THE BINDING OF SMALL MOLECULES TO HAIR--I 455 The water adsorption isotherms obtained were interpreted on the basis of a co-operative binding model derived by Schwarz (16). This model postulates the existence of two types of chemical equilibria between binding sites attached to the polymer and the small molecule: firstly, an equilibrium with sites flanked by two other unoccupied sites K* W + uuu • uwu and secondly, an uptake equilibrium with a site where at least one of the neighbouring sites is already occupied K W + uwu • uww (The symbols W, u, w, K* and K denote a water molecule, an unoccupied site, a site occupied by a water molecule, and the appropriate binding constants, respectively.) The values of K and K* were evaluated from the experimental data and showed that practically all the water binding sites of polar groups in synthetic polypepfides have binding constants and free energies of binding of similar magnitudes (Table II). An important result which also emerged both from our work on polypeptides and from that of Leeder and Watt on wool, is that the free energies of binding seem to be about four to five times larger than the thermal energy, suggesting that, at ambient temperatures, the water is fairly firmly bound to the polar sites of the protein. This argument is also Table II Binding constants and free energies of binding of water K AGo AG½o-op (1 mole -x) (kJ mole -z) (k.l mole -z) PGly I 6.8 x 10 • - 14.4 - 2.2 PGly II +1.5 x 10" +3.5 4-0.4 --COOH • 8.5 x 10 •' -13.1 -4.1 --NH•. 4-1.5 x 10 •' 4-3.5 4-1.0 --COO- Na + • 1.75 X 10 •' - 16.1 - 2.9 --NHa + Br- 4-0.15 X 10 •' 4- 3.5 4-0.5 A G o, Free energy of binding of water A Geo-op, free energy the co-operative interactions between bound water mole- cules.

456 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS supported by results of dielectric measurements which have shown that in proteins about 70•o of hydration water has very limited freedom of move- ment (17), and by results of recent measurements which indicate that water adsorbed on oriented polypeptide films exhibits dichroism of its funda- mental ir frequency suggesting a strong binding of the water to discrete sites which bind water in an oriented way (18, 19). A considerable amount of work has been carried out on the interaction of water with carboxylic, amino and peptide groups attached to small molecules. The results of these investigations are in good agreement and support the results obtained on polypeptides [for a review of this work see the discussion in (15)]. An important question which also requires consideration is whether or not the macromolecular conformation of the polypeptide chains has any influence on the water binding properties of the proteins or polyamides. The detailed work of Puffr and Sebenda (20) on the water adsorption properties of polyamides (Nylon 6 and 66) is highly important in this context. Puffr and Sebenda classified nylon structures into crystalline regions, mesomorphic areas and completely amorphous regions. In a series of detailed studies they measured water binding curves of polyamides containing different proportions of these three regions, and found that the degree of crystallinity, determined by ir and density measurements, in- fluences the water uptake of nylon. Puffr and Sebenda constructed a plot of water adsorption capacity of nylons as a function of the degree of crystallinity. They found by extrapolation that completely crystalline nylon does not adsorb water at all, whereas entirely amorphous polyamides bind 1.5 moles of water per peptide bond (Fig. 7). As an explanation it was c• o Figure 7. Plot of amount of water absorbed by Nylon 66 as a function of O, the degree of crystallinity [reproduced with permission from ref. (20)].