Mixing Schemes in Aqueous Solutions of Nonelectrolytes:  A Thermodynamic Approach

Thermodynamic studies were carried out on aqueous solutions of some nonelectrolytes. The quantities proportional to the second derivatives of Gibbs energy were measured directly and in small increments in mole fraction or temperature. Therefore, we were able to differentiate once more with respect to mole fraction or temperature. Generally, the higher the order of the derivative, the more detailed the information it contains. Using these second and third derivatives, an attempt was made at elucidating the mixing schemes, the way in which solute and solvent H2O molecules mix with each other. For the following nonelectrolytes studied so far, 2-butoxyethanol, tert-butyl alcohol, 2-butanone, isobutyric acid, and dimethyl sulfoxide, there are separate regions in the single-phase domain of the temperature−mole fraction field, in each of which the mixing scheme is qualitatively different from those of the other regions. The details of each mixing scheme were elucidated from the behavior of the second and third derivatives of Gibbs energy. In the water-rich region (I), the effect of a solute was suggested to enhance the hydrogen bonds of H2O in the vicinity of the solute but to diminish the hydrogen bond probability of the bulk H2O away from the solute. When the hydrogen bond probability at a certain region of bulk water decreases to that of the percolation threshold, this mixing scheme is no longer operative, and mixing scheme II sets in. The transition from the mixing scheme of region I to that in region (II) was found to accompany anomalies in the third derivatives of Gibbs energy, in contrast to the normal phase transitions which are associated with anomalies in the second derivatives of Gibbs energy. In the intermediate region (II), it was suggested that the solution consists of two kinds of clusters rich in each component. In the solute-rich region (III), at least for the 2-butoxyethanol and dimethyl sulfoxide cases, the clusters of purely solute molecules exist and H2O molecules are “adsorbed” on the surfaces of such clusters.