Adsorption isotherms: The adsorption data were analyzed to see whether the isotherm obeyed the Langmuir, Freundlich, Dubinin-Radushkevich (D-R) and Temkin isotherm models equationsWhere qmax, the monolayer capacity of the adsorbent (mg/g); KL, the Langmuir constant (L/mg) and related to the free energy of adsorption; qm, the theoretical saturation capacity (mg/g); and ?, the Polanyi potential, which is equal to RT Ln (1 + (1/Ce)), where R (J/mol K) is the gas constant and T (K) is the absolute temperature; ?, a constant related to the mean free energy of adsorption per mole of the adsorbate (mol2/kJ2). Also at Freundlich isotherm KF is adsorption capacity at unit concentration (L/g) and is adsorption intensity. Values indicate the type of isotherm to be irreversible ( = 0), favorable ( ), unfavorable ( ). The A, b, R, T in Temkin isotherm are equilibrium binding constant (L/g) Temkin isotherm constant, universal gas constant (8.314 J/mol K) and temperature at 298 K, respectively. B is the constant related to heat of sorption (J/mol).

The qmax and KL, of Langmuir equation can be determined from the linear plot of 1/Ce versus 1/qe (Fig. 3 a). qm and ? of D-R equation can be determined by plotting Ln qe versus ?2 (Fig. 3 b) and KF and 1/n of Freundlich equation can be calculated from the slope and intercepts of linear plot of log qe versus log Ce (Fig. 3 C).

Temkin isotherm contains a factor that is explicitly entered into the adsorbent–adsorbate interactions. By ignoring the extremely low and large value of concentrations, the model assumes that heat of adsorption (function of temperature) of all molecules in the layer would decrease linearly rather than logarithmic with coverage. As implied in the equation, its derivation is characterized by a uniform distribution of binding energies (up to some maximum binding energy) was carried out by plotting the quantity sorbed qe against Ln Ce and the constants were determined from the slope and intercept (Fig. 3 d).

The Langmuir, Freundlich, Temkin and D-R parameters for the adsorption of Ampicillin onto Mon-nanoparticles were listed in Table 3. The fit of the data for Ampicillin adsorption onto Mon-nanoparticles suggests that the D-R and Langmuir model gave better fittings than of Temkin and Freundlich models, as is obvious from a comparison of the regression coefficient (R2) in Table 3.

The constant ? is related to the mean free energy E (kJ/mol) of adsorption per molecule of the adsorbate when it is transferred to the surface of the solid from infinity in the solution and can be calculated using the relationship