PRESERVATIVES FOR PHARMACEUTICALS 709 As an example of absorption by plastics, Hamdi (18) has shown that cellulose acetate absorbs 23 mg g-• phenol from a 0.1 •o solution, suggesting a plastics/water partition coefficient of about 30 and 19 mg g-• chlorocresol from a 0.025•o solution, indicating a partition coefficient of about 475. These figures indicate that the loss of chlorocresol into a plastics container is more likely seriously to reduce the activity of a preservative than is the loss of phenol. KINETICS OF PRESERVATIVES When bacteria are introduced into a solution of preservative the rate at which they die can for practical purposes (there are theoretical objections) be represented by the first-order reaction equation -dN - KN (I) dt where N is the number of viable organisms m1-1 at time t and K is the death-rate constant. Integrating the equation between viable number No ml 4 at time t =0 and viable number N ml -• at time t and converting to common logarithms, equation I becomes 2.303 No K - log t N- and the reaction may be represented by Fig. 1. Any reduction in the 1¸5 - 10 4 7 • I0• --K .9 o• IC) • t0 20 30 40 50 60 Time ( rain ) •i•u•e 1. Typical representation of the death of mi•m-o•ganisms

710 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS concentration of the preservative will increase the time needed to reach any specified mortality level and reduce the slope of the line in Fig. 1. Con- versely any increase in concentration will reduce the time and increase the slope. The practical worker is likely to be concerned about the increase in time needed to reach the 99.9}/0 mortality level specified by U.S.P. XVIII for ophthalmic solutions resulting from a known concentration of pre- servative being absorbed by the container. This increase in time can be calculated from a knowledge of the concentration exponent of the pre- servative and log K•- log K•. log C•- log Ca ( C• ) n K• or • =K-• where n -- concentration exponent of preservative K• = death rate constant at concentration C• K•. = death rate constant at concentration Now, at concentration C• 2.303 100 K•- t• 1øg 0.1 and at concentration 2.303 100 K•.- t•. log0.1 where t• -- time to reach specified mortality level at concentration C• t•. = time to reach specified mortality level at concentration Ca Equation H indicates that if the concentration of a preservative is plotted against the time taken to reach some specified level of mortality, such as 99.9• or even 100• or sterility, a straight line results with a slope numerically equal to n, the concentration exponent (Fig. 2). Thus, when the concentration exponent has once been determined for a named preservative it can be of great practical value and the writer regards it as the most useful parameter of a preservative. Preservatives belonging to a particular chemical group have approximately the same concentration exponent,