Polarisation permanent

Our discussion of elecfronic effects has concentrated so far on permanent features of the cliarge distribution. Electrostatic interactions also arise from changes in the charge distribution of a molecule or atom caused by an external field, a process called polarisation. The primary effect of the external electric field (which in our case will be caused by neighbouring molecules) is to induce a dipole in the molecule. The magnitude of the induced dipole moment ginj is proportional to the electric field E, with the constant of proportionahty being the polarisability a ... 

The quantum mechanics treatment of diamagnetism has not been published. It seems probable, however, that Larmor s theorem will be retained essentially, in view of the marked similarity between the results of the quantum mechanics and those of the classical theory in related problems, such as the polarisation due to permanent electric dipoles and the paramagnetic susceptibility. f Thus we are led to use equation (30), introducing for rK2 the quantum mechanics value... 

Eo and E (Afi(i)) are respectively the electric fields generated by the permanent and induced multipoles moments. a(i) represents the polarisability tensor and Afi(i) is the induced dipole at a center i. This computation is performed iteratively, as Epoi generally converges in 5-6 iterations. It is important to note that in order to avoid problems at the short-range, the so-called polarization catastrophe, it is necessary to reduce the polarization energy when two centers are at close contact distance. In SIBFA, the electric fields equations are dressed by a Gaussian function reducing their value to avoid such problems. 

All inductive effects are permanent polarisations in the ground state of a molecule, and are therefore manifested in its physical properties, for example, its dipole moment. 

Mesomeric, like inductive, effects are permanent polarisations in the ground state of a molecule, and are therefore manifested in the physical properties of the compounds in which they occur. The essential difference between inductive and mesomeric effects is that while inductive effects can operate in both saturated and unsaturated compounds, mesomeric effects can operate only in unsaturated, especially in conjugated, compounds. The former involve the electrons in a bonds, the latter those in tt bonds and orbitals. Inductive effects are transmitted over only quite short distances in saturated chains before dying away, whereas mesomeric effects may be transmitted from one end to the other of quite large molecules provided that conjugation (i.e. delocalised tt orbitals) is present, through which they can proceed. 

The spectmm from an undulator is very different, and numerous peaks result from interference effects within the undulator. When the electron acceleration is confined to the orbit plane and the emission angle very low, the radiation is strongly elliptically polarised and, in the orbit plane itself, it is to within a few per cent linearly polarised. Use of a sequence of permanent magnets with magnetisation arranged in a spiral sequence enables circularly polarised radiation to be extracted from such a helical undulator and this radiation is particularly important for magnetic studies. 

Fro. IX-1.—Values of the ratio of polarisation P to field strength E for hydrogen chloride gas, as a function of the reciprocal of the absolute temperature. The slope of the line is a measure of the permanent electric dipole moment of the molecules, and the intercept of the line is a measure of the temperature-independent polarizability of the molecules. 

Pyroelectric detectors depend on the use of a thin slice of ferroelectric material (deuter-ated triglycine sulphate (DTGS), Figure 3.14, is the standard example) - in which the molecules of the organic crystal are naturally aligned with a permanent electric dipole. The thin slab is cut and arranged such that the direction of spontaneous polarisation is normal to the large faces. Typically one surface of the crystal is blackened to enhance thermal absorption, and the entire assembly has very low thermal mass. 

If the metal ion to which a ligand is co-ordinated is in a non-zero oxidation state, it will exert an electrostatic effect upon the bonding electrons of the ligand. This will result in the induction of a net permanent dipole in the ligand, with any associated chemical and physical effects. Even zero-oxidation state metal centres may induce a polarisation in the ligand through electronegativity or induced dipole-dipole effects. 

A highly anisotropic polarisability is required in order to enhance intermolecular dispersive interactions. This is favoured by the presence of easily polarisable groups and permanent dipoles. 

Most of the reference electrodes embedded in concrete are used for control of cathodic protection (CP) systems. Potential stability is then less important, compared to corrosion state monitoring. Control of CP systems requires only short-term stability, maximum 24 hours. Corrosion rate measurement, like linear polarisation resistance (LPR) measurements, also requires short-term reference electrode stability. However, regardless of application, a reference electrode which is to be permanently embedded in the test solution, e.g. concrete, must have a long life when exposed to this environment. 

Debye interaction occurs when a permanent dipole induces a dipole in a polarisable atom or molecule. The induced dipole is oriented in such a way that attraction occurs. 

The first term of (3.289) represents a translational Stark effect. A molecule with a permanent dipole moment experiences a moving magnetic field as an electric field and hence shows an interaction the term could equally well be interpreted as a Zeeman effect. The second term represents the nuclear rotation and vibration Zeeman interactions we shall deal with this more fully below. The fourth term gives the interaction of the field with the orbital motion of the electrons and its small polarisation correction. The other terms are probably not important but are retained to preserve the gauge invariance of the Hamiltonian. For an ionic species (q 0) we have the additional translational term... 

Molecular polarisability is the result of two mechanisms (a) distortional polarisation and (b) orientation polarisation. Distortional polarisation is the result of the change of electric charge distribution in a molecule due to an applied electric field, thereby inducing an electric dipole. This distortional polarisation is coined ad. Permanent dipoles are also present in the absence of an electric field. At the application of an electric field they will orient more or less in the direction of the electric field, resulting in orientation polarisation. However, the permanent dipoles will not completely align with the electric field due to thermal agitation. It appears that the contribution of molecular polarisability from rotation is approximately equal to p2/(3kT). Accordingly, the total molecular polarisability is... 

The dielectric constants of an aligned nematic phase are dependent upon both the temperature and the frequency of the applied field at temperatures below the clearing point. The dielectric permitivity, j, measured parallel to all three axes above the clearing point in the isotropic liquid is the same. Therefore, the dielectric anisotropy of the same compound in the liquid state is zero, see Figure 2.10. The sign and magnitude of the dielectric constants and, therefore, the dielectric anisotropy are dependent upon the anisotropy of the induced molecular polarisability, Aa, as well as the anisotropy and direction of the resultant permanent molecular polarisation determined by permanent dipole moments. 

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... 

First consider the application of an external electric field to an assembly of rigid molecular dipoles, i.e. let there be no deformational polarisation. If the permanent moment of each dipole is /i, then the potential energy u of a dipole in the applied field will be ... 

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