Mutual attraction

Dipole-dipole electrostatic interaction perturbs the randomness of orientation. If the dipole on the left is pointing "up," then there is a slightly greater chance that the dipole on the right will point "down" (or vice versa both particles are equivalent in mutual perturbation). By increasing the chances of an attractive mutual orientation, the perturbation creates a net-attractive interaction energy. 

The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range. 

There can be subtle but important non-adiabatic effects [14, ll], due to the non-exactness of the separability of the nuclei and electrons. These are treated elsewhere in this Encyclopedia.) The potential fiinction V(R) is detennined by repeatedly solving the quantum mechanical electronic problem at different values of R. Physically, the variation of V(R) is due to the fact that the electronic cloud adjusts to different values of the intemuclear separation in a subtle interplay of mutual particle attractions and repulsions electron-electron repulsions, nuclear-nuclear repulsions and electron-nuclear attractions. 

Adsorbates can physisorb onto a surface into a shallow potential well, typically 0.25 eV or less [25]. In physisorption, or physical adsorption, the electronic structure of the system is barely perturbed by the interaction, and the physisorbed species are held onto a surface by weak van der Waals forces. This attractive force is due to charge fiuctuations in the surface and adsorbed molecules, such as mutually induced dipole moments. Because of the weak nature of this interaction, the equilibrium distance at which physisorbed molecules reside above a surface is relatively large, of the order of 3 A or so. Physisorbed species can be induced to remain adsorbed for a long period of time if the sample temperature is held sufficiently low. Thus, most studies of physisorption are carried out with the sample cooled by liquid nitrogen or helium. 

Induced dipole/induced dipole forces are the only intermolecular attractive forces available to nonpolar molecules such as alkanes In addition to these forces polar molecules engage m dipole-dipole and dipole/mduced dipole attractions The dipole-dipole attractive force is easiest to visualize and is illustrated m Figure 4 3 Two molecules of a polar substance experience a mutual attraction between the positively polarized region of one molecule and the negatively polarized region of the other As its name implies the dipole/induced dipole force combines features of both the induced dipole/mduced dipole and dipole-dipole attractive forces A polar region of one mole cule alters the electron distribution m a nonpolar region of another m a direction that produces an attractive force between them... 

Neither bromine nor ethylene is a polar molecule but both are polarizable and an induced dipole/mduced dipole force causes them to be mutually attracted to each other This induced dipole/mduced dipole attraction sets the stage for Br2 to act as an electrophile Electrons flow from the tt system of ethylene to Br2 causing the weak bromine-bromine bond to break By analogy to the customary mechanisms for electrophilic addition we might represent this as the formation of a carbocation m a bimolecular elementary step... 

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... 

Newton s law of gravitation states that if two particles are a distance r apart, the mutual attraction force between them can be expressed as follows... 

Incremental Criteria. When mutually exclusive ventures having different levels of investment are compared, an attractive concept is that each increment of investment must itself yield a satisfactory return. This concept has led to a variety of incremental approaches for profitabiUty analysis. Because the risk can vary with investment level and cloud the meaning of satisfactory, any incremental approach to multiyear investment analysis should be viewed with caution. 

Radicals are particularly strongly stabilized when both an electron-attracting and an electron-donating substituent are present at the radical site. This has been called mero-stabilization" or " capto-dative stabilization. This type of stabilization results from mutual reinforcement of the two substituent effects. Scheme 12.3 gives some information on the stability of this type of radical. 

Even the void fraction together with particle size distribution does not provide all of the necessary information on the kind of flow. The mutual forces between distinct particles depend not only on the distance between the particles but also on the surface properties of the particles. The strength of the attractive forces between particles depends on conditions. For instance, the moisture content of the solid is essential for determining the attractiv c forces between particles, especially for hydroscopic materials such as wood. Airflow between particles usually tends to separate particles, whereas the surface forces, adhesion forces, tend to bring them together. 

The terms in square brackets are to do with the nuclear motion the first two of these represent the kinetic energy of the nuclei labelled A and B (each of mass M), and the third term in the square brackets is the Coulomb repulsion between the two nuclei. The fourth and fifth terms give the kinetic energy of the two electrons. The next four negative terms give the mutual Coulomb attraction between the two nuclei A, B and the two eleetrons labelled 1, 2. The final term is the Coulomb repulsion between electrons 1 and 2, with rn the distance between them. As in Chapter 3, I have used the subscript tot to mean nuclear plus electron. 

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