sorptionsisotherm

A sorption isotherm is a relationship that describes how much sorbate is taken up by a solid sorbent at equilibrium as a function of the sorbate’s activity or pressure in the surrounding phase, at a constant temperature. It characterizes the distribution of a substance between the sorbed phase and the phase in contact with the sorbent, such as gas–solid or liquid–solid systems.

Sorption, which includes both adsorption (binding to a surface) and absorption (uptake into the bulk), isotherms focus on the equilibrium state rather than the kinetics of uptake. They are widely used to assess surface properties, porosity, and capacity of materials such as activated carbon, zeolites, and porous polymers. In gas adsorption, the isotherm is often plotted as amount adsorbed versus relative pressure (P/P0) at a fixed temperature; in solution, as amount adsorbed versus concentration.

Common models include:

- Langmuir isotherm: q = (qmax b C)/(1 + b C), reflecting monolayer adsorption on a homogeneous surface with no lateral interactions between adsorbed molecules.

- Freundlich isotherm: q = K_F C^(1/n), an empirical model for heterogeneous surfaces and non-ideal adsorption.

- BET (Brunauer-Emmett-Teller) isotherm: extends Langmuir to multilayer adsorption and is widely used to estimate monolayer capacity qm and surface area from gas adsorption data, using the linear form P/[q(P0−P)] = 1/(qmC) + (C−1)/(qmC)·(P/P0).

Other models (e.g., Redlich-Peterson, Sips) provide flexible fits for complex systems. These isotherms aid material characterization, adsorption process design, and interpretation of surface energetics.