Polarisability molar

Here, k is a factor which converts to units (kcal/mol in this case where the distances are in A and the polarisabilities in A ). G, and Gj are constants chosen to reproduce the well depths for like-with-like interactions. The atomic polarisability values are obtained from an examination of appropriate molecular experimental data (such as measurements of molar refractivity). 

The polarisability, a, of the molecule is proportional to the refractive index increment dn/dc, and to the relative molar mass of the molecule in question. The full relationship is ... 

Molar conductivity measurements are equally applicable to both solid and liquid electrolytes. In contrast, the measurement of current flowing through an electrochemical cell on a time scale of minutes or hours while the cell is perturbed by a constant dc potential is only of value for solid solvents (Bruce and Vincent, 1987) where convection is absent. Because of the unique aspects of dc polarisation in a solid solvent this topic is treated in some detail in this chapter. Let us begin by considering a cell of the form ... 

The group contributions to the molar polarisation (for isotropic polymers) are given in Table 11.1. Application of Eqs. (11.7) and (11.8) permits the calculation of the dielectric... 

TABLE 11.1 Group contributions to molar dielectric polarisation (P) in isotropic polymers (cmVmol)... 

For non-polar materials the relationship between the molar polarisation Pll/ the dielectric constant e and the molecular polarisability a is known as the molar Clausius-Mosotti relation and reads... 

The relationship between the molar refraction RLL/ the refractive index n and the polarisability a is known as the molar Lorentz-Lorenz relation (1880), which reads... 

Sarsfield reported the only three known examples of uranyl bis(imino-phosphorano)-methanides reported to date.52,53 Treatment of the tris-THF adduct of anhydrous uranyl dichloride with one molar equivalent of 2 resulted in the isolation of dimeric 101 when the recrystallisation was carried out in dichloromethane, but monomeric 102 when recrystallised from THF. Both 101 and 102, when treated with two and one equivalents, respectively, of potassium bis(trimethylsilyl)amide afford 103. Complexes 101-103 all exhibit uranyl-methanide contacts in the solid state and these represent noteable examples of out-of-equatorial-plane uranyl coordination. A DFT study concluded that the methanide centre coordinates to the uranyl centre with an orbital of p-type character by a highly polarised cr-type interaction. 

The total molar polarisation, i.e. that due to 1 gramme-molecule of the compound, is given by the Mosotti-Clausius equation —... 

Since the light scattering method yields the mass-average molar mass, hence a may be written as cNAyJ Mni. Combining Eqs. 5.47 and 5.50 and assuming that the polarisability of the solvent, a0 is negligible, we obtain... 

Orientation of molecules is much too slow to contribute to polarisation at these high frequencies. Then substituting (2.34) in (2.33) gives a quantity that is usually called the molar refraction of the material ... 

It is then a simple matter to calculate the molar refraction of any given compound by adding up the values for all its component bonds. Thus the molar refraction for butan-2-one, CH3-CO-CH2-CH3, would be calculated as 20.66 cm3. The observed value is 20.79 cm3 which is in line with the 1% agreement that is usually obtained. The method works well because it inherently takes into account the different polarisabilities of bonding electrons. In the case... 

In contrast to molar polarisation calculated from optical refractivities, that calculated from relative permittivities observed at lower frequencies is by no means always independent of temperature. Actually, materials tend to fall into one of two classes. Those in one class show a relatively constant molar polarisation in accord with the simple Clausius-Mosotti relation, whilst the members of the other class, which contains materials with high relative permittivities, show a molar polarisation that decreases with increase in temperature. Debye recognised that permanent molecular dipole moments were responsible for the anomalous behaviour. From theories of chemical bonding we know that certain molecules which combine atoms of different electronegativity are partially ionic and consequently have a permanent dipole moment. Thus chlorine is highly electronegative and the carbon-chlorine... 

The order of magnitude of such a dipole will be equal to the product of the charge on an electron (1.6 x 10 19 C) and a typical bond length (10 10 m) giving a value of 10" 29 Cm. The old electrostatic Debye unit of molecular dipoles was in fact equivalent to 3.335 x 10 30 Cm. Orientation of such molecular dipoles will clearly produce an extra contribution to the molar polarisation in addition to dipoles induced by the applied field, and it is not unreasonable to expect that the equilibrium degree of orientation in a given field will depend on temperature. 

The complete expression (Debye equation) for the molar polarisation is then ... 

This formula provides a simple way of determining molecular dipole moments from experimental measurements. The method is to plot molar polarisation or effective polarisability against 1/7) as in Fig. 2.8 the slope of... 

The situation is much more complicated in solids because the intermolecular effects can no longer be ignored, i.e. the approximation EM = 0 inherent in the simple formula for the local field (2.29) is not generally true. Consequently, although we can predict the molecular dipole moment from known group moments, it is not possible to calculate the molar polarisation and thereby the relative permittivity, without further elaboration of the dielectric model. In the case of a polymer there are further complications which arise from the flexibility of the long chains. 

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