SOLUBILI•7¾ PARAMETERS IN COSMETIC FORMULATING 321 Prausnitz and Blanks (20) have more accurately determined the London contribution to the solubility parameter by assigning a value equal to the complete solubility pa- rameter of non-polar homomorphs (i.e. compounds with the same general structure but with no polar groups attached). The electrodynamics of light bending by the cohesive field forces is still too poorly understood to provide an accurate measure of solubility parameter based on refractive index. POLAR ATTRACTIONS Polarity was originally considered to be the result of a single phenomenon however, many different causes for polarity emerged from the study of how materials respond to electric charges and fields. By 1930 Debye had discovered that polarity in a molecule produced an additional electromagnetic attractive force caused by elongation of the more spheric London field. This dipole-dipole attraction is calculated to be: U• = - 2/3(u4/r6)(1/kT) where u is the dipole moment, k is the Boltzmann constant, T is the Kelvin temper- ature, and r is the separation. In addition, the dipole moment induces a polarization in its neighbors: Ui = - 2au2/r 6 where a, u, and r = as before. The combined effect of these field deformations was analyzed by Keesom (21) and they now bear his name. However, it was Boettcher (22) who defined the polar contribution to the solubility parameter using the dielectric constant (e) and the refractive index (n): •p = [12108(e - 1)(n 2 q- 2)u2/V2(2e q- n2)] •/2 where u and V = as before. This was simplified by Beerbower (23) to: 8p = 18.3u/(V)V2 where u and V = as before. Unfortunately, both methods have areas of imprecision, with the Beerbower equation showing greater precision with alcohols. Nonetheless, the inclusion of polar contri- butions in calculations using the solubility parameter was the singular technological advance which made the solubility parameter become an effective tool in the polymer and coatings industry. Diagrams such as the one shown in Figure 1 are commonly used in the coatings industry to determine the choice of solvent for any particular resin by comparison of both the polar and total solubility forces. In particular, this graph (24) compares both dipole moment and hydrogen bonding to the solubility parameter to determine the best solvents for the subject resin. Potential solvents are located by their solubility parameter and hydrogen bond strength within the "soluble area." ASSOCIATIVE ATTRACTIONS Consideration of the effects of hydrogen bonding and acid-base interactions has im- proved the accuracy of solubility estimations based on solubility parameters. Martin,

322 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS 4O 3O z o z • 20 o 10 Carbopol Resin - Dodecyl Amine Solubility Curve 5 10 15 20 25 rim-dipole moment SOLUBILITY PARAMETER Figure 1. Comparison of dipole moment and hydrogen bonding to the solubility parameter. Wu, and Beerbower (25) have recently used this expanded approach to study the solubility of methylparaben in 35 different solvents, with relatively good success. Kamlet (26), on the other hand, claims that acid-base interactions are better explained through hydrogen bond strength than through classical electron-donating potentials. The formula describing the hydrogen-bonded electromagnetic field deformations has not been adequately developed from a theoretical standpoint, and estimates of hydrogen bonding are commonly based on infra-red spectral shifts. It is important to note that all the field formulas are divided by the distance of molecular separation to the sixth power. This makes both the polar and non-polar attractions drop off drastically with molecular separation. As a result, both heat and dilution can cause dramatic changes in solvent potential. EXPERIMENTAL Solubility parameters may be used to estimate the co-solubility of two materials through simply assessing their proximity by inspection. For example: Methylparaben (8 = 11.98) is quite soluble in butylene glycol (8 = 13.20) and hexyl alcohol (8 = 10.50), while Glycerin (8 = 16.26) and butyl stearate (8 = 7.68) are comparatively poor