Theory of Dilute Macromolecular Solutions

  • A. Isihara
  • E. Guth
Conference paper
Part of the Advances in Polymer Science book series (POLYMER, volume 5/2)


The object of this paper is to lay the foundations of the Theory of Dilute Macromolecular Solutions in a unified, simplified, and yet rigorous manner. It also aims to acquaint chemists and physicists with a field of rapidly increasing significance, in view of possible applications to biophysics (and biochemistry). The Introduction gives a brief outline of the historical development of macromolecular solution theory. Roughly, one can distinguish between (a) lattice- and (b) gas-type theories, just as in the theory of liquids. The former, because of their apparent simplicity, have enjoyed great popularity for a long time among polymer chemists. However, lately, again just as for liquids, the gas-type approach has been proven to be more fundamental.

Our general approach is a proper adaptation and generalization of the gas-type theories of McMillan and Mayer and of Kirkwood and Buff. These were originally developed for simple (monomer) solutions. We use the cluster development of McMillan and Mayer, which itself is an adaptation of the original (Ursell)-Mayer cluster development. We then combine this procedure with the distribution function approach of Kirkwood and Buff.

Section 2 brings the cluster development for the osmotic pressure. Section 3 generalizes the approach of Section 2 to distribution functions, including a new and simple derivation of the cluster expansion of the pair distribution function. Section 4 presents a new expression for the chemical potential of solvents in dilute solutions. Section 5 contains an application of our general solution theory to compact macromolecular molecules. Section 6 contains the second osmotic virial coefficient of flexible macromolecules, followed in Section 7 by concluding remarks.


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Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • A. Isihara
    • 1
  • E. Guth
    • 1
  1. 1.Oak Ridge National LaboratoryOak Ridge

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