34 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS all Methyl 0.01 • 1 3:2 '1: Propyl Figure 5. Decay curves of methyl and propy/parabens and mixtures at 0.5 g/1 initial concentration in water at 25øC according to the irreversible, incremental model. The abscissa is in arbitrary units proportional to inoculum volume. 2:3 Methyl:Propyl all Propyl I i 2 3 4 kt

PARABENS 35 Assume, now, that the solubilities of the available parabens have been measured directly in the product to be preserved. If the lowest solubility is equal to or greater than the maximum permissible paraben level, which is about 8 g/1 in current practice, then the most efficient system is obtained with this paraben alone all other parabens and mixtures have been shown to be inferior. If this does not suffice, the product cannot be preserved with parabens alone as we have found to be the case with several shampoo and liquid bubble bath formulations in which we find minimum solubilities of 2 to 5%. If, as happens less frequently, one or more of the solubilities is appreciably less than 8 g/l, the optimum system is formulated by taking the saturation concentration of the least soluble, plus the saturation concentration of the next least soluble, and so on until the total is 8 g/1. For example, in water, the solubilities of butyl, propyl, ethyl and preservation, it would be expedient for many good reasons to saturate with only two or three homologues but several precautions should be noted. First, since the solubilities of the parabens increase rapidly with temperature, it is not possible to formulate for saturation at, say 37øC, without risking unsightly and disruptive recrystallization at low storage temperatures. Second, the capacity factor must be considered again. Table II shows the capacity of the first four alkyl parabens at saturation in water for various assumed values of Sc ranging from 0.5 to 0.09. These values were calculated from eq 5 for the single parabens and from the quadratic equation for the capacity of binary mixtures obtained by substitution of eq 4 in eq 2. Considering first the single parabens, it is evident that homologues much less soluble than the butyl ester would make negligible contributions to the capacity regardless of the critical saturation fraction and it would be pointless to include them. The most striking feature in Table II is the enormous advantage of multiple saturation, especially at high values of Sc. This may appear to contradict our earlier dismissal of mixtures, but it must be emphasized that the enhancement of capacity cannot occur in equal weight comparisons it occurs only when the system can be brought to saturation with at least one homologue which is seldom the case with modern cosmetics and toiletties. It should also be emphasized that the enhancement is not a matter of synergistic interaction on the contrary, it follows from the assumptions of independence and simple additivity according to our extension of the Ferguson principle to cumulative saturation fractions greater than one. Table II Capacities of Alkyl Parabens and Mixtures at Saturation Against E. Coli in Water at 25øC Nc X 10 -9 per ml S c Paraben Soly., g/l 0.5 0.75 0.90 0.95 0.99 Methyl 2.5 53 18 5.9 2.8 0.54 Ethyl 1.6 34 11 3.8 1.8 0.34 Prowl O.5 11 3.5 1.2 0.56 0.11 Butyl 0.2 4.3 1.4 0.47 0.22 0.043 Methyl & Ethyl 4.1 179 71 52 47 43 Propyl & Butyl 0.7 21 12 8.3 7.5 6.9