Static electricity statistics

As statistics show, during 10 years in one state and one oil company only, 18 fires have been attributed to static electricity, causing damage and product losses of millions of dollars. ... 

The calculation of the molar polarizabilities, often involves statistical mechanical averaging over orientational distributions of the molecules. An important example is the distribution function w caused by dipole orientation in an externally applied static electric field E° because it describes the process of electric poling of NLO-phores. To second order in the field, the dipolar contributions to this (normalized) function are given by (100),... 

The clasdcal fundamentals of the theory of the Kerr effect are due to Voigt in terms of dectron theory of the atom as an anharmonic oscillator and to Langevin in terms of statistical optical reorioitation of anisotropic molecules in a static dectric fidd. Buckingham proposed a theory and method of measurement of the optical birefringence induced by the gradient of a static electric field permitting the determination of electric quadrupole moments. 

In the EFISH technique (Electric Field Induced Second Harmonic) a solution of the (dipolar) chromophore under consideration is put into a uniform static electric field, obtained for example with parallel metal electrodes. In practice, instead of putting metal electrodes in the solution, the solution is put in a wedge shaped cell bounded by glass windows at which metal electrodes are applied [8]. Owing to the dipolar nature of the chromophores, they statistically orient under the electric field and the whole solution becomes a second order NLO-active polar medium. When a laser radiation crosses the solution, second harmonic radiation is generated and collected. By comparison with a standard nonlinear medium (usually a quartz slab) it is possible to extract the value of the dot product of the chromophore. As we have... 

It is clear that for a substance with dielectric loss, e. g. water and the alcohols, the molecules do not perfectly follow the oscillations of the electric field. For media without dielectric loss, and for the same reasons as under static conditions, the strength of the electric field cannot induce rotation of all polar molecules but, statistically, for a small part only (less than 1%). This means that all the molecules oscillate around an average direction (precession motion), as shown by Fig. 1.5. 

In the absence of external fields the suspension under consideration is macroscopically isotropic (W = const). The applied field h (we denote it in the same way as above but imply the electric field and dipoles as well as the magnetic ones), orienting, statically or dynamically, the particles, thus induces a uniaxial anisotropy, which is conventionally characterized by the orientational order parameter tensor (Piin h)) defined by Eq. (4.358). (We remind the reader that for rigid dipolar particles there is no difference between the unit vectors e and .) As in the case of the internal order parameter S2, [see Eq. (4.81)], one may define the set of quantities (Pi(n h)) for an arbitrary l. Of those, the first statistical moment (Pi) is proportional to the polarization (magnetization) of the medium, and the moments with / > 2, although not having meanings of directly observable quantities, determine those via the chain-linked set [see Eq. (4.369)]. 

First, consider a very dilute gas of molecules [16]. The conventional theory of the static dielectric susceptibility % of such a gas invokes the notion of polarizable molecules with permanent dipole moments that are partially aligned by the external electric field . Standard techniques of statistical thermodynamics produce the Langevin-Debye formula for x Per molecule that reads... 

Statistical Molecular Distribution Functions in a Static and in an Alter-natii Electric Field.— We now shall apply the statistical distribution function expansion (100) to a molecular gas (or dilute solution of polar molecules in a non-polar solvent) immersed in an external electric field E. Not taking into consideration the mutual correlations of molecules but solely their interaction with the field E, we are justified by equation (81) in writing the potential energy to within the square of the field as follows ... 

Most discrete MTP implementations are similar in many respects, e.g., limited expansion up to order 2-4, spherical harmonic description, interaction calculation in the atoms local frames. Hence, what distinguishes these force fields and implementations from each other is primarily in how they treat the other interaction terms. Most importantly, static multipoles only consist of a first-order perturbation of the electrostatic operator. Describing second-order effects leads to polarizability—the charge density s ability to respond to an external electric field—a critical aspect of certain systems (e.g., dielectric changes) [62-64]. Here, possible implementations are ordered in terms of increased overall accuracy (and thus computational investment and larger parametrization effort). Given the heavy requirements of such refined force fields, it is important to point out that "more is not always better," and each system of interest will call for a fine balance of accuracy and statistical sampling. 

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