Refractive index increment dn/dc values when you need them?

In light scattering a crucial parameter that appears together with the Rayleigh Ratio RΘ is the refractive index increment, also known as “dn/dc”. Typically, Kc/RΘ is plotted versus concentration to extrapolate to zero concentration. This is how we can obtain the molecular weight in a batch SLS (static light scattering) measurement. The factor K consists of

Equation displaying K=2 pi^2 n^2/lambda^4 /NA * (dn/dc)^2

where n is the refractive index of the solvent, λ the wavelength of the laser, and NA is Avogadro’s number. Here, the refractive index increment applies to the sample under a specific condition. As a result of this, temperature, laser wavelength, conformation of the molecule, or additives have an effect on the absolute value of dn/dc. Thus for a perfect static light scattering experiment, the exact dn/dc at the conditions under consideration should be determined.

In many practical examples, the value of dn/dc can be taken from prior datasets taken under similar conditions (or from literature references). Since the refractive index is intuitively related to the density / specific volume of molecules, (and for a range of proteins this is quite similar), a typical value of 0.185 mL/g as the dn/dc for an ‘average protein’ is a popularly chosen value. By coincidence, one of the most popular standards for GPC is polystyrene in tetrahydrofuran THF, which happens to also have a dn/dc of 0.185 mL/g.

Table of some common dn/dc values

The table below shows refractive index increment values for light scattering configurations with a red laser [HeliumNeon, 632.8nm] at room temperature [25C]. Refractive increment values are listed for a series of common samples.

Sample/Solid PhaseSolvent/Liquid Phasedn/dc [mL/g]
BiomoleculesAqueous BufferAverage: 0.185
ProteinsAqueous Buffer0.16-0.20, average: 0.185
DNAAqueous Buffer0.17
RNAAqueous Buffer0.17-0.19
AlanineAqueous Buffer0.19
PolysaccharidesAqueous BufferAverage: 0.15
ChitosanAqueous Buffer0.16-0.18
DextraneAqueous Buffer0.14-0.15
Hyaluronic AcidAqueous Buffer0.16-0.18
PullulanAqueous Buffer0.14-0.16
StarchAqueous Buffer0.15
Glucose, Maltose, Lactose, SucroseAqueous Buffer0.14-0.15
SDS micellesWater0.11
CTAB micellesWater0.15
Polystyrene PSTHF0.18-0.19
Polystyrene PSToluene0.08-0.11
Polystyrene PSCyclohexane0.16-0.17
Polystyrene PSDecaline0.12
Polystyrene PSMEK0.21
Polystyrene PSTCB0.052
PEG 4000, PEG 6000Water0.13

DNA = desoxyribonucleic acid ; RNA = ribonucleic acid ; SDS = sodium dodecyl sulfate ; CTAB = cetyltrimethylammonium bromide ; PMMA = poly(methyl methacrylate) ; PVC = polyvinyl chloride ; PEG = poly (ethylene glycol) ; PVP = Polyvinylpyrrolidone ; THF = tetrahydrofuran ; MEK = methyl ethyl ketone ; TCB = 1,2,4-trichlorobenzene ; DMF = dimethylformamide

A useful reference for a wide range of specific dn/dc values is the collection by Theisen, A.; Johann, C.; Deacon, M.P.; Harding, S.E. “Refractive Increment Data-Book for Polymer and Biomolecular Scientists”, Nottingham University Press, Nottingham UK, 2000. ISBN: 1-897676-29-8

Select values in the table were taken from: Tumolo, T.; Angnes, L.; Baptista, M.S. “Determination of the refractive index increment (dn/dc) of molecule and macromolecule solutions by surface plasmon resonance”, Analytical Biochemistry 333 (2004), 273–279; DOI: 10.1016/j.ab.2004.06.010

Also of interest: FAQ – Is it alright to estimate dn/dc for SLS? This document discusses the error of estimating the refractive index increment, specifically the effect that different wavelengths, additives, temperature, or structure/molecular density may have on dn/dc and subsequent influence on Mw and A2.