Quadrupole force

Quadrozyd, n. quadroxide (tetroxide). Quadnipolkraft, /. quadrupole force. quSlen, t.t. mill, crush, disaggregate torment, worry, afflict, distress, qualifizieren, t.t. r. qualify. 

The results of such a calculation, shown in Fig. 8 (52), seem to tell a very different story from the earliest studies. With nondipolar I2 as a solute and C02 as a solvent, the complete domination of the solvent response by the Lennard-Jones forces is impressive, but perhaps not all that startling. One might surmise that the quadupole-quadrupole forces at work in this example are a bit too weak to accomplish much. Yet, when we have a dipolar solute dissolved in the strongly polar solvent CH3CN, we get almost the same kind of complete control by Lennard-Jones forces. Electrostatics now seems totally unimportant. 

O2-N2 systems, although in considerable less detail. Previous results on the N2-N2 system [44] have been reanalyzed, and a characterization of the N2-O2 complex has been presented a subsequent paper [10]. These results indicate that most of the bonding in the dimers comes from van der Waals (repulsion - - dispersion) and electrostatic (permanent quadrupole-permanent quadrupole) forces. On the other hand, chemical (spin-spin) contributions are not negligible for O2-O2, which is an open-shell-open-shell system [4,5]. Therefore the geometrical properties of the three dimers have been found to show interesting differences, to be seen in the next paragraph. 

Thequantity Ef represents the energy of interaction between one water molecule and one ion. If, however, four water molecules surround one ion and one considers a mole of ions, the heat change involved in the formation of a primary solvated ion through the agency of ion-quadrupole forces is given by... 

An important point to recall regarding the dissolution of an ionic crystal (Chapter 2) is that ionic lattices consist of ions even before they come in contact with a solvent. In fact, all that a polar solvent does is to use ion-dipole (or ion-quadrupole) forces to disengage the ions from the lattice sites, solvate them, and disperse them in solution. 

Water, it may be recalled (Chapters 2 and 4), has two modes of solvent action, depending on the nature of the added electrolyte. The water can contact an ionic crystal (e.g., NaCl), detach the ions from the lattice through the operation of ion-dipole (or ion-quadrupole) forces, and convert them to hydrated ions (Chapter 2). 

COEKKICIENTS FOR THE INDUCED DiPOLE-DiPOLE AND DiPOLE-QuADRUPOLE FoRCES... 

The possible relevance of this quadrupole-quadrupole force at colloidal length scales was advanced in references [9,46,47]. As emphasized in reference [9], the natural surface roughness in the nanometer scale of a micrometer-sized spherical particle could conceivably cause a force of this kind. It was also proposed as an explanation of the structures observed experimentally [47] in 2D colloids of nonspherical micrometer particles at a fluid interface. This motivated the theoretical investigation of the anisotropic capillary forces The main difficulty lies in the determination of the capillary charges in terms of given properties of the particles (e.g., wettability and shape). Different simplifications were applied the contact line is approximated by a circle [48-50] or by an expansion in small eccentricity [45] highly elongated shapes are dealt with numerically [51]. 

The range of systems that have been studied by force field methods is extremely varied. Some force fields liave been developed to study just one atomic or molecular sp>ecies under a wider range of conditions. For example, the chlorine model of Rodger, Stone and TUdesley [Rodger et al 1988] can be used to study the solid, liquid and gaseous phases. This is an anisotropic site model, in which the interaction between a pair of sites on two molecules dep>ends not only upon the separation between the sites (as in an isotropic model such as the Lennard-Jones model) but also upon the orientation of the site-site vector with resp>ect to the bond vectors of the two molecules. The model includes an electrostatic component which contciins dipwle-dipole, dipole-quadrupole and quadrupole-quadrupole terms, and the van der Waals contribution is modelled using a Buckingham-like function. 

Forces Molecules are attracted to surfaces as the result of two types of forces dispersion-repulsion forces (also called London or van der Waals forces) such as described by the Lennard-Jones potential for molecule-molecule interactions and electrostatic forces, which exist as the result of a molecule or surface group having a permanent electric dipole or quadrupole moment or net electric charge. 

Dispersion forces are always present and in the absence of any stronger force will determine equihbrium behavior, as with adsorption of molecules with no dipole or quadrupole moment on nonoxidized carbons and silicahte. 

In order to caleulate the force of attraction between the particle and surface. Hays had to estimate the dipole and quadrupole moments on the particle. He did this by assuming that the eharge distribution a 0) around the surface of the particle was given by... 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

While mathematically attractive, this force law is of limited interest physically it represents only the interaction between permanent quadrupoles, and even this with neglect of angles of orientation. However, although the details of the dependence of viscosity upon temperature are affected by the force law used, the general form of the hydrodynamic equation in the Navier-Stokes approximation is not affected. 

Hitherto it has been generally assumed that the repulsive forces between atoms arise from the interaction of the quadrupole (and higher) moments of the atoms, that is, from their departure from spherical symmetry.7... 

Here, disproportionation produces a tight quadrupole A ", 2Na which weakly interacts with the solvent, in contrast to the dipoles A", Na. The gain of entropy resulting from the desolvation of ions becomes a driving force for disproportionation (173). 

The value is derived from a zero-field spectrum recorded at 150 K. A q could not be determined at 4.2 K because the compound is in the limit of slow paramagnetic relaxation and the strong unquenched orbital moment forces the internal field into the direction of an easy axis of magnetization. As a consequence, the quadrupole shift observed in the magnetically split spectra results only from the component of the EFG along the internal field and the orientation of the EFG is not readily known dbabh is a bulky N-coordinating amide... 

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