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# Basics of polarimetry

Polarimetry is used to analyze chiral substances and determine their concentration in solutions. It is applied in quality control, laboratory analytics, as well as in R&D in the pharmaceutical, cosmetics, chemical, food, and medical industries. The basics of polarimetry and chirality are briefly presented in this article.

## Definition of polarimetry

Polarimetry is a superior, sensitive and nondestructive measuring technique for the measurement of optical activity, as exhibited by inorganic as well as organic compounds.

The concentration and physical properties of the solution influence the plane of polarized light and this is detected as the angle of optical rotation by a polarimeter. From this measurement, different parameters can be defined, such as specific rotation, concentration, sugar content, and purity.

## What is chirality

Polarimetry is the key to understanding chiral molecules in terms of optical activity. Chiral molecules are characterized by their property to rotate the plane of polarized light. Therefore, they are called optically active. The effect caused by this property is referred to as optical rotation.

The geometrical property of a molecule that is analyzed with a polarimeter is called chirality; hence molecules with mirror-image geometries are called chiral. They cannot be superimposed on their mirror image. The mirror images are called left- and right-handed enantiomers. Chiral molecules are typically organic molecules and biomolecules, such as sugars, starch, flavors, and essential oils, active pharmaceutical ingredients (APIs), amino acids, and various other biomolecules.

Chiral molecules rotate the plane of polarized light. This property is called optical activity. Left- and right-handed enantiomers turn the polarization plane in opposite directions. The angle by which the polarization plane is rotated is called optical rotation. It is measured in degrees [°OR] with a polarimeter.

Chiral molecules are characterized by the mirror image constitution of their atoms. The mirror image of chiral compounds cannot be superimposed with the original (see Fig. 1). This is in contrast to an achiral object, as for example a symmetric flask, whose mirror image can be superimposed with the original[1].

Figure 1: Chiral and achiral objects. The left hand cannot be superimposed onto its mirror image, the right hand. It is chiral. The mirror image of a symmetric flask can be superimposed onto the original. It is achiral[2].

A precondition for chirality within a molecule is an atom with at least four different substituents displaying distinct physical configurations. Such an atom is called a chiral center. A practical example would be a saturated carbon: with four different substituents bound to one carbon, the molecule is asymmetric. Exchanging one substituent of the chiral center leads to three different substituents (two substituents of four are the same). This creates molecules that can be superimposed with the original (see Fig. 2).

Figure 2: Distinct physical configuration of substituents leads to asymmetric / chiral molecules. Bromochlorofluoromethane (a) is a chiral C atom (*). Its mirror image (turned by 180°) cannot be superimposed onto the original molecule. Dichlorofluoromethane (b) is achiral with only three different substituents. The image of (b) turned by 180° can be superimposed with the original2.

Most chiral substances are organic molecules which are characterized by an asymmetric carbon. Chiral substances do not only occur in organic chemistry but can be made up of any kind of atom that can bind at least four different substituents, like for example phosphor or sulfur. Examples for chiral substances are sugars / carbohydrates, amino acids, DNA, or penicillins.

### Enantiomers

Any molecule with a chiral center can exist in one of two stereo isomeric structures, which are related to each other like image and mirror image. Those compounds are called enantiomers.

Enantiomers of the same substance are composed of the same atomic components and chemical bonds. Therefore, they hardly differ in their physical and chemical properties. However, they differ at a defined point within their geometry. As stated above, polarimetry may be applied to study the geometry of molecules. The ratio of two enantiomers, as well as their purity and their concentration, can be analyzed by the application of polarimetry.

## Optical activity and optical rotation

Chiral molecules are characterized by their property to rotate the plane of polarized light.

Therefore, they are called optically active. The effect caused by this property is referred to as optical rotation. Optically active substances can be pharmaceuticals, flavors and fragrances, amino acids, sugars, and many more biomolecules (see Fig. 3).

The optical rotation can be determined with polarimetry. In polarimetry, plane polarized light is applied. Light sources (e.g. a light bulb, a LED, or the sun) emit electromagnetic light waves. Their electrical field oscillates in all possible planes vertical to their direction of propagation.

If the unpolarized light hits a polarizer, only that part of the light may pass that oscillates in the same plane as the polarization filter is aligned. This plane is called the plane of polarization (see Fig. 4) and the light is called plane polarized light.

The plane of polarization is turned by optically active compounds: the enantiomers. According to the direction in which the light is rotated, the enantiomer is referred to as dextrorotatory (d or +; Latin: right; clockwise) or levorotatory (l or -; Latin: left; counterclockwise). The optical activity of enantiomers is additive. If different enantiomers coexist in one solution, their optical activity adds up.

Solutions with the same concentration of both enantiomers of a chiral compound are called racemates. Racemates are optically inactive as the clockwise and counterclockwise optical rotations cancel each other out.

The concentration and the optical rotation of the optically active substances in the solution are in proportion to each other. When the concentration of a sample is known, polarimetry can be applied to determine its specific rotation (a physical property) to characterize a new substance.

## Polarimeters

### Measuring principle

Figure 4: Measuring system of a modern Modular Circular Polarimeter by Anton Paar and its main components

Polarimetry is the measurement of optical rotation of substances by using a polarimeter. A polarimeter is an instrument which measures the angle of rotation by passing polarized light through an optically active (chiral) substance. To measure optical rotation, a Light Emitting Diode (LED) produces a beam of ordinary light. This light first passes through a polarizer (polarization filter) in order to obtain a defined orientation of the plane of polarization. The polarized light then passes through the sample cell. If the sample is optically active, the plane of polarization becomes rotated. The light with the rotated plane of polarization passes through an analyzer, which is a second polarization filter.

The polarimeter rotates the first polarizer until the photo receiver measures a transmission minimum. If the sample is optically inactive, polarizer and analyzer are now oriented perpendicular to another. If the sample is optically active, the polarimeter rotates the polarizer until the plane of polarization behind the sample cell is again perpendicular to the polarization plane of the analyzer.

The resulting degree of rotation is a direct measure of the optical rotation of the sample. The correct wavelength for the measurement is precisely selected by an interference filter positioned in the beam in front of the photo receiver.

In case of a Modular Circular Polarimeter (MCP), the first polarizer is fixed. The polarized light additionally passes through electromagnetic coils (Faraday modulator) to further enhance the angular resolution. Thereby an oscillation is superimposed onto the plane of polarization by means of the Faraday effect. The Faraday modulator is located in front of the sample cell (see fig. 6). After the polarized light’s transition through the sample cell, the analyzer is rotated automatically until the transmission minimum is reached.

### Measuring range

The measuring range of MCP polarimeters extends from -89.9 °OR to +89.9 °OR. This is the range that can be unambiguously measured with a polarimeter. This results from the fact that one rotation of the analyzer will show two transmission maxima (at 0 °OR and 180 °OR to the plane of polarization) and two transmission minima (at 90 °OR and 270 °OR to the plane of polarization).

Only a range of approx. 180 °OR (i.e. from -89.9 °OR to +89.9 °OR) can give clear results without ambiguity. If, for example, the sample turns the plane of polarization by +110 °OR, a polarimeter would thus show -70 °OR.

Moreover, polarimeters cannot distinguish between single and multiple turns of the polarization plane inside the sample (i.e. a “screw” with a rotation of X °OR + n x 360 °OR).

However, some manufacturers claim to have a measuring range of +/-360 °OR. Without further extrapolation and calculating steps this does not directly lead to unambiguous results: the user has to know in which quadrant the result is to be expected. The estimated optical rotation of the sample has to be known to finally get an idea whether the value is higher than 90 °OR, 180 °OR, or 270 °OR. For this reason, there are no official standards for optical rotations greater than 90 °OR available, and instruments reading above 90 °OR cannot be certified.

In order to obtain a result within +/-89.9 °OR, the sample has to be diluted or the cell length reduced. Both options have a linear effect on the optical rotation value. All official standards follow recipes to ensure optical rotation values between -89.9 °OR and +89.9 °OR.

The specific rotation is the optical rotation for a concentration of 1 g/100 mL and a cell length of 100 mm. For penicillin, this means a polarimeter can already detect small concentrations. For higher concentrations, shorter sample cells can be used so that the measured value is within the range of ±89.9 °OR (this also saves sample volume, yields higher transmission, and gives a better signal).

As penicillin has a specific rotation of 223 °OR, it can be measured with an MCP polarimeter even if it has a measuring range of ±89.9 °OR only. By reducing the path length of the sample cell from 100 mm to e.g. 2.5 mm or reducing the concentration of the sample, the result will be compatible with the measuring range of the polarimeter.

In order to determine the specific rotation of a substance, the MCP polarimeter can use a shorter sample cell than 100 mm. A predefined method works out the scaling to 100 mm automatically.

## Measured parameters and methods

### Optical rotation and related quantities

The measurement of the optical rotation of a sample is called “polarimetry” and is performed using a polarimeter. From the optical rotation, the specific rotation, a material constant of a substance can be derived. It is the optical rotation for a given concentration, sample cell length, temperature, and wavelength.
In turn, if you know the substance’s specific rotation, the concentration can be determined from the optical rotation measurement.

The measured value in a polarimeter is the optical rotation, α [°OR]. From the optical rotation further values can be derived:

a)     Concentration (general) when specific rotation of the substance is known

b)    Sugar concentration (for known specific rotations)

c)     Specific rotation (material constant) when the concentration is known

d)    Purity (in combination with refractive index)

e)     User-defined scales

### Specific rotation

The specific rotation is a material constant. It is the optical rotation for a “given number” of optically active molecules in the light’s way through the sample. This “number of molecules” the light beam meets is determined by:

• Concentration of the optically active substance, c [g/mL]: the higher, the more molecules
• Length of sample cell, l [mm]: the longer, the more molecules along the way
• Temperature, T [°C]: influences density via thermal expansion and may cause changes in molecular structure with effects on the optical rotation

Another influencing parameter on the measured optical rotation is the wavelength of the light, λ [nm].

The substance’s specific rotation $\left[\alpha \right]^T_\lambda$ is defined as the optical rotation for:

• Concentration c = 1 g/mL
• Length of sample cell l = 100 mm
• Temperature T = 20 °C
• Wavelength λ = 589 nm (corresponding to Nad-line)

The relation of optical rotation, α, and specific rotation,$\left[\alpha \right]^T_\lambda$, is summarized by Biot’s law:

To determine a substance’s specific rotation, you have to:

•  measure the optical rotation α
• know the concentration c from sample preparation, and
• know the cell length l from the instrument:

Given the input parameters, the polarimeter works out the specific rotation automatically.

### Concentration

To use the polarimeter for concentration measurements, we have to:

• measure the optical rotation α
• know the specific rotation $\left[\alpha \right]^T_\lambda$ of the optically active constituent in the sample, and
• know the cell length from the instrument l:

Given the input parameters, the polarimeter works out the concentration automatically:

• Sucrose concentration
• Glucose concentration
• °Z (International Sugar Scale)
• % purity (in combination with refractive index)

## Applications

Polarimetry is ideal for measuring the concentration of optically active substances in the pharmaceutical, cosmetics, chemical, and medical industries, as well as for R&D. Measured compounds can, for example, be active ingredients (ingredients in pharmaceutical drugs) in formulation and validation departments. Moreover, polarimetry is used in the sugar industry as for example in payment laboratories to measure the sugar content of incoming sugar beet and sugar cane samples, or in sugar mills for quality control at every stage of production of the raw, intermediate, and final product.