2—the Direct Dyeing of Cellulose: A Method for the Analysis of Equilibrium Absorption Data in Terms of Current Quantitative Theories

Each of the equations derived from current theoretical treatments of the equilibrium between cellulose materials and direct dyes can be reduced to the same form, which expresses a unique relation between the substantivity ratio q and the salt-dye ratio p; this form is here called the p, q equation and it contains two empirical constants A and B. It is a convenient form for testing the fit of experimental absorption data to the quantitative theories. The values of the constants A and B can be readily determined from suitable data that fit the p, q equation. The more fundamental constants used in individual current treatments can easily be calculated from A and B. In particular, values may be calculated for the quantity V having the dimensions of a specific volume, which occurs in all the equations; and for the thermodynamic affinity of the dye for cellulose that occurs in the equation due to Peters and Vickerstaff. In order to illustrate the method, the paper attempts to fit data for the absorption of Chrysophenine G by cotton and mercerized cotton to the p, q equation. Except as an approximation, and over a limited range of salt concentration, no fit is obtained with the data for cotton. The calculation of a constant V, or of thermodynamic affinity, from these data is therefore not possible on the basis of the theories. They fail to correlate the available data for the absorption of the dye at 90°C by mercerized cotton with those available for its absorption by non-mercerized cotton at the same temperature.