The Dubinin-Radushkevich (DR) adsorption isotherm, using Polanyi's potential for sparingly soluble solutes, was applied to phosphorus sorption by 20 soils. The DR isotherm is
where ε, the Polanyi potential, is
X is the amount of phosphorus adsorbed, Xm is the adsorption maximum, and C is the equilibrium phosphorus concentration. B is a constant and is related to the mean energy of adsorption; R is a gas constant; and T is absolute temperature.
The DR isotherm was obeyed so long as phosphorus sorption occurred within the single phase of sparingly soluble phosphorus compounds. The adsorption maxima obtained by the DR isotherm and the Langmuir isotherm were essentially similar. The mean energy of adsorption indicated that diffusion (or anion exchange) controlled the process of phosphorus sorption by soils.