Problems of stability in hydrophobic colloidal solutions II. On the interaction of two colloidal metallic particles: m athem atical theory

Abstract

In this paper we shall develop the mathematical method for determining the energy of interaction of two particles, used in Part I (Levine 1939, referred to as I) to obtain the stability properties of colloidal solutions. Since we apply the Debye-Hiickel theory of electrolytes it is advisable to examine the nature of the approximations so introduced. One of the chief objections to this theory is the neglect of the fluctuation terms. It has been shown by Kirkwood (1934) that the correction to the approximate solution, introduced by Gronwall, La Mer and Sandved (1928) when they solved the original equation, is of the same order of magnitude as the neglected fluctuation terms. Thus the work of the latter becomes questionable, particularly for unsymmetrical electrolytes. Now we have shown in I that such an important property of colloidal solutions as the Schultz-Hardy rule cannot be explained by means of the approximate Debye-Hiickel equation. Further, the ordinary £ potential of colloidal particles is so high that only for the 1-1 type of electrolyte may we assume that the approximate solution can be used with any degree of accuracy. (Of course, at precipitation conditions the £ potential may be sufficiently lowered so as to require only a small correction.) If we treat the particles as equivalent to the ions then we shall have an electrolyte of a very unsymmetrical character and the fluctuation terms will be important. Hence a straightforward application of the complete Debye-Hiickel equation should not be made although this has been done for colloidal electrolytes.