396 jOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS tration while holding the alcohol constant results in a decrease of the FDTT, the effect leveling off at high detergent concentrations. Another method of sectioning Fig. 2 is presented in Fig. 4. Each curve represents compositions of the system which give rise to the same value of the FDTT. The sharp break in each of these isothermals occurs at 0.226 per cent sodium lauryl sulfate and is quite close to the CMC, 0.234 per cent, reported by Mysels (3) for pure sodium lauryl sulfate. The rapid $0 c_ I0-- __ o o I r I 80 85 90 95 I0-t- LoglOZ Figure 5.--Film drainage transition temperature vs. log Z. rise of the curves beyond the CMC illustrates that very much higher ratios of lauryl alcohol to sodium lauryl sulfate are required to give the same FDTT above the CMC than below it. The shape of these isothermals is similar to what is found when the solubility of a long chain alcohol in a detergent is obtained at constant temperature. Above the critical con- centration there is a sharp increase in the quantity of alcohol which dis- solves in the detergent solution. The nearly linear character of the curves

SODIUM LAURYL SULFATE-LAURYL ALCOHOL-WATER SYSTEMS 397 beyond the CMC indicates that the slopes are characteristic of a particular value of the transition temperature. Z = moles of alcohol moles of alcohol q- (moles detergent -- moles of der. at the CMC) Consequentlywe have defined the quantity as the"apparent miceliar mole fraction" which represents the concentration of alcohol in miceliar deter- gent only. The experimental FDTT's are then plotted in Fig. 5 against log Z for all concentrations of detergent above the CMC. The value 0.226 per cent sodium lauryl sulfate is taken from the break in Fig. 4 as repre- senting the CMC for the calculation of Z. The various curves of Fig. 2 except those for concentrations below the CMC, have been reduced in this plot to a single curve. The implications of this plot are the following: 1. Above the CMC, the miceliar composition (mole fraction of alcohol in the micelie) determines the value of'the FDTT which is independent of the number of micelies, i.e., FDTT depends only on the composition of the micelie. 2. Increasing Z results in an increase of the FDTT up to a limiting tem- perature of about 34øC. From consideration of phase data (1'), it appears probable that the intersection of the two branches of the curve in Fig. 5 represents the upper temperature limit for the solution of lauryl alcohol in the micelies and that further addition of lauryl alcohol gives rise to a two-phase system. This calculation neglects the slight correction that should be made for the alcohol which is associated with non-micellar detergent and is not dissolved in the micelies. However, this is essentially of theoretical in- terest and not too significant for this discussion. We have presented a theory of FDTT which is essentially based on the "buffering" action of the micelies and therefore should be confined to the concentrations where micelles are present. INTERMOLECULAR COMPOUNDS Two intermolecular compounds or adducts have been isolated as crystal- line precipitates from the sodium lauryl sulfate--lauryl alcohol--water system. Several of the solubility diagrams have been previously pub- lished (1). These adducts have the following compositions: 1 mole sodium lauryl sulfate: 1 mole lauryl alcohol 2 moles sodium lauryl sulfate: 1 mole lauryl alcohol It is believed that the phenomenon of slow draining films is probably due to the existence of rigid surfaces on the films. The requirement for the formation of high viscosity surfaces is that there'must be present on the sur- face a long chain polar compound which can interact with the detergent