Polarizable molecule

As an exercise, it is not difficult to show that the interaction of a polarizable molecule with a charge q is... 

Derive Eq. VI-12 for the interaction between a polarizable molecule and a charge. 

In the second type of interaction contributing to van der Waals forces, a molecule with a permanent dipole moment polarizes a neighboring non-polar molecule. The two molecules then align with each other. To calculate the van der Waals interaction between the two molecules, let us first assume that the first molecule has a permanent dipole with a moment u and is separated from a polarizable molecule (dielectric constant ) by a distance r and oriented at some angle 0 to the axis of separation. The dipole is also oriented at some angle from the axis defining the separation between the two molecules. Overall, the picture would be very similar to Fig. 6 used for dipole-dipole interaction except that the interaction is induced as opposed to permanent. 

The polarizability of one molecule and the magnitude of the dipole moment of the other are the major factors that determine the strength of the interaction. The larger the dipole moment (//,) of the polar molecule and the higher the polarizability of the other molecule, the greater the strength of the interaction. Mathematically, the energy of the interaction of a dipole with a polarizable molecule can be expressed as... 

The chemical behavior of ions, ion pairs, and polarizable molecules partakes of the same indistinctness as the definitions of these species. Any attempt to make a complete catalog of the reactions of ions will almost certainly include borderline reactions whose intermediates are in fact ion-pairs or even covalent molecules. For many purposes the identification of a reaction as carbonium ion-like, or what the Germans would call Krypto-ionenreaktion, is as useful as the certain knowledge that the intermediate is actually a carbonium ion. Many of the ionic reaction mechanisms in the literature do not represent actual free ions and were not so intended by their authors. The ionic representation is often merely a convenient simplification if it is an oversimplification it is one that is easily rectified when the pertinent data become available. The value of such approximate mechanisms is that... 

The exciting radiation, usually laser light, may be of any wavelength. Interaction is not by absorption and only requires the presence of polarizable molecules. The oscillating electric field of the incident radiation E = E0 cos 27xut induces a dipole moment... 

For molecules having similar structures and dipole moments the more polarizable molecules exhibit the larger effect. 

The fluctuations in the orientation of anisotropically polarizable molecules in liquids also cause frequency broadening of the scattered light, as investigated for CSj in CCI4 239). CS is a highly polarizable molecule with very different polarizabilities along and perpendicular to the internuclear axis. CCU on the other hand, is a poor scatterer because it is an isotropic molecule. Thus, if CSj is mixed with CCI4, the CSj molecules can be studied in a new environment. 

Electrophiles are electron-deficient, electronseeking reagents, and typically have a positive charge (cations) or are polarizable molecules that can develop an electron-deficient centre. 

Other detection modes employed in capillary electromigration techniques include chemiluminescence [69-71], Raman spectroscopy [72,73], refractive index [74,75], photothermal absorbance [76,77], and radioisotope detection [78]. Some of these detection modes have found limited use due to their high specificity, which restricts the area of application and the analytes that can be detected, such as radioisotope and Raman-based detection that are specific for radionuclides and polarizable molecules, respectively. On the other hand, the limited use of more universal detection modes, such as refractive index, is either due to the complexity of coupling them to capillary electromigration techniques or to the possibility of detecting the analytes of interest with comparable sensitivity by one of the less problematic detection modes described above. 

Polar interactions between molecules arise from permanent or Induced dipoles existing in the molecules and do not result from permanent charges as in the case of Ionic interactions. Examples of polar substances having permanent dipoles would be alcohols, ketones, aldehydes etc. Examples of polarizable substances would be aromatic hydrocarbons such as benzene or toluene. It is considered that, when a molecule carrying a permanent dipole comes Into close proximity to a polarizable molecule, the field from the molecule with the permanent dipole induces a dipole in the polarizable molecule and thus electrical interaction can occur. It follows that to selectively retain a polar solute, then the stationary phase must also be polar and contain, perhaps, hydroxyl groups. If the solutes to be separated are strongly polar, then perhaps a polarizable substance such as an aromatic hydrocarbon could be employed as the stationary phase. However, to maintain strong polar interactions with the stationary phase (as opposed to the mobile phase) the mobile phase must be relatively non-polar or dispersive in nature. 

The electric field at a pure metal surface is the origin of the work function Co of escaping electrons. The potential which must be overcome is at the same time a measure of the electron affinity of the metal surface. If adsorption of polarizable molecules occurs on the metal surface, J will be changed by an amount A4>. For a sufficient electronic polarizability of the adsorbed molecule, is negative if the electron affinity of the metal surface predominates so that electrons are shifted toward the metal surface. is positive if the electron affinity of the foreign molecule predominates, in which case metal electrons are shifted in the direction of the adsorbed molecule. 

Dispersion Interactions. Last but not least in the range of solute-solvent electrostatic interactions come the dispersion forces which depend on the polarizabilities of the molecules. Any atom or molecule—non-polar or polar—has a small fluctuating dipole moment as the electrons move around the nuclei. These instantaneous dipoles induce dipole moments in all other polarizable molecules, so that the interaction energy is proportional to the product of the average polarizabilities aM and as of the solute and solvent molecules... 

The strength of the London interaction depends on the polarizability, a (alpha), the ease with which the electron cloud can be distorted. This dependence is reasonable, because the nuclei in highly polarizable molecules have only weak control over the surrounding electrons, so there can be big fluctuations in electron density and hence large instantaneous partial charges. It turns out that the potential energy of the London interaction varies as the sixth power of the separation of two molecules ... 

The high equilibrium selectivity for normal paraffins relative to aromatics observed for H-ZSM-5 and H-ZSM-11, so contrary to that reported for the lower silica/alumina ratio zeolites, may in part be due to the much higher silica/alumina ratio of these relatively hydrophobic zeolites, resulting in reduced polarity and ability to interact with polarizable molecules. However, other zeolites of comparable silica/alumina ratio, such as dealuminized H-morde-nite, exhibited no such enhanced preference for n-paraffins ] ) (see Table II). Clearly, silica/alumina ratio alone is insufficient to account for these differences. The structure of these zeolites, therefore, must play some role in the observed selectivity. 

The structure/property relationships that govern third-order NLO polarization are not well understood. Like second-order effects, third-order effects seem to scale with the linear polarizability. As a result, most research to date has been on highly polarizable molecules and materials such as polyacetylene, polythiophene and various semiconductors. To optimize third- order NLO response, a quartic, anharmonic term must be introduced into the electronic potential of the material. However, an understanding of the relationship between chemical structure and quartic anharmonicity must also be developed. Tutorials by P. Prasad and D. Eaton discuss some of the issues relating to third-order NLO materials. 

The work described in the previous section was essentially concerned with the physical rather than chemical adsorption of some highly polarizable molecules on zeolites. With pyridine, such information can sometimes be obtained as easily using infrared spectroscopy. However, transmission IR spectroscopy cannot so easily be used to study chemisorption on oxides if it is essential to obtain low frequency spectral data (e.g., adsorbent-adsorbate stretching modes) because of the opacity of most oxides over much of the low frequency spectral region. Recent work has shown that the Raman technique can be extremely useful in this context (4). 

The E s of the nonpolar solvents, CF3CI and C2H4, become equal to tnat of n-hexane at a pressure in the range of 1-2 kilobar. Notice that the Hildebrand solubility parameters of these three solvents are roughly equivalent at this condition of constant E. The same result is also observed for the polarizabilities/ volume of these solvents. Again, the molar densities of these supercritical fluids are considerably higher than that of n-hexane at this equivalence point in solvent strength, since the polarizabilities/molecule are lower. 

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