Van der Waals forces between molecules

The van der Waals forces between molecules are rather short range the potential energy decreases with the inverse of the sixth power of the distance of molecules. The van der Waals forces between two molecules 1 and 2 are given by the general expression (for the potential)  

In these equations, ks is the Boltzmann s constant (1.38 X 10 J K ), Tis the temperature, I is the first ionization potential (J), oo,- is the electronic polarizability (C m J ) and p is the dipole moment (p = ql) often given in Debye (1 Debye = 3.336 x 10 Cm). In the dipole moment equation q is the electric charge (C), and I is the distance between the positive and negative charge within a given molecule (m). The electronic polarizabihty is defined as the ease with which the electrons of molecules are displaced by an electric field, e.g. that created by an ion or a polar molecule. The polarizability is expressed in m V or 

There are also weaker (shorter range) forces than the van der Waals ones, e.g. when quadrupoles are present (CO2 is a typical quadrupole), but these are of httle importance in colloid and surface science and will not be discussed further here (for more details on these weaker forces see Prausnitz, Lichtenthaler and de Azevedo, 1999 Kontogeorgis and Folas, 2010). 

When using the Debye and Keesom expressions (induction and polar forces) for interactions in a medium other than vacuum or air, the permittivity of 

Vy = o = zero-frequency contribution due to polar/ induction forces (Keesom/Debye)  

Forces between macroscopic objects result from a complex interplay of the interaction between molecules in the two objects and the medium separating them. The basis for an understanding of intermolecular forces is the Coulomb1 force. The Coulomb force is the electrostatic force between two charges Qi and Q-2- 

The potential energy between two electrical charges which are a distance D apart is 

1 Charles Augustin Coulomb, 1736-1806. French physicist and engineer. 

This is 56 times higher than the thermal energy ksT = 4.12 x 10 21 J at room temperature. 

we have assumed that the distance D is large compared to the extension of the dipole. 

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In the case of an associating fluid with the repulsive-attractive reference system potential, the attractive van der Waals forces between molecules may also be considered in a perturbational manner [114]. The Helmholtz free energy can be written as a sum of three terms... 

The (unbalanced) forces acting in surface layers are diverse in their intensities and character. Physical (van der Waals) forces between molecules are weak and give rise to slight energy effects (up to 20kJ/mol). These forces decrease slowly with increasing distance (i.e., they operate within a relatively wide region) and are responsible for weak physical (often multiplayer) adsorption. 

Increasing surface area => increasing the van der Waals forces between molecules => more energy (a higher temperature) is required to separate molecules from one another and produce boiling. 

The major forms of van der Waals forces between molecules that are not bonded together are the permanent dipole-dipole interaction, the dispersion-induced temporary dipole interaction, and the hydrogen bond. They are short-range forces that operate only when two atoms or molecules are in close proximity. The Lennard-Jones potential of 6-12 is a model of this potential field ... 

It may be added that the difficulty reappeared later, when it appeared that each oscillator has a zero-point energy. This zero-point energy exists also in empty space and is independent of temperature, and may therefore be subtracted from the total energy without affecting the observed facts. However, the difference between the zero-point energy of the field between both mirrors and the vacuum field does not vanish and depends on L. It therefore gives rise to a force between the mirrors, which is a macroscopic version of the Van der Waals force between molecules, nowadays known as the Casimir effect. )... 

Consider the molecules in a liquid. As shown in Figure 3.1, for a liquid exposed to a gas the attractive van der Waals forces between molecules are felt equally by all molecules except those in the interfacial region. This imbalance pulls the latter molecules towards the interior of the liquid. The contracting force at the surface is known as the surface tension. Since the surface has a tendency to contract spontaneously in order to minimize the surface area, droplets of liquid and bubbles of gas tend to adopt a spherical shape this reduces the total surface free energy. For two immiscible liquids a similar situation applies, except that it may not be so immediately obvious how the interface will tend to curve. There will still be an imbalance of intermolecular forces resulting in an interfacial tension and the interface will adopt a configuration that minimizes the interfacial free energy. 

Thixotropy provides a shear thinning effect that is, viscosity decreases as the shear rate increases, and vice versa. This not only allows easy pumping, dispensing, and mixing of the adhesive, but also provides sag resistance once the adhesive is applied. The thixotropic fillers work by forming a temporary structure in the mixture, which can be broken down at high rates of shear. This structure is generally the result of van der Waals forces between molecules. 

An attractive interaction arises due to the van der Waals forces between molecules of colloidal particles. Depending on the nature of dispersed particles, the Keesom forces (or the dipole-dipole interaction), the Debye forces (or dipole-induced dipole interaction), and the London forces (or induced dipole-induced dipole interaction) may contribute to the van der Waals interaction. First, the van der Waals interaction was theoretically computed using a method of the pairwise summation of interactions between different pairs of molecules of the two macroscopic particles. This method called the microscopic approximation neglects collective effects, and, as a consequence, misrepresents the Hamaker constant. For many problems of a practical use, however, specific features of the total interaction are determined by a repulsive part, and such an effective, gross description of the van der Waals interaction may often be accepted [3]. The collective effects in the van der Waals interaction have been taken into account in the calculations of Lifshitz et al. [4], and their method is known in the literature as the macroscopic approach. 

We have mentioned several times that the characteristic of the molecular compounds is that the Van der Waals forces between molecules are small compared to the valence forces holding the atoms together to form a molecule. Thus the substances vaporize at a low temperature, whereas their molecules do not dissociate chemically to any extent except at very high temperatures. For instance, the dissociation H2 = 2H is a typical example of chemical equilibrium, to be handled by the methods... 

This is equivalent to saying that the order formed in the nematic phase is not governed by electric dipole interactions but rather by the molecular shape and the van der Waals forces between molecules. Note that, although entropy is also related to the order of a system, the symbol S used here does not refer to entropy. 

Our recent studies [74-76,85-93] show that almost all prepared polycrystalline adducts of zinc(II)-dithiocarbamates (see previous section) may form solvates, i.e. incorporating small guesf molecules such as benzene, various chlorohy-drocarbons and N-donor bases, which are held by van-der-Waals forces between molecules of the host compound. X-ray diffraction studies [85-91,93] have revealed an ordered system of molecular channels occupied by outer-sphere guest molecules in the crystal lattice of solvated forms of the adducts (see Fig. 23), i.e., clathrate type structures. 

The van der Waals forces between molecules and atoms are well known from their introduction in the so-called van der Waals equation empirically describing the behaviour of a real gas in terms of varying pressure and temperature [2]. The term a[ P- in this equation describes the difference between the ideal and the observed pressure, while h maybe interpreted as the volume occupied by the gas molecules... 

The small differences in stability between branched and unbranched alkanes result from an interplay between attractive and repulsive forces within a molecule (intramolecular forces). These forces are nucleus-nucleus repulsions, electron-electron repulsions, and nucleus-electron attractions, the same set of fundamental forces we met when talking about chemical bonding (see Section 1.12) and van der Waals forces between molecules (see Section 2.14). When the energy associated with these interactions is calculated for all of the nuclei and electrons within a molecule, it is found that the attractive forces increase more than the repulsive forces as the structure becomes more compact. Sometimes, though, two atoms in a molecule are held too closely together. WeTl explore the consequences of that in Chapter 3. 

In practice, in the majority of biphase colloid systems, the number of particles decreases with time, and their size is simultaneously increased. In an emulsion, collision of two drops results in their coalescence with the formation of one drop of greater size. Solid particles undergoing collision do not coalesce, but form aggregates. Aggregation of particles occurs due to attractive Van der Waals forces between molecules. 

The molecular structure not only determines the adsorbate-substrate interactions but also the lateral interactions between the adsorbed molecules. Attractive adsorbate-adsorbate interactions, for example, due to van der Waals forces between molecules with long hydrocarbon chains, result in the formation of condensed, often ordered ad-layer phases ( self-assembled monolayers, see Chapter 2.1 in Volume 10), in which the strength of adsorption is increased. Reciprocally, repulsive interactions (e.g. dipole-dipole interactions) weaken the adsorption. 

The origin of surface tension may be visualized by considering the molecules in a liquid. The attractive van der Waals forces between molecules are felt equally by all molecules except those in the interfacial region. This imbalance pulls the latter molecules towards the interior of the liquid. The contracting force at the surface is known as the surface... 

Van der Waals forces between molecules in vacuum are attractive. As a result, two infinite media 1 and 2 interacting across vacuum attract each other. If they are separated by a gap of constant thickness z, the interaction energy per unit area can be written as ... 

Unfortunately, we do not know a precise expression for the potential energy due to hydrogen bonding but it is considered that the distance dependency is around r, i.e. it is much longer range than the van der Waals forces between molecules and similar to Coulombic forces, though weaker. We can nevertheless present the most qualitative characteristics of the hydrogen bonds and related enhanced interactions. 

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