Attractive forces induction

Induced dipole/mduced dipole attraction (Section 2 17) Force of attraction resulting from a mutual and complemen tary polanzation of one molecule by another Also referred to as London forces or dispersion forces Inductive effect (Section 1 15) An electronic effect transmit ted by successive polanzation of the cr bonds within a mol ecule or an ion... 

In a solution of a solute in a solvent there can exist noncovalent intermolecular interactions of solvent-solvent, solvent-solute, and solute—solute pairs. The noncovalent attractive forces are of three types, namely, electrostatic, induction, and dispersion forces. We speak of forces, but physical theories make use of intermolecular energies. Let V(r) be the potential energy of interaction of two particles and F(r) be the force of interaction, where r is the interparticle distance of separation. Then these quantities are related by... 

When a polar molecule and a non-polar molecule approach each other, the electric field of the polar molecule distorts the electron charge distribution of the non-polar molecule and produces an induced dipole moment within it. The interaction of the permanent and induced dipoles then results in an attractive force. This induction contribution to the electrostatic energy is always present when two polar molecules interact with each other. 

When one molecule is polar and the other nonpolar, the polar molecule induces a dipole in the nonpolar one. The two dipoles are again attracted by electrostatic forces, in this case designated as induction forces. These forces are considerably weaker than orientation forces but stronger than the attractive forces between nonpolar molecules. 

For tliis class of mixtures, interactions between molecules of like species are different in kind for the two species. In particular, two molecules of the polar species experience a direct-electrostatic interaction and a (usually weak) induction interaction, in addition to the usual dispersion interaction here, the attractive forces are stronger than would be observed for a nonpolar species of similar size and geometry. Interactionbetween uiihke species, on the other liand, involves only the dispersion and (weak) induction forces. One therefore expects to be positive, only more so than for otlierwise similar NPNP mixtures. Experiment bears tliis out, on average (Fig. 16.5). 

There are no electrostatic or induction forces between spherical molecules, such as argon, and yet there is clearly a long-range attractive force that causes the liquefaction of argon at low temperatures. This is the dispersion energy, the universal long-range force, which appears at second-order perturbation theory as ... 

Intermolecular forces, sometimes called non-covalent interactions, are caused by Coulomb interactions between the electrons and nuclei of the molecules. Several contributions may be distinguished electrostatic, induction, dispersion, exchange that originate from different mechanisms by which the Coulomb interactions can lead to either repulsive or attractive forces between the molecules. This review deals with the ab initio calculation of complete intermolecular potential surfaces, or force fields, but we focus on dispersion forces since it turned out that this (relatively weak, but important) contribution took longest to understand and still is the most problematic in computations. Dispersion forces are the only attractive forces that play a role in the interaction between closed-shell ( 5) atoms. We will see how the understanding of these forces developed, from complete puzzlement about their origin, to a situation in which accurate quantitative predictions are possible. 

An attractive force between a molecule with a permanent dipole moment and a nonpolar molecule comes about when the first molecule induces a dipole moment in the second. Such attractive forces are called inductive forces. The induced moment obeys the following relation ... 

The van der Waals forces in the strict sense, also called dispersive forces, are the attractive forces between two neutral, nonpolar molecules, for example anthracene molecules, which thus have no static dipole moments. Were the charge dishibution within the molecules rigid, then there would indeed be no interactions between them. However, due to their temporally fluctuating charge distributions, they also have fluctuating dipole moments and these can induce dipoles in other molecules, compare Fig. 2.3. This results in an attractive force, as we aheady calculated in the section on inductive forces. To distinguish the two cases (of a permanent dipole and fluctuating dipoles), these forces due to fluctuations are also termed dispersive forces. 

Surface tension of polymers can be divided into two components—polar (yP) and dispersion (y )— to account for the type of attraction forces at the interfaces. The chemical constitution of the surface determines the relative contribution of each component to the surface tension. The polar component is composed of various polar molecular interactions including hydrogen bonding, dipole energy, and induction energy, while the dispersion component arises from London dispersion attractions. The attractive forces (van der Waals and London dispersion) are additive, which results in the surface tension components to be additive y = y + y. ... 

The stability of an emulsion system towards flocculation and coalescence may be better understood by considering the forces between emulsion droplets. These forces arise from a range of phenomena and vary from system to system. The most ubiquitous of these forces is the van der Waals force of attraction, which arises from momentary fluctuations in the charge distribution across molecules, giving them a flickering dipolar nature. The induction of complementary dipoles in adjacent molecules leads to a weak attractive force between them. A similar attraction occurs between colloidal particles, and the resulting potential decays with the inverse square of the separation between the droplets, as shown schematically in Figure 4.2. 

For polar fluids Bryan and Prausnitz (1987) modified the CS term to account - in addition to the repulsive forces - for orientation-averaged attractive (dipole-dipole) forces this reference system is then combined with a vdW-type perturbation term to account for the additional attractive forces arising from dispersion and induction. 

The intermolecular interactions between species arise from the electronic and quantum nature of atoms. An atom can be viewed as containing a fixed, positively charged nucleus surrounded by a relatively mobile, negatively charged electron cloud. When a molecule is in close enough proximity to another molecule, the electrically charged structure of its atoms can lead to attractive and repulsive forces. The attractive forces include electrostatic forces between point charges or permanent dipoles, induction forces, and dispersion forces. 

We still need to take into account attractive intermolecular forces. In the absence of net electric charge, the attractive forces in the gas phase can include dispersion, dipole-dipole, and induction, all of which have an dependence. However, we do not have distance as a parameter in our equations, but rather volume, which is proportional to the cube of the distance (o r ). We can say, therefore, that all of these terms are proportional to v. ... 

This equation was first proposed by the Dutch physicist van der Waals in 1873. Since it assumes a 1/r dependence for all attractive forces, any force with this functionality (be it dispersion, dipole-dipole, or induction) has been termed a van der Waals force. The parameter a in Equation (4.15) can be related to molecular constants by integrating the Sutherland potential function. This calculation gives a = 2ttN Cq)/. In practice, a and b are treated as empirical constants that account for the magnitude of the attractive and repulsive forces. Can you think of how we might find values for the constants a andfc ... 

There are tliree important varieties of long-range forces electrostatic, induction and dispersion. Electrostatic forces are due to classical Coulombic interactions between the static charge distributions of the two molecules. They are strictly pairwise additive, highly anisotropic, and can be either repulsive or attractive. 

A polar molecule can also induce a dipole on a neighbouring molecule that possesses no permanent dipole. The resultant intermolecular attraction between the permanent and the induced dipole is spoken of as the induction force. Its magnitude is small and independent of temperature. 

As already mentioned molecules cohere because of the presence of one or more of four types of forces, namely dispersion, dipole, induction and hydrogen bonding forces. In the case of aliphatic hydrocarbons the dispersion forces predominate. Many polymers and solvents, however, are said to be polar because they contain dipoles and these can enhance the total intermolecular attraction. It is generally considered that for solubility in such cases both the solubility parameter and the degree of polarity should match. This latter quality is usually expressed in terms of partial polarity which expresses the fraction of total forces due to the dipole bonds. Some figures for partial polarities of solvents are given in Table 5.5 but there is a serious lack of quantitative data on polymer partial polarities. At the present time a comparison of polarities has to be made on a commonsense rather than a quantitative approach. 

In addition to the static induction effects included in I/scf, the hot Drude oscillators give rise to a 1/r6, temperature-dependent, attractive term. This jkg Ta2/r6 term is the classical thermodynamic equivalent of the London quantum dispersive attraction IEa2/r6. It corresponds to a small perturbation to the London forces, because k T is at least two orders of magnitude smaller than the typical ionization energy IE. The smaller the temperature of the Drude motion, the closer the effective potential is to the SCF potential, making Eq. (9-57) independent of mo, the mass of the oscillators. 

Whereas the electrostatic forces arising from permanent moments can be attractive or repulsive (depending on orientation), the induction forces are intrinsically attractive. In the large-R limit, these interactions are generally negligible (i.e., of... 

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