The Zero Time Dynamic Interfacial Tension

ABSTRACT

It has been shown earlier that interfacial tensions between organic liquids and a polar liquid such as water, when measured by drop shape (or drop weight) analysis only closely relate to the mutual solubility of the two liquids as well as to the free energies of interaction between and in the two liquids, when using completely apolar liquids such as alkanes. In all other cases, with partly polar liquids (even including aromatic compounds), the interfacial tension with water (as relates to the mutual solubility of the two liquids) is significantly underestimated by this method, due to unavoidable hysteresis caused by the almost instantaneous orientation of the polar moieties of the organic compound toward the water interface. It is therefore appropriate to introduce the concept of zero time dynamic (ZTD) interfacial tension, where ZTD interfacial tension is designated as γ_ij ^o. Now, two methods for determining ZTD interfacial tensions between polar condensed-phase compounds and water correlate closely to solubilities as well as to free energies of interaction. The first one relates the compound's aqueous solubility to its contactable surface area and its ZTD interfacial tension with water. This approach also allows the determination of ZTD interfacial tensions with very water-soluble solutes, such as sugars. The second one (able to furnish ZTD interfacial tensions between any two condensed-phase materials) utilizes the results of contact angle measurements, interpreted via the Young–Dupré equation, combined with the van Oss–Chaudhury–Good equation for interfacial tension. In some cases the latter approach can be circumvented by using the original Young equation. From the solubility of water in a number of organic solvents, the contactable surface area could be determined for water clusters, at 20^ˆC, at about 4.5 monomeric water molecules per cluster.

Keywords:

• Dynamic interfacial tension
• Solubility
• Surface area
• Zero time dynamic interfacial tension
• Young–
• Dupré
• equation

Acknowledgments

Notes

^*The S_c for (monomeric) water has to be obtained from the known dimensions, bond angles and distances of water molecules, e.g., as given by L. Pauling and R. Hayward, in The Architecture of Molecules, W.H. Freeman, San Francisco, 1964. From their diagrams it can be seen that the most plausible contactable surface area for single water molecules would be about 0.065 nm². However this value is just the contactable surface area between single water molecules, but when the contribution is considered of a single water molecule which is participating in a cluster consisting of one water molecule bonded to four neighboring water molecules, some of the hydrogen bond lengths (e.g., between one O and two H atoms, with the two H atoms belonging to two different monomeric water molecules) are longer than usual (cf. C.N.R. Rao, In: Water, Vol. 1, F. Franks (Ed.), Plenum Press, New York, 1972, pp. 93–114). Also, due to the net repulsions prevailing among water molecules which are located between most of the sites that are not directly undergoing hydrogen bonding attractions, the clusters of water molecules tend to be slightly less dense than bulk water molecules in two of its three dimensions (D. Eisenberg and W. Kauzmann, The Structure and Property of Water, Oxford Univ. Press, Oxford, 1969, pp.164–165). This then somewhat increases the apparent contactable surface area of the average single water molecule when participating in a cluster to approximately 0.08 nm².