Theory of Dilute Polymer Solutions

Assuming the pearl necklace model for a chain polymer molecule in a solution, the theoretical expressions for the mean intermolecular potential and the radial distribution function of polymer molecules are derived. The methods in the theory of Born and Green, which is based on the superposition approximation, are conveniently applied to the case of solution. The results show that the mean intermolecular potential is nearly approximated by the Gaussian function, and it depends on the molecular weight and the temperature; the radial distribution function is also dependent on the molecular weight as well as on the temperature. At critical temperature where the second virial coefficient vanishes, the mean intermolecular potential vanishes and the radial distribution function assumes the constant value which is equal to unity. Theoretical expressions for the second and third virial coefficients are also given.