Optical rotation direct polarization

Polarimetry. Polarimetry, or polarization, is defined as the measure of the optical rotation of the plane of polarized light as it passes through a solution. Specific rotation [ a] is expressed as [cr] = OcjIc where (X is the direct or observed rotation, /is the length in dm of the tube containing the solution, and c is the concentration in g/mL. Specific rotation depends on temperature and wavelength of measurement, and is a characteristic of each sugar it may be used for identification (7). 

Double Polarization. The Clerget double polarization method is a procedure that attempts to account for the presence of interfering optically active compounds. Two polarizations are obtained a direct polarization, followed by acid hydrolysis and a second polarization. The rotation of substances other than sucrose remains constant, and the change in polarization is the result of inversion (hydrolysis) of the sucrose. 

Today, we would describe Pasteur s work by saying that he had discovered enantiomers. Enantiomers, also called optical isomers, have identical physical properties, such as melting point and boiling point, but differ in the direction in which their solutions rotate plane-polarized light. 

FIGURE 16.3 The optically active isomers of [Co(en)3]3+(top) and their directions of rotation of polarized light. 

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.

The presence of chirality introduces an additional component in the y direction. This component will rotate the polarization of die second-harmonic field with respect to the polarization of the incident radiation. The amount of optical rotation will depend on the relative magnitude of the chiral and achiral susceptibility components. Furthermore, Py changes sign between the enantiomers... 

This effect, which is in a loose sense the nonlinear analog of linear optical rotation, is based on using linearly polarized fundamental light and measuring the direction of the major axis of the ellipse that describes the state of polarization of the second-harmonic light. For a simple description of the effect, we assume that the expansion coefficients are real, as would be the case for nonresonant excitation within the electric dipole approximation.22 In this case, the second-harmonic light will also be linearly polarized in a direction characterized by the angle... 

In 1822, the British astronomer Sir John Herschel observed that there was a correlation between hemihedralism and optical rotation. He found that all quartz crystals having the odd faces inclined in one direction rotated the plane of polarized light in one direction, while the enantiomorphous crystals rotate the polarized light in the opposite direction. 

Enantiomers have identical chemical and physical properties in the absence of an external chiral influence. This means that 2 and 3 have the same melting point, solubility, chromatographic retention time, infrared spectroscopy (IR), and nuclear magnetic resonance (NMR) spectra. However, there is one property in which chiral compounds differ from achiral compounds and in which enantiomers differ from each other. This property is the direction in which they rotate plane-polarized light, and this is called optical activity or optical rotation. Optical rotation can be interpreted as the outcome of interaction between an enantiomeric compound and polarized light. Thus, enantiomer 3, which rotates plane-polarized light in a clockwise direction, is described as (+)-lactic acid, while enantiomer 2, which has an equal and opposite rotation under the same conditions, is described as (—)-lactic acid. 

As Louis Pasteur first observed (Box 1-2), enantiomers have nearly identical chemical properties but differ in a characteristic physical property, their interaction with plane-polarized light. In separate solutions, two enantiomers rotate the plane of plane-polarized light in opposite directions, but an equimolar solution of the two enantiomers (a racemic mixture) shows no optical rotation. Compounds without chiral centers do not rotate the plane of plane-polarized light. 

One form (L-form) exhibits the ability to rotate the plane of polarization of plane polarized light to the left (levorotatoiy), whereas the other form (D-form) rotates the plane to the right (dextrorotatory) Although the direction of optical rotation exhibited by these optically active forms is different, the magnitude of their respective rotations is the same. If equal amounts of dextro and evo forms are admixed, the optical effect of each isomer is neutralized by the other, and an optically inactive product known as a racemic modification or racemate is secured. 

A useful model for explanation of optical rotation considers that a beam of plane-polarized light is the vector resultant of two oppositely rotating beams of circularly polarized light. This will be clearer if we understand that circularly polarized light has a component electric field that varies in direction but not in magnitude so that the field traverses a helical path in either a clockwise or counterclockwise direction, as shown in Figure 19-2. 

Enantiomers are labeled (+) or (—), depending on the direction of rotation of the plane of polarization. For example, the isomer of [Co(en)3]3+ that rotates the plane of polarization to the right is labeled ( + )-[Co(en)3]3+, and the isomer that rotates the plane of polarization to the left is designated ( — )-[Co(en)3]3+. A 1 1 mixture of the ( + ) and ( —) isomers, called a racemic mixture, produces no net optical rotation because the rotations produced by the individual enantiomers exactly cancel. 

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

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