Dipolar fluctuations

The correlation pattern depends on the angular momentum transfer K between the core hole and the screening charge. For K = 0 there is a correlation between the radial motion, monopole fluctuation, of the core hole and the screening charge (Fig. 13 g) while for K 1 there is an angular correlation. Fig. 13 h describes the case of dynamic dipolar fluctuation (K = 1) where the core hole no longer is spherically distributed and where the... 

Both formulations stumble when the materials are real conductors such as salt solutions or metals. In these cases important fluctuations can occur in the limit of low frequency where we must think of long-lasting, far-reaching electric currents. Unlike brief dipolar fluctuations that can be considered to occur local to a point in a material, walls or discontinuities in conductivity at material interfaces interrupt the electrical currents set up by these longer-lasting "zero-frequency" fields. It is not enough to know finite bulk material conductivities in order to compute forces. Nevertheless, it is possible to extend the Lifshitz theory to include events such as the fluctuations of ions in salt solutions or of electrons in metals. 

There are monopolar fluctuations of the net charge on the colloid and its surrounding solution there are dipolar fluctuations, the first moment of the ionic-charge distribution around the colloid as well as polarization of the colloid itself. Monopolar and dipolar fluctuations couple to create a hybrid interaction, d-m, again in the limit of the n = 0 sampling frequency at which the ions are able to fluctuate. The salt solution screens even the dipolar fluctuation the same way that the low-frequency-fluctuation term is screened in planar interactions. For dielectric spheres of radius a, ss whose incremental contribution to dielectric response is a =... 

Following the strategy for extracting small-particle van der Waals interactions from the interaction between semi-infinite media, we can specialize the general expression for ionic-fluctuation forces to derive these forces between particles in salt solutions. Because of the low frequencies at which ions respond, only the n = 0 or zero-frequency terms contribute. In addition to ionic screening of dipolar fluctuations, there are ionic fluctuations that are due to the excess number of ions associated with each particle. 

Not only are there fluctuations in the electric fields that create the dipolar fluctuations of most van der Waals forces but there are also fluctuations in electric potential with concomitant fluctuations in the number density of ions and the net charge on and around these small spheres. Monopolar charge-fluctuation forces occur when ion fluctuations in the spheres differ from ion fluctuations in the medium. Perhaps it is better to say that these forces occur when ion fluctuations around the suspended particles differ from what they would have been in the solution in the absence of particles. To formulate these interactions, we allow the ionic population of the spheres to equilibrate with the surrounding salt solution and to exchange ions with that surrounding solution. Then we compare the ionic fluctuations that occur from the presence of the small spheres with those in their absence. To do this we must have a way to count the number of extra ions associated with each sphere compared with the number of ions in their absence. 

DIPOLAR FLUCTUATION FORCES BETWEEN THIN CYLINDERS... 

In the limit at which /cm goes to zero, these functions reduce to the correct form for dipolar fluctuations only. It is the product of these times e 2VpZ+i i that must be integrated over dir and pdp to obtain the interaction of the two arrays A and B. We know in advance that it is the second and third derivatives with respect to l that give us at-an-angle and parallel rod-rod interactions. The second derivative creates a factor 4 (p2 + k ). 

The leading R dispersion term is often described as the correlation in the instantaneous dipolar fluctuations in the charge density of the two molecules. 

In this chapter broadband dielectric spectroscopy (BDS) is employed to polymeric blend systems. In its modem form BDS can cover an extraordinary broad frequency range from 10 " to 10 Hz. Therefore, molecular and collective dipolar fluctuations, charge transport, and polarization effects at inner phase boundaries can be investigated in detail including its temperature dependence. 

Different modes in the dipolar fluctuations characterize the dielectric of chiral smectics. As the fluctuations in the primary order parameter, for instance represented by the tilt vector... 

Finally, quantum dipolar fluctuations of the atomic structure of neutral atoms and molecules lead to the ubiquitous Van der Waals interaction ... 

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