168 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS chemical and electrical interactions. In this we will indulge in a bit of double talk for the discussion will be about double diffuse--double layer-- double particle interactions. In general the positive and negative ions present in an emulsion will dis- tribute themselves between the oil phase and the water phase so as to put a charge on the oil droplets. That is, there will be a higher concentration of ions of one charge than of the other in the oil. This is illustrated dia- grammatically in Fig. 2. In this particular case the negative ions are in excess in the oil phase. Unfortunately the scale is too small to show a distribution of the negative charges of decreasing concentration toward the center of the droplet. The first layer around the droplet, the "solrating layer," consists of strongly bound water molecules, hydrogen atoms pointed toward the oil since the water dipoles will orient in the charge field, and excess positive ions strongly held by the negative charge on the oil. This layer remains bound to the droplet as the oil moves through the water and having an excess of positive ions it reduces the effective net charge of the drop. It is this net charge which is effective in electrokinetic experiments such as electrophoresis measurements. Continuing out toward the body of the water phase distant from the droplet, it is seen that the concentration of the positive ions decreases and that of the nega- tive ions increases much like in Fig. 1. This ion atmosphere is the "diffuse double layer" in the water phase. It is often convenient to consider instead of the double layer itself a shell of charges which would have the same effect as the double layer. What is referred to as the thickness of the double layer is the distance d = 1/K from the droplet to this shell as illus- trated (K2 is proportional to the ionic strength of the solution divided by its dielectric constant). It should be noted that the same type of diffuse double layer is present in the oil phase. Below the diagram in Fig. 2 is a plot of electrical potential, the energy required to bring an electron from infinity to the given point, as a function of distance from the center of the droplet for the region outside the surface of shear. The shape of the potential curve is determined by the ion distribution discussed above. The difference in potential between the surface of shear and a distant point in the water phase is known as the zeta potential or electrokinetic potential. Figure 3 is a plot of the entire potential-distance curve, with the direction of increasing potential reversed when compared with Fig. 2. The difference in potential between the in- teriors of the water and oil layers is denoted by •/• and that portion of the potential difference due to dipole orientation and charges at the interface by chi. It should be noted that most of the potential drop occurs in the oil phase. Implied above was that the water was pure and the only ions present were those from the ionization of water. Although the relative distances

THEORY OF EMULSION STABILITY 169 will be changed the qualitative picture is unchanged if other ions, say a salt, are added to the water as long as they are not surface active. In the absence of surface active ions to a good approximation /x/,' depends only on the species and not on the concentration of the ions present. oil •,at• oil l•,at•r oit watef A • c Figure &--The potential at an oil-water interface. (a) In the absence of surface-active ions. (b) After addition of soap ions, in solution of very low ionic strength. (c) In the presence of soap ions and a large amount of salt. (From Van den Tempel, reference 3.) Upon the addition of a surface active ion the situation changes quite radically as indicated in Fig. 3b and Fig. 3c. The former is the potential curve in the absence of excess salt and the latter in its presence. These curves are both based on the quite artificial assumption that the distribu- tion of the ions in the bulk phases is not changed by the presence of the surface active ion. The scales for a, b, and c in general should be different so comparisons between them are only qualitative. Adsorption of the surface active ion at the interface has produced a deep minimum in the potential curve. These adsorbed ions produce a surface change density on the droplet which is much greater than the original one and, in the case illustrated, is neutralized almost entirely by the increased double layer charge on the aqueous side of the interface. In the presence of an excess of other ions those of charge opposite to that of the surface active ions, the counter ions, nestle in among the surface active ions producing a thin layer of uniform potential 4,0 with respect to the bulk water phase. What are the forces acting between two charged droplets and their diffuse double layers as the droplets move toward each other? In the usual cases in emulsions there are enough ions in the water phase, the counter ions from the soap, so that the double layer thickness, I/g, is less than 0.01 microns which is usuall'y small compared to the droplet radius, r. The problem of the electrical forces acting is not amenable to a complete analytical solution but good approximations are available. These show that in so far as the electrostatics are concerned the droplets will always