Summary
In this paper we present analytical expressions for the osmotic and light-scattering second virial coefficients of polydisperse polymer samples in a good solvent. They are derived using the Schulz and the Lognormal molecular weight distribution respectively. The effect of interpenetrating coils is taken into account. Comparison is made with expressions already derived by Casassa using a hard sphere model. The reduction of the obtained expressions to simple scaling laws is discussed.
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References
H. Yanakawa, “Modern Theory of Polymer Solutions”, Harper & Row, New York, 1971.
P.G. de Gennes, “Scaling Concepts in Polymer Physics”, Cornell University Press, Ithaca, 1979.
J. des Cloizeaux, J. Phys.,42, 635–652 (1981).
E.F. Casassa, Polymer,1, 169–177 (1960).
I. Noda, T. Kitano and M. Nagasawa, J. Polym. Sci., Polym. Phys. Ed.,15, 1129–1142 (1977).
T.P. Wallace and E.F. Casassa, Polym. Prepr.,11, 136–141 (1970).
T. Sato, T. Norisuye and H. Fujita, J. Polym. Sci., Polym. Phys. Ed.25, 1–17 (1987).
M.G. Mennen, PhD Thesis, Leiden University, The Netherlands, September 1989.
E.F. Casassa, Polymer,3, 625–638 (1962).
M.G. Mennen, J.A.M. Smit and M.Mandel, in P.J. Lemstra and L.A. Kleintjens, “Integration of Fundamental Polymer Science and Technology-2”, Elsevier Appl. Sci., London (1988), pp 222–226
W. Krigbaum and P.J. Flory, J. Am. Chem. Soc.,75, 1775–1783 (1953).
J.-Y. Chien, L.-H. Shih and S.-C. Yu, J. Polym. Sci.,29, 117–125 (1958).
V.V. Varadaiah and V.S. Rao, J. Polym. Sci.,50, 31–34 (1961).
M. Fixman, PhD thesis, M.I.T., Cambridge, Mass., 1953.
E.F. Casassa, J.Chem. Phys.,27, 970–971 (1957).
E.F. Casassa and H. Markovitz, J. Chem. Phys.,29, 493–503 (1958).
G. Tanaka and K. Solc, Macromolecules,15, 791–800 (1982).
A.J. Barrett, Macromolecules,18, 196–200 (1985).
E. Straube and K. Oeltze, Acta Polym.,30, 623–627 (1979).
E. Straube, K. Oeltze and G. Helmis, Wiss. Z. Tech. Hochsch. “Carl Schorlemmer”, Leuna-Merseburg,20, 238–248 (1978).
T.A. Witten and J.J. Prentis, J. Chem. Phys.,77, 4247–4253 (1982).
S. Stepanow and E. Straube, Wiss. Z. Tech. Hochsch. “Carl Schorlemmer”, Leuna-Merseburg,29, 403–410 (1987).
Y. Oono and K.F. Freed, J. Phys. A: Math. Gen.,75, 993–1008 (1981).
J.F. Joanny, L. Leibler and R. Ball, J. Chem. Phys.81, 4640–4656 (1984).
G.V. Schulz, Z. Physik. Chem.,B43, 25–46 (1939).
H. Wesslau, Makromol. Chem.,20, 111–142 (1950).
C. Strazielle and H. Benoit, Pure Appl. Chem.,26, 451–479 (1971).
See for example: R. Kniewske and W.M. Kulicke, Makromol. Chem.,184, 2173–2186 (1983). Y. Miyaki, Y. Einaga and H. Fujita, Macromolecules,11, 1180–1186 (1978). M. Fukuda, M. Fukutomi, Y. Kato and T. Hashimoto, J. Polym. Sci., Polym. Phys. Ed.,12, 871–890 (1974)
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Mennen, M.G., Smit, J.A.M. The second virial coefficient of polydisperse polymer samples in a good solvent. Polymer Bulletin 23, 67–74 (1990). https://doi.org/10.1007/BF00983966
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DOI: https://doi.org/10.1007/BF00983966