SHAMPOO PRESERVATIVE TESTING 317 I i r 3.0 3.2 3.4 3.6 1000/T Figure 8. Arrhenius activation energy plot of shampoo preservative system potency determined using E. coli as the challenge organism in preservative efficacy tests on samples stored at 3 ø, 38 ø, and 49øC for 12 months. preservative molar concentration, so that one may determine the molar concentration (or the apparent molar concentration) of active preservative in the formula after any given time and temperature of storage. Calculations of this type may be useful in systems containing only one preservative chemical. Obviously, calculations will be quite complex in products containing multiple surfactants and preservative chemicals because the loss of preservative potency may follow higher-order reaction kinetics. It is believed that determining D-values and Ea' values may be useful in studying the ki- netics of bacterial death, in determining the apparent molar concentration of a preser- vative, and in monitoring the performance of cosmetic preservative systems during stability studies. In discussing accelerated stability testing, Pope used Ea values of 10-20 Kcal/mole for predicting good probability of formulation stability, which he defined as one that de- graded no more than 10.5% in 3 mo. at 45øC (18). He noted that formulations that degrade through solvolysis have Ea values of 10-30 Kcal/mole and that systems with Ea values of this magnitude show marked increases in reaction rates at elevated tempera- tures. The findings in this study revealed that the unstable shampoo preservative system had Ea' values of - 2 to - 16 Kcal/mole, depending on the time period of the determi- nation and the test organism used. It is believed that the difference between the Ea values proposed by Pope and the Ea' values observed in this study (including both absolute magnitude and algebraic sign) may be due to 1) the difference in k for the solvolysis reactions cited by Pope and complexation reactions, such as those involved in the interaction of isothiazolinones and amines (15) and 2) the way in which Ea and Ea' were defined and derived. The shampoo preservative system was satisfactory when examined at the outset of these studies (i.e., at 0 mo.), but it deteriorated during the aging study. Hence, the Ea'

318 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS values for the shampoo decreased with time. By way of contrast, determination of D-values and Ea' values for the test organisms in a proprietary lotion preserved with MP and Quaternium-15 revealed no changes in these values for test samples stored at 3 ø to 49øC for the duration of the stability study. This indicated that the preservative system of the lotion was not changing detectably, as evaluated by the linear regression method. These examples illustrate a useful caveat: the Ea' values should deviate little from the initial, acceptable values if a product is to have satisfactory shelf life. These studies demonstrate that the linear regression method is useful for quantitating the rates of inactivation of bacteria inoculated into stability test samples and illustrate the value of this method for monitoring preservative efficacy of stability test samples. To our knowledge, this is the first report on the use of a quantitative method, which provides via the kinetics of bacterial death, a method to monitor preservative potency at various times during stability studies of cosmetic products. In most instances, preservative efficacy testing demonstrates that the cosmetic preserva- tive system inactivates test organisms rapidly and that the D-values are positive. The preservative system is judged to be inadequate when D-values are greater than accep- tance criteria (4) or when they are negative. For example, the preservative system fails when test organisms grow in the sample. The slope of the survivor curve is positive when growth occurs, which means that the D-value is negative. Negative D-values are rarely, if ever, reported in published literature because they indicate preservative system failure and the need for reformulation. Although negative Ea' values appear to be somewhat anomalous, one must keep in mind that they represent a decrease in potency of the preservative system that occurs on storage and that the rate of preservative deterioration is accelerated by increases in temperature. As noted above, negative D-values are obtained when test organisms grow in the test samples. Negative D-values cannot be used in calculating Ea' values because one cannot take the log of a negative number. This report shows that the linear regression method may be used for predicting the stability and the apparent molar concentration of a preservative system in addition to its already-documented utility in determining the cosmetic preservative efficacy. Thus, examination of the preservative efficacy of a formula after storage at 49øC for 1 to 3 mo. may indicate the system is unstable and that reformulation is necessary. It is recom- mended that formulation chemists quantirate preservative system potency during accel- erated aging studies to determine the likelihood of preservative system failure. ACKNOWLEDGEMENT The authors express their appreciation to Mr. W. E. Dickman for his assistance with stability testing of the samples. REFERENCES (1) U.S. Food & Drug Administration, Human and Veterinary Drugs, Current Good Manufacturing Practice in Manufacture, Processing, Packing, or Holding, Fed. Register, 43, 45014-45087 (1978). (2) D. S. Orth, Principles of preservative efficacy testing, Cosmet. Toilet., 96(3), 43-52 (1981).