In the sample compartment of a conventional spectrophotometer, mounting of a polarizer before sample and an analyzer behind sample allows the determination of the optical rotatory dispersion of optical active media by measurement of the transmission ratio of crossed and parallel arranged polarizer and analyzer. A formula for the determination of the angle of rotation is derived from the transmission ratio. The arrangement is applied to determine the molar optical rotation of D-glucose in water in the wavelength range from 220 nm to 820 nm.
Substances with handed (chiral) structure are optically active (circular birefringent) [1-5]. They have different refractive index dispersion, n (λ), for right and left circular polarized light, i.e. nr (λ) ≠ nl (λ) (circular birefringence), and light absorption is different for right and left circular polarized light, i.e. σr (λ) ≠ σl (λ) or εr (λ) ≠ εl (λ) (circular dichroism, σ is absorption cross-section, is molar decadic absorptivity, λ is wavelength). Linear polarized light can be thought to be composed of equal amount of right and left circular polarized light. Optical active substances cause rotation of the polarization plane of linear polarized light in their transparency region due to different speed of right and left circular polarized light. In the absorption region linear polarized light becomes additionally elliptically polarized because of different attenuation of right and left circular polarized light.
The rotation of polarization at a fixed wavelength is generally measured with a polarimeter consisting of a monochromatic light source, an entrance polarizer, space for the sample, an exit polarizer (analyzer) on a rotation stage, and a detector [
Here the polarizer and analyzer are oriented perpendicular (^) and then oriented parallel (||). In both cases the transmission through polarizer—sample—analyzer (and T||) is measured, and the angle of polarization rotation f is calculated from the transmission ratio. A formula for the relation between f and is derived. The polarizer—sample—analyzer arrangement may be illuminated with a monochromatic light source (laser, light emitting diode, lamp with interference filter) for determination of the optical polarization rotation at a fixed wavelength (polarimeter function), or it may be assembled into the sample chamber of a conventional spectrophotometer to determine the wavelength dependence of the optical polarization rotation (spectropolarimeter function).
The experimental arrangement for the determination of the optical rotation of polarization at a fixed wavelength is shown in the top part of
The light transmission through the P1-S-P2 arrangement is given by
where Sout is the transmitted light power, Sin is the incident light power, TP1 is the transmission through polarizer P1, TS is the transmission through the optical active sample S, and TP2 is the transmission through analyzer P2. The light transmission through the crossed polarizer arrangement with polarization rotation f of the optical active sample is
The light transmission through the parallel polarizer arrangement is
where TP2,0 is the transmission through P2 for parallel orientation of P1 and P2 in the case of f = 0.
The transmission ratio, , is
Solving Equation (2) for the rotation angle f of optical polarization gives
The positive sign applies to dextro-rotatory (= d-rotatory = right-rotatory) samples. The negative sign applies to laevo-rotatory (= l-rotatory = left-rotatory) samples. The rotation sign is determined by rotating the analyzer P2 slightly out of the crossed orientation by an angle δ (|f| > δ > 0) and measuring the transmission ratio (see illustration in lower part of
,(4a)
and for l-rotatory behavior one gets
.(4b)
The analysis above is unambiguous for optical rotation |f| < 90˚ which is accomplishable by reduction of sample length and/or concentration of optical active molecules.
The experimental arrangement for the determination of the optical rotation of polarization as a function of wavelength (optical rotatory dispersion) is shown in
In our experiments calcite Glan polarizers were used for P1 and P2. The polarizer P1 is oriented for horizontal polarized light transmission (after Cary 50 spectrometer horizontal polarized light component is more intense than vertical polarized light component). The light transmissions in the Cary 50 spectrophotometer through the horizontal oriented polarizer P1 alone (dashed curve), through the horizontal oriented polarizers P1 and P2 (solid curve), and through the horizontal oriented polarizer P1 and vertical oriented polarizer P2 (dotted curve) are shown in
The Cary 50 spectrophotometer with polarimeter accessory of
corresponding grape sugar molar density was
and the corresponding molecule number density was
(NA is the Avogadro constant). The experiments were carried out at room temperature (J = 21.5 ± 0.5˚C). The solution was measured in fused silica cells. In the wavelength range from 300 nm to 820 nm a cell length of l = 5 cm was used. In the wavelength range from 220 nm to 300 nm the measurements were carried with a cell length of l = 1 cm.
Light transmissions, T (λ), through the applied grape sugar solution in cell lengths of l = 1 cm (solid curve) and l = 5 cm (dashed curve) in the wavelength range from 200 nm to 820 nm are displayed in
The angle (in radian) of which the plane of polarization rotates in an optical active sample of length l, vacuum wavelength λ, and refractive indices nr and nl is given by [1-5]
where is the wavevector of right (i = r) or left (i = l) circular polarized light.
The specific rotation [f] of an optical active species in a sample is expressed in degrees (1 rad = 180˚/π = 180/π deg) and normalized to mass density or concentration ρ of the optical active species in g·cm-3 and sample length l in dm. The corresponding numerical value equation is
([f] is polarization rotation in deg for sample of density or concentration of ρ = 1 g·cm-3 and sample length of l = 1 dm; f is in rad).
The molar optical rotation [m] of optical active molecules in a sample is expressed in degrees and normalized to the molar density or concentration
in mol dm-3 and sample length l in m (ρ in g·cm-3 and MMol in g·mol-1). The corresponding numerical value equation is [3-5]
([m] is polarization rotation in deg for sample of density or concentration of ρMol = 1 mol·dm-3 and sample length of l = 1 m). The specific optical rotation as well as the molar optical rotation depends on the wavelength λ, the temperature J, the solvent, and in the case of sample dissociation or aggregation on the used concentration. The complete specification is therefore expressed in (solvent, concentration in g per 100 cm3) or (solvent, concentration in mol per 1 dm3).
The wavelength dependence of the optical rotation in the transparency region is related to the absorption spectrum of the optical active sample by the Drude expression [1-5]
where λj is the wavelength of transition from the ground state to the excited state j, and Aj is a constant depending on the absorption strength of this transition.
In the absorption region the absorption band linewidths Δλj (FWHM) have to be considered and the Drude expression changes to the Cotton effect equation [2,4]
(Equation 2.407 in [
).
The transmission measurement results through the polarizer—grape sugar solution—analyzer arrangement in the Cary 50 spectrophotometer are depicted in
The determined optical rotatory dispersion f × 180/π (in degree) of the investigated grape sugar solution is depicted in
data. In the right region (λ ³ 300 nm) D-glucose is transparent and the Drude relation fits well to the experimental curve. The apparent single oscillator transition wavelength is λ0 = 147.49 nm indicating a dominant apparent absorption band there. In the left region (λ < 300 nm) the transmission through the calcite polarizers is small reducing the accuracy of rotation angle dispersion determination. There D-glucose is slightly absorbing (see
The obtained molecule specific molar optical rotatory dispersion [m (λ)] (Equation (7)) of D-glucose is displayed in
The obtained optical rotatory dispersion of D-glucose in Millipore water is in good agreement with published results [
ing specific rotation is (Millipore water, 27.27 g/100 cm3) = 53.2 ± 0.6˚ (Mm = 180.16 g·mol-1 for D-glucose) is in good agreement with results found in the literature ((water, 10 g/100 cm3) = 52.7˚ [
A simple fixed-polarizer-analyzer polarimeter and spectropolarimeter were designed and applied to the measurement of the optical rotatory dispersion of D-glucose. In the arrangements the polarizer and analyzer are aligned perpendicular (T^) and parallel (T||), and the rotation of the polarization plane is calculated from the transmission ratio T^/T||. Besides two polarizers, no extra polarimeter and spectropolarimeter equipment are required for the determination of the specific optical rotation at a fixed wavelength or for the determination of the optical rotatory dispersion over a wide wavelength range.
The author thanks Prof. F. J. Gießibl for his kind hospitality.