A Theory of the Thermodynamic Behavior of Nonelectrolyte Solutions. II. Application to the System Rubber-Benzene

The theories of polymer solutions proposed by Flory, Huggins, Miller, and Guggenheim employ the concept of a coiling polymer molecule which may become entangled with other such molecules in solution, and utilize statistical-mechanical considerations to obtain the thermodynamic relations attending the solution or mixing process. The theories of Flory and Huggins are essentially identical, as are those of Miller and Guggenheim. Further, all theories reduce to practically the same result when the molecular weight of the polymer is high. The present status of these theories may be summarized as follows. Except for dilute solutions, the free energies of mixing predicted by theory agree generally quite well with those measured experimentally; however, the heats and entropies of mixing do not. To correct the situation in the dilute region, Flory and Krigbaum developed a special theory which preserves the original model used by Flory, but attempts to take into account the lesser tangling of polymer chains as the solution is diluted. The latter theory appears to work quite well in very dilute solutions, but it suffers from two shortcomings. First, the theory does not apply to concentrations high enough to overlap the original theories, and hence there is a concentration gap for which no theory is available. Second, the Flory-Krigbaum theory employs parameters which are different in significance from those used at the higher concentrations, and, thus far, no relation has been established between them. The result is that polymer solution behavior at low concentrations is expressed in terms of one set of parameters, that at higher concentrations in another, and no means are available to connect these or to cover the concentration gap to which neither theory applies. Recently Maron7 developed a theory of the thermodynamic behavior of nonelectrolyte solutions which is nonstatistical in character, and which expresses the behavior of solutions in terms of parameters whose significance remains unaltered over the full concentration range of the solution. The purpose of the present paper is to show the application of this theory to the system rubber-benzene, for which Gee and Treloar have determined at 25° C the free energies, heats, and entropies of mixing over the entire range of concentration from pure benzene to pure rubber. Subsequent papers in the series will give applications of the theory to osmotic pressure and light scattering behavior of polymer solutions, as well as to the thermodynamic behavior of solutions of low molecular weight substances.