Electromagnetic dispersion

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

Toumelin, E., Torres-Verdin, C., 2009. Pore-scale simulation of kHz-GHz electromagnetic dispersion of rocks effects of rock morphology, pore connectivity, and electrical double layers. In SPWLA 50th Annual Logging Symposium Transactions, The Woodlands, Texas, 21-24 June. Paper RRR. 

In 1930, London [1,2] showed the existence of an additional type of electromagnetic force between atoms having the required characteristics. This is known as the dispersion or London-van der Waals force. It is always attractive and arises from the fluctuating electron clouds in all atoms that appear as oscillating dipoles created by the positive nucleus and negative electrons. The derivation is described in detail in several books [1,3] and we will outline it briefly here. 

Between any two atoms or molecules, van der Waals (or dispersion) forces act because of interactions between the fluctuating electromagnetic fields resulting from their polarizabilities (see section Al. 5, and, for instance. 

As already mentioned, the results in Section HI are based on dispersions relations in the complex time domain. A complex time is not a new concept. It features in wave optics [28] for complex analytic signals (which is an electromagnetic field with only positive frequencies) and in nondemolition measurements performed on photons [41]. For transitions between adiabatic states (which is also discussed in this chapter), it was previously intioduced in several works [42-45]. 

The focus of this chapter is photon spectroscopy, using ultraviolet, visible, and infrared radiation. Because these techniques use a common set of optical devices for dispersing and focusing the radiation, they often are identified as optical spectroscopies. For convenience we will usually use the simpler term spectroscopy in place of photon spectroscopy or optical spectroscopy however, it should be understood that we are considering only a limited part of a much broader area of analytical methods. Before we examine specific spectroscopic methods, however, we first review the properties of electromagnetic radiation. 

In the second broad class of spectroscopy, the electromagnetic radiation undergoes a change in amplitude, phase angle, polarization, or direction of propagation as a result of its refraction, reflection, scattering, diffraction, or dispersion by the sample. Several representative spectroscopic techniques are listed in Table 10.2. 

Table 3.1 summarizes the details of typical sources, absorption cells, dispersing elements and detectors used in different regions of the electromagnetic spectrum. 

This model was later expanded upon by Lifshitz [33], who cast the problem of dispersive forces in terms of the generation of an electromagnetic wave by an instantaneous dipole in one material being absorbed by a neighboring material. In effect, Lifshitz gave the theory of van der Waals interactions an atomic basis. A detailed description of the Lifshitz model is given by Krupp [34]. 

Such efforts have met with limited success, and the reason usually advanced is our lack of understanding of the frequency dependence of molecular NLO properties. In classical electromagnetism, we refer to properties that depend on the frequency of radiation as dispersive and we say that (for example) dispersion is responsible for a rainbow. The blue colour of the sky is a dispersion effect, as is the red sky at night and morning. There is more to it than that, and you might like to read a more advanced text (Hinchliffe and Munn, 1985). 

The field strength is scanned by an electromagnet, and the dispersion of adjacent masses (i.e. the resolution) decreases with increasing ion mass. The high secondary ion extraction voltage employed results in efficient transmission of secondary ions from the sample surface to the detector, although it is difficult to analyse samples with surfaces that are fractured or rough. 

The four rather distinct forms of chemical bonding between atoms are metallic, ionic, covalent, and dispersive (Van der Waals). All of them are sub-topics of quantum electrodynamics. That is, they are all mediated by electronic and electromagnetic forces. There are also mixed cases, as in carbides and other compounds, where both metallic and covalent bonding occur. 

All spectrometers have the following basic units a source of electromagnetic radiation, a dispersion device, sample holder, optical devices for collimating and focusing, a detection device and a data readout or storage system. There are also a variety of ways in which these parts are assembled into the entire spectrometer. 

As with prisms, there are other devices that have been historically used for dispersing or filtering electromagnetic radiation. These include interference filters and absorption filters. Both of these are used for monochromatic instruments or experiments and find little use compared to more versatile instruments. The interested reader is referred to earlier versions of instrumental analysis texts. 

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