Optical rotation defined

An example of a chiral compound is lactic acid. Two different forms of lactic acid that are mirror images of each other can be defined (Figure 2-69). These two different molecules are called enantiomers. They can be separated, isolated, and characterized experimentally. They are different chemical entities, and some of their properties arc different (c.g., their optical rotation),... 

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). 

Physical Properties. Oligosaccharide antibiotics are colodess soHds, which are often crystalline and have defined melting poiats and optical rotations, [cc] (see Tables 1 and 2). They have a characteristic uv spectmm resulting from the phenoHc ester residue, 285 nm (s ca 22), which shifts... 

Quantitative measurements of optical activity are usually expressed in terms of the specific rotation, defined as... 

To express optical rotations in a meaningful way so that comparisons can be made, we have to choose standard conditions. The specific rotation, [a ]D, of a compound is defined as the observed rotation when light of 589.6 nanometer (nm 1 nm = 10-9 m) wavelength is used with a sample pathlength / of 1 decimeter (dm 1 dm = 10 cm) and a sample concentration C of 1 g/mL. (Light of 589.6 nm, the so-called sodium d line, is the yellow light emitted from common sodium lamps.)... 

Because of their high molecular weight and their defined structure, dendrimers offer themselves for studying the expression of chirality on a macromolecular level. The construction of configurationally uniform macromolecules is otherwise a complex task but can be achieved more easily with dendrimers because of repetitive synthesis from identical (chiral) building blocks. Comparison of optical rotation values and circular dichroism (CD) spectra should demonstrate what influence there is of the chiral building blocks on the structure of the whole dendrimer. 

If polarized light passes through a medium that exhibits optical rotation, the motion along one of the circular vectors is slower than that of the other. The resultant vector is thus displaced from the original vector by some angle, . Figure 16.5 shows the vector model in which the phase difference is [Pg.588]

Define plane-polarized light, optical rotation, optical activity, asymmetric carbon atom, enantiomers, racemic mixture, polarimeter, and specific rotation. 

The recorded angle of rotation of an optically active gas, liquid, solid or solution is called optical rotation and is denoted by the symbol a. The magnitude of the optical rotation (a) of a pure liquid is affected by the cell path length, density, temperature and wavelength. Hence, the specific rotation of pure (neat) liquids is defined as follows ... 

Circular dichroism and optical rotation for particulate media may be operationally defined in terms of the Stokes parameters (2.80), which in the circular polarization representation are written... 

If optical rotation 4>7 for a collection of particles is defined as the change in azimuth of a horizontally polarized incident beam (y, = 0) after it is... 

In the previous sections the MCD equations were developed starting from the transition moment definition of MCD. As described in the introduction, MCD has also been defined through the complex optical rotation ... 

Figure 6.5 Temperature dependence of the characteristics of sodium k-carrageenan particles dissolved in an aqueous salt solution (0.1 M NaCl). The cooling rate is 1.5 °C min-1, (a) ( ) Weight-average molar weight, Mw, and (A) second virial coefficient, A2. (b) ( ) Specific optical rotation at 436 nm, and ( ) penetration parameter, y, defined as tlie ratio of the radius of the equivalent hard sphere to the radius of gyration of the dissolved particles (see equation (5.33) in chapter 5). See the text for explanations of different regions I, II, III and IV.

The specific rotation, [a]o°, of lactose in solution at equilibrium is +55.4° expressed on an anhydrous basis ( + 52.6° on a monohydrate basis). The specific rotation is defined as the optical rotation of a solution containing 1 g ml"1 in a 1 dm polarimeter tube it is affected by temperature (20°C is usually used indicated by superscript) and wavelength (usually the sodium D line (589.3 nm) is used indicated by subscript). 

The optical activity of a stereoisomer is expressed quantitatively by its optical rotation, the number of degrees by which plane-polarized light is rotated on passage through a given path length of a solution of the compound at a given concentration. The specific rotation [ci ff c of an optically active compound is defined thus ... 

Physical Properties. Oligosaccharide antibiotics are colorless solids, which are often crystalline and have defined melting points and optical rotations. 

Figure B3.5.3 The relation of ellipticity to the differential absorption of circularly polarized radiation. The oscillating radiation sine wave, 01, is proceeding out of the plane of the paper towards the viewer. (A) Plane-polarized radiation is made up of left- and right-handed circularly polarized components, OL and OR, respectively. Absorption by a chromophore in a nonchiral environment results in an equal reduction in intensity of each component, whose resultant is a vector oscillating only in the vertical plane—i.e., plane-polarized radiation. (B) Interaction of the radiation with achiral chromophore leads to unequal absorption, so that combination of the emerging vectors, OL and OR, leads to a resultant that describes an elliptical path as it progresses out of the plane of the paper. The ratio of the major and minor axes of the ellipse is expressed by tan 0, thus defining ellipticity. The major axis of the ellipse makes an angle (q) with the original plane, which defines the optical rotation. This figure thus demonstrates the close relation between optical rotation and circular dichroism.

Chiral molecules are optically active. They rotate a beam of plane-polarized light. They are dextrorotatory (+) or levorotatory (-), depending on whether they rotate the beam to the right or left, respectively. The rotations are measured with a polarimeter and are expressed as specific rotations, defined as... 

The crystal structures of the alkaloids containing a hydroxyl group at C-2 have not been determined. The stereochemistry of erythratine (42) was established as 2R,3R,5S by Barton et al. (79) and that of erythratidine (39) as 2S,3R,5S by the same group (27) on the basis of optical rotation and NMR data for both pairs of C-2 epimers (see Section II,C,4b). The configuration at C-2 for erysosalvine (45), erysotine (48), and erysopitine (50) has not been defined. 

When plane-polarized light passes through a sample of chiral molecules with an excess of one enantiomer, its plane of polarization is rotated. This phenomenon, called optical rotation, is usually described quantitatively by the specific optical rotation [a]m, defined as... 

The assignment of an asymmetric centre as (R) or (S) has nothing to do with whichever direction the molecule rotates plane-polarised light. Optical rotation can only be determined experimentally. By convention, molecules which rotate plane-polarised light clockwise are written as (+) or d. Molecules which rotate plane-polarised light counterclockwise are written as (-) or 1. The (R) enantiomer of lactic acid is found to rotate plane-polarised light counterclockwise and so this molecule is defined as (R)-(-)-lactic acid. 

The criteria for a substance to exhibit either optical rotation or optical rotatory dispersion is that (nL - n ) not equal zero. Within an absorption band it can be concluded that if (nL - n ) does not equal zero, then (kL - kR) will not equal zero either. The quantity (kL - kE) is defined as the circular dichroism (CD). 

In addition to the optical rotation tensor fi, the gyration tensor is often used as the basis of computing optical rotations, since it is more straightforward to define working equations for it in the frequency domain. The relation to the OR tensor is... 

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