the polarizability can change. This problem of additivity is completely avoided in the macroscopic theory developed by Lifshitz [118,119]. Lifshitz neglects the discrete atomic structure and the solids are treated as continuous materials with bulk properties such as the... 

The major disadvantage of this microscopic approach theory was the fact that Hamaker knowingly neglected the interaction between atoms within the same solid, which is not correct, since the motion of electrons in a solid can be influenced by other electrons in the same solid. So a modification to the Hamaker theory came from Lifshitz in 1956 and is known as the Lifshitz or macroscopic theory." Lifshitz ignored the atoms completely he assumed continuum bodies with specific dielectric properties. Since both van der Waals forces and the dielectric properties are related with the dipoles in the solids, he correlated those two quantities and derived expressions for the Hamaker constant based on the dielectric response of the material. The detailed derivations are beyond the scope of this book and readers are referred to other publications. The final expression that Lifshitz derived is... 

This chapter aims to give guidelines on how to use adsorption methods for the characterization of the surface area and pore size of heterogeneous catalysts. The information derived from these measurements can range from the total and available specific surface area to the pore sizes and the strength of sorption in micropores. Note that this spans information from a macroscopic description of the pore volume/specific surface area to a detailed microscopic assessment of the environment capable of sorbing molecules. In this chapter we will, however, be confined to the interaction between sorbed molecules and solid sorbents that are based on unspecific attractive and repulsive forces (van der Waals forces, London dispersion forces). 

The method considered here for determination of these forces is the modified Lifshitz macroscopic approach, considering the microscopic approach results. This approach uses the optical properties of interacting macroscopic bodies to calculate the van der Waals attraction from the imaginary part of the complex dielectric constants. The other possible approach—the microscopic theory—uses the interactions between individual atoms and molecules postulating their additive property. The microscopic approach, which is limited to only a few pairs of atoms or molecules, has problems with the condensation to solids and ignores the charge-carrier motion. The macroscopic approach has great mathematical difficulties, so the interaction between two half-spaces is the only one to be calculated (Krupp, 1967). 

The van der Waals equation (1.11) describes the macroscopic properties of a real gas where the intermolecular forces and thermal molecular movements are in mutual balance. From a molecular point of view the real gas is a transition state between the ideal gas and the condensed, liquid and solid states. 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

Within the core region the profile of a drop is modified by surface forces, such as long-range van der Waals and electrostatic double-layer forces [220], These forces affect the profile in a range of 1-100 nm. They can cause a difference between the microscopic contact angle and the macroscopic one (which enters into Young s equation) [268,269], If the liquid is attracted by the solid surface and this attraction is stronger than the attraction between the... 

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