Thermodynamics of Mixing of n-Alkanes with Polyisobutylene

The volume changes on mixing polyisobutylene (PIB) with n-pentane, n-hexane, n-heptane, n-octane, n-decane, and n-hexadecane have been determined by direct measurements at 45°, and for n-heptane at 0 and 50° as well. They are negative in every case; the magnitude of the excess volume decreases with chain length, and increases with temperature. These results on volume changes, which are beyond the scope of conventional theories of polymer solutions, are rationally taken into account by the recent statistical mechanical theory of solutions which relates properties of the mixture to characteristics of the pure liquids manifested in their equation-of-state parameters. The negative enthalpies of mixing found by Delmas, Patterson, and Somcynsky for all of these systems with the exception of PIB-n-hexadecane are similarly shown to arise from negative equation-of-state contributions to the enthalpy which reflect differences between the liquid characteristics of n-alkane and PIB. The energy contributed by interchange of neighbor species in contact is shown to be small but positive, as should be expected for the nonpolar molecules involved. It diminishes with chain length of the alkane, becoming little greater than zero in the limit of an infinite alkane chain (polymethylene). Osmotic pressures of concentrated solutions (∼ 15–50%) of PIB in n-octane at 25° yield values of the residual chemical potential, expressed in terms of the conventional parameter χ, which are well reproduced by the theory without arbitrary parameters. The partial molar enthalpy and entropy of dilution are dominated by equation-of-state contributions rendering both of them negative, despite the large positive combinatory entropy. The appearance of critical miscibility at higher temperatures is thus predicted by the theory without resort to special explanations.