Polarized ion model

According to the polarized-ion model, however, the nonideality is not sufficiently described by the coulombic interactions alone, and the chemical state... 

The irreversible dehydration process indicates that the underlying dielectric continuum approach used in the anisotropic primitive model does not hold. Further numerical simulations are presently imdertaken at the atomic scale in the frame of the polarized ion model (so-called shell model ) in order to give a better description of Tobennorite dehydration/rehydration and cohesive property of cement [24]. 

The polarized ion model considers the fact that cations can be polarized by anions, whereupon the polarization ability rises with increasing cation size, resulting in angular structures. 

A study of debrominations of vtc-dibromides promoted by diaryl tellurides and din-hexyl telluride has established several key features of the elimination process the highly stereoselective reactions of e/7f/tro-dibromides are much more rapid than for fhreo-dibromides, to form trans- and cw-alkenes, respectively the reaction is accelerated in a more polar solvent, and by electron-donating substituents on the diaryl telluride or carbocation stabilizing substituents on the carbons bearing bromine. Alternative mechanistic interpretations of the reaction, which is of first-order dependence on both telluride and vtc-dibromide, have been considered. These have included involvement of TeAr2 in nucleophilic attack on carbon (with displacement of Br and formation of a telluronium intermediate), nucleophilic attack on bromine (concerted E2- k debromination) and abstraction of Br+ from an intermediate carbocation. These alternatives have been discounted in favour of a bromonium ion model (Scheme 9) in which the role of TeArs is to abstract Br+ in competition with reversal of the preequilibrium bromonium ion formation. The insensitivity of reaction rate to added LiBr suggests that the bromonium ion is tightly paired with Br. ... 

A new theory of electrolyte solutions is described. This theory is based on a Debye-Hiickel model and modified to allow for the mutual polarization of ions. From a general solution of the linearized Poisson-Boltzmann equation, an expression is derived for the activity coefficient of a central polarized ion in an ionic atmosphere of non-spherical symmetry that reduces to the Debye-Hiickel limiting laws at infinite dilution. A method for the simultaneous charging of an ion and its ionic cloud is developed to allow for ionic polarization. Comparison of the calculated activity coefficients with experimental values shows that the characteristic shapes of the log y vs. concentration curves are well represented by the theory up to moderately high concentrations. Some consequences in relation to the structure of electrolyte solutions are discussed. 

The ion-pair model stipulates that formation of an ion-pai. occurs in the aqueous mobile phase (16, 18, 20). The retention time is governed by the extraction coefficient of the ion-pair. A longer alkyl chain on the pairing agent simply makes a less polar ion-pair, with a resulting higher extraction coefficient, and the retention of the ion-pair increases as a result of its greater affinity for the stationary phase. 

In this scheme a full positive charge of -FI is assumed. In fact, the polarity of the chemical bonds will be lower. The same is true, however, for the classical carbenium ion model. It was shown by Kazansky 316) that surfece protons in zeolites are, in reality, O—H bonds with a finite dipole moment likewise the carbenium ions assumed in isomerization reactions, etc., in acid zeolites are merely transition states of alkoxy groups with a finite dipole moment of the O—C bond. In the same manner the ions in the above reaction scheme should be read as limiting structures of a complex with nonnegligible polarity. 

An electrostatic hydration model, previously developed for ions of the noble gas structure, has been applied to the tervalent lanthanide and actinide ions. For lanthanides the application of a single primary hydration number resulted in a satisfactory fit of the model to the experimentally determined free energy and enthalpy data. The atomization enthalpies of lanthanide trihalide molecules have been calculated in terms of a covalent model of a polarized ion. Comparison with values obtained from a hard sphere modeP showed that a satisfactory description of the bonding in these molecules must ultimately be formulated from the covalent perspective. 

How Polar Bonds and Geometry Affect Molecular Polarity Ions, Polar Molecules, and Physical Properties MiniLab 9.2 Modeling Molecules ChemLab What colors are in your candy ... 

Ii3/2 multiplets. Frequencies and polarization vectors of phonons in the LiYp4 crystal were obtained at 8000 points in the irreducible part of the Brillouin zone using the rigid ion model of lattice dynamics derived on the basis of neutron scattering data. Matrix elements of electronic operators Vds) were calculated with the wave functions obtained from the crystal-field calculation. The inverse lifetimes of the crystal-field sublevels determine the widths of corresponding absorption lines. 

A subsequent description by Bockris and associates drew attention to further complexities as shown in Figure 15. The metal surface now is covered by combinations of oriented structured water dipoles, specifically adsorbed anions, followed by secondary water dipoles along with the hydrated cation structures. This model serves to bring attention to the dynamic situation in which changes in potential involve sequential as well as simultaneous responses of molecular and atomic systems at and near an electrode surface. Changes in potential distribution involve interactions extending from atom polarizability, through dipole orientation, to ion movements. The electrical field effects are complex in this ideal polarized electrode model. 

Several models have been proposed to account for the overall effect of these three forces on the motion of the ion, and some of the classical models are discussed here in brief, and their usefulness in predicting the mobility of polyatomic ions in different drift gases is examined. Two simple models are considered first the rigid sphere model and the polarization limit model. Next, a more refined yet relatively simple-to-use model is described in which a 12,4 hard-core potential represents the ion-neutral interaction. The more complex three-temperature model is not discussed because ions in linear IMS are traditionally regarded as thermalized. This is the one-temperature assumption, in which ion temperature is assumed to be equal to the temperature of the drift gas. 

According to the polarization limit model, the polarization is added to the interaction between the ion and the drift gas molecule. If the neutral molecule does not have a permanent dipole or quadrupole moment and if there are no ion-neutral repulsive forces, then the interaction between the ion and the neutral molecule is due solely to the ion-induced dipole interaction. This interaction is a function of the polarizability of the neutral molecule a. The interaction potential varies as a function of the distance r between the ion and the neutral molecule (this r is not to be confused with from Equations 10.10 and 10.11), according to Equation 10.18 ... 

The number 13.853 is obtained for Kp i when is in units of A, m and M are in daltons, and K has units of square centimeters per volt per second at 273 K and 760 torr. When the mass of the ion is much larger than the mass of the neutral molecule, 1/m in the reduced mass term is negligible compared to 1/Af, so that the mobility is essentially independent of the ion mass, and the redueed mass simply becomes the mass of the drift gas. This contradicts physical intuition as well as experimental observations. In summary, the polarization limit model provides a poor description of several empirical observations in IMS. 

In the rigid sphere model, the sum of the radii of the ion and the neutral molecule d will increase slightly as the chain length and ion mass in the homologous series increase. In the polarization limit model, the ion size is totally neglected, whereas in the hard-core potential model, (the minimum in the interaction potential) depends on the ion mass, as shown in Equation 10.22 ... 

FIGURE10.3 The measured inverse mobility of protonated acetyl compounds in air at 200°C as a function of ion mass. Curve a was calculated according to the rigid sphere model with Tq= 2.60 A curve b according to the polarization limit model curve c according to the hard-core model with a = 0.2, z = 0 A/amu, and Tq = 2.40 A curve d with a = 0.2, z = 0.0013 A/amu, and Tq= 2.20 A. (From Berant and Karpas, Mass-mobility correlation of ions in view of new mobility data, /. Am. Chem. Soc. 1989, 111, 3819-3824. With permission.)... 

The motion of ions in a buffer gas is governed by diffusive forces, the external electric field and the electrostatic interactions between the ions and neutral gas molecules. Ion-dipole or ion-quadrupole interactions, as well as ion-induced dipole interactions, can lead to attractive forces that will slow the ion movement, mainly due to clustering effects. The interaction potential can be calculated according to different theories, and three such approaches—the hard-sphere model, the polarization limit model, and the 12,4 hard-core potential model— were introduced here. Under... 

The above potential is based on a rigid-ion-model (RIM), as no effect of atomic polarization is taken into account. A shell model (SM) was also developed, which considers a split core-shell structure for polarizable O atoms. As usual [23], core and shell are coupled by an elastic spring of force constant k, and are characterized by different electric charges zqc and ZQs- In addition to k, and zqs, also the core-shell displacement, is to be optimized, and contributes three positional parameters (unless reduced by symmetry) for eaeh O atom in the asymmetric unit. When an O atom is involved in the two-body interaction, the repulsive and, possibly, dispersive energy is eomputed by reference to the 0 shell position. All other atoms and interactions are treated as for the RIM case. 

Implicit solvation models developed for condensed phases represent the solvent by a continuous electric field, and are based on the Poisson equation, which is valid when a surrounding dielectric medium responds linearly to the charge distribution of the solute. The Poisson equation is actually a special case of the Poisson-Boltzmann (PB) equation PB electrostatics applies when electrolytes are present in solution, while the Poisson equation applies when no ions are present. Solving the Poisson equation for an arbitrary equation requires numerical methods, and many researchers have developed an alternative way to approximate the Poisson equation that can be solved analytically, known as the Generalized Born (GB) approach. The most common implicit models used for small molecules are the Conductor-like Screening Model (COSMO) [96,97], the Dielectric Polarized Continuum Model (DPCM) [98], the Conductor-like modification to the Polarized Continuum Model (CPCM) [99], the Integral Equation Formalism implementation of PCM (lEF-PCM) [100] PB models and the GB SMx models of Cramer and Truhlar [52,57,101,102]. The newest Miimesota solvation models are the SMD (universal Solvation Model based on solute electron Density [57]) and the SMLVE method, which combines the surface and volume polarization for electrostatic interactions model (SVPE) [103-105] with semiempirical terms that account for local electrostatics [106]. Further details on these methods can be found in Chapter 11 of reference 52. 

We have seen that the electric dipole moments of the gaseous alkali metal halides estimated from the spherical ion model are significantly larger than the experimental values. The assumption that the ions remain spherical as they are brought close to each other is, in fact, an unreasonable one particularly for the anions which are easily polarized. 

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