The attractive force

In 1873, van der Waals [2] first used these ideas to account for the deviation of real gases from the ideal gas law P V= RT in which P, Tand T are the pressure, molar volume and temperature of the gas and R is the gas constant. Fie argried that the incompressible molecules occupied a volume b leaving only the volume V- b free for the molecules to move in. Fie further argried that the attractive forces between the molecules reduced the pressure they exerted on the container by a/V thus the pressure appropriate for the gas law isP + a/V rather than P. These ideas led him to the van der Waals equation of state ... 

The attractive force is called hydrogen bonding and is normally represented by a dotted line, for example A—H A—H it is this... 

This term describes the repulsive forces keeping two nonbonded atoms apart at close range and the attractive force drawing them together at long range. 

The hydrogen atom is a three-dimensional problem in which the attractive force of the nucleus has spherical symmetr7. Therefore, it is advantageous to set up and solve the problem in spherical polar coordinates r, 0, and three parts, one a function of r only, one a function of 0 only, and one a function of [Pg.171]

Atoms combine with one another to give compounds having properties different from the atoms they contain The attractive force between atoms m a compound is a chemical bond One type of chemical bond called an ionic bond, is the force of attraction between oppositely charged species (ions) (Figure 1 4) Ions that are positively charged are referred to as cations, those that are negatively charged are anions... 

The H—O—H angle m water (105°) and the H—N—H angles m ammonia (107°) are slightly smaller than the tetrahedral angle These bond angle contractions are easily accommodated by VSEPR by reasoning that electron pairs m bonds take up less space than an unshared pair The electron pair m a covalent bond feels the attractive force of... 

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

Dipole/mduced dipole and dipole-dipole attractive forces make alcohols higher boiling than alkanes of similar molecular weight The attractive force between —OH groups is called hydrogen bonding... 

Dipole moment (Section 1 5) Product of the attractive force between two opposite charges and the distance between them Dipole moment has the symbol p- and is measured in Debye units (D)... 

All heteronuclear diatomic molecules, in their ground electronic state, dissociate into neutral atoms, however strongly polar they may be. The simple explanation for this is that dissociation into a positive and a negative ion is much less likely because of the attractive force between the ions even at a relatively large separation. The highly polar Nal molecule is no exception. The lowest energy dissociation process is... 

An exception to the mle that lowering the temperature causes transitions to phases with iacreased order sometimes occurs for polar compounds which form the smectic phase. Decreasiag the temperature causes a transition from nematic to smectic but a further lowering of the temperature produces a transition back to the nematic phase (called the reentrant nematic phase) (22). The reason for this is the unfavorable packing of the molecules ia the smectic phase due to overlap of the molecules ia the center of the layers. As the temperature is lowered, the steric iateractions overpower the attractive forces, causiag the molecules to pack much more favorably ia the nematic phase. The reentrant nematic phase can also be produced from the smectic phase by iacreasiag the pressure (23). 

V n der W ls Interactions. Van der Waals iateractions result from the asymmetric distribution of electronic charge surrounding an atom, which induces a complementary dipole in a neighboring atom, resulting in an attractive force. In general, the attractive force of van der Waals interactions is very weak (<4.2 kJ/mol (1 kcal/mol)) but may become significant if steric complementarity creates an opportunity to form a large number of van der Waals attractions. 

The atoms of a molecule are held together by primary bonds. The attractive forces which act between molecules are usually referred to as secondary bonds, secondary valence forces, intermolecular forces or van der Waals forces. 

The molecules of liquids are separated by relatively small distances so the attractive forces between molecules tend to hold firm within a definite volume at fixed temperature. Molecular forces also result in tlie phenomenon of interfacial tension. The repulsive forces between molecules exert a sufficiently powerful influence that volume changes caused by pressure changes can be neglected i.e. liquids are incompressible. 

In the above analysis, Johnson et al. [6] assume that the interfacial forces act only when the surfaces are in contact, i.e. the attractive forces are considered to be of infinitesimally short range. This analysis ignores the forces acting just outside the edge of the contact circle. Because of this, the theory predicts an infinite tensile stress at the edge of the contact. If the attractive force between the surfaces is allowed to have a finite range, the infinity in the tensile stress disappears. The stress at the edge of the contact circle is still tensile, but it remains finite. 

To account for some of the shortcomings of the JKR theory, Derjaguin and coworkers [19] developed an alternative theory, known as the DMT theory. According to the DMT theory, the attractive force between the surfaces has a finite range and acts outside the contact zone, where the surface shape is assumed to be Hertzian and not deformed by the effect of the interfacial forces. The predictions of the DMT theory are significantly different compared to the JKR theory. 

By combining Hertz s contact theory (Eq. 1) and with Hamaker s functional form for the attractive force (Eq. 17), the Derjaguin model takes the form... 

Equilibrium is established when the attractive surface forces are balanced by elastic repulsion forces between the materials. The DMT model states that the elastic repulsion force is related to the attractive force within the contact region Fs by... 

The equilibrium contact radius is determined by substituting the attractive force experienced by the particle into Eq. 33. Accordingly,... 

An alternative explanation has been proposed by Quesnel [62]. Assuming that the adhesion-induced deformation could be treated as a Hertzian indentor, with the load due to the force arising from the surface energy, Quesnel calculated the indentation in a self-consistent manner. That is to say, Quesnel recognized that the attractive force would vary as the particle or substrate deformed, owing to the increased circumference of the contact patch. He also recognized that, due to... 

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