Polarisation dipole

In the dielectric of a condenser the dipole polarisation would increase the polarisation charge and such materials would have a higher dielectric constant than materials whose dielectric constant was only a function of electronic polarisation. 

There is an important practical distinction between electronic and dipole polarisation whereas the former involves only movement of electrons the latter entails movement of part of or even the whole of the molecule. Molecular movements take a finite time and complete orientation as induced by an alternating current may or may not be possible depending on the frequency of the change of direction of the electric field. Thus at zero frequency the dielectric constant will be at a maximum and this will remain approximately constant until the dipole orientation time is of the same order as the reciprocal of the frequency. Dipole movement will now be limited and the dipole polarisation effect and the dielectric constant will be reduced. As the frequency further increases, the dipole polarisation effect will tend to zero and the dielectric constant will tend to be dependent only on the electronic polarisation Figure 6.3). Where there are two dipole species differing in ease of orientation there will be two points of inflection in the dielectric constant-frequency curve. 

When dipoles are directly attached to the chain their movement will obviously depend on the ability of chain segments to move. Thus the dipole polarisation effect will be much less below the glass transition temperature, than above it Figure 6.4). For this reason unplasticised PVC, poly(ethylene terephthalate) and the bis-phenol A polycarbonates are better high-frequency insulators at room temperature, which is below the glass temperature of each of these polymers, than would be expected in polymers of similar polarity but with the polar groups in the side chains. 

In the case of polymer molecules where the dipoles are not directly attached to the main chain, segmental movement of the chain is not essential for dipole polarisation and dipole movement is possible at temperatures below the glass transition temperature. Such materials are less effective as electrical insulators at temperatures in the glassy range. With many of these polymers, e.g., poly(methyl methacrylate), there are two or more maxima in the power factor-temperature curve for a given frequency. The presence of two such maxima is due to the different orientation times of the dipoles with and without associated segmental motion of the main chain. 

With polar molecules the value of the dielectric constant is additionally dependent on dipole polarisation and commonly has values between 3.0 and 7.0. The extent of dipole polarisation will depend on frequency, an increase in frequency eventually leading to a reduction in dielectric constant. Power factor-frequency curves will go through a maximum. 

The dielectric properties of polar materials will depend on whether or not the dipoles are attached to the main chain. When they are, dipole polarisation will depend on segmental mobility and is thus low at temperatures below the glass transition temperatures. Such polymers are therefore better insulators below the glass temperature than above it. 

Where dipole polarisation occurs it may be shown that... 

Because of a small dipole polarisation effect the dielectric constant is somewhat higher than that for PTFE and the polyolefins but lower than those of polar polymers such as the phenolic resins. The dielectric constant is almost... 

The dipole polarisability calculated in the present basis has components 0 = 62.38 and ax = 34.52, giving a mean value of a = 43.81 and Aa = 27.87, all in units of e2afiE 1 1.648778 x 10 41 C2m2J-1. These values are all close to the CHF results reported in ref (9) where correlation effects were estimated and found to lower ay by 0.9 and raise ax by 1.6 e2a2E 1, respectively, and zero-point vibrational effects were predicted to give increases in both Aa and a by only 0.1 e2a%E 1. The present value of a is within the spread of values obtained from measurement of the refractive index of the gas(10) (43.4 e2alEJ 1) and the liquid(ll) (46.6 e2a%EZ1) and the radio-frequency dielectric constant of the vapour(12) (47.2 e2a E 1), all as quoted in ref. (9). Some further remarks on polarisability values are made in ref. (8). 

Energies 2.3. Oscillator strengths, dipole polarisabilities and nuclear shielding 208... 

Table 2 Oscillator strengths and dipole polarisabilities of a hydrogen atom confined in a spherical box of radius R (the superscripts (asy) and (num) denote, respectively, asymptotic analytical and precise numerical values)...

The dipole polarisability a of a hydrogen-like atom confined in its Is ground state is... 

Table 12 Comparison of perturbation and precise numerical electric dipole polarisabilities for a hydrogen atom confined at the centre of a spherical box of radius K.The numbers in parentheses indicate the power of 10...

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