Electric vector

On metals in particular, the dependence of the radiation absorption by surface species on the orientation of the electrical vector can be fiilly exploited by using one of the several polarization techniques developed over the past few decades [27, 28, 29 and 30], The idea behind all those approaches is to acquire the p-to-s polarized light intensity ratio during each single IR interferometer scan since the adsorbate only absorbs the p-polarized component, that spectral ratio provides absorbance infonnation for the surface species exclusively. Polarization-modulation mediods provide the added advantage of being able to discriminate between the signals due to adsorbates and those from gas or liquid molecules. Thanks to this, RAIRS data on species chemisorbed on metals have been successfidly acquired in situ under catalytic conditions [31], and even in electrochemical cells [32]. 

The transition probability R is related to selection mles in spectroscopy it is zero for a forbidden transition and non-zero for an allowed transition. By forbidden or allowed we shall mostly be referring to electric dipole selection mles (i.e. to transitions occurring through interaction with the electric vector of the radiation). 

When the vector components are not in phase with each other, the projection of the tip of the electric vector onto a plane perpendicular to the beam propagation direction traces out an ellipse, as shown in Figure 2b. 

The handedness (righthanded rotation of the electric vector describes clockwise rotation when looking into the beam)... 

Consider an absorption band in the infra-red spectrum associated with a vibration where the transition dipole moment n for a typical unit of structure makes an angle p with the electric vector E. The absorption of infra-red radiation A is given by... 

For a uniaxially oriented sample, with the electric vector parallel to the symmetry axis (parallel dichroism), the absorption A ( will be given by... 

It may readily be shown that for the electric vector perpendicular to the symmetry axis (perpendicular dichroism) the absorption Ax is given by... 

The classical scheme for dichroism measurements implies measuring absorbances (optical densities) for light electric vector parallel and perpendicular to the orientation of director of a planarly oriented nematic or smectic sample. This approach requires high quality polarizers and planarly oriented samples. The alternative technique [50, 53] utilizes a comparison of the absorbance in the isotropic phase (Dj) with that of a homeotropically oriented smectic phase (Dh). In this case, the apparent order parameter for each vibrational oscillator of interest S (related to a certain molecular fragment) may be calculated as S = l-(Dh/Di) (l/f), where / is the thermal correction factor. The angles of orientation of vibrational oscillators (0) with respect to the normal to the smectic layers may be determined according to the equation... 

For a vibrating molecule to absorb radiation from an incident IR beam at the frequency of a particular normal mode it must be situated at a position of finite intensity and with an orientation such that there is a finite component of the dipole derivative du /dQ in the direction of the electric vector of the radiation field, where duj is the change of dipole for the change of normal mode coordinate dQ. At a... 

FIGURE 27.23 Electric (E) and magnetic (H) vectors in a linearly polarized light wave. The plane of polarization contains the electric field vectors in space. At a fixed focation, the tip of the electric vector traces a straight line as a function of time. (From Muller, 1973, with permission from Wiley-VCH.)... 

The angular distributions of the 0(3P2) fragments show the degree of correlation between the product recoil velocity (v) with the electric vector of the dissociating light and are typically characterized by the lab frame anisotropy parameter (/ ) given in the equation,52,53... 

Here 0 is the recoil angle relative to the electric vector of the dissociating light and P2 is the second-order Legendre polynomial. 

Figure 2.10. Direction of electric vector in (a) unpolarized and (b) polarized light the direction of propagation of the light wave is along the horizontal from left to right.

The values of P range from + to — (0 = 0 or 90°). This equation would be considerably simpler if only those molecules with their transition moments parallel to the electric vector were capable of absorption or if the molecules were perfectly aligned, that is, 0 = 0. Then the angle between the two transition moments could be directly determined from the observed degree of polarization P. 

Figure 2.41 The direction of the electric vector for light polarised in the S- and P-directions before being incident at a planar surface at an angle 6, and the resolution of the electric vector of the P-polarised light into its components parallel and perpendicular to the reflective surface.

Figure 2.42 The variation in the amplitude or the electric vector of the standing wave, < >, ratioed to the intensity of the incident ray, < ( ), as a function of the angle of incidence at a reflecting surface, n = 3.0 and k = 30, in contact with a medium with n = 1.0 and k = 0. From J.K, Foley, C. Korzeniewski, J.J. Daschbach and S. Pons in Electroanalytical Chemistry, A Series of Advances, A J, Bard fed ), Vol. 14, Marcel Dekker, New York, 1986,...

The path followed by the tip of the electric vectors of the individual components after reflection can be described by the equations ... 

---