Differential refractometer

A differential refractometer (DRI), or refractive index detector (RI or RID) is a detector that measures the refractive index of an analyte relative to the solvent. They are often used as detectors for high-performance liquid chromatographyand size exclusion chromatography. They are considered to be universal detectors because they can detect anything with a refractive index different from the solvent, but they have low sensitivity.

Principles of operation

Light will bend or refract at different angles when entering solutions of different refractive indices. In a differential refractometer, light is passed simultaneously through a reference and a sample solution, and the difference in how much the light bends is collected. The difference appears as a peak in the chromatogram.

Refractive Index and Concentration

Refractive index measures how much light changes when it enters one medium from another. If we assume the refractive index of a solution changes proportionally solute concentration, then we get

$$n=n_{0}+k\cdot C$$

$$\Delta n=k\cdot C$$

Where:

• ${\textstyle n}$ is refractive index of the sample solution
• ${\textstyle n_{0}}$ is refractive index of the reference solution
• ${\textstyle k}$ is the refractive index increment, and is specific to the polymer sample-reference solution system
• ${\textstyle C}$ is the concentration of the solvent

Refractive Index Increment

The refractive index increment is crucial to the use of a differential refractometer. ${\frac {dn}{dC}}$, often expressed as mL/g, tells us the change in a solutions' refractive index relative to change in concentration. Accuracy of the refractive index increment is important in determining properties like molecular weight and molecular interactions with solvent. The refractive index increment can be found with a differential refractometer where the change in concentration is plotted against the change in refractive index.

The refractive index is affected by solvent, temperature, wavelength of light, environmental conditions and solute (polymer type).

Equipment Components

Light Source

Depending on the wavelength of choice, an appropriate light source is used, and a beam of light is directed at both cells. Sources include Helium–neon laser, Argon-ion laser, Sodium-vapor lamp and more.

Flow Cells

There are two compartments or flow cells, one holding the sample solution and the other holding the reference solution. Depending on the wavelength of light chosen, the cell material must be chosen so the wavelength is transmissible through the cell.

Optical Wedge or Prism

The optical wedge or prism sits after the cells and separates the light coming from the flow cells. The difference in refractive index causes the light paths to reflect at different angles. This difference is magnified by the optical wedge/prism.

Detector

A detector that can measure of range of wavelengths, usually a Photodiode array, measures the position of the two light paths. The detector quantifies the angle of refraction, which is proportional to the refractive index.

Signal Processor

The signal processor takes the signals from the detector and changes it to a chromatogram.

Temperature Control System

Because solutions are sensitive to temperature, a temperature control system regulates the solution temperature to ensure consistent readings.

General Operation

Common Differential Refractometer Brands

There exist various brands of differential refractometers. Popular models include:

• Waters 2414 Refractive Index Detector
• Agilent 1290 Infinity II Refractive Index Detector
• Thermo Scientific RefractoMax521 Refractive Index Detector

Set-up

The key general set-up and installation steps of a differential refractometer are as follows:

1. Select a suitable location with consistent temperature
   • Since the refractive index of a fluid depends on its temperature, it is crucial that the temperature of the environment is stable for most accurate outputs. To ensure the temperature of the detector and mobile phase are both consistent and the same, instruments typically include heat sinks.
2. Secure connections
   • The detector must be connected to numerous components, such include:
     • Grounded AC power source and input
     • Solvent waste line
       • Extra care for installing and positioning of the solvent waste line must be taken as the flow cell is sensitive to possible backpressure through this entry.
     • Ethernet
     • Additional detectors
3. Power on and configure the differential refractometer according to the manufacturer's manuals and desired applications

Instrument Calibration and Quality Control

All refractive index detectors require calibration upon first setting up the instrument as well as periodic quality control. Most manufacturer's recommend calibration with pure water and a sucrose calibration solution of a known refractive index. Once the instrument is in calibration mode, the pure water acts as a zero baseline reading, while the sucrose solution compares its known RI to the output, and the machine is adjusted accordingly.

After the pump has not been used for a while, it is necessary to purge the tubes of any contaminant air that has diffused into the channels. This is typically accomplished with isopropyl alcohol.

Data Utility

Differential refractometers are often used for the analysis of polymer samples in size exclusion chromatography. Other types of information that can be gathered from differential refractometers are:

Molecular Weight

Since the molecular weight (or extent of polymerization) of a solute will correspond to a specific refractive index increment, the relationship between increasing solute weight and refractive index increment can be plotted to determine the exact molecular weight of an unknown solute.

Interactions with Solvent

Increasing addition of solute will alter the solvent's viscosity and polarizability, which cannot be measured by instruments that rely on low viscosity. Since differential refractometer is an external tool, the solvent viscosity does not pose a physical barrier to measurement, making them universal detectors.

General Shape

The shape of a solute will influence it's induced dipole. This will affect the solvent polarizability, which affects the refractive index.

Practical Considerations

There are many practical factors that can affect the accuracy of a differential refractometer.

Solute Properties

When solutes are added to a solvent, they change the solution's optical density. The size, polarizability and shape and molecular structure of a solute all have effects on the refractive index of a solution. Generally, a Gaussian distribution is observed, although deviations occur.

Temperature

A controlled temperature is needed to ensure accurate measurements, as temperature affects many properties of a solution. If the temperature changes between measurements, this variance will be reflected in the measured refractive index.

Wavelength of Light

Cauchy's equation and Sellmeier equation describe the effect of wavelength on refractive index of medium.

Applications

The use of and results from differential refractometers are valuable in numerous fields of science, with its theory and function applied in various research directions, including drug analysis and nanoparticle tracking.

The nature of refractive indexes allows RIDs to be used in conjunction with additional analytical chemistry instruments. Following the use of other machines, differential refractometers can immediately (further) characterize compounds eluting from chromatographers, spectrometers, and detectors, including:

• High Performance Liquid Chromatography (HPLC)
• Ultraviolet-Visible Spectroscopy
• Mass Spectrometry
• Evaporative Light Scattering Detection (ELSD)