Optical Activity and Polarimetry

Optical activity is the ability of a chiral substance to rotate the plane of polarized light, measured with a polarimeter, and expressed as the specific rotation [α] = α / (l × c), where α is the observed rotation, l the path length in decimeters and c the concentration in g/mL. In brief: a solution of 10.0 g of sucrose in 100 mL in a 10 cm tube rotates the light by +6.65° (the specific rotation of sucrose is +66.5°), and fructose rotates it in the opposite direction (−92.4°).

Optical rotation was the first property that distinguished enantiomers, and it is still used in the sugar industry, in the pharmaceutical industry and in research to measure the concentration and the purity of chiral compounds. This article explains plane-polarized light and how a polarimeter works, defines specific rotation and gives a table of values, shows how to calculate concentrations and enantiomeric excess, and explains mutarotation and the inversion of sucrose with worked examples.

What is plane-polarized light?

Ordinary light consists of waves whose electric fields oscillate in all directions perpendicular to the direction of travel. A polarizing filter lets through only the waves that oscillate in one plane, and the transmitted light is plane-polarized. If a second filter (the analyzer) is placed behind the first and rotated by 90°, no light gets through. Polarizing sunglasses use this principle to cut the glare from horizontal surfaces.

What is optical activity?

When plane-polarized light passes through a solution of a chiral compound, the plane of polarization is rotated by an angle α. The compound is optically active. One of a pair of enantiomers rotates the light clockwise (as seen by an observer looking toward the light source): it is dextrorotatory, designated (+) or d. The other rotates it by the same amount counterclockwise: it is levorotatory, (−) or l. A racemic mixture, which contains equal amounts of both, shows no rotation, and achiral compounds, such as water or acetone, do not rotate the light. The cause of the rotation is that the two circularly polarized components of the light interact differently (have different refractive indices) with a chiral molecule. The sign of rotation (+ or −) cannot be predicted from the R/S configuration.

How does a polarimeter work?

1. A monochromatic light source, usually a sodium lamp (the D line, 589 nm), or a LED, emits light.
2. A polarizer produces plane-polarized light.
3. The light passes through a sample tube of known length (typically 1 dm = 10 cm) containing the solution.
4. An analyzer, which can be rotated, is adjusted until the maximum or minimum light intensity is reached. The angle through which it was rotated is the observed rotation α.

Modern instruments use electronic detectors and give the reading digitally, with a resolution of 0.001° or better. The sign is determined by the direction in which the analyzer must be turned. For small angles, it is not possible to tell +10° from −170° with a single measurement, so the measurement is repeated at a different concentration or tube length.

What is specific rotation?

The observed rotation depends on the number of molecules in the path of the light, so it is proportional to the concentration and the path length. The specific rotation is a characteristic constant of the compound:

[α]λT = α / (l × c)

where α is the observed rotation in degrees, l the path length in decimeters and c the concentration in g/mL (the units of [α] are deg·mL·g⁻¹·dm⁻¹, usually written just as degrees). It is reported with the temperature and the wavelength, for example [α]_D²⁰, where D means the sodium D line, and with the solvent and concentration, since these can change the value. For a pure liquid, the density (g/mL) is used for c.

Specific rotations of common compounds

Worked examples

Example 1: the expected rotation

What rotation is observed for a solution of 10.0 g of sucrose in 100.0 mL in a 10.0 cm (1.00 dm) tube? c = 10.0 g / 100.0 mL = 0.100 g/mL. α = [α] × l × c = 66.5 × 1.00 × 0.100 = +6.65°.

Example 2: finding the concentration

A solution of an unknown sugar sample in a 2.00 dm tube gives α = +13.3°. The sample is sucrose, so c = α / ([α]l) = 13.3 / (66.5 × 2.00) = 0.100 g/mL.

Example 3: enantiomeric excess

A chemist prepares a sample of a chiral compound for which the pure (+) enantiomer has [α] = +50.0°. The sample gives [α] = +30.0°. The optical purity (and enantiomeric excess, ee) is 30.0 / 50.0 × 100 = 60 %. The sample contains (100 + 60)/2 = 80 % of the (+) enantiomer and 20 % of the (−) enantiomer. The ee is the excess of the major over the minor enantiomer: 80 − 20 = 60 %.

Example 4: the inversion of sucrose

Sucrose is hydrolyzed by acid or by the enzyme invertase: sucrose + H₂O → glucose + fructose, an equimolar mixture. The specific rotation of the mixture is the average (for equal masses; the two sugars have the same molar mass): (+52.7 + (−92.4))/2 = −19.9°. The sign changes from + to −, which is called the inversion, and the mixture is called invert sugar. It is sweeter than sucrose, because fructose is the sweetest of the common sugars, and it is used in confectionery because it does not crystallize easily.

Example 5: the effect of the path length

If the tube in Example 1 is replaced with one of 20.0 cm (2.00 dm), the observed rotation doubles to +13.3°. Doubling the concentration at the same path length has the same effect.

What is mutarotation?

When crystalline α-D-glucose ([α] = +112.2°) is dissolved in water, the rotation falls with time to +52.7°. When β-D-glucose ([α] = +18.7°) is dissolved, the rotation rises to the same value. The cause is the interconversion of the two forms through the open-chain aldehyde until an equilibrium is reached: x × 112.2 + (1 − x) × 18.7 = 52.7, so 93.5x = 34.0 and x = 0.364. The equilibrium mixture contains 36 % α and 64 % β (plus a very small amount of the open-chain and furanose forms). The more stable β form has all the substituents on the ring in the equatorial position.

Where is polarimetry used?

• Sugar industry: saccharimeters measure the sucrose content of syrups, beets and sugar, in “degrees Brix” or “degrees Z”.
• Pharmaceuticals: checking the identity and enantiomeric purity of chiral drugs, and following stereoselective reactions.
• Food and flavor: quality of essential oils, honey and juices.
• Research: studies on reaction kinetics (the inversion of sucrose was one of the first studied reactions) and the structure of molecules. Related methods, optical rotatory dispersion and circular dichroism, give the secondary structure of proteins.

Who discovered optical activity?

Étienne-Louis Malus discovered the polarization of light by reflection in 1808. Jean-Baptiste Biot found in 1815 that quartz crystals, and then liquids such as turpentine, rotate the plane of polarized light, and in 1830s established the laws of optical rotation and used it to study sugars. Louis Pasteur showed in 1848 that the two forms of tartaric acid rotate light in opposite directions, and connected optical activity with the asymmetry of molecules. Ludwig Wilhelmy used a polarimeter in 1850 to follow the rate of inversion of sucrose, in the first quantitative study of a reaction rate.

Which mistakes are common?

• Using the wrong units: l is in decimeters and c in g/mL.
• Equating (+) with R or D: the sign of rotation does not follow from the configuration.
• Forgetting to quote conditions: temperature, wavelength, solvent and concentration all matter.
• Assuming that zero rotation means an achiral compound: a racemate or a meso compound also gives zero.
• Mixing up optical purity and yield: they measure different things.