602 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS gives an approximate radius for the equivalent sphere of 3.0 A. This is in fair agreement with the determined value of 3-7 A. Valuesof (D•)lare plottedagainstrdinFig.lineofbestThe2. is drawn through these points. The intercept of 7.4 A indicates that the holes are 14.8 2k across. This is intermediate between the values which WiNmann found and those predicted by Speakman. Considerably more data are required, however, to attach any confidence to the result. 10. o z 4 6 $ • (4) Figure 2 The effect of diffusant radius on the relative diffusion constant. Diffusion coefficients have been determined for one dye (C) at different temperatures. At 25 ø C, the value is 257 X 10-" cm2/sec, but at 60 ø C it is 4,422 x 10-" cm=/sec. This corresponds to an activation energy of 16,450 cal/mole/ø C. This is not exceptionally high for a fibre, and is a reflection of the large change in the viscosity of the water within the fibre as the temperature rises. This is not uncommon. For instance, if we calculate the theoretical activation energies of diffusion in a sucrose solution from viscosity data, we have the results in Table III. Table III Activation energies of diffusion in sucrose solutions Sucrose 0 20 25 70 75 cal/mole 4,735 5,442 5,689 14,948 18,588

DIFFUSION PROCESSES IN HUMAN HAIR 603 It is seen that the activation energies in the more concentrated sucrose solutions are very similar to those in hair. The high activation energy alone is sufficient to account for the dramatic increase in the rate of dye uptake observed at high temperatures. The application of some of the above ideas, many of which have been extensively applied in the textile industry, will lead us to a better under- standing of the processes occurring in hair during many cosmetic treatments. (Received: 13th February 1964.) REFERENCES (1) I(. W. Herrmann Trans. Faraday Soc. 59 1663 (1963). (2) F. Perrin J. phys. radium 7 1 (1963). (3) J. Hill Proc. Roy. Soc. London B 104 39 (1928). (4) J. Crank Trans. Faraday Soc. 53 1083 (1957). (5) J. H. Skinkle Textile Research J. 25 861 (1955). (6) J. A. Medley and M. W. Andrews Textile Research J. 29 398 (1959). (7) J. B. Speakman Proc. Roy. Soc. London A 132 167 (1931). (8) H. Wilsmann J. Soc. Cosmetic Chemists 12 490 (1961). (9) J. B. Speakman, E. Stott and H. Chang J. Textile Inst. 24 T273 (1933). (10) L. J. Gosling Advances in Protein Chemistry Chapter XI 487 (1956) (Academic Press, New York) (11) L. G. Longsworth J. Am. Chem. Soc. 75 5705 (1953). Introduction by the lecturer When I first started looking at the process of dyeing hair, I found that there was a fair amount of knowledge about what was involved. It was one of the points that the hair consisted of a sort of sieve which had holes, but there was some disagreement about the size of these holes. I decided to look at the effects of diffusion of molecules in the hair and see, if by this technique, we could get some idea of these holes. I propose to expand a little on the way I calculated this. If one takes a cross-sectional area, one has a flux through this area, but if part of the area is not available for diffusion, the total flux will be reduced. The real flux through the system multiplied by the area gives the apparent flux. The apparent diffusion constant divided by the available area is the KT real diffusion constant. Now D -- We are concerned here with hair, 6•r ' so D is the diffusion constant in hair, and • the viscosity of water in hair. What we in fact determine is the apparent diffusion constant, and so D has to be corrected by an area term. By simple arithmetic, we have Dh •,v Dw •h We now have to evaluate the area term. If one takes a hole, and one has to get an infinitely small molecule through it, the effective area is obviously