Fluctuating Dipoles

The physical origin of the dispersion interaction is often described in terms of a quasi-classical induced-dipole-induced-dipole picture. The quantum-mechanical fluctuations of the electronic distribution about its spherically symmetric average can be pictured as leading to an instantaneous (snapshot) dipole /za(mst) on monomer a, which in turn induces an instantaneous dipole tb(mst) on b. Thus, if the dipole fluctuations of the two monomers are properly correlated, a net attraction of the form (5.25) results. As remarked by Hirschfelder et al,28... 

S.9.a. Induced-dipole-induced-dipole fluctuation correlation... 

A final interesting observation is the existence of a frequency scale, 3x10 see in Eq. (2-39). This is the frequency at which the electronic cloud around an atom fluctuates it is therefore the rate at which the spontaneous dipoles fluctuate. Since the electromagnetic field created by these dipoles propagates at the speed of light c = 3 x lO cm/sec, only a finite distance c/v 100 nm is traversed before the dipole has shifted. Since the dispersion interaction is only operative when these dipoles are correlated with each other, and this correlation is dismpted by the time lag between the fluctuation and the effect it produces a distance r away, the dispersion interaction actually falls off more steeply than r when molecules or surfaces become widely separated. This effect is called the retardation of the van der Waals force. The effective Hamaker constant is therefore distance dependent at separations greater than 5-10 nm or so. 

J. Heinrichs. Contribution of dipole fluctuations in the quantum theory of electronic polarizability of crystals. Phys. Lett., 73 251-252 (1965). 

J. Heinrichs. Role of quantum dipole fluctuations in the theory of excitations and of the dielectric constant of crystals. Phys. Rev., 188 1419-1430 (1969). 

Loosely speaking, the theory shows that two bodies (or macromolecules) sense and feel their different frequencies of inter-oscillations at different distances. The zero frequency (microwave, non-retarded) classical or non quantum mechanical coupled permanent dipole fluctuations guide orientation and interactions at large distances. At distances 200-500A, the infra-red locks in and at distances below about 50A, the strong ultraviolet correlations take over. At smaller distances still chemistry takes over, as the far ultraviolet correlations lock in. 

ABSTRACT The principle of electrical spectrography and its measurement system is discussed. The phenomenon of noise in electrolytes and interfaces receives attention. Noise spectrography is found to have applications in some biomolecular systems, viz., DNA helix-to-coil transition, thermal transconformation, and salt-free premelting effects. Noise conductivity emission spectra of collagen solutions gave information on permanent dipole fluctuations and hydrodynamic properties of the system. 

Demonstration of the Permanent Dipole Fluctuations of Collagen Molecules... 

Let us first consider spectroscopy. Linear-response theory, in particular the fluctuation dissipation theorem - which relates the absorption of an incident monochromatic field to the correlation function of (e.g. dipole) fluctuations in equilibrium - has changed our perspective on spectroscopy of dense media. It has moved away from a static Schrodinger picture -phrased in terms of transitions between immutable (but usually incomputable) quantum levels - to a dynamic Heisenberg picture, in which the spectral line shape is related by Fourier transform to a correlation function that describes the decay of fluctuations. Of course, any property that cannot be computed in the Schrodinger picture, cannot be computed in the Heisenberg picture either however, correlation functions, unlike wave-functions, have a clear meaning in the classical limit. This makes it much easier to come up with simple (semi) classical interpretations and approximations. 

Mode of activation Convection currents Electronic excitation Electron transfer at the electrode Cavitation Dipole fluctuation Mechanical... 

The second approach, referred to as a continuum theory, has been pursuit by theorists using classical or quantum statistical mechanics with the common focus on solvent dipole fluctuation as a major factor controlling the charge transfer [5,6]. 

A nonpolar molecule is nonpolar only in a statistical sense. At any instant, the random motion of the electrons will lead to a dipole moment, but this fluctuates as the electrons move around and its average value is zero. Thus a hydrogen atom at any given instant has a dipole moment since the electron and proton are at different points in space as the electron moves around the proton, the direction and size of the dipole fluctuate, the average value being zero. When two neutral molecules are close together, the electrostatic interactions between them cause the electrons to correlate these motions so that the instantaneous dipole moments of the molecules lead to a net attraction. These attractive forces, due to electron correlation between adjacent molecules, are called Heitler-London dispersion forces, usually abbreviated to dispersion forces. 

The electrical charges in permanent dipoles fluctuate slightly in their distribution. Vhen dipole-dipole forces are present between two molecules, those fluctuations also cause London forces to be present. In general the London forces will be weaker than the dipole-dipole forces, but both contribute to the attractions between molecules. If a molecule also exhibits hydrogen bonding, dipole-dipole and London forces will both be present and contribute to the attractions between molecules. 

Broadhurst et al. assumed that the dipoles fluctuate within the crystalline lamella [253]. The total dipole moment m, contributed from both the fluctuation ci crystalline dipoles and the space charges trapped at the interfacial part between the crystallite and amorphous region, is expressed approximately by... 

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