EMULSION STABILIZATION 161 where v is the number of polymer chains per unit area of the surface. It should be mentioned that G el is always repulsive and becomes very high on considerable overlap of the polymer chains. Plots of G m ix and G el versus h are illustrated in Figure 8. This figure shows that G m ix increases very rapidly with a decrease in h as soon as h becomes smaller than 28 (and X 0.5). G el also increases very rapidly with a decrease in h on further overlap. Combi- nation of G mix ' G e1 , and G A (the van der Waals attraction) results in the total Gr - h curve shown in Figure 8. This curve shows a minimum (G mi n) at h - 28, but when h 28, Gr increases very rapidly with a further decrease in h. The depth of the minimum, G min ' depends on the adsorbed layer thickness. With an increase of 8, G min decreases, and at sufficiently high values of 8 (of the order of 5-10 nm), it reaches small values (fraction of kT units). This shows that with sterically stabilized dispersions, there is only weak attraction at relatively long distances of separation, which in most cases is over- come by Brownian diffusion. Thus, one can say that the net interaction is repulsive, and this ensures the long-term stability of the emulsion. From the above discussion one can summarize the main criteria for effective steric stabilization. First, there should be enough polymer to ensure complete coverage of the surface by the chains. This will prevent any attraction between the bare patches or bridging by the polymer chains (which can adsorb simultaneously on more than one particle). Secondly, the chains must be strongly adsorbed ("anchored") to the surface. This prevents any displacement on close approach. In this respect, block and graft copolymers containing an anchoring chain (such as the alkyl groups of HMI) for oil droplets are the best stabilizers. The third criteria for effective steric stabilization is to ensure that the stabilizing A chain remains in good solvent condition at all times and G h h Gmin Figure 8. Schematic representation of the variation of Gmix' Ge1, GA, and GT with b.

162 JOURNAL OF COSMETIC SCIENCE under all conditions. As discussed above, for systems where water is the continuous medium, polyfructose (inulin) is the most suitable A chain. This polymer chain is highly soluble in water and remains solvated up to high temperatures. It can also tolerate reasonable amounts of electrolyte. For dispersions, where the continuous medium is a hydrocarbon oil (e.g., W/0 emulsions) poly(hydroxystearic acid) is the most suitable A chain(s). The last criterion for effective stearic stabilization is to have a sufficiently thick adsorbed layer to avoid any weak flocculation. This is particularly important for con- centrated emulsions. A value of o of the order of 5-10 nm is usually sufficient. O/W EMULSION STABILIZATION USING HYDROPHOBICALL Y MODIFIED INULIN (HMI) BASED POLYMERIC SURFACTANT As mentioned above, the graft copolymer based on inulin (hydrophilic polyfructose chain) on which several alkyl groups have been grafted (INUTEC® SPl) was recently evaluated as an effective stabilizer for 0/W emulsions. This polymeric surfactant was prepared using inulin (INUTEC® N25) with a degree of polymerization greater than 23. The inulin chains were hydrophobically modified by grafting several alkyl chains on the inulin backbone. Two oils, Isopar M (supplied by Exxon) and cyclomethicone (supplied by Dow Corning) were used to prepare the 0/W emulsions (10). Most emulsions consisted of 50/50 (v/v) ratio oil in water, and the polymeric surfactant concentration was changed from 0.25 (w/v)% to 2 (w/v)%. The emulsions were prepared using a high- speed stirrer, an Ultra-Turrax (CAT X620). The emulsion quality was assessed by optical microscopy. Samples of the emulsions were stored at room temperature and at 50°C, and the droplet size was qualitatively assessed by taking optical micrographs at various intervals of time. Figure 9 shows typical micrographs of diluted 50/50 Isopar M/water emulsions con- taining 2 (w/v)% INUTEC® surfactant that were stored for periods of 1.5 and 14 weeks at 50°C. As can be seen, there is no apparent increase in droplet size during this storage time, and this was taken as an index of stability against coalescence. Similar results were A B Figure 9. Optical micrographs of diluted 50/50 Ispoar M/water emulsions containing 2(w/v)% INUTEC® SPl that were stored at 50°C for 1.5 (A) and 14 (B) weeks.