Calculation of the dispersion of specific refractive index
increments
Citation for published version (APA):
Laven, J., Esker, van, M. W. J., & Vrij, A. (1975). Calculation of the dispersion of specific refractive index
increments. Journal of Polymer Science, Polymer Physics Edition, 13(2), 443-444.
https://doi.org/10.1002/pol.1975.180130220
DOI:
10.1002/pol.1975.180130220
Document status and date:
Published: 01/01/1975
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JOURNAL OF POLYMER SCIENCE: Polymer Physics Edition VOL. 13 (1975)
Calculation of the Dispersion of Specific Refractive
Index Increments
Values of the specific refractive index increment, Y
=
an/&, are needed for the deter- mination of molecular weights by light scattering. In particular for the study of co-polymers it is often important to mask one of the monomers, i.e., to make Y of that monomer (nearly) zero by choosing an appropriate solvent and wavelength. The finer adjustments of Y can be achieved by the selection of the wavelength. It would therefore be convenient if dispersions in Y could be calculated in a simple way. From the Lorenz- Lorentz equation one may derive1 for c + 0
Here n is the refractive index of the solution; cis the polymer concentration; n1 is the r e
fractive index of the solvent; p 2 and pl are the densities of polymer and solvent; M2 and
RZ are the molecular weights and the molar refractions of the repeating units of the poly- mer; and M I and R1 are those of the solvent. Although it is well-known that eq. (1)
gives rather poor results for the absolute values of Y , i t might be expected to give much better accuracy for the dispersion in Y . In Table I, calculated and experimental values of A 3 ~ ( 4 3 6 nm)
-
4546 nm) are compared. Only Y'S specified to four significant figures were used as tabulated by Huglin.2 Values of R were calculated from Eisen- lohr's bond refractions;J nl and p1 were obtained from tabulations of H u g h 4 a t 20°C,and p2 from tabulations of Van Krevelen.6 The molar refractions of the phenyl group
were obtained from averaged values of the molar refractions of monosubstituted benzene derivatives minus the bond refractions of the subst,ituents (R(C6Hs) = 25.20, 25.96, 26.44, respectively, at 656.3, 486.1, 434 nm). The molar refractions of the monosub stituted benzene derivatives were calculated from densities and refract,ive indexes, using the Lorenz-Lorentz equation.
Apparently the accuracy of the calculated A is 0.0020 ml/g or better. The following additional comments can be made:
1. There is no correlation between the magnitude of A and of A(ca1c)
-
A(exp).2. When neither polymer nor solvent contains benzene rings, A is several times smaller
3. A is negative when only the solvent contains a benzene ring. The existence of than when polymer or solvent contain benzene rings.
negative values of A is not always recognized.6 TABLE I
DisDersion of Refractive Index Incrementsz
Polymer Solvent &ale. Acale.
-
Aexp.Poly(ethy1 acrylate) Poly(propy1ene oxide) Poly(methy1 methacrylate) Poly(n-butyl methacrylate) Poly(propy1ene oxide) Poly(propy1ene oxide) Poly(methy1 methacrylate) Poly(methy1 methacrylate) Polystyrene Polystyrene Poly (a-methylstyrene) butanone isooctane isoamyl acetate acetone benzene chlorobenzene benzene toluene cy clohexane butanone carbon tetrachloride Poly (a-methylstyrene) cy clohexane
Polystyrene benzene
Polystyrene toluene 443
@ 1975 by John Wiley & Sons, Tnc.
0.0014 0.0007 0.0020 0.0014 -0.0100 -0.0100 -0.0056 -0.0052 0.0105 0.0109 0.0086 0.0098 0.0026 0.0029 0.0000 0.0007 0.0000 0.0001
-
0.0018 -0.0020 0.0015 0.0021-
0.0008 -0.0017 -0.0014 -0.0022-
0.0006 -0.0005444 NOTES References
1.
J.
W.
Lorimer, Polymer, 13.46 (1972).2.
M.
B.
Huglin in Light Scattering from Polymer Solutions, M. B. Huglin, Ed., 3. F. Eisenlohr, 2. Phys. C h a . , 75,585 (1910); 79,129 (1912).4. Ref. 2, p. 29.
5. D.
W.
van Krevelen in Properties of Polymers, Elsevier, Amsterdam, 1972, Ap-6. Ref. 2, p. 195.
Academic Press, London, 1972, Chap. 6.
pendix 2.
J. LAVBN
M. W. J. VAN DEN EWER A. VRIJ
Van’t Hoff Laboratorium voor Fysische en Colloidchemie der Rijksuniversiteit
Padualaan 8
Utrecht, The Netherlands
