Specific Rotation Equation vs. Optical Rotation – What’s the Difference?

Por Angelo DePalma, PHD

La polarimetría con polarímetros mide el grado de rotación de la luz polarizada cuando pasa a través de un material ópticamente activo.

If you’re learning about Polarimetry you might come across  the terms specific rotation and optical rotation. What is the specific rotation equation and optical rotation? What are the differences between the two?  We will cover this below.

Polarimetry was discovered by Étienne-Louis Malus, a French engineer who was studying reflective glass. Several years later another Frenchman, Jean-Baptiste Biot, found that molecules such as sugar could rotate polarized light as well. It was not until 1874 that Dutch chemist Jacobus Henricus van’t Hoff proposed that carbon’s tetrahedral structure was responsible for the optical activity – the ability to rotate plane-polarized light – of many organic compounds.
Optical activity is a property unique to chiral substances. For example 2-butanol, which possess a chiral center (one carbon bound to four different ligands). Figure 1 illustrates that 2-butanol exists as two mirror-image isomers, or enantiomers. The atomic connectivity in the S-isomer is identical to that of its mirror-image R-isomer, except that two of the groups attached to carbon were interchanged.
Las designaciones R y S se basan en las reglas del Prelog de Cahn-Ingold para asignar prioridad a los grupos sustitutivos. Visualiza el sustituto más pequeño apuntando hacia abajo por debajo del plano del papel o de la pantalla del ordenador. Los tres grupos restantes están clasificados por peso molecular. Si la dirección del grupo más pesado, el siguiente más pesado y el más ligero es en el sentido de las agujas del reloj, la molécula se designa como R; si es en sentido contrario a las agujas del reloj, la designación es S.
Cuando los isómeros d y l están presentes en concentraciones exactamente iguales, siguen siendo quirales, pero sus rotaciones se anulan y la muestra se denomina racemato o mezcla racémica.

How Polarimetry Works

La luz monocromática normal que emerge de una bombilla consiste en un número infinito de ondas oscilantes en todos los planos posibles perpendiculares a la línea de propagación. Un polarizador es un tipo especial de rendija o abertura que permite que la luz que se propaga en un plano pase a través de ella. Cuando esta luz interactúa con una sustancia quiral se acelera o se ralentiza, siendo el efecto neto una aparente rotación en el plano de la luz polarizada.

Unfortunately no correlation exists between the absolute configuration of the molecule (e.g. R- or S-) and the direction in which it rotates polarized light. Molecules that shift the angle clockwise are known as dextrorotatory (“right-turning”), d or (+) Those molecules that shift the angle counter-clockwise are called levorotatory (“left-rotating”), l, or (-). Predicting the precise rotation of a molecule with more than one chiral center is difficult since both chiral centers contribute to optical rotation.

In this 3D projection of 2-butanol the structure on the left has the R-configuration, while its mirror image on the right is the S-isomer according to the Cahn-Ingold-Prelog rules. However, the structure on the left rotates plane-polarized light counter-clockwise. It is designated as (-) or l, while the S-isomer is (+) or l.
Por si esto no fuera suficientemente confuso, la bioquímica emplea una tercera nomenclatura que emplea las minúsculas mayúsculas D y L. Este sistema está relacionado con la R y la S pero no sigue estrictamente el Prelog de Cahn-Ingold ni se relaciona directamente con la rotación óptica. Por lo tanto, está fuera del alcance de este artículo. Aquí nos ocupamos sólo de la D y la L o (+) y (-), respectivamente.

Specific Rotation Equation

Specific rotation equation, [α], is a fundamental property of chiral substances that is expressed as the angle to which the material causes polarized light to rotate at a particular temperature, wavelength, and concentration.
The term for specific rotation equation is given by

where T is the measurement temperature, λ is the wavelength of light employed (normally the sodium D-line, or 589 nm), α is the observed rotation. l is the path length, and c is the concentration in grams per milliliter (for pure substances the density) or grams per 100 milliliters. The solvent (often ethanol, methanol, DSMO, acetone, water, etc.) is also specified. Specific rotation may also be expressed as degrees per mole of the substance where the conditions of measurement (i.e. solvent, light source, and path length) are also specified.

Uso de varias longitudes de onda en la polarimetría para controlar la sensibilidad

El uso de longitudes de onda inferiores a 589 nm, que están disponibles con las líneas de lámparas de mercurio y de deuterio aisladas a través de filtros para proporcionar longitudes de onda de 578, 546, 436, 405 y 365 nm, puede a veces proporcionar ventajas en cuanto a la sensibilidad. En general, la rotación óptica observada a 436 nm es aproximadamente el doble y a 365 nm alrededor del triple que a 589 nm.

Fuentes de luz del polarímetro

It is now common practice to use other light sources such as xenon or tungsten halogen. With appropriate filters, these light sources offer advantages of cost, long life, and broad wavelength emission range over traditional light sources.
Los polarímetros miden la rotación observada designada por la letra griega minúscula α. A partir de este valor y del conocimiento de la rotación específica, se pueden calcular fácilmente las concentraciones de ambos isómeros de una sustancia pura. Por ejemplo, es posible determinar la conversión de un material aciral en una sustancia quiral, o las concentraciones relativas de los isómeros ópticos, conocidas como exceso enantiomérico.

Digamos que un químico intentaba fabricar (-)-2-butanol puro, que tiene una rotación específica de -13,5º en condiciones de medición estándar. Pero cuando el producto líquido se coloca en una celda de un polarímetro como solución limpia, la rotación observada es sólo de -4,5º, o un tercio de la rotación específica. Esto nos dice que un tercio del 2-butanol de la muestra consistía en el isómero l o (-), y los dos tercios restantes consisten en el racemato (cantidades iguales de (+) y (-). Por lo tanto, dos tercios del butanol son (-)-2-butanol, y un tercio es (+)-2-butanol.

Observed Rotations

More relevant to industry are observed rotations of mixtures. For example of food ingredients, perfumes, flavorings, chemicals, pure or formulated pharmaceuticals – virtually any industry that produces or uses chiral organic molecules in pure or diluted form. In these situations, polarimetry provides a rapid, reliable, quality check. This eliminates the need of using conventional analysis like liquid chromatography. This can take an hour to do what the polarimeter accomplishes in minutes.
Polarimetry provides an additional check on a pure substance before it is added to an expensive batch. This determines the ingredient’s concentration or purity. For example a 25% glucose syrup will have an observed rotation that is five-sixths that of a 30% syrup.

Similarly the optical rotation of a mixed-component ingredient, intermediate, or finished product will have a characteristic optical rotation that may arise from the presence of several chiral compounds. Once a standard is determined for the composite observed rotation, one can establish quality criteria based on optical rotation. In these situations the polarimeter measurement becomes a type of screen for further testing. This determines which ingredient is out of specification.

Conclusión de la polarimetría

In conclusion, Optical rotation is an indispensable quality and identity assay for a wide range of critical industries. Research organic chemists use polarimetry to test the effectiveness of catalysts and asymmetric synthetic processes. Food, drug, as well as flavors industries utilize polarimetry as a quality attribute for raw ingredients and finished products.

Los polarímetros en los laboratorios de hoy en día

Although polarimetry is a mature technique, today’s instrumentation provide features and benefits that purely manual-optical systems do not. Busy labs process multiple samples per day. They  now have the option of automated data capture, variable wavelength and temperature. Labs can now get readouts accurate to 0.0001°Arc (optical rotation, α).  This is a high level of precision for process industries and formulators.  Armed only with a polarimeter,  labs can set extremely narrow quality standards based on optical rotation.