The Surface Tension of Debye-Hückel Electrolytes

As has been shown by Wagner, the increase of the surface tension caused by the addition of a strong electrolyte to water is mainly due to the repulsion of ions from the surface by the electrostatic image force. Due to the shielding action of the ``ionic atmospheres,'' of radius 1/κ, the image force is appreciable only within distances of the order 1/κ from the surface. The computations become very complicated if, as Wagner did, one attempts to allow for the variation of κ with the depth in accordance with the decreased concentration of ions in the surface layers. Fortunately, a detailed analysis of the problem shows that this refinement may be dispensed with as a first approximation, and that the formulas thus derived will be accurate for not too high concentrations. The same analysis tends to show that Wagner's procedure supplies only a part of the intended correction, so that the results will be applicable only over a slightly wider range of concentrations than the convenient explicit formulas which are derived from the simplified theory. In the limit of low concentrations, the increment of the surface tension is proportional to c log c. The theory accounts reasonably well for the observed surface tensions up to 0.2 N concentration. The discrepancies, while partly due to mathematical approximations, may be of some physical significance and would mean that for small distances the repulsion from the surface is greater than expected from Coulomb's law. Nevertheless, the agreement obtained verifies Coulomb's law for univalent ions at distances greater than a molecular diameter from the surface.