Monopole attraction

Ionic crystals Atomic or molecular anions and cations are bound by the electric monopole-monopole attraction (e.g., NaCl, NH4CIO4). 

The bonding mechanism is the electric monopole-monopole attraction between atomic or molecular anions and cations, Eq. 5.31 ... 

London23 has treated the case of the attractive force between anisotropic molecules on the dipole-dipole interaction basis as well as on the monopole basis mentioned above. The small anisotropy found for the chlorine atom makes the dipole-dipole formulation appropriate. For the symmetrical orientation in the Cl2 molecule the London formula is... 

The term molecular crystal refers to crystals consisting of neutral atomic particles. Thus they include the rare gases He, Ne, Ar, Kr, Xe, and Rn. However, most of them consist of molecules with up to about 100 atoms bound internally by covalent bonds. The dipole interactions that bond them is discussed briefly in Chapter 3, and at length in books such as Parsegian (2006). This book also discusses the Lifshitz-Casimir effect which causes macroscopic solids to attract one another weakly as a result of fluctuating atomic dipoles. Since dipole-dipole forces are almost always positive (unlike monopole forces) they add up to create measurable attractions between macroscopic bodies. However, they decrease rapidly as any two molecules are separated. A detailed history of intermolecular forces is given by Rowlinson (2002). 

In practice a molecule with a dipole moment is often mobile. If the dipole is free to rotate and close to a positive charge it tends to rotate until its negative pole points towards the positive charge. On the other hand, thermal fluctuations drive it away from a perfect orientation. On average, a net preferential orientation remains and the dipole is attracted by the monopole. The average potential energy is... 

When a charge approaches a molecule without a static dipole moment, all energies considered so far would be zero. Nevertheless, there is an attractive force. Reason The monopole induces a charge shift in the non-polar molecule. An induced dipole moment arises, which interacts with the charge. The Helmholtz free energy is... 

Though this looks like an extensive quantity, its thermodynamic limit is infinite if Ai. = /dry rniy) is non-zero for both i = m and i = n. (The Coulomb repulsion of an infinite set of monopoles is infinite.) The problem can be removed by including the nuclear Coulomb attraction. Consider the charge distribution 5)n(r)... 

It is interesting to look at the antibaryon-nucleus system from somewhat different point of view. An antibaryon implanted into a nucleus acts as an attractor for surroimding nucleons. Due to the uncompensated attractive force these nucleons acquire acceleration towards the center. As the result of this inward collective motion the nucleons pile up producing local compression. If this process would be completely elastic it would generate monopole-like oscillations around the compressed SBN state. The maximum compression is reached when the attractive... 

Interactions become shorter-ranged and weaker as higher multipole moments become involved. When a monopole interacts with a monopole. Coulomb s law says u r) oc r But when a monopole interacts with a distant dipole, coulombic interactions lead to u r) oc r (see Equation (21.26)). Continuing up the multipole series, two permanent dipoles that are far apart interact as u(r) oc r Such interactions can be either attractive or repulsive, depending on the orientations of the dipoles. Table 24.2 gives typical energies of some covalent bonds, and Table 24.3 compares covalent to noncovalent bond strengths. 

This result shows that at large distances the attractive energy between a monopole and a dipole varies as R. ... 

SOLUTION Use Eq. 10.14 for the monopole-dipole energy, and Coulomb s law for the attraction in the ionic bond ... 

The strongest of these (non-chemical bonding) interactions is the monopole-dipole attraction between an ion and a polar molecule, which is proportional to the dipole moment and the ion charge q ... 

As with the neutral weakly bonded clusters, the binding energy in these clusters generally increases with cluster size. Flowever, the first few molecules added to the ionic cluster occupy the best sites to take advantage of the strong monopole-dipole or monopole-induced dipole attraction to the ion. As coordination sites around the ion get more crowded, the binding energy of additional... 

The electrostatic component is generally the dominant attractive contribution in the case of polar molecules, i.e., systems with nonspherical charge distributions, usually manifested as appreciable permanent dipole and/or quadrupole moments. The classical Coulomb interaction between the respective charge distributions of the interacting molecules is conveniently formulated in terms multipole expansions that consist of dipole/dipole, dipole/quadrupole, quadrupole/quadrupole, etc. type terms, with distance (R) dependences R, R, R, ... (In the case of charged systems the monopole (net charge) terms must of course be also included in the expansion, that give rise to R, ... dependent terms.)... 

---