PREDICTION OF THE RHEOLOGIC AGING OF COSMETIC LOTIONS H. WOOD, PH.D., and GP, EGOP,¾ CATACALOS, B.S.* Presented September 20, 1962, Seminar, New York Cily I• studying the aging of cosmetic lotions after preparation, the cosmetic formulator often finds himself on the horns of a major dilemma: how to predict from short periods of time what will happen during the nor- mally accepted shelf life. The normal rule of the chemist for determining shelf life is to set samples at a series of temperatures and to evaluate a classic rate constant for the reaction. The formulatot is beset by the problem that his creations frequently have extremely complex behavior when stored at various elevated temperatures, for example, the classic heat hardening of many soap-containing formulations. In such a case, from the phase rule viewpoint, his formula is simply moving at reasonable rates into the ever present gel regions characteristic of long chain com- pounds in water. However, at lower temperatures this often never hap- pens, for the rates are so much slower. Alternately, the elevated temperatures lead to the melting of one or more components and hence a complete change in the nature of the formu- lation. Often high temperatures maintain an impurity in solution so that the high temperature forms remain satisfactory when those stored at lower temperatures soon become cosmetically unelegant. Thus, though the formulatot uses accelerated testing as a guide, he feels forced to rely ulti- mately on room temperature behavior. Certainly the standard Arrhenius relation seldom is of use to him, and his systems rarely obey conventional kinetics. The formulator usually uses observing periods of roughly doubled time intervals--thus 1, 2, 4, 7 and 14 days 1, 3, 6 and 12 months. Experience has taught him that in these time intervals he may expect to see sufficient change to justify the observations. More frequent observation is usually impossible because of the demands on his time. However, the normal frame of reference is based on the linear time scale and it is often said that the changes are leveling off. That is, there is an asymptotic approach to a limit, since as much change occurs in going from one to three months as occurred in one to three days. * Bristol-Myers Products Division, Bristol-Myers Co., Hillside 5, N.J. 147

148 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Several years ago, as a matter of convenience, one of us (G. C.) began using logarithmic plots as a convenient compacting device to consolidate rheological data from days to months onto a reasonable plot that would give equal weight to all observations. It was soon evident. that for many viscosity plots a reasonably good straight line was obtained for a plot of the logarithm of viscosity against logarithm of time, using any suitable units. The first tentative mention of this was over a year ago (1). Since that time, we have sought to examine the possible generalization of such a re- lationship and the underlying logarithmic time dependency in order to assess the reliability of the generalization and hence in turn the significance of any departure from such a behavior. Of course, empirical line straightening and data compaction are often obtained by the use of square root or higher roots of the variable. To ob- tain a crude linearity between a root plot and a logarithmic one, it is necessary to use a root power at least 0.5 greater than the number of log- arithmic decades considered. Therefore, for four or more time decades the power root dependency on time is theoretically not probable. OCCURRENCE OF THE LOGARITHM TIME DEPENDENCY First it is well to examine how significant is the aging property depend- ence on logarithm of time, as evidenced from published literature. The examples chosen are not intended to be complete but rather were chosen because they were known to the authors as cases where a logarithmic time dependency was found empirically necessary. Two examples of emulsion stability were available. The first by Menczel el a[. (2) clearly demonstrated by a colormetric technique that the logarithm of the per cent separation of internal phase was directly related to the logarithm of time for time periods from minutes to several days. These authors suggested an emulsion stability grading system based on this re- lationship. A similar relationship was found by Christian (3) for the cream- ing rates of various emulsions using radio isotopic measurements for the ratio present at the top and the bottom of a cylinder. We have recently reported (4) that the viscosity build-up by hydration of Veegum©*, a bentonire type clay, regardless of the temperature of storage, is related to the age of the suspension by a linear log-viscosity log-time re- lationship, holding over a time range of hours to months. In a recent paper, Levy (5) reports the build-up with time of the various rheologic parameters useful to characterizing a bentonire gel, dynamic and static yield value, thixotropic area, and plastic viscosity. As may be seen from Fig. 1, these properties are well characterized when plotted on a log- property log-time plot by a straight line relation. Chong (6) showed that the growth of anti-thixotropy for a magnesia * Veegum is a trade name of the R. T. Vanderbilt Co., Inc.