Point-cloud potential

And each proton is attracted to one of the electron clouds through the point-cloud potential (Equation 3.7). The attractive force is given by the gradient of the point-cloud potential ... 

From the preceding sections it can be seen that surfactants can be extremely important in many facets of the petroleum industry. From a knowledge of some of the basic properties of a surfactant (i.e., the erne, Krafft point, cloud point, adsorption level and surface or interfacial tension at the cmc), some predictions may be made as to the performance of the surfactant in a given potential oil recovery process. However, it is also clear that there are severe limitations on the extent to which equilibrium micellar properties can be used to predict what are frequently, in practical application, dynamic phenomena. Subse-... 

The problem of explosion of a vapor cloud is not only that it is potentially very destructive but also that it may occur some distance from the point of vapor release and may thus threaten a considerable area. If the explosion occurs in an unconfined vapor cloud, the energy in the blast wave is generally only a small fraction of the energy theoretically available from the combustion of all the material that constitutes the cloud. The ratio of the actual energy released to that theoretically available from the heat of combustion is referred to as the explosion efficiency. Explosion efficiencies are typically in the range of 1 to 10 percent. A value of 3 percent is often assumed. 

A more deterministic estimate of a vapor cloud s blast-damage potential is possible only if the actual conditions within the cloud are considered. This is the starting point in the multienergy concept for vapor cloud explosion blast modeling (Van den Berg 1985). Harris and Wickens (1989) make use of this concept by suggesting that blast effects be modeled by applying a 20% TNT equivalency only to that portion of the vapor cloud which is partially confined and/or obstructed. 

If, on the other hand, a vapor cloud s explosive potential is the starting point for, say, advanced design of blast-resistant structures, TNT blast may be a less than satisfactory model. In such cases, the blast wave s shape and positive-phase duration must be considered important parameters, so the use of a more realistic blast model may be required. A fuel-air charge blast model developed through the multienergy concept, as suggested by Van den Berg (1985), results in a more realistic representation of a vapor cloud explosion blast. 

When two atoms approach each other so closely that their electron clouds interpenetrate, strong repulsion occurs. Such repulsive van der Waals forces follow an inverse 12th-power dependence on r (1/r ), as shown in Figure 1.13. Between the repulsive and attractive domains lies a low point in the potential curve. This low point defines the distance known as the van der Waals contact distance, which is the interatomic distance that results if only van der Waals forces hold two atoms together. The limit of approach of two atoms is determined by the sum of their van der Waals radii (Table 1.4). 

Similarly, all points within a metal, which consists of an ordered rigid lattice of metal cations surrounded by a cloud of free electrons, are electrically neutral. Transport of charge through a metal under the influence of a potential difference is due to the flow of free electrons, i.e. to electronic conduction. The simultaneous transport of electrons through a metal, transport of ions through a solution and the transfer of electrons at the metal/solution interfaces constitute an electrochemical reaction, in which the electrode at which positive current flows from the solution to the electrode is the cathode (e.g. M (aq.) + ze M) and the electrode at which positive flows from it to the solution (e.g. M - M (aq.) -)- ze) is the anode. 

This expression is exact within our original approximation, where we have neglected relativistic effects of the electrons and the zero-point motions of the nuclei. The physical interpretation is simple the first term represents the repulsive Coulomb potential between the nuclei, the second the kinetic energy of the electronic cloud, the third the attractive Coulomb potential between the electrons and the nuclei, and the last term the repulsive Coulomb potential between the electrons. 

The key point here is to determine if flammable or combustible materials are being processed under conditions of temperature and pressure such that, if a release occurs, a significant quantity of the material may be released into the air as either a gas, vapor, mist, or aerosol. If such conditions are present, the user should assume that the potential for a vapor cloud explosion exists. Otherwise, VCE hazards can be ignored. 

The Lewis dot formalism shows any halogen in a molecule surrounded by three electron lone pairs. An unfortunate consequence of this perspective is that it is natural to assume that these electrons are equivalent and symmetrically distributed (i.e., that the iodine is sp3 hybridized). Even simple quantum mechanical calculations, however, show that this is not the case [148]. Consider the diiodine molecule in the gas phase (Fig. 3). There is a region directly opposite the I-I sigma bond where the nucleus is poorly shielded by the atoms electron cloud. Allen described this as polar flattening , where the effective atomic radius is shorter at this point than it is perpendicular to the I-I bond [149]. Politzer and coworkers simply call it a sigma hole [150,151]. This area of positive electrostatic potential also coincides with the LUMO of the molecule (Fig. 4). 

The problem of the explosion of an unconfined vapor cloud is not only that it is potentially very destructive but also that it may occur some distance from the point of vapor release and may thus threaten a considerable area. 

Parallel to these works, from 1987 onwards I proceeded along a clear line of development that led to my present-day projects. My first conception of this type was a multidimensional sculpture for the University of Trier, a visionary design as a symbol for the interplay of solar energy, clouds and rainbows. The university seemed to me to be exactly the right place for an innovation of this type. I wanted to point the way to the potential positive interaction of environment and energy. 

Ethylene oxide is an important fuel for FAEs and has proved its potential as one of the best fuels for them. It has wide explosive limits and low boiling point (10.5 °C) which facilitates its vaporization faster at room temperature and results in the formation of a cloud with air which is detonated. However, EO has a tendency to polymerize during storage thereby decreasing its shelf-life as well as the performance of EO-based weapons. The phenomenon of polymerization of EO, effect of temperature and materials of construction of weapons on polymerization and retardation of EO polymerization by the addition of well-known anti-oxidants have been studied by Agrawal et al. [293]. The addition of anti-oxidants retards EO polymerization and enhances the shelf-life of EO but does not meet the requirements of the Services, stipulating a shelf-life of minimum 10 years for... 

All symbols have their usual meaning in the c.g.s. system of units, as given in Ref. 3. The common interpretation that the central ion sees its ionic cloud at a distance k 1 away is valid for the point-charge model only. For the DH second approximation the ionic cloud can be reduced to a charge located on a spherical surface at k 1 so as to maintain a constant potential at the surface of the central ion. Therefore, it cannot be replaced by a point charge. 

A molecule may be viewed as a number N of nuclear charges, Z e, of a certain arrangement given by their position vectors, Rt for i = 1... JV, surrounded by an electronic cloud of charge density p(r) of finite dimensions. The potential of the electrostatic field at the point R outside the electronic cloud is given by... 

Jj( 1) is the potential energy of interaction between the point charge of electron 1 and electron 2 considered to be smeared out into a hypothetical charge cloud of charge density (charge per unit volume) - e)Hartree-Fock method considers average interelectronic interactions, rather than instantaneous inter-... 

Borazine is isoelectronic with benzene, as B=N is with C=C, (Fig. 16.21). in physical properties, borazine is indeed a close analogue of benzene. The similarity of the physical properties of the alkyl-substituted derivatives of benzene and borazine is ever more remarkable. For example, the ratio of the absolute boiling points of the substituted borazines to those of similarly substituted benzene is constant. This similarity in physical properties led to a labeling of borazine as "inorganic benzene." This is a misnomer because tbe chemical properties of borazine and benzene are quite different Both compounds have aromatic rr clouds of electron density with potential for delocalization over all of the ring atoms. Due to the difference m electronegativity between boron and nitrogen, the cloud in borazine is "lumpy" because more electron... 

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