156 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Many items must be accounted for in any complete treatment however, the more important factors in diffusion from solution to interface are these: 1. All other things being equal, the higher the concentration of dye in solution, the more dye will reach the fiber in a given time. Some dyes ac- tually are used in concentration above solubility in the form of a dispersion which dissolves and replenishes the bath as it is exhausted. Hydrophilic groups also are synthesized into the molecules to increase their solubility and hence their concentration at the interface. 2. The rate at which any particle moves in a solution is called that par- ticle's diffusion constant in that particular solution. The larger the parti- cle, the slower it diffuses. The size of dye particles frequently exceeds that suggested by molecular weight because aggregation of dye molecules into micelles is so common. Hydration also increases the effective size of the particle in solution. The addition of dispersing agents greatly increases diffusion rate by reducing the size of the dissolved entities. 3. Viscosity of the solution plays a simple part in diffusion rate. The more viscous the dye solution, the slower is the movement of the molecules therein. 4. Very important to the textile dyer is temperature. Diffusion through the solution depends upon the random motion of the solvent molecules which bombard the larger dye solute entities. The higher the temperature, the more rapid and energetic is the bombarding, and hence the more rapid is the diffusion of the dyes to the fiber. From the dye-solution interface, dye molecules must diffuse into the fiber itself. The pore size of wool or human hair usually is considered compa- rable to, or smaller than, the molecular size of the dyes used to color it. The energy in the fiber causes its network to vibrate, and occasionally random oscillations with the help of energy supplied by bombarding water molecules momentarily will open holes large enough for a dye molecule to penetrate. Without the optimizing of many factors, the process is im- practically slow. Some of the factors affecting diffusion within the fiber are these: 1. Molecular weight or particle size is very important The diffusion rate varies over many orders of magnitude with the range of molecular sizes employed for dyeing. Associated molecules which are much too large to penetrate sometimes can be broken down by a change in pH, solvent or dispersing agent. 2. Fibers tend to carry a net electrostatic charge, especially near ionizable groups. Keratin normally is negatively charged. Therefore, negatively charged dye ions tend to be repelled and penetrate slowly. The distance through which these fiber charges can effectively repel or restrict movement can be decreased by increasing the ionic strength of the dye solution. Some salts also may compete for sites of adsorption so that less

BASIC ELEMENTS OF DYEING HUMAN HAIR 157 total dye is adsorbed, but the movement of the dye through the fiber still is faster unless so much salt is added that fiber swelling is reduced. 3. The effect of fiber charge also can be reduced and penetration rate increased if a nonionic dye molecule or one of opposite charge is employed. 4. Leveling or even distribution of a dye is important in all fields of coloring. The initial penetration of dye never is uniformly distributed geometrically in a fiber because of local breaks in the fiber surface or un- intentional isolation of one fiber by its neighbors. Some dyes are adsorbed so strongly and completely on contact that they tend to remain where they happen to be first bound. They can be redistributed around the fiber by adding an agent that competes for adsorption on the same sites to which the dyes are adsorbed. This agent is called a "leveler." Dyes that are adsorbed only weakly by the fiber automatically give a much more level dyeing because they freely redistribute through a process of exchange be- tween fiber and solution. 5. Most textile dyeing is carried out at very high temperatures. With elevation in temperature there is a great increase in random motion of the solvent and fiber network. More important, keratin fibers swell greatly in water above 75 ø to 80øC., and too, most dyes are more soluble at these temperatures. In the textile industry, aqueous dye baths may be heated under pressure to achieve temperatures above 100øC. Under these con- ditions diffusion rates are increased by many orders of magnitude so that huge dye particles can be driven into the fiber. 6. The condition of a keratin fiber, especially of its surface, vastly affects the rate at which it can be penetrated. Morphological studies also show that wool or hair has several layers. Of these, the cuticle, or sheath of scales, and the epicuticle, a thin continuous outer cover of about 1013 A., are most resistant to penetration (7, 8). An analysis of the rate of sorption of simple salts like sodium sulfate or sodium bromide in human hair also shows that the epicuticle and cuticle form a resistant barrier that is pene- trated 10 to 100 times slower than the cortex in virgin hair (9). Chemical or physical damage of these barriers greatly accelerates diffusion (8). Bleaching, dyeing, waving or even swimming in chlorinated pools, es- pecially with exposure to sun, will break down these diffusion barriers and subsequent penetration by dyes as well as by other cosmetics is vastly accelerated (10). 7. To insure that adequate diffusion of dye occurs even into intact virgin hair, swelling agents can be added. Water probably is one of the best swelling agents for hair, but dilute ammonia or even disulfide reducing agents favorably augment the swelling. Other miscellaneous agents perform a combination of effects--wetting, dispersing, swelling, etc. When dye intermediates are employed, the next step in the dyeing process is color development. Typical dyes used in intermediate forms are azo