Kinetic study and thermodynamic equilibrium modeling of the Co(II) and Mn(II) bioadsorption using the Rhodococcus opacus strain

Microbial biomass is considered a renewable and environmentally friendly re-source. Thus, the research conducted a kinetic study and thermodynamic equilibrium modeling of the cobalt (Co) and manganese (Mn) bioadsorption process using the Rhodococcus opacus (RO) strain as a biosorbent. The inactive biomass subject-ed to 0.1 M NaOH pretreatment was brought into contact with synthetic solutions of Co and Mn. The experimental data for the Co(II) and Mn(II) bioadsorption process were fit to the Langmuir model with kads of 0.65 and 0.11 L.mg -1 , respectively. A better statistical fit was also obtained for the pseudo-second order kinetic model ( R 2Co(II) = 0.994 and R 2Mn(II) = 0.995), with 72.3% Co(II) and 80% Mn(II) removals during the first 10 min. In addition, a higher affinity of RO for the Co(II) ion was observed, with maximum uptake values of 13.42 mg.g -1 ; however, a higher adsorption rate was observed for Mn(II) ion (k = 0.21 g.mg -1 .min -1 at 318 K). The bioadsorption process was spontaneous and dependent on temperature, being endothermic and irreversible for the Co(II) ion (∆H = 2951.91 J.mol -1 ) and exothermic and reversible for the Mn(II) ion (∆H = -2974.8 J.mol -1 ). The kinetic and thermodynamic equilibrium modeling allowed to identify the main mechanisms involved in the biosorption process of both metals.

Some metals such as cobalt (Co) and manganese (Mn), belonging to the group of so-called microelements are considered essential because they are related to biochemical and physiological functions in humans, animals and plants; however, their requirement is in low concentrations (Hejna et al., 2018). Excessive exposure of these microelements in high concentrations has been linked to cellular and systemic disorders, representing a considerable source of contamination (Rossi et al., 2014). Symptoms related to Co contamination are hair loss, vomiting, bleeding, diarrhea, vasodilation, cardiomyopathy, coma and even sterility and death (Ozdemir et al., 2020;Thirulogachandar et al., 2014). Meanwhile, Mn contamination causes drowsiness, weakness, emotional disturbances, recurrent leg cramps and paralysis (Thirulogachandar et al., 2014).
Co is present in wastewater from nuclear and mining-metallurgical plants, electroplating processes, paints, pigments and the electronics industry (Al-Shahrani, 2014). While Mn comes from the ferrous metallurgical, chemical, food electrochemical and pharmaceutical industries (Patil et al., 2016). Both pollutants are present in wastewater from lithium batteries (Qiao et al., 2020) and purified terephthalic acid (PTA) production, and in the petrochemical industry (Lin et al., 2020).
Technologies related to the removal of heavy metals from contaminated ef-fluents include chemical precipitation, ultrafiltration, ion exchange, reverse osmosis, electrowinning and phytoremediation. All of the above techniques have several disadvantages associated with them, such as low removal efficiency, sludge generation, energy requirements and very high reagent costs, among others (Beni and Esmaeili, 2020;Kanamarlapudi et al., 2018). However, the use of low-cost bioadsorbent may be an alternative (Li et al., 2019).
Bioadsorption is defined as a passive and metabolically simple physicochemical process involving the use of previously inactive adsorbents of biological origin that have demonstrated high metal removal efficiency and do not generate solid residues or toxic substances during operation.
Furthermore, this process is simple to operate, low-cost, highly efficient, does not increase chemical oxygen demand (COD), is environmentally friendly and allows regeneration of the biosorbent. (Chojnacka, 2010;Costa and Tavares, 2016).
It is common to compare the adsorption capacity between different types of biosorbents, as well as the affinity of different substances for biosorbents by means of adsorption isotherms. (Fomina e Gadd, 2014). Some isotherm models even describe the mechanism of the bioadsorption process and the distribution at equilibrium. Among the most commonly used isotherms are Langmuir, Freundlich and Temkin. (Beni and Esmaeili, 2020;Kanamarlapudi et al., 2018).
The kinetic study of the bioadsorption process indicates the speed with which the pollutants are removed from the aqueous medium, and among the variety of models, the most commonly used are the pseudo-first order and pseudo-second order (Beni and Esmaeili, 2020;Calero et al., 2009). Therefore, the research carried out a kinetic study and thermodynamic equilibrium modeling of the Co(II) and Mn(II) bioadsorption using the Rhodococcus opacus (RO) strain. For this purpose, the influence of time and temperature on the biadsorption process was studied, and the experimental data were evaluated using the pseudo-first order and pseudo-second order kinetic models, as well as the Langmuir and Freundlich isotherms.

Introduction
The RO bacteria was acquired from the André Tóselo Foundation, Sao Paulo, Brazil. It was cultivated in a liquid medium composed of 10 g.L -1 of glucose, 5 g.L -1 of peptone, 3 g.L -1 of malt extract and 3 g.L -1 of yeast extract, at pH 7.2. The incubation was carried out at 28ºC and 125 rpm for 72 h in a Cientec incubator (CT-712, Brazil). Subsequently, the cellular biomass was concentrated, quantified and stored according to the methodology described by Pimentel (2011).
To obtain the bioadsorbent, the biomass was treated with a 0.1M NaOH solution, considering a ratio of 30 ml of NaOH solution per 100 ml of biomass. After stirring, the biomass was washed with deionized water and the pH was adjusted with 0.1M HCl solutions.
The concentrations of both metals were determined with an atomic absorption spectrophotometer (Perkin-Elmer; model 1100B, USA), considering a margin of error of 5% in the results obtained.

Preparation of Co(II) and Mn(II) solutions
The pseudo-first and pseudo-second order models are the most common and are used to explain the adsorption of met-als using biological material.
The linear form of the pseudo-first order (Kowanga et al., 2016) and pseudo-second order (Ho and McKay, 1999) model are presented in Equation 1 and Equation 2, respectively.
The thermodynamic equilibrium modeling was carried out using the Langmuir and Freundlich isotherms.  Figure 1-b show a rapid adsorption of metal ions in the first 10 minutes for a temperature of 298 K, reaching removal values greater than 50%. In the case of Co(II) ion, the uptake increases as the temperature increases, and remains almost constant after 10 minutes because equilibrium is reached. On the contrary, it is perceived with the Mn(II) ion, where the highest uptake and removal are obtained at 298 K, with values of 1.07 mg.g -1 and 79.9%, respectively.
Bioadsorption can involve two phases, the initial phase where rapid adsorption occurs through mechanisms of physical adsorption or ion exchange, and the other phase refers to a slow adsorption that could involve complex formation, micro precipitation or satu-ration of active sites (Esmaeili and Beni, 2015). On the other hand, temperature can have a positive or negative effect on the bioadsorption process, increasing or decreasing the adsorption capacity (Kanamarlapudi et al., 2018). Additionally, increases in temperature can improve removal but can also cause structural damage to the bioadsorbent (Park et al., 2010).
The experimental data of Co(II) and Mn(II) bioadsorption fitted well to both models evaluated (Langmuir, Fig. 1-c and Freundlich, Fig. 1-d). However, the best correlations were obtained with the Langmuir model, with correlation coefficients (R 2 ) of 0.987 and 0.995 for Co(II) and Mn(II), respectively. This indicates that metal adsorption occurs in monolayers and at specific and uniform sites in the biomass, considering that metals can chelate with chelating effect groups on the biomass surface (Altıntıg et al., 2017). The Langmuir (q max and K ads ), Freundlich (K F and n F ) and R L separation parameters are shown in Table 1.
Where: q e (mg.g -1 ), is the amount of metal retained in the adsorbent at equilibrium; q max (mg.g -1 ), is the Langmuir parameter related to the adsorption capacity; K ads (L.mg -1 ), is the Langmuir constant and C (mg.L -1 ), is the concentration of the ion in the solution at equilibrium.
Likewise, the dimensionless constant R L is obtained by Equation 4 and is known as the separation factor or equilibrium parameter, and indicates the form and nature of the process (Weber and Chakravorti, 1974).
The Freundlich isotherm explains a physical adsorption and is expressed by Equation 5 (Edzwald, 2011): Where: K f and N, are the empirical constants that represent the adsorption capacity and affinity or adsorption intensity to metals.
Where: K 1 (min -1 ) and K 2 (g.mg -1 .min -1 ), are adsorption rate constants; q e (mg.g -1 ), is the amount of metal adsorbed per amount of biomass in equilibrium, q t (mg.g -1 ) is the amount of metal adsorbed per amount of biomass at time t and t, is the adsorption time.
(3) From the data presented in Table  1-a, a greater affinity of the RO biomass for the Co(II) ion than the Mn(II) ion is observed with bioadsorption capacity values of 13.42 and 6.91 mg.g -1 , respectively. It was also observed that the K ads and K F constants of the Langmuir and Freundlich models are higher for Co(II) bioadsorption due to the higher uptake of this metal. (Fathollahi et al., 2021) reported that 30.3% of Mn(II) bioadsorption investigations using Bacillus sp. achieved adsorption capacities higher than 98.12 mg.g -1 .
On the other hand, the Langmuir isotherm can be expressed through the constant R L , called the separation factor or equilibrium parameter. If R L > 1, the bioadsorption process is unfavorable; 0 <R L <1, the process is favorable; R L = 0, the process is classified as irreversible and R L = 1, represents linearity (Vilvanathan e Shanthakumar, 2015). Therefore, according to the results presented in Table 1-b, the R L values obtained varied between 0 and 1, indicating that the bioadsorption process is favorable for the removal of both metal ions.
Similar results were obtained in the investigations carried out by Din et al. (2013) and Vilvanathan and Shanthakumar (2015) for the adsorption of Co(II), using Saccharum bengalense Table 1 -a) Langmuir and Freundlich isotherm constants for Co(II) and Mn(II) bioadsorption and b) R L parameters for Co(II) and Mn(II) bioadsorption.

Kinetic study
Figure 2-a shows the Co(II) and Mn(II) concentrations as a function of time, distinguishing two stages of bioadsorption. The first one occurs in the first 10 min of the process and corresponds to a fast adsorption with a rising behavior for both metal ions, and the second stage occurs after 10 min with a slow adsorption and a different behavior for each metal ion. According to Hamidpour et al. (2018), fast bioadsorption with high metal removal involves physical and chemical adsorption and ion exchange, and slower adsorption involves other adsorption mechanisms, such as microprecipitation and complex formation.
In the bioadsorption of Co(II), a removal of 72.3% is reached in the first 10 minutes of the process, and subsequently, the adsorption is slow and removal values of 84.2% are obtained in 180 minutes. Meanwhile, in the bioadsorption of Mn(II), a high removal (80%) is observed in the first 10 minutes, subsequently the adsorption decreases which increases the concentration of metal ions in the solution. This behavior can be explained by the high solubility of Mn(II) in aqueous media (Bhattacharya and Elzinga, 2018).
The results of the pseudo first and second order kinetic analysis are presented in Figure 2 Table 2, the kinetic parameters of the bioadsorption of Co(II) and Mn (II) ions are shown. It shows that the values of k and q e were higher for the pseudo second order model, confirming its best fit. On the other hand, it was observed that the bioadsorption rate of Mn(II) (k = 0.15 g.mg -1 .min -1 ) is greater than Co(II) (k = 0.026, g.mg -1 .min -1 ), indicating that the metal ions of Mn(II) have greater mobility in solution with respect to the metal ions of Co (II). In this regard, several investigations reported that the pseudo-second order model best fits both Mn(II) (Zhang et al., 2014) and Co(II) (Din et al., 2013;Vilvanathan and Shanthakumar, 2015) bioadsorption data. Meanwhile, Esmaeili and Beni (2015) reported a better fit of the pseudo-first order model in the Co(II) bioadsorption.  From the values of the bioadsorption rate constants of the pseudosecond order model presented in Table  2-b, the activation energy (E a ) of the bioadsorption process for both metal ions was obtained using the linearized Arrhenius equation (Figure 3-a). The E a value provides information regard-ing the type of adsorption (physical or chemical) that occurs in the process. The Arrhenius equation is presented in Equation 6 (Tassist et al., 2010).
Where: K 0 is the independent factor of temperature (g.mg -1 min -1 ) and R is the constant of the ideal gas law (8.314 J.mol -1 K -1 ).
The E a values of Co(I I) and Mn(II) bioadsorption were 58.16 and 3.2 kJ mol -1 respectively. The relatively high E a value for the Co(II) ion indicates chemical adsorption and this was different from that reported by Din et al.
(2013), who obtained a lower activation energy value (E a = 0.007 kJ mol -1 ) related to physical adsorption. For the Mn(II) ion, Ea had relatively small values, suggesting the existence of physical adsorption by Van de Waals forces.
Thermodynamic parameters such as enthalpy (∆H), Gibbs free energy (∆G) and entropy (∆S) variations were estimated using variations of the equilibrium constant with temperature. These relationships were established by the Van't Hoff equation, presented in Equation 7 (Lin et al., 2020;Vilvanathan and Shanthakumar, 2015). The values of ∆H and ∆S were obtained from the slope and intercept of the plot of lnK vs 1/T.
The equilibrium constants were expressed in terms of the variation of the adsorption enthalpy as a function of temperature using Equation 8, whereas, the Gibbs free energy and the equilibrium constant using Equation 9. The values of K ads ∆G, ∆H and ∆S are presented in Table 3. The effect of temperature on the Co(II) and Mn(II) bioadsorption was shown in Figure 2-d and Figure 2-e, respectively. It was observed that the values of k and q are higher as the temperature increases, i.e., the bioadsorption process is favored by the increase in the kinetic energy of the aqueous medium. Moreover, the bioadsorption rate values were higher for Mn(II) than for Co(II) because the mobility of Mn(II) is more favored with increasing temperature. Din et al. (2013) and Vilvanathan and Shanthakumar (2015) also observed that Co(II) bioadsorption is favored by increasing temperature. However, Meitei and Prasad (2014) reported that there is an inverse relationship between temperature and Mn(II) ion uptake.

a)
Metal q max (mg.g -1 ) Pseudo-first order kinetic Pseudo-second order kinetic k 1 (min -1 ) q e1 (mg.g -1 ) R 2 1 k 2 (g.mg -1 .min -1 ) q e2 (mg.  Table 2 -a) Kinetics parameters for Co(II) and Mn(II) bioadsorption and b) Kinetics parameters for Co(II) and Mn(II) bioadsorption using the pseudo-second order model at temperatures of 298, 308 and 318 K. The thermodynamic results for the bioadsorption of Co(II) ions were positive values of both ∆H and ∆S and negative value of ∆G, indicating an endothermic (chemical nature), irreversible and spontaneous process favored by increasing temperature. Positive ∆S values also indicate a decrease in randomness at the solid/solution interface (Saleh et al., 2017a;Saleh et al., 2017b) or a structural change between the adsorbent and the metal (Altıntıg et al., 2017). Similar values of ∆G and ∆H for Co(II) bioadsorption were reported by Vilvanathan and Shanthakumar (2015) and Elanza et al. (2017). For the bioadsorption of Mn(II) ions, the ∆H, ∆S and ∆G values were negative, indicating an exothermic (physical nature), reversible and spontaneous process not favored by increasing temperature. Singh et al.   The bioadsorption process of the metal ions is fast, reaching removal values of 72.3% for Co(II) and 80% for Mn(II) during the first 10 minutes. Experimental bioadsorption data for Co(II) and Mn(II) ions best fit the Langmuir model (R 2 Co(II) = 0.987 and R 2 Mn(II) = 0.995), with maximum adsorption values of 13.42 and 6.91 mg.g -1 , respectively. Moreover, in the bioadsorption of Co(II) and Mn(II), there is a direct relationship between the adsorption rate and temperature, following the pseudo-second order kinetic model (R 2 Co(II) = 0.994 and R 2 Mn(II) = 0.995) with adsorption rates of 0.026 and 0.15 g.mg -1 .min -1 , respectively. On the other hand, the activa-tion energy values showed that there is chemical adsorption for Co(II) ion and physical adsorption for Mn(II) ion. Finally, the variations of ∆G, ∆H and ∆S indicated a spontaneous, endothermic and irreversible process for the Co(II) ion and a spontaneous, exothermic and reversible process for the Mn(II) ion.