Molar ellipticity relation

The characteristic of the molecule is sometimes expressed as the molar ellipticity in deg d/-moP dm . This is related to the difference in extinction coefficients by... 

The Kronig-Kramers relation is of fundamental importance for optics and for physics in general13). Here, these equations do not seem practical because of the integration of the wavelength from 0 to oo. However, these are very useful for calculating the molar ellipticity magnitude from the observed ORD curve 14). 

All commercially available CD instruments measure AA = Al - Ar which is readily converted to Ae by Eq. (3). However, most instruments are calibrated in terms of molar ellipticity, an alternative measure of CD which is mainly of historical interest. The ellipticity is an angular measure which is related to AA as follows ... 

Commonly, for the sake of comparison, the molar ellipticity [6>] = 100 Ofcd in units of deg cm dmol" is recorded, where c is the concentration in mol and d is the optical path length. If, in the case of polymers such as proteins, the molar concentration is related to the molar mass of the residue, i.e. to the repeating (base) unit, the mean residue weight ellipticity [0]mrw is obtained. 

Optical activity of a substance leads at least to three spectroscopic phenomena which are, however, related Optical Rotatory Dispersion (ORD), i.e. the rotation of the plane of linearly polarized light by traversing the substance. Circular Dichroism, expressed as Ae = e - e (if the relative molar mass of the molecules is known, or - in case of biopolymers - the mean residual relative molar mass), and Molar Ellipticity, [e] = 3300 x Ae. A necessary condition for optical activity of a substance is the Chirality of its molecules, i.e. the property of being not superposable onto its mirror image. This allows still the presence of (proper) axes of rotation Cp, but not improper ones (Sp, including... 

Before moving further, we mention here that the decadic molar extinction coefficient, also known as molar absorptivity, is not the only quantity employed by experimentalists to report their measurements of circular dichroism. Two other quantities often employed are the specific ellipticity [ J/] and the molar ellipticity [ ]. The former is given in degrees cm dm g and is related to the absolute ellipticity ij/, usually given in degrees, by the relationship... 

In a series of works, Tokura and coworkers have systematically studied the CD induced in a number of carboxylic acids through their association with optically active amines [14-17]. Salts of 1 1 stoichiometry were formed as contact ion pairs, with limiting values normally being obtained for the observed ellipticities at equivalent molar amounts. The degree of salt formation could be related to the polarity of the solvent medium, as has been summarized in Table 1. The data in the table illustrate that, as the degree of solvent polarity increases, the limiting ellipticity induced in the carboxylate carbonyl band decreases. 

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