SOLUBILITY PARAMETERS IN COSMETIC FORMULATING 327 From Kauri-Butanol point (KB)-ASTM D1133 (Sevestre) (36): 8 = .O2 KB + 7.O for KB 35. From GLC activity coefficients (Alessi) (13): lnX = V/RT[(SDS - 8D) 2 + (1 - 2m)(Sps -- 8p) 2] q- [(lnV/Vs + (1 - V/Vs)] where X = activity coefficient, m = structural constant, and S indicates solvent. From HLB (Beerbower) (33): 8 = [118/(54 - HLB)] + 6.0 CALCULATIONS AND TABLES In the past, solubility parameters have not been commonly used in the cosmetics and toiletries industry for reasons of expedience. Using solubility parameters is a compar- ative technique. Ideally, when one would like to know the solubility or compatibility of two materials, one most easily compares their solubility parameters. A difference of 2.0 usually indicates mutual solubility, although polar forces and hydrogen bonding are known to greatly affect this span. A mathematical model has recently been published by Kamlet and Taft (44) which uses the solubility parameter combined with measures of polarity and hydrogen bonding as was graphically demonstrated herein. They call their approach "solvatochromic" and achieve excellent predictive results however, their method requires prior determination of solubility parameter, polarity, and strength of hydrogen bonding. This is admittedly a severe limitation. A practical approach is to make an estimate of solubility based on inspection of a table of solubility parameters or to use such a table to help determine appropriate solvents to use in a limited solubility study. This approach, made with an awareness of polar and hydrogen-bonding groups, can be expected to yield results more accurate and more rapid than the predominant rule-of-thumb, "Like dissolves like." In the past, the rule-of-thumb has predominated as a matter of practicality. Neither was a body of solubility parameter values for cosmetic materials available nor was there an easy method for determining the solubility param- eter from easily determined or readily available physical constants. Our work with solubility parameters addresses both the above needs. Below is a listing of a computer program which will operate on the IBM PC or the Apple Macintosh with Microsoft Basic or on the Radio Shack Color Computer. It will determine the total solubility parameter of any chemical material based on boiling point, molecular weight, and density at a given temperature. It uses Hildebrand's method, including the empirical adjustments for ketones, aldehydes, and alcohols. This is the most common method used in the literature. Boiling points must be converted from reduced pressure values to 760 mm before calculating. A convenient nomogram for this purpose may be found in many handbooks or you may consult the original reference (45). The computer program is written in BASIC. SOLUBILITY PARAMETERS OF COSMETIC MATERIALS The need for a body of calculated solubility parameters of cosmetic materials is addressed here. The following table of cosmetic chemicals is listed by CTFA nomenclature in

328 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS 10 'Solparam 20 CLS 30 PRIET"Solubility Parameters by Hildebrand's Method" 40 PRINT"Program by CHRIS VAUGHAN" 50 PRINT" copyrighted 1985" 60 FOR X= 220 TO 880 STEP 20 70 SOLTND X,2:NEXT:CLS 80 INPUT"chemical name" C$ 90 INPUT "Molecular Wt." MW 100 INPUT"Boiling Pt. at 760 mm" BP 110 INPUT"Density" DEN 120 INPUT"at what temp" T 130 S0L = ((23.7'(BP + 273) +.02*(BP + 273)^2-2950)-(1.986'(273+ T)))/ (MW/DEN) 140 SOL= SOL^.5 150 PRINT" Is the Chemical an Alcohol(a), Ester(e), Ketone(k), or Neither(n)?" 160 IS= INKEY$ 170 180 190 200 210 220 230 240 250 260 270 IF IS = "a" TI-IEN SOL = SOL + 1.4 IF IS = "e" TI-IEN SOL = SOL + .6 IF IS ="k" TI-IEN SOLTND 1000,4: IF BPm100 TI-IEN SOL=SOL+.5 IF IS = "n"TI-IEN 220 IF IS ="" TI-IEN 160 PRINT"The Solubility Parameter of:" C$ "is " SOL "at " T "Degrees C." PRINT: PRIET,"want a hardcopy?? (Y) or (N)" AS = INKEY$:IF AS ="" TI-IEN 240 IF AS = "y" TI-IEN 260 ELSE 270 LPRINT "The Solubility Parameter of:" C$ " is " SOL " at " T "Degrees C." GOT0 80 Figure 4. Computer program in BASIC for solubility parameter calculations. order of increasing solubility parameter, grouping the co-soluble materials together. The values listed here were either calculated by the BASIC computer program or taken from other literature(*). The physical constant data used to make the computations were taken from various handbooks, journal references, tables, and supplier's data sheets, or were supplied to the author by individual request. As such, they are subject to error and variation. For this reason we have cross referenced these computed results with other published solubility parameters where they exist and evaluated these results for compliance with general trends of structure/function. Several trends are readily evident from inspection, such as the uniform reduction of cohesive strength by increased branching or progressive chain length. However, some exceptions were substantiated by several sources. These have been retained in the table. CONCLUSION Solubility parameters can operate as an effective tool for the cosmetic chemist by shedding light on the most basic process in formulation, intermolecular cohesion. This is the force which gives stability and compatibility to products and packaging that are required by today's sophisticated consumer. It is also the same force which controls