# Refractive index increment dn/dc values

18 June 2013 No Comment

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

In light scattering a crucial parameter which 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 and obtain the molecular weight in a batch SLS (static light scattering) measurement. The factor K consists of

$K=\frac{2 \pi^2 n^2}{\lambda^4 N_A} (\frac{dn}{dc})^2$

where n is the refractive index of the solvent, λ the wavelength of the laser, and NA is Avogadro’s number. The refractive index increment applies to the sample under a specific condition. For example, 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 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, which happens to also have a dndc of 0.185 mL/g.

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

### Table of select dn/dc values

Sample/Solid Phase Solvent/Liquid Phase dn/dc [mL/g]
Biomolecules Aqueous Buffer Average: 0.185
Proteins Aqueous Buffer 0.16-0.20, average: 0.185
DNA Aqueous Buffer 0.17
RNA Aqueous Buffer 0.17-0.19
Alanine Aqueous Buffer 0.19
Polysaccharides Aqueous Buffer Average: 0.15
Chitosan Aqueous Buffer 0.16-0.18
Dextrane Aqueous Buffer 0.14-0.15
Hyaluronic Acid Aqueous Buffer 0.16-0.18
Pullulan Aqueous Buffer 0.14-0.16
Starch Aqueous Buffer 0.15
Glucose, Maltose, Lactose, Sucrose Aqueous Buffer 0.14-0.15
Liposomes
Phospholipids Water 0.16
SDS micelles Water 0.11
CTAB micelles Water 0.15
Polymers
Polystyrene PS THF 0.18-0.19
Polystyrene PS Toluene 0.08-0.11
Polystyrene PS Cyclohexane 0.16-0.17
Polystyrene PS Decaline 0.12
Polystyrene PS MEK 0.21
Polystyrene PS TCB 0.052
PMMA THF 0.09
PMMA Toluene 0.01-0.02
PVC Cyclohexanone 0.08
PVC DMF 0.08
PVC THF 0.10
PVP Water 0.17
PEG 4000, PEG 6000 Water 0.13

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 dndc for SLS? This document discusses the error of estimating the refractive index increment, specifically the effect that different wave lengths, additives, temperature, or structure/molecular density may have on dn/dc and subsequent influence on Mw and A2.