A theory of the thermodynamic behavior of nonelectrolyte solutions. III. The osmotic pressure of polymer solutions

Data on the osmotic pressures of both dilute and concentrated polystyrene and polyisobutylene solutions in various solvents have been examined in terms of Maron's theory. It is shown that for each polymer‐solvent system at a given temperature the behavior over the entire concentration range studied can be characterized by a single interaction parameter μ, whose dependence on volume fraction v2 of polymer is given by where μ° and σ° are constants. For two systems, where data are available, this linear relationship has been found to hold from v2 = 0 up to v2 = 0.90. With this relationship for μ, Maron's theory leads to functional plots for dilute solutions which are linear even in systems where the usual II/C vs. C plots are not straight lines. These plots yield the molecular weights from the intercepts and the quantities (μ° − σ°) from the slopes. However, the individual values of μ° and σ° cannot be obtained from dilute solution data. To arrive at these, data are required at concentrations higher than those customarily used for molecular weight determinations. The μ°'s show values which are frequently larger than 0.50 and which vary quite appreciably with change of solvent or temperature. Similarly the σ°'s are quite sensitive to these variables, and both positive and negative values have been observed for this quantity. On the other hand, the difference (μ° − σ°) is much less sensitive to these variables and consistently yields values of 0.50 or less. It is also shown that the parameter χ of the Flory‐Huggins theory does not measure explicitly the interactions in either dilute or concentrated solutions. Consequently, the dependence of χ on solution variables does not reflect directly the effect of such variables on the polymer‐solvent interactions in solution.