378 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS nents and, where possible, to compare these predictions with experimentally determined yields. So far results have been evaluated only for a single competition (i.e., one primary intermediate and two couplers, or two primary intermediates and one coupler). These results may not be directly translated into colors produced on hair from similar mixtures because factors such as diffusion rates of the various species also have to be considered. However, when dye yield in solution is compared with that predicted from the appropriate competing rate constants, generally good agreement is obtained. For example, when imine (2) was formed by ferricyanide [FC] oxidation in the presence of ten-fold molar excesses of two couplers, the ratio of the two indo dyes were, as predicted, for a first-order competition, in the ratio of the two coupling rate constants: coupler Iq dye [ 1] (2) • ß dye [2] coupler [2] then: dye [l]/dye [2] = k•/k2 This is demonstrated in Table I for competition of either p-phenylenediamine [PPD] or p-aminophenol [PAP] with m-phenylenediamine [MPD] and m-aminophenol [MAP]. Table I Competition for meta Couplers Under First-order Kinetic Conditions at pH 8.6 and 30 ø Relative Concentrations ' PPD PAP MPD MAP Expt % Para-MPD b Theory' 1 -- 10 -- 100 100 1 -- 0 10 0 0 1 -- 10 10 12 20 1 - 15 5 30 43 1 -- 17.5 2.5 49 63 -- 1 0 10 0 0 -- I 10 0 100 100 -- I 10 10 17 18 -- 1 15 5 31 40 -- 1 17.5 2.5 61 61 •Multiples of 9.3 x 10 -5 M. bDetermined spectrophotometrically. 'Rate constants: PPD-MPD, 298 PAP-MPD, 11 PPD-MAP, 1200 PAP-MAP, 49 1. mol-•s -•. Significant error is involved in determining experimental product yields spectropho- tometrically since the two products generally have similar spectra. Even so, the agreement between experiment and theory is good. A second example is shown in Table II, for competition of m-phenylenediamine and m-aminophenol for p-aminophenol (molar ratio 10:10:1) at various pH values.

HAIR COLORANTS 379 Table II Competition for PAP by MAP and MPD at Various pH Values and 30 ø % PAP - MPD Product pH Experimental Calculated 6.5 8O 68 7.1 65 62 7.8 34 3O 7.9 34 27 8.7 18 17 9.4 4 8 10.1 0 0 The trends predicted from the effects of pH on the individual coupling rate constants are reflected closely in the product yields from the competition experiments. Although these meta competition reactions are easy to evaluate, the corresponding para competitions are much more difficult because first-order kinetic conditions cannot be used. Thus a reaction stoichiometry such as a 10 PPD: 10 PAP: 1 coupler would show significant product formation from para self-coupling or cross-coupling or para addition to the coupled product. In addition, if a deficit of oxidant is used, some competition for oxidant will be evident and equilibria such as PAP q- Di-imine • Monoimine q- PPD .... (i) will be established, resulting in consecutive rather than competitive product formation (6). Product yields for the competitive system PPD - PAP - MAP are given in Table III. Table III Competition between PAP and PPD for MAP at pH 8.6 and 30 ø Relative Concentrations • % PAP Reacted % PPD Reacted % PPD Product PPD PAP MAP in Mixture Found Theory Found Theory 1 -- 1 100 0 0 100 100 1 0.5 1.5 74 50 50 75 75 1 1 2 52 48 50 53 50 0.5 1 1.5 43 57 50 86 100 -- 1 1 0 100 100 0 0 •Concentrations are multiples of 9.87 x 10 -• M 4 molar equivalents of FC added. Kinetic equations for competing second-order reactions have not been derived, but they are not needed for a quantitative understanding of these data. When a deficit of oxidant is used with a mixture of PPD and PAP, the PAP product is formed first even when the PAP coupling rate constant is very much less than the PPD rate constant. This is due to oxidation of PAP to monoimine by diimine by equilibrium (i), which effectively means that all the PAP is oxidized first. Any remaining ferricyanide is then used to oxidize PPD to diimine. Since diimine couples faster than monoimine under the experimental conditions, any remaining ferricyanide is used to