Theory of Dilute Polymer Solution. I. Excluded Volume Effect

A statistical theory of the excluded volume effect in a polymer molecule is developed, making use of a pearl necklace model with a continuous medium approximation. For the mean square end-to-end distance 〈R2〉 and the mean square radius of gyration 〈S2〉, the theory leads to the same expressions as Zimm, Stockmayer, and Fixman's. Taking solutions of polystyrene in cyclohexane as an example, it is illustrated that, in the vicinity of the Flory temperature, the expression for 〈S2〉 enables to give a complete quantitative interpretation to light scattering data. The distribution function for distance Rkl between segments k and l, its 2mth moment 〈Rkl2m〉, and the mean square distance 〈Sk2〉 between segment k and the center of molecular mass are also calculated to make clear the nature of the excluded volume effect. Finally, the influence of the volume effect upon light scattering measurement is discussed somewhat in detail.