2.4.3. Adsorption Isotherms

The adsorption isotherm describes the relation between the amounts of metal ion adsorbed onto adsorbent surface and the concentration of the metal ion remaining in the solution at a particular temperature when the adsorption process reaches equilibrium conditions. Various amounts of G1H20 nanoparticles (0.025, 0.035, 0.045, 0.055, 0.065 and 0.075 g) were added to 50 mL of 100 ppm of copper solutions at pH of 6 and 60 °C. The mixture was agitated in a shaking bath at 100 rpm for 720 min. The adsorption data were fitted with two commonly used isotherm models, Langmuir and Freundlich, to understand the adsorption behavior of copper ions onto PGA-AP nanoparticles.

The Langmuir isotherm model is based on monolayer adsorption onto a homogeneous adsorbent surface without any interactions between adsorbed molecules [23]. The Langmuir equation is given by:

The linear form is as follows:

where q_m (mg/g) corresponds to the maximum amount of copper ions adsorbed per gram of adsorbent to form a complete monolayer on the surface. K_L (L/mg) is the Langmuir equilibrium constant related to the bonding-energy of the adsorbate to the adsorbent. The constants q_m and K_L can be determined from the slope and intercept of the linear plot between C_e/q_e and C_e.

The important characteristic of the Langmuir isotherm is the dimensionless separation factor (R_L), which confirms the favorability of the adsorption process and is expressed as follows:

where C₀ (mg/L) corresponds to the highest initial copper ion concentration in the solution.

The Freundlich isothermal model indicates the heterogeneity of the adsorbent surface and describes multilayer adsorption with an energetic nonuniform distribution [24]. The adsorption capacity is related to the concentration of copper ions at equilibrium and can be expressed as:

The linear form is as follows:

where K_F [(mg/g)/(mg/L)^–1/n] and 1/n are the Freundlich constants related to the capacity and intensity of the adsorption, respectively. The constants K_F and 1/n can be determined from the intercept and slope of the linear plot between lnq_e and lnC_e.