How do I determine what dn/dc I should use for my sample? - WKB319062
OBJECTIVE or GOAL
To determine the appropriate dn/dc value for a sample in a specific mobile phase, which is essential for accurate molar mass and concentration measurements using ASTRA software.
ENVIRONMENT
- Optilab (for differential refractive index measurements)
- ASTRA software
PROCEDURE
The dn/dc value can be determined by measuring it directly using batch injections with an Optilab, referencing literature values, estimating from UV data, or assuming 100% mass recovery. For direct measurement, prepare at least five concentrations of the sample in the mobile phase and measure dRI for each using Optilab. Plot dRI versus concentration to obtain the slope, which is the dn/dc value. Alternatively, use the ASTRA method “dndc from UV” if the UV extinction coefficient is known. For systems with full mass recovery, use injected mass and RI data to estimate dn/dc.
ADDITIONAL INFORMATION
How do I determine what dn/dc I should use for my sample?
When calculating molar mass of your sample in your mobile phase, it's important that you are using the correct value for the specific refractive index increment, also known as dn/dc. This value will be specific to the sample and the mobile phase used to dissolve the sample.
What is dn/dc and how does ASTRA use this value?
For a solute (your sample) in a solution (your mobile phase), dn/dc is related to the polarizability of the solute. The value of dn/dc describes how much the refractive index of the solution changes as a function of the sample's concentration. dn/dc has units of [mL/g], which can be thought of as how much the refractive index of a solution will change for unit change in concentration of the solute. The value of dn/dc is important in two contexts:
1) Measuring molar mass via light scattering measurements
The amount of light scattered by the sample is proportional to the molar mass, sample concentration, and the square of the sample's dn/dc value. A sample's dn/dc will impact the intensity of scattered light intensity, so for accurate molar mass measurements we need to use an appropriate value for dn/dc. It's important to note that dn/dc is required for molar mass determination regardless of the concentration detector that is used; however, dn/dc can also be used to determine concentration as discussed next.
2) Measuring concentration via differential refractive index (dRI) measurements:
In many cases, we need to know the concentration of our sample at each data slice. Differential refractive index (dRI) measurements with an Optilab are one way to determine this. ASTRA then uses the value of dn/dc to determine the concentration of your sample based on this change by dividing the dRI signal by the sample's dn/dc.
What causes dn/dc to change?
Solvent refractive index dependence:
Changing the solvent can impact dn/dc. If the refractive index of the new solvent is significantly different (greater than 1%) from the previous one, the dn/dc must be updated. A new dn/dc can be estimated using a specific equation involving the partial specific volume and refractive index of the solvent.
Wavelength dependence:
dn/dc typically increases as the wavelength decreases. For molar mass calculations, use the dn/dc value at the wavelength used by the light scattering instrument (~660 nm). Curve fitting can be used to estimate dn/dc at a desired wavelength if values are known at several wavelengths.
Molar Mass dependence:
Above a certain molar mass, dn/dc can be considered constant. For low molecular weight polymers, dn/dc may vary and can be modeled using the equation: dn/dc = d + e/Mw.
How can I determine what dn/dc I should use for my sample in my mobile phase?
Measurements of dn/dc with an Optilab
Measure dn/dc by performing batch injections of your sample at various concentrations and plotting dRI versus concentration. The slope of the plot is the dn/dc value.
Literature values for dn/dc
If measurement is not possible, use literature values from the Wyatt dn/dc database or bibliography.
Estimation of dn/dc using UV data
If the UV extinction coefficient is known, use UV and RI data together in ASTRA to estimate dn/dc using the “dndc from UV” method.
Estimation of dn/dc by assuming 100% mass recovery
In systems with full mass recovery, estimate dn/dc using injected mass, sample concentration, injection volume, and flow rate. This method is described in TN4001: Online dndc Determination.