POLARIMETRY

Summary

Polarimetry is is a very useful method to analyze chiral substances. The magnitude and direction of rotation of the plane of polarized light by a chiral compound is a specific physical property of the compound that can be used to characterize it. Most biomolecules are chiral and hence rotate polarized light. In this experiment you will study the optical rotation of a series of mixed carbohydrate solutions and determine the relative concentrations of them that produce an optically inert mixture. Carbohydrates are so named because they generally contain C, H, and O in the ratio C_m(H₂O)_n. The smallest carbohydrate molecules are called monosaccharides and these are the basic building blocks for larger carbohydrate molecules, the disaccharides and polysaccharides. Monosaccharides and disaccharides are collectively referred to as sugars because of their often-sweet taste. Polysaccharides include the starches and cellulose. Most monosaccharides can exist as either an open-chain or a cyclic structure, with these two forms being in equilibrium with each other. The cyclic structure contains a new chiral carbon not present in the open-chain form. Monosaccharides are classified as aldoses if they contain an aldehyde group in their open-chain form, or as ketoses if they contain a ketone group. Glucose is an example of an aldose and fructose is a ketose. The most common disaccharide, sucrose or table sugar, is a combination of glucose and fructose.

The instrument used to study optical rotation in chiral molecules is called a polarimeter. A polarimeter takes light vibrating in all planes, isolates the light vibrating in a single plane, projects the light through a tube filled with a solution of chiral compound, and measures the amount of rotation.

Introduction

This experiment demonstrates a physically observable consequence of quantum mechanics. From organic chemistry, we know that non-superimposable mirror-image molecules rotate the plane of polarization of light. We also understand that two mirror-image molecules (enantiomers) rotate the plane of polarization in opposite directions. However, a typical organic class does not explain why or how this occurs. Why do different molecules rotate the plane of polarization by different amounts? Why is the angle of rotation different at different wavelengths? The following discussion should help to explain these questions.

Electromagnetic radiation consists of sinusoidally varying electric and magnetic fields whose directions lie in mutually perpendicular planes. The directions of the vibrations of the electric and magnetic fields are perpendicular to the direction of propagation. To understand polarized light we need only to study the electric field. In ordinary unpolarized light, a series of "snapshots" would reveal that the electric field orientation randomly varies among all possible angles in the plane normal to the direction of propagation (for a layman's explanation see http://www.colorado.edu/physics/2000/polarization/polarizationII.html). But, if the electric vibrations are confined to a single plane in one particular direction, the light is said to be plane polarized.

Unfortunately, this simple view of plane-polarized light does not explain why a collection of chiral molecules, with random orientations in solution, will rotate the plane of the light. We can explain this effect if we visualize plane-polarized light as a superposition of right- and left-circularly polarized light.

The relative velocity of light in different media is given by v₁/v₂ = n₂/n₁ where v_i is the velocity of the light in medium i with refractive index n_i. Chiral molecules possess different refractive indices for right and left circularly polarized light, and thus slow one component more than the other. The end result is an apparent change in the angle of the plane of polarization. The angle of rotation of the molecule can be written as:

where L is the path length, l is the light wavelength, and (n_L-n_R) is the difference in the left and right refractive indices. The refractive index is different for different substances and is also wavelength-dependent. The refractive index is a bulk molecular property. There are a number of theories to explain the rotatory power of a molecule, with different degrees of formality (see Condon for a complete but lengthy and mathematical treatment of the subject). The mechanism of the light-medium interaction is very complicated, involving all the electronic excited states of the molecule. A less formal theory by Born and Kuhn in classical mechanics and Kirkwood in quantum mechanics describes a molecule as a set of charge clouds (bonds) at fixed orientations to one another. When the oscillating electromagnetic field of a polarized light beam passes by, the charge clouds are set into oscillations which interact with one another in a way based on their orientations to each other. The molecule´s induced oscillating electric dipoles produce a secondary beam of electromagnetic radiation which is polarized in the same direction as the original beam, but is out of phase with the original beam. A symmetric molecule (i.e., one which is superimposable on its mirror image) will oppose the left and right circularly polarized light equally often when all possible orientations of the molecule are taken into account. Chiral molecules will not be able to do the same because of the asymmetric arrangements of the interacting charge-clouds. Finally, the more the charge clouds oscillate given a certain external electromagnetic field, the more they will "oppose" that field.

Light may be polarized in a variety of ways. The most widely used technique is to pass a beam of ordinary light through a pair of anisotropic crystal prisms (such as calcite) glued together with optical cement. The velocity of light in any material is lower than in vacuum (the frequency is unchanged) and is easily calculated from the refractive index, n, for the material (n = v_vacuum/v_material). An anisotropic crystal has different refractive indices for different crystal axes and so the components of unpolarized light travel at different speeds through the crystal. The prism can be adjusted so that the incident angle of one component exceeds the critical angle on entry to the second prism and will not be transmitted. The result is the transmission of plane-polarized light (the other component is totally reflected and absorbed by a black coating applied to the prism).

If a substance rotates the plane of polarized light clockwise (looking toward light source) it is said to be dextrorotatory with a reported as positive. If the rotation is counterclockwise the substance is termed levorotatory and a is reported as negative. This angle is determined by rotating another pair of prisms at the opposite end of the material to produce maximum (or minimum) transmission of light of a given wavelength. An optically inert substance is first placed between the prism (for calibration) and then the optically active substance is added. The difference in rotation angles is the optical rotation of the active substance. Customarily, a is reduced to specific rotation by the definition:

Specific rotations found in tables are usually reported in "degrees", but actually correspond to inserting the path length L in decimeters, the density of the solution r in g cm^-3, the concentration of the optically-active solute c in g cm^-3, and the weight percent of solute in the solution w as a unitless number (i.e. degree cm³dm^-1g^-1 units). Occasionally, [a]^T_l are reported in biots (1 biot = 10^-3rad cm²g^-1). The superscript T is the temperature in °C and the subscript l is the wavelength of the incident monochromatic light. You will often see specific rotations in tables reported as [a]^T_D values: the "D" refers to the sodium D yellow line (a doublet at 589.0 and 589.6 nm) light source.

To make polarimetry accurate enough for analytical purposes the analyzer prism is adjusted to yield the minimum brightness (a small absolute change in light intensity will then be a large relative change). It would be difficult to locate the point of minimum intensity visually so a split-field polarimeter will be employed. This technique uses a smaller third prism to split the visual field into two halves. This prism will be set at a small angle to the polarizer and rotates the plane of polarization of half the visual field (this is the half-shade angle referred to later).

The analyzer may now be set at a certain angle to the other two prisms so that the two halves of the field will be maintained at the same intensity with no optically active material present. When an optically active compound is inserted the plane of polarization of the incident polarized light will be rotated through some angle. The two half-fields will now have different intensities since the plane of polarization of the light in the two halves of the field will be at different angles. The analyzer may now be rotated through the same angle that the active material rotated the plane of polarization of the incident light to restore the equal intensities in the two halves of the visual field. This then determines the angle of rotation, a.

Experiment

You will use a pair of sugars. One will be levorotatory and the other dextrorotatory. At some mole fraction a mixture of these materials in water will be optically neutral. You will find the correct mixture for optical inertness in this experiment by making a series of mixtures of different percent composition. Before beginning the experiment you should tabulate the following:

1. Length (2 dm) and diameter (9 mm) of the tubes.
2. Light source used (mercury lamp - it produces many wavelengths, but we select the 546.1-nm green line) NEVER look directly at the light source - it could cause blindness.
3. Aperture size (should be set at 6 mm)
4. Half-shade angle (generally 5°)
5. Correction for blank (+ or -)

The mercury lamp needs a 15 minute warm-up period so turn on the instrument when you first enter the laboratory. Make up your stock solutions with distilled water and then make the sample mixtures of different fractional composition (see procedure below). Keep the mixtures in covered containers to prevent water evaporation.

The polarimeter tubes are filled as follows: Unscrew the window holder in the widest diameter of the tube. Be careful with the window which could fall out. Remove the window from the holder trying to only handle it by it's edge. Hold the tube in a vertical position and pour in just enough mixture to fill above the rim. Then slide the window across the top of the tube so that no air bubbles become trapped inside. If an air bubble forms, you must remove the window, top up the tube and try again. The filled tubes must not contain any air. Screw on the window cap, holding the window in place. Tighten just enough to seal the tube. If you over tighten the stress in the glass will make the window optically active and will cause errors in your measurement.

The analyzer unit is at the front of the instrument. The eyepieces can be pushed in and out to allow you to focus on the vernier scale (be careful not to pull too far as they can easily be pulled from their sockets). The knurled ring in the center adjusts the focus of the half shade.

Look in the scale viewer and turn the adjustment dial until the two zero lines are aligned. One zero line is in the left side of the dial, and this is the units zero. The other in the right side is the decimal zero. The correction angle is found by looking in the half angle viewer. Inside you should see a green circle vertically cut with one side darker than the other. Turn the half-shade angle adjuster to one side or the other. One half of the circle will turn from dark to green and the other side will do the opposite. Turn the adjuster so that the two halves of the circle become uniformly dark (not uniformly green). Then record the half shade angle in your notebook. If the number is greater than 180° you should subtract 360° from it and use the negative number in your calculations. Do not move that dial again until you start the next sample.

To measure the optical rotation of a sample, look into the half-angle viewer and turn the adjustment dial on the front panel to make the circle evenly dark. Then read the scale shown and note this measurement in your data sheet. Before making any measurements we need to measure any rotation due to the glass tube filled with water. To make this blank measurement fill the tube with distilled water and place it in the instrument. Read the rotation and record this blank value in your notebook. Note of the position of the tube in the instrument and try to put all later tubes into the instrument in the same way. You should repeat this measurement two more times (a total of 3 measurements). All readings should agree within ±0.1°. Take the average of these measurements. This is the "zero" point.

Remove the tube from the polarimeter and carefully place a tube containing a sample solution of known concentration into the polarimeter. The difference between these readings and the "zero" point is a measure of the rotation of the light by the optically active material. The reading you obtain is the observed rotation

PROCEDURE

1. Prepare two stock solutions by accurately weighing 12.5 g samples of each and then dissolving each sample in 250 mL of water. Use two 250 mL graduated flasks and weigh your sample to the nearest mg.
2. Use the stock solutions to make the following sample mixtures

3. Clean and dry the sample tubes (including the brass ends) before each run so that all solution concentrations are accurate.
4. Fill the tube with the solution to be measured and look through the tube. If the solution is not clear and bubble free, do not take a measurement. The solutions must be thoroughly mixed to avoid any concentration gradients.
5. Place the tube into the instrument. Look into the half-angle viewer and make the circle evenly dark.
6. Read and record the values from the viewer. You should always write down the positive number given. If the number is greater than 180° you should subtract 360° from it and use the negative number in your calculations (e.g. read 335.7°; use 335.7 - 360.0 = -24.3°).
7. Obtain three (3)measurements of the optical rotation of this solution. All readings should agree within ±0.1°. If the eyepiece was rotated clockwise when the sample was measured, the sign of rotation is (+). Counter-clockwise rotation corresponds to a (-) rotation.
8. Repeat steps 3-6 for all remaining solutions.

You will be given two sugars from the following list.

CALCULATIONS

Correct all readings with the blank reading. Calculate [a]^T₅₄₆ for each run using equation (2). Determine the identity of your sugars and report the percent error for these single component calculations. Calculate the mole fractions for each of your mixtures and then plot the specific rotation versus mole fraction of sample A. Calculate the mole fraction of A required to produce an optically-inert mixture.

LITERATURE

1. D. P. Shoemaker, et al., Experiments in Physical Chemistry, McGraw-Hill Book Company, Sixth Edition, 1996.
2. P. W. Atkins and J.de Paula, Physical Chemistry 7th edition, W. H. Freeman and Company, New York, (2002).
3. E. U. Condon, Reviews of Modern Physics 7, 432 (1937).
4. T. R. P. Gibb, Jr., Optical Methods of Chemical Analysis, McGraw-Hill Book Company, 1942, pp. 343 ff.
5. R. E. Lyle and G. G. Lyle, A Brief History of Polarimetry, J. Chem. Ed., 41, 308-313 (1964).
6. H. B. Thompson, The Criterion for Optical Isomerism, J. Chem. Ed., 37, 308-313 (1960).

© 2003, S.C. Foster and Mississippi State University.