London dispersion forces characteristics

Typical potential energy curves for the interaction of two atoms are illustrated in Figure 11.3. There is characteristically a very steeply rising repulsive potential at short interatomic distances as the two atoms approach so closely that there is interpenetration of their electron clouds. This potential approximates to an inverse twelfth-power law. Superimposed upon this is an attractive potential due mainly to the London dispersion forces. This follows an inverse sixth-power law. The total potential energy is given by... 

Intermolecular forces, known collectively as van der Waals forces, are the attractions responsible for holding particles together in the liquid and solid phases. There are several kinds of intermolecular forces, all of which arise from electrical attractions Dipole-dipole forces occur between two polar molecules. London dispersion forces are characteristic of all molecules and result from the presence of temporary dipole moments caused by momentarily unsymmetrical electron distributions. A hydrogen bond is the attraction between a positively polarized hydrogen atom bonded to O, N, or F and a lone pair of electrons on an O, N, or F atom of another molecule. In addition, ion-dipole forces occur between an ion and a polar molecule. 

Meanwhile, in the London dispersive force Eq. (7), the characteristic electronic vibrational frequency, v, is directly related to the deformation polarizability, ao, of the molecule by [61,63,64]... 

The title dispersion arises because, from the more theoretical development of this concept, an important parameter, characteristic of each molecule, is involved. This constant is proportional to the dispersion of the refractive index with frequency, and this in turn is approximately proportional to the ionization energy of the molecule. Hence the title. However, since the word Dispersion has other connotations and could be misleading, the name London , the name of the man who initially developed this theory, is frequently included in the title to give London Dispersion Forces . 

In the last 40 years, techniques to directly measure surface forces and force laws (force vs. separation distance between surfaces) have been developed such as the surface forces apparatus (SFA) [6] and AFM. Surface forces are responsible for the work required when two contacting bodies (such as an AFM tip in contact with a solid surface) are separated from contact to infinite distance. Although the physical origin of all relevant surface forces can be derived from fundamental electromagnetic interactions, it is customary to group these in categories based on characteristic features that dominate the relevant physical behavior. Thus, one speaks of ionic (monopole), dipole—dipole, ion—dipole interactions, electrostatic multipole forces (e.g., quadrupole), induced dipolar forces, van der Waals (London dispersive) interactions, hydrophobic and hydrophilic solvation, structural and hydration forces,... 

Hamaker Constant In the description of the London-van der Waals attractive energy between two dispersed bodies, such as particles. The Hamaker constant is a proportionality constant characteristic of the internal atomic packing and polarizability of the particles. Also termed the van der Waals-Hamaker constant. See also Dispersion Forces. 

There is an important characteristic of polarizability that we have not yet mentioned, namely, its dynamic (time-varying) nature. Because the electrons in a molecule are in constant motion, it is possible that at some particular instant—purely by chance—electrons are concentrated in one region of a molecule. This displacement of electrons causes, for example, a normally nonpolar species to become momentarily polar. An instantaneous dipole is formed. That is, the molecule has an instantaneous dipole moment. After this, electrons in a neighboring molecule may be displaced to produce a dipole— an induced dipole. Taken together, these two events lead to an intermolecular force of attraction (Fig. 12-3). We can call this interaction an instantaneous dipole-induced dipole attraction, but the names more commonly used are dispersion force and London force, the latter in honor of Fritz London who, in 1928, offered a theoretical explanation of these forces. 

In 1930, London [1,2] showed the existence of an additional type of electromagnetic force between atoms having the required characteristics. This is known as the dispersion or London-van der Waals force. It is always attractive and arises from the fluctuating electron clouds in all atoms that appear as oscillating dipoles created by the positive nucleus and negative electrons. The derivation is described in detail in several books [1,3] and we will outline it briefly here. 

Interparticle forces are a determinant factor for most properties of dispersions, including rheological behavior. They are produced by the molecular forces on the surfaces of the particles, due to their nature or to adsorbed molecules, that modify the interface. These are electrical forces arising from charges on the particles and London-van der Waals attraction forces. The role of these forces on suspension stability has been extensively study and is known as the DLVO theory. In addition, sterical forces encountered on dispersions stabilized with nonionic species also exert an important influence on rheological behavior. The nature of these forces will not be considered since they are matters of discussion in Chapters 1-4. However, from a rheological point of view it is impwtant to understand how these factors modify the flow characteristics of dispersions. 

The characteristic feature of dispersion (London) forces is their additivity. 

A characteristic feature of the dispersion (London) forces is their additivity. A molecule induces periodic dipoles in several neighboring molecules. The induced dipole is attracted to the original dipole. In view of this, the energy of attraction between the two bodies may be regarded as the sum of the energies of attraction between the corresponding pairs of molecules forming the bodies in question. 

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