SOLUBILITY PARAMETERS IN COSMETIC FORMULATING 325 D I E 20 L E C T R I 15 C C O N 10 S T A N T S DIHETItICONE o.1% OCTANE 0.4% ACFTONoe PLG-4 23.2% 7.4% BLNZALDEI!YDE 35.5% B•IBK BENZYL A[ COilO L 17.5% 14.9% ACETIC ACID 3.8% 1• CETOi• ITRI LE , ?,PROPYLENE 14.6 % L•9JCARBO,•,iATE 12.4% ETHYL ACETATE 21.5% 6 • 7 8 9 10 11 12 13 14 SOLUBILITY PARAMETER Figure 3. Results of the solubility study plotted with respect to solubility parameter and dielectric constant. is greatly affected by its bulk solubility. As a result, the foaming or foam-suppressing capacity of a surfactant is readily indicated by solubility parameter. The thermal change in this effect has been demonstrated for sodium stearate and block polyoxyethylene copolymers (33). Both these materials foam at high temperature but suppress foam when cold. Emulsion stabilization can be effected in a manner similar to the stabilization or de- stabilization of foams. Beerbower (34) has shown a method of pre-calculating the requirements for a "perfect" stable emulsion and claims to have used his method to produce stable asphalt emulsions without trial and error. In this method the solubility parameter of the hydrophobic or lipophilic tail of the sufactant is matched to the solubility parameter of the emulsified oil. In any case, the concept of cohesive forces explains the mechanics of surfactant action. As Schott (35) has recently shown, the solubility parameter offers a more effective method for assessing the activity of a sur- factant than Griffin's HLB system. This is because the HLB system took only the molecular weights of the two parts of a surfactant into account, while the cohesive approach accounts for its actual attractive force regardless of molecular weight. DETERMINING SOLUBILITY PARAMETER Many methods have been developed for the determination of the solubility parameter, ranging from essentially theoretical calculations, such as the Hildebrand/Scatchard

326 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS equation, to totally empirical correlations, such as the Kauri-Butanol number conver- sion published by Sevestre (36). Siddiqui made a comparison of several methods uti- lizing structural group contributions to the solubility parameter of n-propyl acetate (37). These are methods where portions of a molecule are given values which contribute to the total solubility parameter of the whole molecule. Hildebrand's method was chosen for computation of solubility parameters in this paper because this method is widely accepted and easily applied. It relies on molecular weight, boiling point, and density data which are commonly available for many materials and yields values which are usually within the range of other treatments. Moreover, the conversion from the calculated heat of vaporization (AHv) is the standard because this is the value originally defined by Hildebrand as the solubility parameter. This method is also preferred because it uses physical properties determined at the same ambient conditions under which many predictions may be desired. Sometimes the boiling point and density or molecular weight are not available for a material of interest, and so some alternate methods drawn from the literature have been included although the accuracy of these alternatives may be limited. From heat of vaporization (AHv) (Scatchard) (38): 8 = (AHv) •/2 From boiling point (Hildebrand) (39): 8 = [23.7T•3 + .02T• 2 - 2950 - 1.986Kø/(MW/Density)] 1/2 where T•3 = boiling point @ 760 mm and K ø = density measurement temperature Kelvin. From thermal expansion (Burrell) (40): 8 = (aT/B) •/2 where B = compressibility, a = coefficient of thermal expansion, and T = temper- ature of liquid. From surface tension (Lee) (41): 8 = 4.1 (•t/V•/•) 0'43 where •/ = surface tension and V = molecular weight/density. From refractive index (Lawson): (42) • = [C(n 2 - 1)/(n 2 + 2)]•/2 where n is the refractive index and C is a constant. From gas law correction constants (Van der Waals) (40): 8 = 1.2 al/2/V where a = Van der Waals constant and V = molecular weight/density. From aniline point-ASTM D611 (Francis) (43): 8 = 10.6 - [(4R/1.8)(A + 460/V + 91.1)] •/2 where A = aniline point and R = Boltzmann constant.