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. n_r (λ) ≠ n_l (λ) (circular birefringence), and light absorption is different for right and left circular polarized light, i.e. σ_r (λ) ≠ σ_l (λ) or ε_r (λ) ≠ ε_l (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 [6]. The analyzer is rotated to crossed position (blocking of linear polarized light transmission) in accordance of the rotation of the linear polarization of the optical active sample under investigation. The optical rotatory dispersion (wavelength dependence of optical rotation) is measured with spectropolarimeters consisting of a broadband light source, a spectrometer, and a polarimeter [6].

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 Figure 1(a)" target="_self">Figure 1(a). The light source (here a He-Ne laser with λ = 632.8 nm) emits monochromatic light along the z-direction through the polarizer (P1)—sample (S)—analyzer (P2) arrangement. The polarizer orientations and the optical polarization rotations of right (dextro) rotatory and left (laevo) rotatory samples are illustrated in the bottom part of Figure 1(a)" target="_self">Figure 1(a).

The light transmission through the P1-S-P2 arrangement is given by

where S_out is the transmitted light power, S_in is the incident light power, T_P1 is the transmission through polarizer P1, T_S is the transmission through the optical active sample S, and T_P2 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 T_P2,0 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 Figure 1(a)" target="_self">Figure 1(a)). For d-rotatory behavior one gets

,(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 Figure 1(b). The P1-S-P2 polarizer-sample-analyzer assembly is mounted in the sample chamber of the applied UV-Vis spectrophotometer Cary 50 from Varian. The wavelength range of this spectrophotometer is 190 nm to 1100 nm.

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 Figure 2. Below 390 nm the transmission through calcite begins to decrease remarkably and below 218 nm the transmission through calcite becomes diminishingly small (transmission behavior of calcite is found in [7,8]). For optical rotatory dispersion measurement in the wavelength range from 200 nm to 390 nm the calcite Glan polarizers should be replaced by α-BBO Glan polarizers with better transmission performance (BBO = barium borate = BaB₂O₄) [9].

The Cary 50 spectrophotometer with polarimeter accessory of Figure 1(b) was applied to determine the molar optical rotation [1-5] of grape sugar (D-glucose) in Millipore water in the wavelength range from 220 nm to 820 nm. Grape sugar from Frießinger Mühle, Bad Wimpfen (www.friessinger-muehle.de) was purchased in a supermarket and used without further purification. Its composition is D-glucose with crystal water, the sum formula is C₆H₁₂O₆·H₂O (molar mass M_m = 198.18 g·mol^-1). It was dissolved in Millipore water. A mass concentration of C_m = 0.3 g·cm^-3 was prepared (near saturation concentration) and used in the experiments. The

corresponding grape sugar molar density was

and the corresponding molecule number density was

(N_A 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 Figure 3. The inset shows the absorption cross-section spectrum σ (λ) of the applied grape sugar in the UV spectral region. It was calculated by the relation. Absorption shoulders at 325 nm and 215 nm, and an absorption peak at 268 nm with σ (268 nm) = 5.64 × 10^-22 cm² are observed.

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 n_r and n_l 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 M_Mol 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 ρ_Mol = 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 λ_j is the wavelength of transition from the ground state to the excited state j, and A_j is a constant depending on the absorption strength of this transition.

In the absorption region the absorption band linewidths Δλ_j (FWHM) have to be considered and the Drude expression changes to the Cotton effect equation [2,4]

(Equation 2.407 in [2] rewritten to λ dependence using leading to

).

The transmission measurement results through the polarizer—grape sugar solution—analyzer arrangement in the Cary 50 spectrophotometer are depicted in Figure 4. The concentration was C_m = 0.3 g·cm^-3. The right part shows the transmissions through the cell of 5 cm length and the left part shows the transmission through the cell of 1 cm length. The solid curves belong to T_^(λ) and the dashed curves belong to T_||(λ). The dotted curves shows the ratio T_^(λ)/T_||(λ). The shape of T_||(λ) is mainly determined by the transmission behavior of the calcite polarizers. The finite transmission T_^(λ) is caused by the rotation of the polarization direction by the optical active D-glucose solution. The transmission ratio is relevant for the calculation of optical rotation of polarization (Equations (2) and (3)).

The determined optical rotatory dispersion f × 180/π (in degree) of the investigated grape sugar solution is depicted in Figure 5. It was obtained from Figure 4 by application of Equation (3). The left part belongs to a cell length of 1 cm and the right part belongs to a cell length of 5 cm. The dash-dotted curve on the right part is the single-term regression fit of the Drude expression Equation (8) to the experimental

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 Figure 3) causing a slight structuring of the optical rotatory dispersion curve due to the Cotton effect dispersion [1-5].

The obtained molecule specific molar optical rotatory dispersion [m (λ)] (Equation (7)) of D-glucose is displayed in Figure 6. It shows the optical rotation in degree (˚) of 1M (1 mol·dm^-3) glucose in a cell of 1 m length. Over the whole displayed wavelength range from 220 nm to 820 nm the dispersion fits well to the singleterm Drude formula. Some Cotton effect dispersion is seen in the D-glucose absorption region. The D-glucose absorption in the 220 to 300 nm region (see inset of Figure 3) is too weak to influence markedly the polarization rotatory dispersion which is determined by strong absorption in the vacuum UV spectral range.

The obtained optical rotatory dispersion of D-glucose in Millipore water is in good agreement with published results [10]. The here determined molar optical rotation at λ_D = 589.3 nm is (Millipore water, 1.514 mol·dm^-3) = 95.8 ± 1 deg mol^-1·dm³·m^-1. The correspond-

ing specific rotation is (Millipore water, 27.27 g/100 cm³) = 53.2 ± 0.6˚ (M_m = 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˚ [11]).

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.