Nernst Distribution Isotherm

Chemical potentials of species A in organic and aqueous phases are represented by 

When the distribution equilibrium is attained, = p is hold, and the next relation is derived as 

Considering only the reactions in two-bulk phases, the formation constants of metal complexes, and the distribution constants of the ligand and the complex, Kq and 

FIGURE 2.1 Conceptual drawing of the driving force of the distribution in terms of the differenee of standard chemical potentials between the aqueous phase and organic phase (see Equation 2.3). 

are primary factors governing the extraction constant, as written by the equation 

---

The Nernst partition isotherm applies to each individual species in an equilibrium mixture. The analyst is more directly concerned with the experimentally determinable distribution ratio, D, defined as... 

When two immiscible solvents are placed in contact, any substance soluble in both of them will distribute or partition between the two phases in a definite proportion. According to the Nernst partition isotherm, the following relationship holds for a solute partitioning between two phases a and b ... 

I he simplest is the partition of a solute between two immiscible solvents. In this case [0] /[Z)], = K, where K is the partition coefficient. This equilibrium is often referred to as the Nernst distribution. When [Z)], is plotted against [Z)], at constant temperature the curve is a straight line which terminates at the point when both the fibre and the dyebath are saturated. There are slight deviations from the linearity of the curve, particularly as the solutions become more concentrated. This system is probably exhibited in its ideal form when dyeing cellulose acetate rayon from an alcoholic dye solution, but it is also essentially true in the case of the application of disperse dyes in aqueous suspension to cellulose acetate, because the dyes are all soluble in water to a very limited extent and the undissolved particles act as a reservoir to maintain the concentration of the solution. The curve for this isotherm is shown in Fig. 12.14. 

Effect of various dosing profiles on levelness of dye distribution through the package for a Nernst adsorption isotherm. 

Isotherms plot of distribution ratios K, that is, a plot of concentration of the component in the stationary phase versus concentration in the mobile phase. Isotherms represent the relative attraction of a solute for the stationary and mobile phases, the plot is linear for a symmetrical Gaussian peak, non linear isotherms lead to unsymmetrical peaks, e.g. peak fronting and tailing. Langmuir isotherms describe the equilibrium process in adsorption chromatography, Nernst isotherms relate to partition chromatography. 

The conclusions above are drawn from Figs. 6.22 and 6.23, for the Nernst type adsorption isotherms. In the case of Freundlich adsorption isotherms, the simulation shows the same trend (see Figs 6.24 and 6.25) in both CDEP and DDF, although the dyeing system with a Freundlich adsorption isotherm seems to give a better dye distribution through the package. 

---