Kinetic and Thermodynamic Study of the Adsorption of Malachite Green Dye Using Graphene Nanoplatelets

2.1.

Materials

Commercial-grade GNPs were procured from Cheap Tubes Inc. (VT, USA). The provider data indicated that they were Grade 3, with 97% purity, average thickness of 8–15 nm, 2 μm in length, and specific surface area (SSA) of 500–700 m²⋅g⁻¹. They were used as received. MG dye was commercially sourced from Jalmek Scientific (NL, MX), and deionized water was used as the solvent. The spectrophotometer employed for analyte quantification was a Thermo Scientific model, Multiskan SkyHigh (MA, USA).

2.2.

Methods

Figure 1 presents a general overview of the methodology followed for the various adsorption tests conducted in this study.

2.3.

Effect of adsorbent mass

For the experiments, 10, 20, and 30 mg of GNPs were used, with a contact time of one hour at room temperature under constant agitation. The initial concentrations of MG dye used were 250–750 ppm, using a total volume of 5 mL. After the contact time, the samples were filtered and analyzed at a wavelength of 620 nm. The obtained absorbance readings were evaluated using the MG calibration curve to determine the dye concentrations in the solution.

2.4.

Effect of pH

To determine the optimal pH for the best adsorption of MG dye, experiments were conducted at a dye concentration of 500 ppm, using 10 mg of GNPs and varying pH levels of 4, 7, and 9.

2.5.

Effect of contact time (Kinetics)

An adsorption kinetics study was performed to observe the adsorption behavior of MG dye on GNPs over time. The initial concentration was 600 ppm, and contact time ranged from 0 to 180 minutes. Each trial used a fixed mass of adsorbent and 5 mL of MG solution.

2.6.

Kinetic study of MG adsorption on GNPs

Adsorption kinetics describes the rate at which the solute adsorbs and the contact time of the adsorbate at the solid-liquid interface, i.e., it is related to the efficiency of the adsorption process. The adsorption rate depends on the number of particles adsorbed onto the adsorbent surface per second and the number of particles in contact with a unit area per second [34].

The Elovich model assumes that the rate of the adsorption reaction decreases with increasing surface area of the adsorbent. The kinetic model represents the chemisorption of gases onto solid surfaces, with no desorption of the product [35], and the mathematical equation representing this model is given by Equation (1). This model is commonly used, assuming the adsorbent surface is energetically heterogeneous [34].

where, 𝛼 represents the initial adsorption rate (mg⋅g⁻¹ min⁻¹) and 𝛽 denotes the desorption constant (g⋅mg⁻¹).

The pseudo-first-order model (PFO), Equation (2), was also applied. It is suitable for describing physisorption and reversible interactions between the gas and solid surface component.

where, q_e is the adsorption capacity of the adsorbent at equilibrium (mg⋅g⁻¹), q_t is the adsorption capacity of the adsorbent at time t (mg⋅g⁻¹), and k_t is the rate constant for PFO adsorption (min⁻¹).

The reaction time is directly proportional to the difference in concentration and the rate at which the adsorbate is removed over time [34].

The pseudo-second-order (PSO) kinetic model is a widely used model to fit rate data for the adsorption of metal ions, dyes, and other compounds from aqueous solutions. A literal interpretation of the model assumes that different adsorption sites on a solid substrate collide with each other [36].

The published evidence on the validity of the mechanistic assumptions underlying the application of the PSO model for adsorption kinetics has been considered. This mathematical model is expressed in Equation (3).

where, q_e is the adsorption capacity of the adsorbent at equilibrium (mg⋅g⁻¹), q_t is the adsorption capacity of the adsorbent at time t (mg⋅g⁻¹), and k_t is the rate constant for PSO adsorption (g⋅mg⁻¹⋅min⁻¹).

After the results from the contact time experiments were obtained, the data were tested against Elovich, PFO, and PSO kinetic models, which were the basis for the equations used to analyze the obtained data.

2.7.

Adsorption isotherms of MG on GNPs

Adsorption isotherms describe the interaction between the adsorbent and the adsorbate, making them essential for optimizing the use of any adsorbent. The shape of an isotherm provides information about the stability of these interactions and the adsorption affinity of molecules. Adsorption isotherms are described in various mathematical models; few are based on simplified physical descriptions of adsorption, while others are empirical and must be correlated with experimental data [34].

To understand the behavior of the system at equilibrium, isotherms were performed at three different temperatures (10, 40, and 50 °C), with initial concentrations ranging from 600 to 2100 ppm using a fixed mass of adsorbent and a volume of 5 mL.

The Freundlich adsorption isotherm is used to quantify the equilibrium relationship between the amount of adsorbate removed per unit weight of adsorbent and the concentration remaining in the solution. The mathematical equation that describes the Freundlich adsorption model is given in Equation (4).

where, n is a constant related to the efficiency and sorption energy, k_f is the adsorption constant, q_e is the amount of adsorbate removed per unit weight of adsorbent, and C is the equilibrium concentration of the adsorbate in solution [34].

The Temkin isotherm is described in Equation (5).

where, q_e represents the amount of adsorbate removed per unit weight of the adsorbent, k_t (dm³⋅g⁻¹) represents the optimal binding energy, C_e is the equilibrium concentration of the adsorbate in solution, b_T (J⋅mol⁻¹) is a constant related to the heat of adsorption, R is the ideal gas constant (8.314 J⋅K⁻¹⋅mol⁻¹), and T is the absolute temperature [34, 37, 38].

The Langmuir isotherm is described in Equation (6) [34, 39].

where, q_e represents the amount of adsorbate removed per unit weight of the adsorbent, Q° is a constant related to the monolayer adsorption capacity, b is the constant that quantifies the surface energy of the adsorption process, and C is the equilibrium concentration of the adsorbate in solution.

2.8.

Thermodynamic parameters

Adsorption enthalpy (𝛥H°) provides insights into whether the process is exothermic or endothermic. It allows for estimating energy activation and helps differentiate whether the process occurs via physisorption or chemisorption. If the enthalpy values range between −40 and −120 kJ⋅mol⁻¹, the adsorption is classified as chemical.

Adsorption entropy (𝛥S°) predicts the changes occurring on the adsorbent surface. Significant surface structure alterations affect the process’s reversibility, resulting in a negative adsorption entropy value. Conversely, a positive 𝛥S° indicates a high likelihood of reversibility [40].

Using van’t Hoff’s assumptions, it is possible to estimate thermodynamic properties such as enthalpy, entropy, and Gibbs free energy of adsorption processes. Once the data are plotted, the thermodynamic parameters can be determined using the intercept and slope of the linear equation, along with the ideal gas constant R.

The Gibbs free energy (𝛥G°) determines whether a process is spontaneous. Negative 𝛥G° values indicate a spontaneous process, whereas positive values imply that energy input is required to proceed. 𝛥G° is calculated using Equation (7), leading to Equation (8) [40].

Rearranging lnK, Equation (9) is obtained, commonly known as the van’t Hoff equation. By combining these two equations, a plot of lnK on the ordinate axis and T⁻¹ on the abscissa should yield a linear relationship, with the intercept corresponding to 𝛥S°⋅R⁻¹ and the slope numerically equal to 𝛥H°⋅R⁻¹. K represents the adsorption constant obtained from the adsorption model used to fit the experimental data.

3.1.

Effect of adsorbent mass

Adsorption experiments were conducted using adsorbent masses of 10, 20, and 30 mg of GNPs, with initial dye concentrations of 250, 500, and 750 ppm, as described in the methodology section.

The adsorption percentages of MG with GNPs for the three tested masses (10, 20, and 30 mg) are presented. Although adsorption reached 100% with 20 and 30 mg, non-total adsorption was required for subsequent experiments. Therefore, the lowest mass (10 mg of GNPs) was selected, which exhibited a removal efficiency of 87%, corresponding to approximately 652 ppm.

The adsorbent dosages used in this study were 2, 4, and 6 g⋅L⁻¹, with complete dye adsorption occurring at the two highest dosages. Consequently, the lowest dosage was selected. Fadhila et al. [5] used a CoCr₂O₄/ZnO nanocomposite for MG degradation, with adsorbent loadings ranging from 0.04 to 0.12 g⋅L⁻¹. However, their initial concentration was only 5 ppm, and the highest degradation efficiency (90%) was achieved using 0.08 g⋅L⁻¹, removing 4.5 ppm of the dye. Similarly, Piriya et al. [28] reported using acid-activated coconut shell charcoal for MG adsorption. Their initial dye concentrations ranged from 20 to 80 ppm, achieving a maximum adsorption capacity of 32 mg/g. The adsorption capacity of the GNPs in MG in percentage and in mass, of the present study are shown in Figure 2.

3.2.

Effect of pH

Adsorption tests were conducted at three different pH values: 4, 7, and 9, as detailed in the methodology section. During the quantification process, a precipitate was observed at acidic pH, making dye quantification unreliable despite achieving removal of up to 230 ppm. At neutral pH, a removal efficiency of approximately 60% (300 ppm) was obtained, while at basic pH, the removal decreased to 150 ppm (∼30%). Consequently, neutral pH was selected for further experiments. In the present study the influence of pH on adsorption capacity of the GNPs in MG in percentage and in mass is shown in Figure 3.

These findings align with those reported by Bulut et al. [41], who also determined that pH 7 was optimal for MG removal using bentonite as an adsorbent. Likewise, Fu et al. [42] reported that the most efficient pH for MG removal with activated carbon was 7, while adsorption rates significantly decreased at pH values below 4 or above 9. MG dye reacts with H⁺ and OH⁻ ions, influencing its adsorption rate.

3.3.

Effect of contact time

To determine the optimal contact time, adsorption kinetics were evaluated at an initial MG concentration of 600 ppm. Under ambient temperature and stirring at 250 rpm, contact times ranged from 0 to 180 minutes.

As shown in Figure 4, the adsorption process occurred rapidly, with adsorption percentages approaching 40% (equivalent to 240 ppm) within the first 15 minutes. The removal efficiency gradually increased, reaching approximately 90% (540 ppm) at 180 min. Based on these results, a contact time of 2 h is recommended for optimal adsorption performance.

Choudhary et al. [8] posited that activated biochar derived from Opuntia ficus-indica adsorbed MG dye, Cu²⁺, and Ni²⁺ from water. The material achieved an adsorption capacity of 165 ppm within a maximum contact time of 120 minutes and a removal efficiency of 99%. In the present study, a removal efficiency of 87% was obtained under the same contact time, corresponding to 522 ppm. This indicates that the material used in this work is more efficient for MG removal.

3.4.

Kinetic models

The kinetic analysis data were applied to the Elovich, PFO, and PSO models, as described by Equations (1), (2) and (3), to better understand the adsorption behavior of MG onto GNPs. These models help determine whether the adsorption mechanism is chemisorption or physisorption. PSO model provided the best fit (Table 1), as shown in Figure 5, indicating that adsorption depends on the number of available active sites on the adsorbent surface [43].

Although acceptable R² values were obtained for all three kinetic models, the experimental data for the kinetics from 0 to 180 minutes, at ∼40 °C, and with an initial analyte concentration of 600 ppm, fit best to the PSO model (98.8%). This indicates that the rate-controlling factor during the first 3 h was related to the adsorption mechanism, leading to the inference that the adsorption of the dye onto GNPs can be described as a chemical process [7, 44]. Furthermore, using the slope of the linear plot, it was possible to calculate the rate constant for the PSO model (k₂), which was determined to be 35.71 mg/g. This relatively high value confirmed the rapid adsorbent and adsorbate interaction.

3.5.

Isotherms

Adsorption isotherms were conducted at 10, 40, and 50 °C, as shown in Figure 6. The initial concentrations ranged from 600 to 2100 ppm, with 10 mg of GNPs and 5 mL of solution rendering different R² for the Langmuir isotherm. The values were 0.9896, 0.9345 and 0.9899, respectively.

Another parameter that can be determined using the Langmuir model is the maximum adsorption capacity of the material. As presented in Equation (10), the method for obtaining q_max is outlined, providing a quantitative measure of the adsorption potential of the material.

q_max = maximum adsorption capacity (mg⋅g⁻¹ or mol⋅g⁻¹). KCe = Langmuir constant, related to the affinity of the adsorbate for the adsorbent (L⋅mg⁻¹ or L⋅mol⁻¹) [19]. The Langmuir model estimated a maximum adsorption capacity of 1000 mg/g at 40 °C in this study. Table 2 compares different values of q_max reported in the literature for different materials.

3.6.

Determination of thermodynamic parameters

Adsorption enthalpy (𝛥H°) provides information about the exothermic or endothermic nature of the process. It can estimate the activation energy and elucidate whether the process occurs via physical or chemical adsorption. If the 𝛥H° values range between −40 and −120 kJ/mol, the adsorption is classified as chemical. Using van’t Hoff’s assumptions, it is possible to estimate the range of thermodynamic properties, such as enthalpy, entropy and Gibbs free energy, for the adsorption process, as shown in Figure 7.

Based on the slope and intercept values of the graph and considering the ideal gas constant R, it is possible to determine the adsorption enthalpy (𝛥H°) and adsorption entropy (𝛥S°). Once these values are calculated, the Gibbs free energy change (𝛥G°) can be determined. Table 3 presents these values, where the mass of 10 mg was consistent in all cases.

A positive enthalpy value indicated that the adsorption process was endothermic, i.e., it required energy to occur. Similarly, a negative entropy value suggested a decrease in system randomness, indicating that the adsorption process was ordered and irreversible. This also confirmed that GNPs have a strong affinity for MG dye possibly due the interaction of 𝜋–𝜋 bonds in their chemical structure. The Gibbs free energy value also confirmed that the system required an external energy input and that the process was non-spontaneous [49]. These thermodynamic parameters indicated that this adsorption model required an external energy supply for optimal performance. The optimal temperature was 40 °C.