Polarisability orientational

We now consider the radiative decay of the excited ensemble of atoms. The angular distribution and polarisation of the emitted photons can be conveniently described in terms of the Stokes parameters I, t]i, t]2, and (Born and Wolf, 1970). The emitted photons can be observed in the direction n making polar angles 6 and azimuthal angles with respect to the collision frame (fig. 8.1). It is convenient to choose the coordinate system in which the direction of observation n of the radiation is chosen as the z axis. The polarisation vector of the photons is restricted to the plane perpendicular to n by the two unit vectors i = (0 + 90°, 0) and 2 = (0,light emitted in the direction n and I y) the intensity transmitted by a linear polariser oriented at an angle y with respect to the i-axis, then the Stokes parameters are defined by... 

In the infra-red region, dichroic measurements are conveniently made on double beam instruments, the sample and polariser each being placed in the usual sample beam, and the spectra recorded with the polariser orientation successively parallel and perpendicular to the sample reference axis. If wire grid polarisers are employed, errors due to polariser... 

Any system in which the spatial distribution of angular momentum or axial vectors is not isotropic is said to be polarised. Oriented distributions are ones in which the odd moments are non-zero aligned distributions are ones in which the even moments... 

Reference solvent 1,4-dioxane Monte-Carlo method from PCM surface from PCM volume mean of b and c induction polarisation orientation polarisation... 

For isolated atoms, the polarisability is isotropic - it does not depend on the orientation of fhe atom with respect to the applied field, and the induced dipole is in the direction of the electric field, as in Equation (4.51). However, the polarisability of a molecule is often anisotropic. This means that the orientation of the induced dipole is not necessarily in the same direction as the electric field. The polarisability of a molecule is often modelled as a collection of isotropically polarisable atoms. A small molecule may alternatively be modelled as a single isotropic polarisable centre. 

The halogen substituents ( — 7 +M) owe their o p-orientating effect, achieved in spite of the deactivation, to polarisability by the conjugative process. The strength of the inductive deactivation is seen in the sequence of the two ratios quoted. 

Fig. 8. Principle of the magnetooptical read-out of domain patterns by the polar Kerr effect. The polarisation plane of the incoming laser beam is rotated clock- or counterclockwise according to the orientation (up or down) of the magnetic moments.

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. 

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. 

Pq the dipole or orientation polarisation P itself is defined by the Clausius-Mosotti Equation... 

An interesting point concerns polarisation effects in the Raman spectra, which are commonly observed in low-dimensional materials. Since CNTs are onedimensional (ID) materials, the use of light polarised parallel or perpendicular to the tube axis will give information about the low dimensionality of the CNTs. The availability of purified samples of aligned CNTs would allow us to obtain the symmetry of a mode directly from the measured Raman intensity by changing the experimental geometry, such as the polarisation of the light and the sample orientation, as discussed in this chapter. 

Fig. 3. Raman intensities as a function of the sample orientation for the (10, 10) armchair CNT. As shown on the right, 0 and 62 are angles of the CNT axis from the z axis to the x axis and the y axis, respectively. 63 is the angle of the CNT axis around the z axis from the x axis to the y axis. The left and right hand figures correspond to the VV and VH polarisations [12].

Another example of the coupling between microscopic and macroscopic properties is the flexo-electric effect in liquid crystals [33] which was first predicted theoretically by Meyer [34] and later observed in MBBA [35], Here orientational deformations of the director give rise to spontaneous polarisation. In nematic materials, the induced polarisation is given by... 

The factors Kn are elastic constants for the nematic phase and Icb is the Boltzmann constant. Therefore a combination of molecular electronic structure, orientational order and continuum elasticity are all involved in determining the flexoelectric polarisation. Polarisation can also be produced in the presence of an average gradient in the density of quadrupoles. This is... 

In EMIRS and SNIFTIRS measurements the "inactive" s-polarlsed radiation is prevented from reaching the detector and the relative intensities of the vibrational bands observed in the spectra from the remaining p-polarised radiation are used to deduce the orientation of adsorbed molecules. It should be pointed out, however, that vibrational coupling to adsorbate/adsorbent charge transfer (11) and also w electrochemically activated Stark effect (7,12,13) can lead to apparent violations of the surface selection rule which can invalidate simple deductions of orientation. 

Combined dipole moment and Kerr effect studies are regularly used by Russian workers for the conformational analysis of phosphorus heterocyc1es.135 230 In a study of the interaction of phenol with phosphoryl groups the Kerr effect was used to evaluate not only the extent of hydrogen bonding but also the influence of changes in polarity and polarisation upon stability constants.231 In a similar study the orientation of the aryl groups of 1,3,5-triazaphosphorines (82) were shown to be less coplanar than biphenyl in the gas phase. 2 3 2... 

In applying RAIRS to CO adsorption, the contribution from CO molecules in the gas phase to the absorption spectrum at CO pressures above 10-3 mbar completely obscures the weak absorption signal of surface adsorbed CO. Beitel et al. found it possible to subtract out the gas phase absorption by coding the surface absorption signal by means of the polarization modulation (PM) technique applied to a conventional RAIRS spectrometer, p-polarised light produces a net surface electric field which can interact with adsorbed molecules, whereas both polarization states are equally sensitive to gas phase absorption because gas phase molecules are randomly oriented. By electronic filtering a differential spectrum is computed which does not show contributions from the gas phase and which has much higher surface sensitivity than a conventional RAIRS setup. 

Addition is initiated by the positively polarised end (the less electronegative halogen atom) of the unsymmetrical molecule, and a cyclic halonium ion intermediate probably results. Addition of I—Cl is particularly stereoselective (ANTI) because of the ease of formation (and relative stability compared with carbocations) of cyclic iodonium ions. With an unsymmetrical alkene, e.g. 2-methylpropene (32), the more heavily alkyl-substituted carbon will be the more carbocationic (i.e. the less bonded to Br in 33), and will therefore be attacked preferentially by the residual nucleophile, Cle. The overall orientation of addition will thus be Markownikov to yield (34) ... 

Litvinenko KL, Webber NM, Meech SR (2001) An ultrafast polarisation spectroscopy study of internal conversion and orientational relaxation of the chromophore of the green fluorescent protein. Chem Phys Lett 346 47-53... 

Thermoplastic polymer macromolecules usually tend to become oriented (molecular chain axis aligns along the extrusion direction) upon extrusion or injection moulding. This can have implications on the mechanical and physical properties of the polymer. By orienting the sample with respect to the coordinate system of the instrument and analysing the sample with polarised Raman (or infrared) light, we are able to get information on the preferred orientation of the polymer chains (see, for example, Chapter 8). Many polymers may also exist in either an amorphous or crystalline form (degree of crystallinity usually below 50%, which is a consequence of their thermal and stress history), see, for example, Chapter 7. 

The surface selection rule operates in addition to the normal IR selection rules in determining which vibrational modes are observed. As a result of the SSR the relative intensities of the fundamental IR adsorption bands of an adsorbed species can be used to give information on the orientation of the species with respect to the surface. Both S- and P-polarised light interact equally with the randomly oriented solution species. 

Dust particles appear to become oriented in interstellar magnetic fields, aligning themselves with the field lines to produce preferential absorption of light polarised... 

---