Fluctuating electric dipoles

There are two general cases of dipole-dipole forces those between molecules in which the distribution of electronic charge is centrosymmetric and those in which it is not. In the first case, there are no permanent electrical dipoles, whereas there is a permanent dipole if the charge distribution is non-centro-symmetric. When permanent dipoles are not present, there are nevertheless fluctuating dipoles as a result of atomic vibrations. These are always present because of zero-point motion. At temperatures greater than 0°K, thermal energy further excites the molecular vibrational modes which create fluctuating electric dipoles. 

When infrared light interacts with the fluctuating electric dipole caused by the vibration of the constituent atoms in molecules or crystals, absorption may occur when the energy of the radiation matches that of the vibration. This fluctuating electric dipole can be considered to arise if two centers (atoms) of equal and opposite charge ( Q) are separated by a distance r, when the dipole moment ( x) will be ... 

Guided by the result in classical mechanics, that the amount of energy radiated by an oscillating charge is related to the dipole moment, the new quantum theory attempts to construct in terms of wave functions the quantity which will represent a fluctuating electric dipole moment. The function... 

Intermolecular forces in saturated hydrocarbons are practically entirely due to the London dispersion forces. These forces are the result of the interaction of fluctuating electric dipoles with the induced dipoles they contribute to the cohesion in all substances, but their magnitude depends on the type of material and its density. Many substances have other intermolecular forces in addition to the dispersion forces. In the case of mercury, the interatomic forces involve the dispersion forces and the metallic bond in the case of water, they involve dispersion forces and dipole interactions (mainly hydrogen bonds). Since the dispersion forces are not appreciably influenced by other intermolecular forces, one can assume dispersion forces and other intermolecular forces generally to be additive. Thus, in the case of the surface tension of water, the surface tension can be considered the sum of a contribution resulting from dispersion forces, y and a contribution resulting from the dipole interactions, mainly hydrogen bonds,... 

An attractive force between neutral molecules can be explained to some extent by a dipole-dipole interaction when the particles carry a dipole moment. Such an attractive force even exists between nonpolar molecules as a result of the influence of electron motion in one atom on the motion in the other atom. This force was elucidated by London on the basis of wave mechanics. The charge fluctuations in one atom or molecule induce a fluctuating electric dipole in the other atom or molecule. A dipole-induced dipole interaction is thus set up, which in turn leads to an attractive interaction between the atoms or molecules. The attractive potential due to this force is expressed as... 

FIGURE 5.5 The rapid fluctuations in the electron distribution in two neighboring molecules result in two instantaneous electric dipole moments that attract each other. The fluctuations flicker into different positions, but each new arrangement in one molecule induces an arrangement in the other that results in mutual attraction. 

Non-polar Solutes in Polar Solvents the (Solvent Stark EffecP. At first sight a non-polar solute molecule cannot polarize the surrounding solvent since it develops no electric field. However, the solvent fluctuates around the non-polar solute, so that there is a small instantaneous electric field which acts on the solute to produce a fluctuating induced dipole which leads to... 

The electrons in a molecule are in constant motion so that at any instant even a non-polar molecule such as H2 possesses an instantaneous electric dipole which fluctuates continuously in time and orientation. The instantaneous dipole in one molecule induces an instantaneous dipole in a second molecule, and interaction of the two synchronized dipoles produces an attractive dispersion energy (known as London energy). In the case of interaction between two neutral, non-polar molecules the dispersion energy is the only contribution to the long-range energy. 

The London energy between two inducible dipoles at separations small compared with the wavelengths of their fluctuating electric fields (Table S.8.c, the first equation) ... 

In addition to the direct interaction of magnetic dipoles, spin-lattice relaxation can proceed by way of interactions between the magnetic dipole of the target nucleus and fluctuating electric fields in the lattice. This is why neighboring quadrupolar nuclei (those with / >, Section 2.1) can bring about very efficient spin-lattice relaxation (short T values). 

Van der Waals forces are the electrostatic a ttractions between the electrons in one molecule and the nuclei of an adjacent molecule minus the molecules inter electronic and intemuclear repulsive forces. In about 1930, Fritz London showed that these forces are caused by the attraction between an electric dipole in some molecule and the electric dipole induced in an adjacent one. Therefore, van der Waals forces result from random fluctuations of charge and are important only for molecules that are very close together—in particular, for neighboring molecules. 

Fluctuations of the Molecular Fields. The second right-hand term of Kerr s constant (191), in the case of dipolar molecules, leads directly to the result (178). We shall now show that this part of the Kerr constant is non-zero even in liquids composed of non-dipolar molecules. This is due to the circumstance that in dense media, even if no external field is applied, intense molecular fields fluctuating in time and space have to be considered locally. The molecular fields Fm induce electric dipoles in the molecules in such regions, giving rise in the medium to the non-zero total dipole moment A/q occurring in the second part of the constant (191). In fact, we have in a linear approximation ... 

In non-dipolar dielectrics sufiSciently dense for molecular interaction, the temperature-dependent polarization (241) is generally non-zero. Such interaction will lead to an effect consisting in the induction, in any given molecule immersed in the dense medium, of a dipole moment M by the fluctuating electric field of the permanent quadrupoles, > octu-poles, >hexadecapoles, and in general multipoles" of its nei bours. 

Gamier and Ciliberto verified an FR for work (equivalent to Q in this paper ) of the form given by eqn (1.1), and a heat fluctuation relation as predicted by van Zon et They studied fluctuations in the power injected to an electrical dipole... 

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