Polarization electric rotational

Figure 9.2 Quantitative description of optical rotation. A vertically polarized electric field Em is incident on chiral system and induces vertically directed dipole moment i and magnetic moment m. Both act as sources of radiation, p, giving rise to vertically polarized field, m giving rise to horizontally polarized field. Sum of both fields is a new field E0ut with polarization rotated over angle 0.

Figure B3.6.12 Depolarization of fluorescence indicates rotation of the chromophore. Monochromatic radiation from the source (S) has all but the vertically polarized electric vector removed by the polarizer (P). This is absorbed only by those molecules (see Fig. B3.6.5) in which the transition dipole of the chromophore is aligned vertically. In the case where these molecules do not rotate appreciably before they fluoresce ( no rotation"), the same molecules will fluoresce (indicated by shading) and their emitted radiation will be polarized parallel to the incident radiation. The intensity of radiation falling on the detector (D) will be zero when the analyzer (A) is oriented perpendicular to the polarizer. In the case where the molecules rotate significantly before fluorescence takes place, some of the excited chromophores will emit radiation with a horizontal polarization ( rotation ) and some with a vertical polarization. Finite intensities will be measured with both parallel and perpendicular orientations of the analyzer. The fluorescence from the remainder of the excited molecules will not be detected. The heavy arrows on the left of the diagram illustrate the case where there is rotation.

Molecular dynamics simulations on artificial surface-mounted molecular rotors have been performed and extensively reviewed.33 55 The theoretical rotational motion, driven by a circularly polarized electric field, of a dipolar chiral rhenium complex rotor attached to a molecular grid was also studied.56 In vacuum and at... 

One possible such mechanism for fixing a pattern is to have a phase transition. For example, if the pattern is in terms of a distribution of large molecules on the outer membrane surface, as in the Fucus-like models discussed here, then a membrane phase transition from a more liquid-like to a more crystal-like state of the membrane could essentially immobilize the membrane bound species and freeze in the pattern. In fact several hours after fertilization in Fucus the lability (rotatability) of the polar axis significantly decreases. Indeed this freezing of the Fucus patterning is not easily explained in terms of a Turing mechanism since the rotational symmetry of the Fucus egg, as discussed previously, implies that the electrical polarity is not stable (or more precisely is marginally stable) to polar axis rotation. 

Fig. 2. Schematic representation of an experimental set-up for measuring the polar Kerr rotation. (After van Engen 1983). The light passes a fixed polarizer P and, after being reflected by the magnetized sample S, passes respectively through a linear phase retarder R, a Faraday modulator M and an electrically adjustable analyser A before reaching the detector D.

If the linearly polarized electric field E is decomposed into a sum of two counter-rotating circularly polarized fields... 

In polar materials, rotational movements will be caused by the torque experienced by permanent dipoles in electric fields. 

If a polarizer which rotates the polarisation plane of the incident wave is placed between two crossed linear polarizers (Fig. 2.13) the electric vector of the input beam will be turned and the crossed polarizer transmits only a fraction of the input intensity which depends on the turning angle 9 of the rotating polarizer. The Jones formahsm yields the output electric vector as... 

Fig. 1.17 Apparatus for measuring fluorescence anisotropy. In the main drawing (a top view), a polarizing filter or prisim (PI) polarizes the excitation light so that the electric vector is normal to the plane of the paper. The intensity of the fluorescence is measured through a second polarizer (P2), which is oriented either parallel or perpendicular to PI. The drawing at the lower right shows a perspective view of the sample and the polarizers. To check for bias of the detection monochromator in favor of a particular polarization, measurements also are made with polarizer PI rotated by 90°. The fluorescence signal then should be same with either orientation of P2 because both orientations are perpendicular to PI. L lamp, 5 sample, PD photodetector...

The oriented sample and the polarizer are placed in the spectrometer beam and spectra are taken with the electric vector of the radiation parallel and perpendicular to the orientation direction of the sample. If the sample is not uniform in thickness or shape, it may be left stationary while the polarizer is rotated so that the same part of the sample is used. Errors are caused by this method because of the inherent polarization in the spectrometer. To avoid the above difficulty, measurements may be made with the sample and polarizer oriented 45° from the vertical and then with the polarizer rotated 90° to a position 45° on the other side. If the sample is uniform enough, the polarizer is left stationary in the direction of maximum transmission while the sample is rotated 90°. This is the most satisfactory way to make polarization measurements. 

If a beam of unpolarized electromagnetic radiation is transmitted in the z direction, the amplitudes of the components of the sinusoidally varying electric field in the x and y planes are identical. When the beam is passed through a polarizer, the component of the electric field in one plane is transmitted, as described in more detail in Chapter 12. For unoriented samples such as all gases and liquids and isotropic solids, the absorbance of all bands in the spectrum is independent of the orientation of the polarizer. If the molecules in a certain sample are preferentially oriented in a given direction, however, the component of the dynamic dipole moment derivative of each vibrational mode, d i./dQ, in the direction that the radiation is polarized will change as the polarizer is rotated. 

Molecules that have a plane of symmetry interact with photons of both circular polarizations in the same way. A molecule without a plane of symmetry appears different to the two kinds of photons, and the speed of light of the two kinds of photons can be different. The rotation of one circularly polarized electric field contribution lags behind the other, and the plane of polarization is rotated as shown in Figure 23.22b. 

It is another mechanism proposed for the microwave heating, which involves the movement of charged particles by the back and forth motion present in the solution, finally the collisions with the siurounding molecules leads to the generation of heat [13], The two mechanisms are diagrammatically represented in Fig. 10.3, and it explains how the polar molecules rotate veiy quickly with the alternating electric field [13]. 

A dipole in a cavity in a polarizable solvent will polarize the medium and create an electric field at its own position. The simplest model is that of a dipole ]1 at the center of a spherical cavity of radius a embedded in a dielectric. We already encountered its results in Section 9.5. The way Nee and Zwanzig [16] came to their results is as follows Outside the cavity there is a dielectric with dielectric constant c (o)), and inside the cavity we assume only electronic polarization C or vacuum (fj = 1). The frequency dependence of the outside dielectric constant derives from the fact that the molecules in the solvent can rotate to change the polarization. This rotation is diffusional, so the dipoles need time to adjust to a new situation. This does not have an effect on the solution of the boundary value problem. At the boundary, the usual boundary conditions apply the transverse component of the electric field is continuous, as is the normal component of the displacement field. Using these boundary conditions, it is possible to find the fields inside and outside the cavity. Solving this problem gives the electric and displacement fields inside and outside the cavity. The important field is the field created by the outside polarization inside the cavity, the so-called Onsager reaction field [23] E ... 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

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