3.4. Batch Biosorption Procedure and Data Analysis

The batch biosorption tests were performed by adding an appropriate amount of CDA into glass beakers containing 50 mL of CV or CR dyes. All biosorption experiments of CV and CR dyes onto CDA were carried out separately using monocomponent dye solutions. The impact of operational factors like pH of the solution (from 2.1 to 11.8), CDA dose (from 0.1 to 2 g/L), initial dye concentration (from 20 to 400 mg/L), biosorption time (from 0 to 240 min), and temperature (from 25 to 55 °C) has been studied on the extent of CV and CR dye removal. The initial pH was adjusted by adding a few drops of concentrated HCl or NaOH solutions. After each biosorption experiment, the adsorbent was separated by filtration on a 0.45 μm membrane filter. A UV-2300 spectrophotometer was used to quantify the dye concentration of the filtrate at the maximum absorption wavelengths of CV and CR dyes presented in Table 1. The uptake capacity (Q_e) and removal efficiency (%R) were calculated using

where C₀ and C_e are dye concentrations (mg/L) before and after biosorption, respectively, m (g) is the mass of the CDA, and V (L) is the volume of adsorbate solution.

In the present study, the experimental kinetic data for adsorption of CV and CR dyes on the CDA surface were analyzed using pseudo-first-order,⁵⁶ pseudo-second-order,⁵⁷ and intraparticle diffusion⁵⁸ models, which are expressed according to the following equations:

In eqs 5–7, Q_t (mg/g) is the experimental uptake capacity at time t (min); Q_e (mg/g) is the theoretical biosorption capacity at equilibrium calculated by kinetic models; β (mg/g) is the intraparticle diffusion model constant related to the thickness of the boundary layer; k₁ (1/min), k₂ (mg/g·min), and k_int (mg/g·min^0.5) are the biosorption rate constants of pseudo-first-order, pseudo-second-order, and intraparticle diffusion, respectively.

Langmuir and Freundlich isotherms were used to describe the interactions between the CV and CR dyes and the CDA biosorbent when the adsorbent–adsorbate equilibrium is reached. The Langmuir isotherm model is based on the assumption that the biosorption mechanism occurs as a monolayer coverage of adsorbate molecules on the same binding sites distributed homogeneously throughout the adsorbent surface, without intermolecular interactions between adsorbed species.⁵⁹ The Freundlich isotherm model suggests that the biosorption process tends to be multiple layers over the heterogeneous adsorbent surface with different affinities of active sites.⁶⁰ The following formulas give the expressions of Langmuir and Freundlich models

In eqs 8 and 9, C_e (mg/L) is the equilibrium dye concentration, Q_e (mg/g) is the equilibrium uptake capacity, Q_m (mg/g) represents the maximum monolayer uptake capacity, K_L (L/mg) is the Langmuir constant, K_F is the equilibrium constant of the Freundlich isotherm related to uptake capacity, and n_f is the factor heterogeneity.

The values of crucial thermodynamic parameters such as Gibbs free energy change (ΔG°), enthalpy change (ΔH°), and entropy change (ΔS°) are determined by applying the van’t Hoff law (eq 10) to biosorption experimental data at different temperatures.⁴⁴

The equilibrium constant (K_e°) was expressed as^61,62

where K_L (L/mg) is the Langmuir equilibrium constant, R is the universal gas constant (8.314 J/K·mol), T is the investigated temperature in Kelvin, M(Adsorbate) is the molecular weight of the dye, γ represents the coefficient of activity, and [Adsorbate]° denotes the standard concentration of the solute (1 mol/L).