*2.3. The Influence of Di*ff*erent Physicochemical Parameters on the Biosorption of Co2*<sup>+</sup> *by PLEM*

Experiments to evaluate the effect of several physicochemical variables on the biosorption of Co2<sup>+</sup> by *PLEM* were carried out in 500 mL Erlenmeyer flasks. They contained 120 mL of a solution with a known concentration of Co2<sup>+</sup> at a predetermined pH value. Subsequently, an addition was made of 0.12 g of PLEM at a certain particle size, thus achieving a biosorbent concentration of 1 g (dry weight) L−<sup>1</sup> . The suspensions were left at 18 ◦C (rt) for 2 h under constant agitation at 140 rpm in an orbital shaker (All Sheng™, Hangzhou Allsheng Instruments Co, Ltd., Hangzhou, China). The pH of the solutions was adjusted to the desired value and maintained constant throughout the assay by adding 0.1 M HCl and 0.01 M NaOH.

Firstly, the pH varied (2, 3, 4, 5, 6, and 7), while maintaining the initial concentration of Co2<sup>+</sup> (*Cini*) at 100 mg L−<sup>1</sup> and the particle size of *PLEM* at 0.3–0.5 mm. Later, distinct particle sizes (0.3–0.5, 0.5–0.8, 0.8–1.4, 1.4–2.0, and 0.3–0.8 mm) were utilized, while maintaining *Cini* at 100 mg L−<sup>1</sup> and the pH at 7.0. Finally, different initial values of *Cini* (10, 20, 40, 60, 80, 100, 200, and 300 mg L−<sup>1</sup> ) were used, while maintaining the pH at 7.0 and the particle size at 0.3–0.8 mm.

During the experiment, samples were taken at various exposure times and filtered to afford a solution free of biosorbent. The filtrate of each flask was diluted properly for the posterior quantification of the cobalt concentration. From the values obtained, the biosorption capacity of Co2<sup>+</sup> by *PLEM* was calculated at a series of exposure times using Equation (1):

$$q = \frac{V}{M}(\mathbb{C}\_{\text{ini}} - \mathbb{C}) \tag{1}$$

where *q* (mg g−<sup>1</sup> ) is the capacity of biosorption of Co2+, *V* (L) is the total volume of the solution, *M* (g) is the biosorbent mass, and *Cini* and *C* (mg L−<sup>1</sup> ) correspond to the initial concentration of Co2<sup>+</sup> in the solution and its concentration at time *t* (h), respectively. When the system reaches equilibrium, *t* = *teq*, *C* = *Ceq* and *q* = *qeq*. Based on the values of biosorption capacity found, the most suitable pH of the solution and the best particle size for the removal of Co2<sup>+</sup> were selected for the rest of the biosorption experiments. For each of the parameters examined, controls free of biosorbent were established and analyzed for possible changes in the concentration of cobalt.

### *2.4. Kinetic Modeling of the Biosorption of Co2*<sup>+</sup> *by PLEM*

For the kinetic modeling of the biosorption of Co2<sup>+</sup> by *PLEM*, the equations of pseudo-first-order, pseudo-second-order, and fractional power were employed (Table 1).


#### *2.5. Biosorption Isotherm Studies at Di*ff*erent Temperatures*

In 125 mL flasks were poured 30 mL of solutions of Co2<sup>+</sup> at distinct concentrations (20, 40, 60, 80, 100, 200, and 300 mg L−<sup>1</sup> ), adjusting the pH to 7.0. Then 0.03 g of *PLEM* (particle size = 0.3–0.8 mm) was placed in each flask to ensure a concentration of 1 g L−<sup>1</sup> of *PLEM*. The suspensions were left for 2 h at 18, 30, 40, 50, or 60 ◦C to reach biosorption equilibrium. Subsequently, the samples from each flask were filtered, and the residual concentration of Co2<sup>+</sup> was quantified in each filtrate. With the experimental results of the biosorption capacity found at equilibrium (*qeq*) and the residual concentration of cobalt at equilibrium (*Ceq*) for each initial concentration of metal assayed (*Cini*), the isotherm for adsorption was calculated. It was then possible to select the best mathematical model for describing the experimental behavior. With this objective in mind, models of two (Langmuir and Freundlich) and three parameters (Sips and Redlich-Peterson) were used (Table 1).

#### *2.6. Determination of the Thermodynamic Parameters*

The thermodynamic parameters examined were the changes in Gibbs free energy (∆*G* 0 , J mol−<sup>1</sup> ), in standard entropy (∆*S* 0 , J mol−<sup>1</sup> K −1 ), and in standard enthalpy (∆*H*<sup>0</sup> , J mol−<sup>1</sup> ). With the data on the isotherms for biosorption at equilibrium, the coefficient of distribution (*Kd,* L g−<sup>1</sup> ) was obtained for each temperature and concentration assayed using Equation (2) [21]:

$$K\_d = \frac{q\_{eq}}{\mathcal{C}\_{eq}} \tag{2}$$

In the graph of Ln *K<sup>d</sup>* vs. *Ceq* for each temperature, the point at which the ordinate crosses the origin corresponds to Ln *K*<sup>0</sup> (*K*<sup>0</sup> being the sorption constant at equilibrium, L g−<sup>1</sup> ). These values were substituted in Equation (3) to find the change in Gibbs free energy [22]:

$$
\Delta G^0 = -RT\,\ln K\_0 \tag{3}
$$

where *R* is the constant of the ideal gases (8.315 J mol−<sup>1</sup> K −1 ), and *T* is the absolute temperature (K) during biosorption. The change in standard entropy (∆*S* 0 ) was found by Equation (4):

$$
\Delta S^0 = \frac{\partial \Delta G^0}{\partial T} \tag{4}
$$

The slope of the graph of ∆*G* <sup>0</sup> vs. *T* indicates the mean value of ∆*S* 0 . The change in the standard enthalpy was furnished by Equation (5):

$$
\Delta \mathbf{G}^0 = \Delta H^0 + T\Delta \mathbf{S}^0 \tag{5}
$$

### *2.7. Desorption of Co2*<sup>+</sup> *from the Biosorbent*

To evaluate desorption, the biosorbent was first saturated by exposing *PLEM* (1 g L−<sup>1</sup> , with a particle size of 0.3–0.8 mm) to a solution of Co2<sup>+</sup> (300 mg L−<sup>1</sup> , pH 7.0, rt) under constant agitation at 140 rpm for 2 h. Upon completion of this time, the biosorbent was washed with deionized water several times to eliminate the excess cobalt and then dried in an oven at 60 ◦C for 48 h. Finally, it was stored in hermetically-sealed bottles until further use.

For the desorption of Co2<sup>+</sup> from *PLEM*, diverse solutions were tested as eluents: Water at rt (H2O rt, the control), water at 60 ◦C (H2O 60 ◦C), various acidic solutions (HCl, H2SO4, HNO3, C2H2O4, KH2PO4, and NH4Cl) and three alkaline compounds (NaOH, NaHCO3, and K2HPO4). The concentration of all compounds was 0.1 M. Desorption was carried out by placing 120 mL of one of the distinct eluent solutions in each Erlenmeyer flask and adding the saturated biosorbent at a concentration of 1 g L−<sup>1</sup> . The material was maintained under constant agitation at 140 rpm and 18 ◦C for 2 h, collecting and filtering samples from each of the flasks at different times. The concentration of desorbed metal on each filtrate was quantified. The percentage of desorption at time *t* was calculated with Equation (6) [23]:

$$E\_D(\%) = \frac{V(\mathcal{C}\_D - \mathcal{C}\_{ini})}{M \, q\_{eq}} \times 100\tag{6}$$

where *Cini* and *C<sup>D</sup>* (mg L−<sup>1</sup> ) are the initial concentration of metal in the solution (*t* = 0 h) and the concentration of Co2<sup>+</sup> eluted from the solution at time *t*, respectively, and *qeq* (mg g−<sup>1</sup> ) is the amount of Co2<sup>+</sup> retained per gram of biosorbent (determined experimentally). The results of the percentage of the desorption were compared to select the adequate solution for eluting Co2<sup>+</sup> from *PLEM*.

#### *2.8. Biosorption-Desorption Cycles*

*PLEM* was saturated with Co2<sup>+</sup> for 2 h, as described in the previous section. Upon completion of this time, samples of the solution were taken to assess the biosorption capacity of *PLEM* in the first stage (Equation (1)). Subsequently, the saturated biosorbent was washed, dried, and subjected to the desorption of Co2<sup>+</sup> (as already explained) by putting 1 g L−<sup>1</sup> of the material in a solution with the selected eluent and leaving it under constant agitation at 140 rpm and rt for 2 h. Samples were then taken to quantify the concentration of Co2<sup>+</sup> in the solution and calculate the percentage of desorption for the first cycle (Equation (6)). *PLEM* was washed with deionized water and dried at 60 ◦C for 48 h to be submitted to posterior cycles. Three cycles of biosorption/desorption were carried out under the same conditions, allowing for the comparison of the capacity of biosorption and percentage of desorption from one cycle to another.

### *2.9. Scanning Electron Microscope Coupled to Energy-Dispersive X-ray Spectroscopy (SEM-EDX)*

The possible changes in the structure and composition of the surface of *PLEM*, due to the process of biosorption and the posterior desorption of Co2<sup>+</sup> were explored on a scanning electron microscope (SEM). The three types of samples of *PLEM* (unexposed to Co2+, saturated, and desorbed in the first cycle) were dried for 24 h at 60 ◦C. Subsequently, they were covered with carbon to be later observed with a JEOL high-resolution scanning electron microscopy (HR-SEM) (model JSM7800F, Jeol Ltd., Tokyo, Japan) with an acceleration voltage of 5 kV.

#### *2.10. Analytical Methods*

Co2<sup>+</sup> was quantified by the dimethylglyoxime (DMG) method, with which a compound is formed with an intensity of color proportional to the concentration of Co2<sup>+</sup> present in the solution [24]. The measurement of absorbance was conducted in a Spectronic Genesys UV/Vis 10 spectrophotometer (Thermo Electron Scientific Instruments Corp, Madison, WI, USA) at 400 nm. The concentration of Co2<sup>+</sup> was established by constructing metal-type curves with at least 10 distinct known concentrations.

#### *2.11. Statistical Analysis*

Each experiment was performed independently at least twice, and the determinations of residual cobalt were made at least three times, with the aim of attaining the appropriate statistical power. Data are expressed as the mean ± standard deviation (SD) of the values obtained experimentally. Regarding the values from the kinetics of biosorption and the experimental biosorption capacity at equilibrium (*qeq*), differences between groups were examined with two-way ANOVA and Tukey's test (with a confidence interval of α = 0.05) on the GraphPad Prism® Ver 8.4 program 2020 (GraphPad Software Inc, San Diego, CA, USA). The kinetic and equilibrium parameters were scrutinized by nonlinear regression on the same software, selecting the best model in accordance with a variety of error functions: The correlation coefficient (*R* 2 ), the absolute sum of squares (*ASE*), the standard deviation of the residuals (*Sy.x*) and Akaike's information criterion (*AICc*). The data from the three cycles of biosorption/desorption were compared with one-way ANOVA and Dunnett's test (confidence interval, α = 0.05) on the GraphPad Prism® Ver 8.4 program 2020 (GraphPad Software Inc., San Diego, CA, USA).

#### **3. Results and Discussion**

No change in the concentration of Co2<sup>+</sup> was found for the *PLEM*-free solutions, used as controls for the evaluation of the influence of the physicochemical conditions herein tested. Thus, the removal of Co2<sup>+</sup> from the aqueous solution can be fully attributed to the effect of biosorption produced by *PLEM*.

### *3.1. The E*ff*ect of pH*

The level of pH is one of the physicochemical factors that most influence the biosorption of heavy metals [25]. The pH values of 2–7 were presently employed because the precipitation of cobalt was observed experimentally as of pH 8, likely due to the formation of cobalt hydroxide [26,27]. At each pH value, the biosorption capacity was evaluated with respect to time (Figure 1a). With the pH at 2 or 3, the cobalt removal capacity was near 0.

*3.1. The Effect of pH* 

**3. Results and Discussion** 

*PLEM*.

2020 (GraphPad Software Inc., San Diego, CA, USA).

ANOVA and Tukey's test (with a confidence interval of α = 0.05) on the GraphPad Prism® Ver 8.4 program 2020 (GraphPad Software Inc, San Diego, CA, USA). The kinetic and equilibrium parameters were scrutinized by nonlinear regression on the same software, selecting the best model in accordance with a variety of error functions: The correlation coefficient (*R*2), the absolute sum of squares (*ASE*), the standard deviation of the residuals (*Sy.x*) and Akaike's information criterion (*AICc*). The data from the three cycles of biosorption/desorption were compared with one-way ANOVA and Dunnett's test (confidence interval, α = 0.05) on the GraphPad Prism® Ver 8.4 program

No change in the concentration of Co2+ was found for the *PLEM*-free solutions, used as controls for the evaluation of the influence of the physicochemical conditions herein tested. Thus, the removal of Co2+ from the aqueous solution can be fully attributed to the effect of biosorption produced by

The level of pH is one of the physicochemical factors that most influence the biosorption of heavy metals [25]. The pH values of 2–7 were presently employed because the precipitation of cobalt was observed experimentally as of pH 8, likely due to the formation of cobalt hydroxide [26,27]. At each pH value, the biosorption capacity was evaluated with respect to time (Figure 1a). With the pH at 2

**Figure 1.** Capacity of biosorption of Co2<sup>+</sup> by pretreated *Lemna gibba (PLEM)*: (**a**) At various pH values of the solution (*Cini* = 100 mg L−<sup>1</sup> , particle size = 0.3–0.5 mm), (**b**) with distinct particle sizes of *PLEM* (*Cini* = 100 mg L−<sup>1</sup> , pH = 7.0), and (**c**) at different initial concentrations of the metal (pH = 7.0, particle size = 0.3–0.8 mm). The continuous lines were predicted by the pseudo-second-order kinetic model.

The sorption capacity was enhanced with each increment in pH from 4 to 7, which can be easily explained by considering the pH of the plant material (1.67), which results in zero point of charge (ζ0) [17]. When the pH of a solution is less than that found at ζ0, the net charge of the surface of the biosorbent is positive. Hence, an electrostatic repulsion exists between the positive charge of both the metal ions and the surface of the biosorbent [28]. In contrast, when a solution has a pH value above that at ζ0, the net charge of the surface of the biosorbent is negative, and there is an attraction with the positively charged metal ion [29]. A pH value of 5–7 herein afforded the fastest biosorption of Co2<sup>+</sup> during the first 10 min (0.17 h) of the experiment. After this time, however, the velocity of removal of the metal decreased until reaching equilibrium, at which point the velocity of net transfer was 0. The initial rapid biosorption was due to the greater number of sites on *PLEM* available for the uptake of the sorbate and the higher concentration of Co2<sup>+</sup> in the aqueous solution. As time passed, the available sites and the concentration of free cobalt ions were both diminished, leading to a gradual decline in the velocity of the removal of Co2<sup>+</sup> until reaching the equilibrium dynamic. It was observed that as the pH increased, the biosorbent removed more Co2+, and therefore, required more time to reach equilibrium

(*teq*). The same phenomenon has been reported for the effect of pH on the biosorption of other divalent metal ions [29].

A summary of the of Co2<sup>+</sup> removal capacity at experimental equilibrium (*qeq*), the time to reach equilibrium (*teq*), and the values of the parameters and error functions for each model and at each pH value assayed are provided in Table 2. None of the kinetic models employed fit the experimental results at pH 2 or 3, probably owing to the minimal biosorption of Co2<sup>+</sup> under these conditions. At pH 4, a reduction in the removal capacity was only found after 0.75 h (Figure 1a), a time period not included in the process of biosorption. Hence, the corresponding data was not considered when determining the values of the parameters for the kinetic models. With a pH of 4–7, the pseudo-second-order model had the highest correlation coefficient (*R* 2 ) and the lowest values for *ASE, Sy.x*, and *AICc* compared to the other two models (pseudo-first-order and fractional power). The Elovich model was also evaluated, but is not listed in the tables because the *R* <sup>2</sup> was too small, and the parameters obtained had exaggerated *SD* values. Given that a pH of 7 produced the greatest biosorption capacity at equilibrium, this value was used for further testing.

**Table 2.** Kinetic parameters of the biosorption of Co2<sup>+</sup> by *PLEM* at various pH values of the solution (*Cini* = 100 mg L−<sup>1</sup> , particle size = 0.3–0.5 mm).

