In this work, n-GCHM was used for the removal of Cu2+ and Co2+ from wastewater. The adsorbent material (n-GCHM) was characterised using SEM and TGA. The following optimum conditions were obtained: a contact time of 120 min and pH 5 for the removal of Cu2+ and Co2+. The maximum adsorption capacity of Cu2+ and Co2+ was 5.8343 mg/g using n-GCHM. The highest percentage removal of Cu2+ and Co2+ on n-GCHM at pH 5 was 80 and 80.5%, respectively. The experimental data successfully fitted to pseudo-second-order kinetic, and also fitted well to the Freundlich isotherm model. The process of adsorption was spontaneous and exothermic in nature. To obtain extensive information on the adsorption process of metal ions on the functional groups of adsorbents, the quantum adsorption mechanism was investigated using DFT. The molecular orbital approach has shown that the HOMO and LUMO were located on –NCN– and LUMO on –NCO–. The quantum adsorption mechanism has shown that the binding energies of Cu2+ and Co2+ on imine functional groups were −60,604.399 and −53649.06 eV, respectively. On the –NCO– functional group, the binding energy was −58587.608 and −51632.618 eV, respectively, for Cu2+ and Co2+. Quantum mechanical methods using the ANN approach have been demonstrated to be accurate.

  • The highest percentage removal of Cu2+ and Co2+ on n-GCHM at pH 5 was 80 and 80.5%, respectively.

  • Experimental data fitted well to pseudo-second-order and to Freundlich isotherm model.

  • The quantum adsorption mechanism has shown that the binding energy of Cu2+ and Co2+ on imine functional group was −60604.40 and −53649.06 eV, respectively.

  • On the –NCO– functional group, the binding energy was −58587.61 and −51632.62 eV, respectively, for Cu2+ and Co2+.

Heavy metals such as Cu2+ and Co2+ in water are toxic and non-biodegradable (Almomani et al. 2020). Chemical precipitation, membrane separation, ion-exchange, reverse osmosis, adsorption, electrochemical treatment, electrodialysis, photodegradation, supercritical fluids extraction, and solvent extraction have been successfully applied for the removal of these metals from wastewater (Negm et al. 2015; Fan et al. 2017; Kabuba & Banza 2021). However, these removal processes have their own capabilities and limitations (Elwakeel et al. 2018). The adsorption process has been found to be the most used process for the removal of Cu2+ and Co2+ from wastewater. This process is relatively simple, efficient, cost-effective, and flexible in design (Garcia-Diaz et al. 2018; Yin et al. 2022; Pete et al. 2023). Moreover, many researchers investigated the adsorption process to make it more efficient for the removal of heavy metals from wastewater and more recent experimental studies have been increased with theoretical support, to investigate it completely (Moreno et al. 2020). Theoretical methods not only produce insight into the removal efficiency of heavy metals and binding preference amid numerous metal ions but simultaneously, can produce detailed information concerning the changes taking place in energies and geometries throughout the process (Mishima et al. 2018). Energies of binding interaction at numerous sites of adsorbent material, their preferences for various heavy metal ions and the feasible mode of connection are some other significant benefits presented by the theoretical method studies of the adsorption process (Malik et al. 2022). Adsorption parameters such as adsorption energy, favoured adsorption sites, and structural dynamics of adsorbent materials are difficult to acquire from the experimental studies. Under such circumstances, quantum adsorption's mechanism makes significant complementary support for better understanding the adsorption process of heavy metal ions efficaciously and precisely. This method has been also found quite efficient in studying the adsorption process in terms of the estimation of the site adsorption, to conclude the relative possible and stability structure of different adsorption sites existing in an adsorbent material (Paredes-Doig et al. 2020).

An artificial neural network (ANN) is a technique of data processing established on the structure of a biological neural system. It has been successfully applied in different areas of engineering studies due to its ability to apprehend the non-linear relationships of variables in complex systems (Khan et al. 2017; Kabuba & Banza 2020). Because of the complex nature of the adsorption process, the ANN appeared to be one the most auspicious numerical simulation techniques to produce reliable predictions. In order to acquire extensive information on the adsorption process of metal ions on the functional groups of adsorbents, the quantum adsorption mechanism was investigated using the DFT (density functional theory). Chen et al. (2019) synthesized a multi-functional group-modified cellulose for the removal of Cd2+ to enhance the electronegativity, and carbonyl sulfide, the amide, and secondary amino groups could extend the adsorption sites and discussed the thermodynamic studies, kinetic and isotherm models for better understanding the adsorption mechanism. The binding ability of Cd2+ with cellulose-based adsorbents, adsorption sites, and interaction between the functional groups were investigated by chemical quantum simulations. To the best of the author's knowledge, the quantum adsorption mechanism using ANN has not yet been reported in the literature. The aim of this work is to develop an ANN technique to accurately predict the adsorption efficiencies using the Gelatin Cellulose Hydrogel Membrane (GCHM) for the removal of Cu2+ and Co2+ from wastewater. The adsorption process using quantum mechanism methods was also investigated.

Chemicals

All chemicals employed in this study were supplied by Sigma Aldrich and LabChem. and were of analytical reagent grade (98–99.5%). Adequate quantities of cellulose nanocrystals (CNCs) (from wood pulp) and gelatin (from porcine skin) dried powder (purity ≥ 98%) were obtained from the Council for Scientific and Industrial Research (CSIR) in Pretoria, South Africa.

GCHM preparation

CNCs and gelatin were dissolved in 50 mL of distilled water. CNC suspension was then homogenized to obtain a uniform solution. 4 g of gelatin was then added to the CNC suspension. The homogenous viscous solution was obtained at 55 °C. The cross-linking agent (EDTA 1%) was then added. After 4 h, the homogenous solution was poured into a petri dish and dried in the oven at 45 °C. Hydrogel films were discharged from the petri dish and washed with distilled water. The acetone was used to remove the unreacted chemicals from the hydrogel.

Preparation of the synthetic solution

The synthetic solutions were produced by dissolving CuSO4·5H2O and CoCl2·6H2O in distilled water, and different concentrations were obtained by gradient dilution. The pH solution was adjusted with 0.1 M NaOH or 0.1 M HCl solution. All experiments were conducted in triplicate and the results obtained were at a 95% confidence level.

Quantum chemical simulation

The binding potentiality between Co2+, Cu2+, and GCHM was evaluated by the DFT. All DFT calculations were performed using Gaussian 03 and Gaussian 3.09 software. The optimization, electrical calculations, and quantum molecular descriptions were achieved using the Becke-three parameters-Lee-Yang-Parr (B3LYP) method I gas and aqua phases. For Co2+ and Cu2+, LanL2DZ basis set was employed. Frontier molecular orbital (MO), molecular electrostatic potential (MEP) plots, bond distances, and bond angles were investigated using DFT calculations.

Gelatin as the main constituent of GCHM was used to run the quantum calculations (Malik et al. 2017). The DFT calculations were used to explain the intermolecular bonds formed between the functional groups of hydrogel membrane and hydrated metal ions. The technique was also used to correlate the different quantum parameters with the perceived experimental data and hence, a novel mechanism of adsorption was proposed.

For a better understanding of the adsorption preferential sites, the Lowest Unoccupied Molecular Orbital (LUMO) of Co2+ and Cu2+E(LUMO), Highest Occupied Molecular Orbital (HOMO) energy of adsorbent E(HOMO), and energy gaps Eg = E(HOMO)–E(LUMO) were calculated (Rad & Kashani 2015). Comparing the Co2+ and Cu2+ binding potentiality of different functional groups of GCHM and describing the preferential adsorption sites.

ANN experimental set up

ANN technique was carried out using Neural Network Toolbox V4.0, MATLAB, 2022a. The feed-forward neural network (FFNN) had the following input variables: solution pH, contact time, and initial concentration. The output variable was decided upon as being the effectiveness of the Co2+ and Cu2+ removal. Levenberg-Marquardt back-propagation (BP) algorithm was selected as the appropriate training algorithm in consideration of the minimum value of mean square error (MSE). Experimental data points were used for a three-layer ANN structure with a tangent sigmoidal transfer function (tansig) at the hidden layer, and a linear transfer function (purelin) at the output layer. The adsorption percentage capacity of the input variables was employed as a target. The experimental data sets were divided for training (70%), testing (30%), and validation (30%).

All the data (input and output) were normalized between 0.1 and 0.9 to prevent computational problems.

Physical structure

SEM analysis of n-GCHM

The SEM analysis image presented in Figure 1 was used to observe the change in the morphological structure of the n-GCHM. The SEM image was taken by employing 10 kV voltage with different magnification times for the clarification of the surface.
Figure 1

SEM image of the n-Gelatin Cellulose Hydrogel Membrane.

Figure 1

SEM image of the n-Gelatin Cellulose Hydrogel Membrane.

Close modal

The SEM image in Figure 1 indicates the presence of bigger particles with irregular shapes. The porosity characterization of the hydrogen membrane is based on the presence of open pores which are related to properties such as permeability and surface area of the porous structure. Figure 1 shows the cavities of different shapes and sizes. The big pores between the particles could be observed which will be considered for the solution permeating through the hydrogel membrane and enhancing adsorption performance.

The high porosity provides favourable adsorption of Cu2+ and Co2+. The presence of such granules enhances the surface area of the hydrogel membrane which is suitable for effective adsorption of Cu2+ and Co2+. Small openings and holes on the surface enhance the contact of the adsorption and consequently lead to pore diffusion during the adsorption process (Kabuba 2019). The morphology changes as the gelatin concentration increases and therefore many pores have been observed.

TGA of n-GCHM

The TGA monitors the thermal stability and degradation behaviour of the membrane, as a function of temperature in controlled surroundings. Figure 2 presents the degradation of all films starting at the temperature from 350 to 800 °C with the mass weight loss ranging from 11 to 2 mg. This observation is the result of the decomposition of highly connected amino acid groups in the protein films (Samiee et al. 2019). The incorporation of cellulose into the gelatin film-forming solution can improve the thermal stability of the films due to its crystalline structure. The thermal decomposition of gelatin cellulose bend films is shifted regarding higher temperatures as correlated to gelatin films. The temperature increased to 800 °C, the membrane was carbonised, and the weight loss of cellulose due to more energy was required to cleave C = N bonds. The increase in thermal stability of gelatin cellulose films can be ascribed to the intramolecular and intermolecular interaction between the polymers.
Figure 2

TGA curve of the membrane.

Figure 2

TGA curve of the membrane.

Close modal

Physical and rheological properties of n-GCHM

The surface potential of n-GCHM under different pH values was characterized by a solid surface zeta potential. The isoelectric point (pI) of the solution occurred at pH 6, at which a pHz = 0 (Figure 3). Gelatin can present charges depending on the pH. At pH < pI, the gelatin solution presented a net positive charge, which was ascribed to the protonation of the amino groups, while pH > pI presented a net negative charge and this was attributed to ionization of the carboxyl groups. The pHz value was found to be negative regardless of the pH for the CNC suspension. The pHz (< −40 and >+ 40 mV) could maintain a stable colloidal system because of the repelling forces between particles. Electrostatic charges are one of the main driving forces for interactions between charge biopolymers in aqueous solutions.
Figure 3

Effect of pH on zeta potential.

Figure 3

Effect of pH on zeta potential.

Close modal

Adsorption study

Effect of pH on the removal

The degree of ionization, specification, and equilibrium pH are all impacted by the surface charge of the adsorbent membrane. The removal percentage of Cu2+ and Co2+ adsorbed by n-GCHM and GCHM@Fe3O4 as a function of pH is depicted in Figure 4(a) and 4(b), respectively. The findings showed that the equilibrium pH has a great impact on the elimination of Cu2+ and Co2+ from wastewater. In an acidic medium, the adsorption process was minimal as the equilibrium pH rose, it became more intense. The maximum removals were 70.5% and 63.8% for Cu2+ and Co2+ at pH 5 with n-GCHM (Figure 4(a)), respectively. It was reported by Kumaruzaman et al. (2017); (El-Sheikh et al. 2012; Al-shahrani 2014; Akpomie et al. 2015), that at low solution pH from 3 to 5, the adsorption process of Cu2+ and Co2+ was low due to the large quantities of protons (H+) compete with the removal cations for the functional group's sites on GCHM. As the equilibrium pH increases, the number of positively charged available sites decreased while the negatively charged active sites increased.
Figure 4

Effect of pH on the removal of Cu(II) and Co(II) using n-GCHM and GCHM@Fe3O4.

Figure 4

Effect of pH on the removal of Cu(II) and Co(II) using n-GCHM and GCHM@Fe3O4.

Close modal

The equilibrium pH plays a crucial role in the adsorption process of Cu2+ and Co2+. Figure 4(b) shows that the effect of the external magnetic field had a significant impact on this yield. Thus, the highest adsorption efficiencies of the two metal ions were, respectively, 61.6% for Cu2+ and 89.4% for Co2+. It has been shown that the effect of the internal or external magnetic field can significantly promote the removal efficiency of Cu2+ and Co2+ (Wang et al. 2021). In this case, the effect of the external magnetic field showed a very high affinity for Co2+.

Effect of contact time

Figure 5 presents the effect of contact time on the percentage removal efficiency of Cu2+ and Co2+ into n-GCHM and GCHM@Fe3O4 for different values of pH. Liu et al. (2015) stated that the percentage removal was a function of contact time. The contact time was 15–120 min, and the initial concentration was 100 mg/L, while the doses of n-GCHM and GCHM@Fe3O4 were 0.25 g/100 mL of Cu2+ and Co2+ and the solution pH was kept constant at 5. The removal of Cu2+ and Co2+ gradually increased to attain at 120 min. This is because of the abundant availability of the active sites on the adsorbent surface and can also be attributed to the fact that all adsorbent sites are vacant (Kumaruzaman et al. 2017). The long time needed for adsorption to reach equilibrium can be attributed to the low adsorption efficiency of the n-GCHM or can also be attributed to the high initial concentration of Cu2+ and Co2+ and the mass adsorbent (0.25 g/100 mL) (Akpomie et al. 2015; Kumaruzaman et al. 2017).

Effect of equilibrium concentration

The sorption of Cu2+ and Co2+ was carried out at different equilibrium concentrations ranging from 50 to 125 mg/L, at pH 5, at 250 rpm with 120 min of contact time using n-GCHM and GCHM@Fe3O4. The uptake of Cu2+ and Co2+ is decreased by increasing the initial concentration to reach saturation at higher metal concentrations as shown in Figure 6 (Al-Shahrani 2014). When the initial Cu2+ and Co2+ concentration increased from 50 to 125 g/L, the uptake capacity of n-GCHM and GCHM@Fe3O4 decreased from 85 to 66.3% for Cu2+ and 87.1 to 58.4% with n-GCHM; 64.2 to 39.1% for Co2+ and 77.7 to 57.1% with GCHM@Fe3O4.
Figure 5

Effect of time on the removal of Cu2+ and Co2+, using n-GCHM and GCHM@Fe3O4.

Figure 5

Effect of time on the removal of Cu2+ and Co2+, using n-GCHM and GCHM@Fe3O4.

Close modal
Figure 6

Effect of equilibrium concentration on the removal of Cu2+ and Co2+: (a) n-GCHM and (b) GCHM@Fe3O4.

Figure 6

Effect of equilibrium concentration on the removal of Cu2+ and Co2+: (a) n-GCHM and (b) GCHM@Fe3O4.

Close modal

Analysis of adsorption mechanism

The Langmuir, Freundlich, and Dubinin–Radushkevich (D–R) adsorption isotherm models were applied to examine the mechanisms of the adsorption process (Hamza et al. 2021). The Langmuir and Freundlich isotherm models are well described in a linear form as presented in Equations (1) and (2) (Kabuba 2021):
formula
(1)
formula
(2)
where qe is the amount of ion adsorbed at equilibrium (mg/g); Ce is the equilibrium concentration (mg/L), qm is the amount of ion required to occupy the available site in the unit weight of the solid sample, BL is the Langmuir constant (L/mg), KF and 1/n are Freundlich constants relating to the adsorption capacity and adsorption intensity. The parameters of Langmuir and Freundlich models were calculated from the slope–intercept of the plot of Ce/qe versus qe and log qe versus log Ce, respectively.

Table 1 presents the fitting parameters for both adsorption isotherms. For the Freundlich model, the correlation coefficient (R2) is 0.9393, higher than the R2 of the Langmuir model, demonstrating that the adsorption of both Co2+ and Cu2+ onto the n-GCHM could be better described by the Freundlich model. This indicated a heterogeneous energetic distribution of the active sites on the n-GCHM surface with interaction between Co2+ and Cu2+. The value of n > 1 is indicative of good adsorption affinity and illustrates favorable adsorption of Co2+ and Cu2+ onto n-GCHM. KF value suggests that the adsorption ability is strong.

Table 1

Parameters for the Cu2+ and Co2+ adsorption by n-GCHM according to isotherm models (T = 298 K)

Langmuir   
 qmax (mg/g) KL (L/mg) R2 RL range 
Cu2+ 58.12 0.016 0.886 0.1–0.84 
Co2+ 57.86 0.014 0.894 0.1–0.84 
Freundlich   
 1/n KF R2  
Cu2+ 0.418 4.20 0.9674  
Co2+ 0.412 4.18 0.9343  
D–R   
 qs (mg/g) E (kJ/mol) R2  
Cu2+ 14.34 11.31 0.960  
Co2+ 22.51 14.48 0.950  
Langmuir   
 qmax (mg/g) KL (L/mg) R2 RL range 
Cu2+ 58.12 0.016 0.886 0.1–0.84 
Co2+ 57.86 0.014 0.894 0.1–0.84 
Freundlich   
 1/n KF R2  
Cu2+ 0.418 4.20 0.9674  
Co2+ 0.412 4.18 0.9343  
D–R   
 qs (mg/g) E (kJ/mol) R2  
Cu2+ 14.34 11.31 0.960  
Co2+ 22.51 14.48 0.950  

The D–R isotherm model offers a three parameter-equation, used to represent solute adsorption data on heterogeneous surfaces.
formula
(3)
where qe is the amount of ion adsorbed in (mg/g), qmax is the D–R monolayer capacity (mg/g), k is energy constant in (mol2/kJ2), and β is the Polanyi potential which is related to the equilibrium concentration which is defined in Equation (4)
formula
(4)
where R is the gas constant 8.314 in kJ/mol.K, T is the temperature in K. The slope of the plot of ln qe versus β gives k and of the intercept yields the adsorption capacity qmax (mg/g). The energy required to remove each molecule of metal ions from the solution to the adsorption site can be calculated using Equation (5).
formula
(5)

The value of free energy E is vital and can be obtained in the nature of the adsorption process.

The D–R model was successful in analyzing experimental data for the considered metal ions with R2 values ≥0.93. The energy values for these ions are, respectively, 14.48 and 11.31 kJ/mol for Cu2+ and Co2+. These values are greater than 8 kJ/mol, this indicates that the adsorption process is not physical (Kabuba 2021).

The effect of temperature was better estimated using thermodynamic parameters such as enthalpy change (ΔH), entropy change (ΔS) and Gibbs free energy of adsorption (ΔG). The parameters were calculated using Equations (6)–(8) (Almughamisi et al. 2020; Elwakeel et al. 2021):
formula
(6)
formula
(7)
formula
(8)

The plot of ln kd versus 1/T gives a straight line and the value of enthalpy change ΔH and entropy change ΔS can be calculated from intercept and slope, respectively.

In Table 2, the values of ΔG were negative in the range of 283–313 K indicating that the adsorption of Co2+ and Cu2+ onto n-GCHM is spontaneous. A similar finding was reported by Borandegi & Nezamzadeh-Ejhieh (2015). The positive values of ΔH indicate that the adsorption is endothermic. The positive value of ΔS confirmed an increase of randomness at the interface n-GCHM and solution during the adsorption process.

Table 2

Thermodynamic parameters for the adsorption of Cu2+ and Co2+ by n-GCHM

Cu2+ 
Parameter T (K) n-GCHM 
ΔG (kJ/mol) 283 −18.56 
 293 −19.66 
 303 −21.09 
 313 −22.15 
ΔH (kJ/mol) – 15.74 
ΔS (kJ/mol.K) – 0.120 
Co2+ 
Parameter T (K) n-GCHM 
 283 −17.67 
 293 −18.77 
 303 −20.10 
 313 −21.26 
ΔH (kJ/mol) – 14.75 
ΔS (kJ/mol.K) – 0.118 
Cu2+ 
Parameter T (K) n-GCHM 
ΔG (kJ/mol) 283 −18.56 
 293 −19.66 
 303 −21.09 
 313 −22.15 
ΔH (kJ/mol) – 15.74 
ΔS (kJ/mol.K) – 0.120 
Co2+ 
Parameter T (K) n-GCHM 
 283 −17.67 
 293 −18.77 
 303 −20.10 
 313 −21.26 
ΔH (kJ/mol) – 14.75 
ΔS (kJ/mol.K) – 0.118 

The adsorption kinetic models such as the pseudo-first-order, pseudo-second-order and Elovich were fitted to predict the adsorption mechanism. These models are presented in Equations (9)–(11):
formula
(9)
formula
(10)
formula
(11)
where qe and qt represent the amount of heavy metal ions adsorbed in (mg/g) at equilibrium and at time t, respectively. k1 is the rate constant of the pseudo-first-order kinetics. The value from the straight-line plot of log (qe–qt) versus t, k2 is the rate constant of pseudo-second-order models and it was calculated from the plot t/qt and time. α is the initial sorption rate (mg g−1min−1), and β is the desorption constant (g.mg−1) during any one experiment.

The kinetic parameters presented in Table 3 showed that the R2 values for both metal ions derived from the pseudo-second-order were greater than the first order. The adsorption of Co2+ and Cu2+ into n-GCHM followed the pseudo-second-order kinetic model and the rate-limiting step may be chemical adsorption involving valences forces through the exchange of electrons between Co2+ and Cu2+ and n-GCHM (Xu et al. 2018). The Elovich model showed that Co2+ and Cu2+ complexed with the functional groups in n-GCHM. The values of α and β indicate more activated adsorption sites and stronger electron donating ability of n-GCHM.

Table 3

Kinetic parameters (Co = 200 m/L)

Pseudo-first-order 
 K1 (m−1qe (cal) R2 
Cu2+ 0.036 16.66 0.970 
Co2+ 0.047 15.77 0.962 
Pseudo-second-order 
 K2 (g.mg−1. min−1qe (cal) R2 
Cu2+ 4.22 × 10 − 3 119.60 0.996 
Co2+ 3.99 × 10 − 3 118.10 0.989 
Elovich model 
 α β R2 
Cu2+ 151.09 0.055 0.801 
Co2+ 150.20 0.049 0.812 
Pseudo-first-order 
 K1 (m−1qe (cal) R2 
Cu2+ 0.036 16.66 0.970 
Co2+ 0.047 15.77 0.962 
Pseudo-second-order 
 K2 (g.mg−1. min−1qe (cal) R2 
Cu2+ 4.22 × 10 − 3 119.60 0.996 
Co2+ 3.99 × 10 − 3 118.10 0.989 
Elovich model 
 α β R2 
Cu2+ 151.09 0.055 0.801 
Co2+ 150.20 0.049 0.812 

Analysis of binding ability and preferential adsorption sites

The structural characterizations and mechanistic analysis discussed showed that n-GCHM has more active adsorption sites and stronger adsorption ability. The Cu2+ and Co2+ chemisorption by n-GCHM can be considered the electron transition between the HOMO of n-GCHM and the LUMO of Cu2+ and Co2+.

The cellulose in the hydrogel formed a matrix in which the gelatin could be dissolved. Being the main constituent of synthetic hydrogel, gelatin was the molecule on which the quantum study was carried out (Malik et al. 2017).

In this section, the theoretical study was to determine the preferential sites and adsorption mechanism of Cu2+ and Co2+ (by forming the metallic complex with the gelatin) on the different functional groups of gelatin based on the difference of energies. To achieve this, we proposed to apply the MO approach to determine the HOMO and LUMO and energy gap on the substrate (Tsuji & Yoshizawa 2021). The DFT/B3LYP levels in the Gaussian 03W package program with the 3–21G basis set were used for all calculations and optimizations in this work. Figure 7 represents the optimized gelatin and its chemical quantum parameters are recorded in Table 4.
Table 4

Quantum chemical parameters of gelatin

DescriptorsValue of descriptors
Total energy −7,002,499.647 kJ/mol 
Dipole moment 5.351 Debye 
EHOMO −6.099 eV 
ELUMO −6.019 eV 
Egap −0.081 eV 
DescriptorsValue of descriptors
Total energy −7,002,499.647 kJ/mol 
Dipole moment 5.351 Debye 
EHOMO −6.099 eV 
ELUMO −6.019 eV 
Egap −0.081 eV 
Figure 7

Optimized structure of gelatin.

Figure 7

Optimized structure of gelatin.

Close modal
It appears from Table 4 that the total energy of gelatin optimized was −7,002,499.65 kJ/mol with a dipole moment of 5.35 Debye. The energies of HOMO and LUMO were, respectively, −6.099 and −6.019 eV. The difference in energies between HOMO and LUMO (ΔE or Egap) was −0.081 eV. Constituting different amino acids such as guanine, arginine, glutamine, optimizing gelatin using the MOs approach, it has been shown that HOMO was on arginine while LUMO was on glutamine. The HOMO and LUMO of the gelatin are represented in Figure 8.
Figure 8

(a) HOMO and (b) LUMO of gelatin.

Figure 8

(a) HOMO and (b) LUMO of gelatin.

Close modal

HOMO on arginine is located at the level of imine function (–NCN–) and LUMO on glutamine at the level of amino acid function (–NCO–) and have the hard Lewis base properties. These two functional groups are susceptible sites for adsorbing and binding the copper and cobalt ions. Hard Lewis bases include –OH, –NH2, and –COC groups, while the electron cloud on the aromatic ring may function as a soft base (HSAB principle). Hard Lewis acids have a minimal positive charge, totally filled atomic orbitals, tiny ionic radii, and low energy LUMOs. Due to their empty ‘d’ orbitals, Cu2+ and Co2+ can therefore be considered as Lewis acids (Tsuji & Yoshizawa 2021).

Quantum adsorption of Cu2+ and Co2+

Quantum adsorption of Cu2+ and Co2+ was performed on HOMO and LUMO to determine the preferential adsorption site of each metal ion. Figure 9 shows the adsorption of both metal ions on arginine and glutamine (Figure 10) taken separately. The data from the optimization of arginine and glutamine alone, complex arginine with Cu2+ and Co2+, and the complex of glutamine with (Cu2+ and Co2+) are given in Table 5.
Table 5

Quantum parameters of adsorption of Cu2+ and Co2+

Arginine optimized Electronic energy (kJ/mol) −1,583,639.740 
μD (Debye) 4.528 
Glutamine optimized Electronic energy (kJ/mol) −1,388,410.080 
μD (Debye) 3.177 
Arginine/Cu2+ (HOMO) Electronic energy (eV) −60,604.399 
μD (Debye) 9.553 
Glutamine/Cu2+ (LUMO) Electronic energy (eV) −58,587.608 
μD (Debye) 7.660 
Arginine/Co2+ (HOMO) Electronic energy (eV) −53,649.06 
μD (Debye) 6.553 
Glutamine/Co2+ (LUMO) Electronic energy (eV) −51,632.618 
μD (Debye) 4.247 
Arginine optimized Electronic energy (kJ/mol) −1,583,639.740 
μD (Debye) 4.528 
Glutamine optimized Electronic energy (kJ/mol) −1,388,410.080 
μD (Debye) 3.177 
Arginine/Cu2+ (HOMO) Electronic energy (eV) −60,604.399 
μD (Debye) 9.553 
Glutamine/Cu2+ (LUMO) Electronic energy (eV) −58,587.608 
μD (Debye) 7.660 
Arginine/Co2+ (HOMO) Electronic energy (eV) −53,649.06 
μD (Debye) 6.553 
Glutamine/Co2+ (LUMO) Electronic energy (eV) −51,632.618 
μD (Debye) 4.247 
Figure 9

(a) Arginine/Cu2+ and (b) Arginine/Co2+.

Figure 9

(a) Arginine/Cu2+ and (b) Arginine/Co2+.

Close modal
Figure 10

(a) Glutamine/Cu2+ and (b) Glutamine/Co2+.

Figure 10

(a) Glutamine/Cu2+ and (b) Glutamine/Co2+.

Close modal

It appears from Table 5 that both complexes that the arginine has formed with the Cu2+ and Co2+, have an energy of −60,604.399 and −53,649.06 eV, respectively, for Cu2+ and Co2+. The other complexes formed with glutamine have an energy of −58,587.608 and −51,632.618 eV, respectively, for Cu2+ and Co2+.

From the above, since the energy of the arginine/Cu2+ complex is lower than that of arginine/Co2+, it is deduced that the adsorption site (imine functional group) is more favorable for Cu2+ than for Co2+. The same observation was made for the glutamine/Cu2+ and glutamine/Co2+ complexes, Cu2+ showed an affinity for the carboxylic acid functional group. With complexes whose energies are lower than the energies of the complexes with Co2+, Cu2+ showed a preference for HOMO and LUMO. However, since the energy of the Arginine/Cu2+ complex is lower than that of glutamine/Cu2+, Cu2+ would have a preference for HOMO and a competition of both metal ions on the functional groups is very high.

Artificial neural network

Figure 11 shows the setup used for configuration, which consists of a three-layer system with three neuron inputs pH, contact time, and initial concentration, a hidden layer and one output layer. BP-ANN trains the algorithm using a first-order gradient descent technic. The Marquardt-Levenberg BP learning approach was selected as the BP method. The log-sigmoid transfer function for all data sets in ANN (logsig) was employed in the hidden layers. The optimum algorithm appeared to be Levenberg-Marquardt BP for training, validation, and test MSE. The Levenberg-Marquardt BP (trainlm) algorithm derived in a R value of 0.99993 throughout training, 0.99998 during validation, 0.9993 during testing, and a summary of all the stages derived in a R of 0.99984 as shown in Figure 12.
Figure 11

ANN architecture for both Co2+ and Cu2+.

Figure 11

ANN architecture for both Co2+ and Cu2+.

Close modal
Figure 12

Training, validation and test MSE for the LMA for the Levenberg-Marquart back-propagation (trainlm) algorithm for both Co2+ and Cu2+.

Figure 12

Training, validation and test MSE for the LMA for the Levenberg-Marquart back-propagation (trainlm) algorithm for both Co2+ and Cu2+.

Close modal

The adsorbent material (n-GCHM) was used for the removal of Cu2+ and Co2+ from wastewater and the effects of experimental conditions were studied. The optimum conditions obtained were 120 min and pH 5 for both metal ions. The maximum adsorption capacity of Cu2+ and Co2+ was 5.834 mg/g using n-GCHM. The highest percentage removal of Cu2+ and Co2+ on n-GCHM at pH 5 was 80 and 80.5%, respectively. The experimental data successfully fitted to pseudo-second-order kinetic, and was well described by the Freundlich model. Thermodynamic studies demonstrate the exothermic and spontaneous nature of the adsorption process. The DFT was used for the quantum adsorption mechanism. The MO approach has shown that the HOMO and LUMO were located on the arginine (–NCN–) and LUMO on glutamine (–NCO–). The quantum adsorption mechanism has shown that the binding energy of Cu2+ and Co2+ on the imine functional group (arginine) was of −60,604.399 and −53,649.06 eV, respectively. On the –NCO– functional group (glutamine), the binding energy was of −58,587.608 and −51,632.618 eV, respectively, for Cu2+ and Co2+. Quantum mechanical methods using the ANN approach have been proven to be accurate in studying complex terms involved in the adsorption processes of heavy metal ions.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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