Excluded Volume in Polymer Chains

This discussion is concerned with the excluded volume effect in polymer chains, i.e., the mathematical problem of random flights with correlations between the flights, which is of importance in relating the mean size of a chain to its structure. A general formulation of the problem is set up and compared with the theory of Markoff processes. It is shown that although an integral equation of the Markoff form for the distribution function exists, it contains a complicated function whose exact evaluation is difficult. Since the same function occurs in the problem of the osmotic second virial coefficient, it is natural to relate the excluded volume effect to the second virial coefficient. The results of preliminary numerical calculations for the relation between the mean square radius of the chain and the second virial coefficient, in good agreement with experiment, are given. It is concluded that the volume effect is certainly not negligible for real chains, except when the second virial coefficient is zero,...

[1]  Bern,et al.  Zur mathematisch‐statistischen Theorie der Kettenmoleküle , 1950 .

[2]  T. B. Grimley.  High-polymer solutions , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  T. B. Grimley.  The Volume Effect in Polymer Chains , 1953 .

[4]  Elliott W. Montroll,et al.  Markoff Chains and Excluded Volume Effect in Polymer Chains , 1950 .

[5]  J. Kirkwood.  Statistical Mechanics of Fluid Mixtures , 1935 .

[6]  C. I. Carr,et al.  Light Scattering Investigation of the Structure of Polystyrene , 1950 .

[7]  P. Flory,et al.  Statistical Mechanics of Dilute Polymer Solutions. II , 1950 .

[8]  H. Benoǐt.  Calcul de l'écart quadratique moyen entre les extrémités de diverses chaînes moléculaires de type usuel , 1948 .

[9]  Paul J. Flory,et al.  The Configuration of Real Polymer Chains , 1949 .

[10]  P. Flory.  Summary report on polymer symposia held in conjunction with the international conference on theoretical physics, tokyo and kyoto, japan, september 11 to 23, 1953 , 1954 .

[11]  P. Flory.  Principles of polymer chemistry , 1953 .

[12]  C. Tchen.  Random Flight with Multiple Partial Correlations , 1952 .

[13]  Bruno H. Zimm,et al.  Application of the Methods of Molecular Distribution to Solutions of Large Molecules , 1946 .

[14]  S. Chandrasekhar.  Stochastic problems in Physics and Astronomy , 1943 .

[15]  R. Rubin.  The Excluded Volume Effect in Polymer Chains and the Analogous Random Walk Problem , 1952 .

[16]  H. James.  The Volume Exclusion Effect in Flexible Chains , 1953 .

[17]  W. Kuhn,et al.  Über die Gestalt fadenförmiger Moleküle in Lösungen , 1934 .

[18]  M. Klamkin,et al.  The Excluded Volume of Polymer Chains , 1952 .

[19]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion II , 1945 .

[20]  W. J. Taylor.  Average Square Length and Radius of Unbranched Long‐Chain Molecules with Restricted Internal Rotation , 1947 .

[21]  M. Fixman,et al.  DILUTE SOLUTIONS OF BRANCHED POLYMERS , 1953 .

[22]  F. Bueche.  The Effects of Interactions in Real Polymer Chains , 1953 .

[23]  Bruno H. Zimm,et al.  The Dimensions of Chain Molecules Containing Branches and Rings , 1949 .