Polarizability volumes

Polarizability volume (47reo cm ) coulomb squared-(meter squared per joule) 1.112 65 X 10- ... 

Apart from the factor of 4rreo, the polarizability of an atom is determined in this model by the volume. If we had been working in cgs (old-fashioned electromagnetic quantities) rather than SI (modem ones), we would have found a = a and for this reason people speak of the polarizability volume. 

This expression reproduces the experimentally measured ionization efficiency curves surprisingly well, considering the simplicity of the model on which it is based. There is a discontinuity in the function at the maximum (when X = Xmax) but this affects only a small region of the ionization efficiency curve, and satisfactory values of the cross section are still obtained over this region. A great advantage of this method is that it is very simple to apply, depending on only three parameters the molecular polarizability volume, the ionization potential, and the maximum electron impact ionization cross section. These can be measured or calculated values (from the ab initio EM method described above, for example). 

This expression introduces a dependence of ionization efficiency on a, the polarizability volume, a = a/(4jt Q). 

Combining the highest electronegativity (4,0) with a rather small polarizability volume which amounts to not more than 0.5 makes fluorine a unique element. Its incorporation into hydrocarbon frameworks results in different electrostatic effects, which are sometimes rarely predictable. However, the influence of fluorine substituents on the acidity of nearby functional groups such as OH, NH,... 

Solvatochromic data, specifically absorption or transition energies (E s), have been obtained for the dye phenol blue in supercritical fluids as a function of both temperature and pressure. These data will be used to compare the "solvent strength" of these fluids with liquid solvents. He will use the terms "solvent strength" and "Et" synonymously in this paper such that they include the magnitude of the polarizability/volume as well as the dipole moment. The "solvent strength" has been characterized by the spectroscopic solvatochromic parameter, E, for numerous liquid solvents (9 JU, J7,JJ3). 

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. 

At this pressure, the polarizability/volume of SF CO2 is a little less than that of n-hexane, which suggests that there are other molecular interactions between CO2 and phenol blue in addition to dispersion and induction. The likely possibilities include electron donor-acceptor forces and dipole-quadrupole interactions. 

In this equation, Vmc represents the molecular van der Waals volume (in A ) and indicates the cavity size needed in the solvent matrix to accommodate the solute. The polarizability index, tii, is obtained by dividing the polarizability volume by the molecular volume, to give a alternatively size-independent quantity that indicates the ease with which electrons may move throughout the solvent molecule. The solvent HBD... 

Molecular polarizability can also be approximated by simply summing atomic polarizabilities over all the molecule atoms. Moreover, molecular polarizability a expressed as polarizability volume is called polarizability volume and is defined as ... 

Acid-base interactions have been explored as a function of density in SCFs using solvatochromic probes. The basicity of SCF CO2 was found to be relatively constant with respect to density(13L although the polarizability/volume is a linear function of density. The acidity of SCF CHF3 was also observed to be density insensitive, over a range from 4 to 18 mol/L(S). Although it appears that hydrogen-bond interactions become fairly saturated at a relatively low density, further experimental and theoretical work is required to understand this behavior more quantitatively. 

COMMENT. The agreement of the value of n with Table 18.1 is exact, but the polarizability volumes differ by about 8 percent. 

Hosoya266 has discussed implications of graph-theoretical techniques and the Coulson-Longuet-Higgins atom-atom polarizability in an analysis of -electron networks. The internal energy as a state function of the polarizability volume and the diamagnetic susceptibility has been discussed by deVisser.265... 

PI 8.3 The equations relating dipole moment and polarizability volume to the experimental quantities r and p are... 

O2 can be derived from the polarizability volumes tabulated in Lide (2004-2005). Data of the adsorbent properties... 

The fraction a = a/ 47tso) has the dimension (length) and is referred to as the polarizability volume. This is the parameter that is normally listed in reference works. The polarizabilities atoms or monatomic ions in the gas phase are not accurately known, but recommended values for polarizability volumes of neutral alkali metal and halogen atoms and ions are listed in Table 3.4. 

Table 3A. Recommended values for the polarizability volumes a (in 10 m ) of some atoms and monatomic ions in the gas phase [5].

Table 3.4 also contains the polarizability volumes of some common monatomic ions. It is seen that removal of the most loosely held electron in an alkali metal atom leads to a dramatic reduction of the polarizability. Similarly, addition of an electron to a halogen atom to form an anion leads to an increase of the polarizability. Comparing cations and anion, we see that halogen anions have considerably higher polarizabilities than alkali metal cations. 

Recommended values for the polarizability volumes of gaseous atoms have been taken from T. M. MiUer and B. Bederson, Adv. At. Mol. Phys, 1977, 13, 1 polarizabUity volumes for alkali metal cations and halide anions from S. Hati, B. Datta and D. Datta, J. Phys. Chem., 1996,100,... 

It is common to divide the polarizability by 4 7reo to obtain what is called the polarizability volume, which typically has units of A . According to equation 1, if the two vector quantities n and E are not of the same direction, then a must be a tensor. Generally for a molecule one may write the polarizability tensor as (7)... 

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