Introduction

Li-ion battery waste are electronic product waste containing large amounts of key raw materials such as cobalt, lithium, manganese and nickel, as well as hazardous substances [1,2,3,4,5]. On one hand. If lithium-ion (Li-ion) battery waste is not properly managed, these valuable metals and toxic substances end up in the environment and cause environmental and public health issues [6,7,8]. Effective management and recycling of dead Li-ion batteries is critical to protect nature, ensure sustainable resource management and stimulate a circular economy [9,10,11]. On the other hand, more conventional methods using a combination of pyrometallurgic treatment with hydrometallurgical processing have been widely studied to recover metals from Li-ion battery waste [12,13,14,15,16]. Also there are other methods for the recovery of these metals from industrial waste such as liquid–liquid extraction [17, 18], chemical precipitation [19], adsorption on activated carbon [20, 21], ion exchange on resins[22], and membrane process techniques [23,24,25,26,27]. Membrane processes have advantages over other conventional techniques, such as good selectivity, lack of phase change during separation operations, modularity and low consumption of energy compared to other processes [28]. These membranes techniques are based on the properties of a semi-permeable barrier working under the effect of a transfer force, thus allowing certain molecules to pass selectively and to retain others [29].

In this present study, we focused on the use of polymer inclusion membranes (PIM) which consist of a polymer supports, polyvinyl alcohol (PVA) containing three types of extractive agents Nitrilotriacetic acid (NTA), ethylenediaminetetraacetic acid (EDTA) and tris (2-aminoethyl) amine (TREN) (Fig. 1). In order to quantify the performances of the elaborated PIM, we determined the macroscopic parameters, the membrane permeability P and the initial flux J0, and the microscopic parameters, the constant association Kass and the apparent diffusion coefficient D* obtained from the Fick's first law. Moreover, to explain the substrate process of extractions and recovery of Nickel (II) ions from Li-ion battery waste by the elaborated membranes, and to elucidate its mechanistic aspects, the activation energy Ea, the association enthalpy ΔH≠ and the entropy ΔS≠, the thermodynamic enthalpy (ΔHth) and dissociation enthalpy (ΔH≠diss) were determined and the obtained results show that the suggested orientation process takes place due to successive jumps.

Fig. 1
figure 1

Structure of extractive agents; a EDTA, b TREN, c NTA

Full size image

Therefore, these energetic values can be used to explain the performance of the used membranes and elucidate the energetic and structural kinetic aspects that control the mechanisms of oriented processes through the PIM membrane.

Materials and Methods

Calculations

The permeability P and the initial flux J0 are determined from the following equations [30,31,32]:

$$ {\text{P }}\left( {{\text{t}} - {\text{tL}}} \right){ } = { }\left( {\ell {\text{*V}}/2{\text{*S}}} \right){\text{ Ln}}\left( {{\text{C}}_{0} { }/{\text{ C}}_{0} - { }2{\text{C}}_{{\text{R}}} { }} \right){ } $$
(1)
$$ {\text{P }} = {\text{ a*V*}}\ell { }/2{\text{*S and J}}_{0} { } = {\text{P * C}}_{0} /\ell { } $$
(2)

a: the slope value of the linear representation of -Ln(C0-2Cr) = f(t). ℓ: the membrane thickness. S: the active surface of the barrier membrane in contact with the aqueous solutions. V: the volume of the receiving phase.

Kass and D* are calculated by the following equation:

$$ 1/{\text{ J}}_{0} { } = 1/{\text{ D*}}\left( {\left( {1/\left[ {\text{T}} \right]_{0} {\text{ *K}}_{{{\text{ass}}}} {\text{ *C}}_{0} } \right) + { }1/\left[ {\text{T}} \right]_{0} { }} \right){ } $$
(3)
$$ {\text{K}}_{{{\text{ass}}}} { } = { }\frac{{{\text{intercept }}\left( {{\text{o}}.{\text{o}}} \right)}}{{{\text{slope }}\left( {\text{p}} \right)}} $$
$$ {\text{D* }} = \left( {\frac{1}{{{\text{o}}.{\text{o}}}}} \right){ *}\left( {1/\left[ {\text{T}} \right]_{0} } \right) $$
(4)

where p are the values of the experimental line slope and O.O the intercept of 1/J0 = f(1/C0). [T]0: the total and fixed concentrate of the extractive agent in the membrane phase.

The initial flux is related to the temperature, according to the Arrhenius law by the follow equation:

$$ J\left( T \right){ } = {\text{ AjExp}}\left( { - {\text{E}}_{{\text{a}}} /{\text{RT}}} \right) $$
(5)

R: Ideal gas constant, Aj: pre-exponential factor, Ea: activation energy for the transition state of the kinetically determining step which is the diffusion of the substrate S through the membrane by the intermediate entity (ST).

After linearization we have the following relation

$$ {\text{LnJ}}_{0} = { } - {\text{E}}_{{\text{a}}} /{\text{R}} \times { }\left( {1/{\text{T}}} \right){ } + {\text{ lnAj}} $$
(6)

The value of Ea parameter is determined from the slope of the line segment ln(J0) = f(1/T). It is known from the activated complex theory that Ea is related to the activation enthalpy parameter ΔH♯ass as follows:

$$ {\mathbf{\Delta Hass}}^{{\mathbf{\# }}} \; = \; {\mathbf{Ea}}\;{-}\;2500\;{\text{J}}\;{\text{mol}}\; - \;1\;{\mathbf{at}}\; 298\;{\text{K}} $$
(7)

While the entropy parameter ΔS♯ is related to the pre-exponential factor by the relation:

$$ \Delta {\mathbf{S}}^{{\# ~}} \; = \;~R~\left( {LnAj{-}30,46} \right)\;{\text{J}}\;{\text{mol}}^{{ - 1}} \;{\text{at}}\;298\;{\text{K}} $$
(8)

Elucidation and quantification of energy and/or kinetic pathways associated with Nickel (II) ions are carefully designed membrane. The value of ΔHth, which is the enthalpy of equilibrium substrate S and the extractive agent T in the membrane phase was determined. Integral of Van't Hoff's law (dLnKass/dT = ΔHth/RT2) expresses the evolution of the associated constant parameter (Kass) as Temperature.

$$ Ln\left( {Kass} \right) = {-}\Delta Hth/RT + cste $$
(9)

The slope of the linear representation Ln(Kass) = f(1/T) allows to determine the value of the ΔHth related to the activation parameters (ΔH#ass and ΔH#diss) which is based on following expression.

$$ \Delta Hth = \Delta H\# ass{-}\Delta H\# dis $$
(10)

Chemicals

All chemicals, reagents and solvents were pure commercial products of analytical grade (Aldrich, Fluka). The polymer support used PVA was supplied by (Loba Chemie).

Extraction experiments

The double cell used to carry out the experiments of the facilitated transport of Nickel (II) ions consists of two glass compartments separated by the examined membrane. A compartment containing the feed phase of Nickel (II) ions at the examined concentration and a compartment containing the receiving phase consisting of distilled water. The system is immersed in a thermostat bath containing water in order to keep the temperature constant throughout the experiments. A multi-position stirrer is used to ensure the homogeneity of the two phases [33,34,35]. Micro volumes samples were taken from the feed phase at regular time intervals and analyzed by a Mettler Toledo UV–visible spectrophotometry device.

Preparation of the PIM membranes:

The preparation of the membranes consists of mixing 10 g of PVA with 20 ml of Dimethylsulfoxide (DMSO) and 80 ml of distilled water (DE) as solvent in a tightly closed bottle to prevent evaporation. The mixture is stirred for 24 h at a temperature of 393 K to solubilize the PVA in the solution. To this solution we added 0.5 g of transporter (NTA, EDTA and TREN). The whole mixture is stirred for 6 h at 333 K, using a hot plate. Finally, we casted the membrane into a Petri dish and then put it in an oven at 338 K to dry. The following notations were adopted for the prepared PIM membranes. We used a Mitutoyo Palmer electronic device, with an accuracy of 0.001 mm for the measurement of the thickness of the obtained membranes is determined by performing an average calculation on the values measured in twelve different places and we found E (PVA-NTA) = 0.102 mm, E(PVA-EDTA) = 0.15 mm and E(PVA-TREN) = 0.17 mm.

Results and discussion

Characterization of the developed membranes by FTIR

Analysis by the (Fourier-Transform Infrared Spectroscopy) FTIR spectrometric technique (Fig. 2) was used to study and identify the functional groups of the PIM membranes that were developed. The PVA polymer support membrane alone and the other membranes prepared from the PVA support and the various extractive agents NTA, EDTA, TREN with 6% (w/w) of the total polymer membrane mass. The characteristic peaks typical of the PVA support located between 3100 and 3500 and at 1707 cm−1 related respectively to the stretching vibrations of the bound O–H bonds, and to the stretching vibrations of the C=O bonds of the acetate group present after the production of PVA from the hydrolysis of the polymer and its dehydration [36]. Nevertheless, the peak at 3100–3500 cm−1 of membranes containing NTA and EDTA is more intense due to the inclusion of O–H functions between the PVA chains. While it is observed that there is a change in the shape of the peak towards at 3240–3370 cm−1 in the membrane containing the TREN agent compared to that of stretching of the hydroxyl groups in the spectrum of the PVA support. The bands at 1093, 1420 and 2941 cm−1 are respectively attributed to the stretching vibrations of the C–O, C–H bonds of the PVA. After the inclusion of each of the carriers in the polymeric support, a new peak was detected at 1650 cm−1 in the spectra of the PVA-NTA and PVA-EDTA membrane, which was attributed to the vibration of the carboxylic group C=O and in the spectrum of the PVA-TREN membrane, the vibration bands of the NH2 groups can be observed at 1640 cm−1 which corresponds to the deformation of the N–H bond (primary amine). A new peak at 3010 cm−1 appears in the TREN-modified PVA membrane, which is probably attributed to stretching vibrations of the –CH2-groups in TREN. All these findings consolidate the conclusion that our extractive agents have been successfully included in the polymeric PVA matrix.

Fig. 2
figure 2

FTIR spectra relative to the different constituents of the developed PIMs membranes: PVA/ NTA-EDTA-TREN

Full size image

Characterization of the Elaborated Membranes by SEM

The morphology surfaces of the PVA, PVA-EDTA, PVA-NTA and PVA-TREN membranes were explored by (Scanning Electron Microscopy) SEM and are presented in the Fig. 3a–d. The micrographs show that upon incorporation of the extractive agents into the matrix of the PVA support, the membranes surfaces obtained have become smoother and more porous than the PVA support membrane alone. This result confirms that the extractive agents and the PVA matrix have intermolecular interactions via hydrogen bonds, resulting in the formation of a larger number of crystal-phase PVA [37].For the PVA-EDTA membrane Fig. 3b, the surface is more porous than the other two membranes, which is certainly due to the outward orientation of the hydrophilic nitrogen groups of the EDTA agent.

Fig. 3
figure 3

SEM; a PVA support alone, b PVA-EDTA, c PVA-NTA and d PVA-TREN

Full size image

Effect of the Nature of the Extractive Agent and the Initial Concentration (C0) the Substrate Nickel (II) Ions

The extractive agent (carrier) is the main component of a polymeric affinity membrane for the oriented processes of transport and facilitated extraction from substrates (metal ions or organic compounds). This element must have an appropriate structure with groups capable of interacting in a targeted manner with the extracted substrates. Therefore the nature and the chemical structure of the carrier are the most important factors to ensure efficient and selective facilitated transport of the substrates through the adopted membranes [38, 39]. Studies of the nature and the chemical structure of the extractive agent on the evolution of the facilitated transport processes of Nickel (II) ions through the PVA-NTA, PVA-EDTA and PVA-TREN membranes have been carried out. The experiments were conducted under the following conditions: pH 1, T = 298 K, initial concentrations of Nickel (II) ions ranging from 0.200 M, 0.100 M, 0.050 M to 0.025, extractive agents used: NTA, EDTA and TREN, polymer matrix: PVA; solvent/non-solvent: DMSO/water). The technique of UV–visible spectrophotometry made it possible to quantify the evolution of the absorbance of the receiving phase as a function of time and to calculate the CR concentration of the Nickel (II) ions according to Beer Lamber's law and to present the evolution of the kinetic term predicted by the adopted model (Eq. 1) − Ln(C0-2CR) = f(t) (Fig. 4).

Fig. 4
figure 4

Representation of the lines − ln (C0-2CR) = f(time) of the transport of Nickel (II) ions through the three PIMs studied at pH = 1 and T = 298 K

Full size image

The line segments obtained confirmed the compatibility of the kinetic model developed with the experimental results. From the slopes of these segments of the function − Ln (C0 − 2CR) = f(t), we were able to determine the values of the macroscopic parameters P and J0 for the process studied (Table 1).

Table 1 Experimental results for the process of facilitated transport of Nickel (II) ions
Full size table

The results illustrated in Fig. 4 show a linear evolution which confirms the validity of the kinetic model, with the substrate diffusion through the membrane phase as the kinetically determining step. For the same type of membrane (PIM) and the same polymer support (PVA), the values of the parameters P and J0 associated with the membranes performance depend on the chemical nature of the used extractive agent, hence the importance of the choice of the carrier agent, as well as the initial concentration of substrate to improve the properties, the efficiency and the performance of this type of PIMs [40,41,42].The analysis of these results indicates that the membrane with the NTA extractive agent with three carboxylic groups and a tertiary amine exhibits the highest permeability and initial flux for this oriented processes of facilitated extraction and transport of Nickel (II) ions compared to its counterparts with EDTA and TREN agents. For the three examined membranes, an increase in the substrate initial concentration (C0) leads to a decrease in P permeability parameter, while an increase in the flux J0. In order to establish more correct interpretations and comparisons on the performance of each membrane adopted, we examined the evolution of the microscopic parameters, Kass and D*, linked to the association of Nickel (II) ions with the semi-mobile sites of the extractive agents in the membrane phases during their diffusion through these organic phases [43, 44]. The Lineweaver–Burk representation 1/J0 = f(1/C0) predicted by the thermodynamic model (Eq. (3)) indicates linear segments shown in Fig. 5. with positive slopes, which helps to confirm the validity of the proposed thermodynamic model, and the establishment of interactions between the Nickel (II) ions and the extractive agents with the formation of a pseudo-entity of composition (1/1), during the diffusion of the Nickel (II) ions at the membrane phase of each of the adopted PIM membranes. From the slopes and the ordinates at the origin of these straight lines, we were able to calculate the values of Kass and D* according to the expressions of Eq. (4). The values indicated in Fig. 6, for these parameters and their evolution are specific for each extractive agent and vary in opposite direction with respect to each other.

Fig. 5
figure 5

The Lineweaver–Burk representation for the facilitated transport of Nickel(II) ions through the three membranes (PIM(1), PIM(2), PIM(3))

Full size image
Fig. 6
figure 6

Graphic representation of the evolution of the D* and Kass microscopic parameters related to the facilitated extraction of Nickel (II) ions by the three PIMs studies

Full size image

The analysis of the results grouped in Fig. 6, confirms that for equal numbers of moles in transporters, the PVA-NTA membrane is the most efficient than its counterpart PIMs PVA -TREN/EDTA for the processes of the extraction and transport of Nickel (II) ions. This result is also well justified by the values of the Kass and confirms that these D* and Kass parameters are specific to the type of membrane adopted, to the substrate transported and to the nature of the used extractive agent [45,46,47]. Indeed, the experimental results for P and J0 indicate that the PVA-NTA membrane is more efficient for the facilitated transport of Nickel (II) ions, in agreement with the values of the Kass and D* parameters, with a high value of the D* and a low value of the Kass. This result is certainly linked to the NTA structure which presents sites of interaction with unfavorable orientations and which interacts with Nickel (II) ions to form pseudo-entities (Nickel(II)-AT) which are not very stable and easily dissociated than their counterparts EDTA and TREN.

Analysis of the Influence of the Temperature Factor

The influence of the temperature factor on the evolution of different parameters related to the facilitated extraction phenomenon on of the Nickel (II) substrate through the three PIMs are of paramount importance in order to explain the performance of these membranes, and to elucidate the mechanisms related to this extraction processes across the adopted membranes. To examine this influence of this parameter, several experiments were conducted at the optimal acidity found (pH 1) and at three temperatures 298, 303 and 308 K. The kinetic law − Ln(C0 − 2CR) = f(t), for these experimental results, allow to identify the values of the parameters P and J0 for the three temperatures studied. Table 2, summarizes the values obtained of these parameters.

Table 2 Evolution of P and J0 parameters according to temperature factor for the facilitated extraction process of Nickel (II) ions substrate through elaborated membranes
Full size table

This data indicates a clear improvement of macroscopic P and J0 parameters as a function of the temperature factor and show that an increase of this important factor leads to an improvement of the membrane performance. In the temperature interval studied from 298 to 308 K, a better evolution of P and J0 parameters for the adopted membranes (PVA-EDTA and PVA-TREN), while for PVA-NTA membrane the performances are higher at the analyzed temperatures. To understand and to interpret these results and determine the movement nature of the substrate S through the membrane phase, it is necessary to study the effect of temperature factor on the evolution of microscopic parameters Kass and D*. Based on the Lineweaver–Burk representation of the function 1/J0 = f (1/C0) (Eq. (3)), the line shown by the graph in the following figure can be exploited to obtain the values of these specific parameters (Fig. 7).

Fig. 7
figure 7

Lineweaver–Burk representations [1/J0 = f(1/C0)] for facilitated extraction process of Nickel (II) ions substrate across the adopted membranes at studied temperature (a = 298 K, b = 303 K and c = 308 K)

Full size image

The slopes and intercepts of these line segments are used according to the terms of (Eq. (4)) to determine the values of the parameters Kass and D*. The values calculated for these microscopic parameters at the three temperatures studied are summarized in the table below (Table 3).

Table 3 Influence of temperature factor on the evolution of Kass and D* parameters to facilitated extraction process of Nickel (II) ions substrate through the adopted membranes
Full size table

According to the results obtained grouped in Table 3, we observe a clear influence of the temperature factor on the evolution of the microscopic parameters. When the temperature of the medium increases, the apparent diffusion coefficient D* of the Nickel (II) ions increases, while the association constant Kass of these ions with each of the transporting agents decreases. Consequently, this evolution explains the better performance of the membranes adopted at high temperature. The analysis of all the results clearly shows that the PIM membrane prepared based on the transporter agent NTA is the most efficient, because it allows to obtain the best values of permeabilities (P) and initial fluxes (J0) as well as high values of the coefficient D* which correspond to low values of the Kass constant for these facilitated transport processes of Nickel (II) ions. The PIM membrane prepared based on the extractive agent EDTA (PVA-EDTA) comes in second position in terms of performance, followed by the PIM membrane prepared based on the agent TREN. All these membranes were successfully used for the first time for these oriented processes of facilitated- transport and extraction of Nickel (II) ions.

On the other hand, an increase in the temperature factor leads to a decrease in the stability of the substrate-extractant (ST) entity, and a rapid dissociation. This significant result shows that the movement of the substrate (S) through the organic membrane phase is based on its interaction with the extractive agent (T) in opposite reactions (association/dissociation) whose rates increase with temperature. Thus, the passage of the Nickel (II) substrate through the membrane phase is an apparent movement of diffusion, by successive jumps of the molecules of the substrate from one site to another of the extracting agent. (Fig. 8).

Fig. 8
figure 8

Apparent diffusion movement of the substrate by successive jumps from one site to another of the extractive agent across the membrane organic phase

Full size image

To confirm these results and elucidate the real mechanism related to the process studied through each type of adopted membrane, we determined the values of the activation and the thermodynamic parameters (Ea, ΔH#ass, ΔS#, ΔH#diss and ΔHth) for the transition state of the diffusion step of the substrate through the membrane phase (rate-determining step). For this, we have examined the evolution of J0 and Kass values with temperature factor according to Arrhenius [Ln (J0moy) = f (1/T)] and Van’t Hof [Ln (Kass) = f(1/T)] relationships (Eqs. 6 and 9). The values of the slopes and intercepts of the straight segments obtained were used to determine the values of the parameters of Ea and Aj so that the values of the activation thermodynamic parameters were determined at 298 K according to the expressions in Eqs. 7, 8 and 10). All obtained data is presented in Table 4.

Table 4 Evolution of activation and the thermodynamic parameters for the facilitated extraction-oriented process of Ni (II) ions through membrane types: PVA-NTA, PVA-EDTA and PVA-TREN
Full size table

The results in Table 4, indicate the values of a low and close energy parameters. These parameters are relative to the transition state of the rate-determining step, and the negative values of the parameter ∆S# confirm that in the transition state there is an association of Nickel (II) ions with the extractive agents sites. The interaction of each agent adopted, to form an entity (Nickel (II)-AT) whose structure is a function of the nature and structure of the interaction site of the extractive agent AT [46, 48]. However, the negative values are very close to the entropy of activation parameter (ΔS≠) for the transition states of the entities (Nickel (II)-AT) formed with the agents NTA and EDTA (-288.43 and -251.75 J/mol.K) indicating for the mechanisms of the processes reflects late transition states, whose structures are close and with similar bidentate chelation sites. Whereas, the transition state for the entity (Nickel (II)-TREN) which is also late, whose value of ΔS≠ is less negative (-243.86 J/mol.K), indicates that this transition state whose structure is less ordered and different from those of NTA and EDTA and which also corresponds to a bidentate chelation site. The low values of the activation and thermodynamic parameters (Ea, ΔH#ass, ΔS#, ΔH#dis and ΔHth) explain the good performances of described membranes and make it possible to explain the difference between these performances, especially for the PVA-TREN membrane whose values of parameters ΔH#ass and ΔH#dis are the highest (Table 4), explain its weaker performance. This difference in performance certainly lies in the number of favorable orientations of chelation sites which is low in the case of the PVA-TREN membrane [49, 50]. In addition, the difference between the values of this important parameter ΔH#diss, perfectly explains the order of observed performances for the adopted membranes.

Conclusion

For this study, we prepared three affinity membranes namely PVA-NTA, PVA-EDTA and PVA-TREN intended for the oriented processes of the facilitated extraction and recovery of Nickel (II) ions from Li-ion battery waste. These membranes contain chelating compounds as extractive agents or carriers including NTA, EDTA and TREN. The characterization methods verified the inclusion or the functionalization of PVA polymer support by the carrier transporting agents, to develop the three elaborated membranes. Experiments relating to oriented processes of transport and extraction, showed that the presence of carboxylic and amine groups in the membrane phases led to a significant improvement in the membrane transport efficiency of Nickel (II) ions through theses phases. Then we studied the influence of two factors on the extraction phenomenon, in particular, the carrier agent chemical nature and the concentration of substrate in the medium. Macroscopic (permeability P and initial flux J0) and microscopic (apparent diffusion coefficient D* and the association constant Kass) parameters have been quantified. Finally, the important studies on the influence of temperature factor have also made it possible to determine the activation and thermodynamic parameters (Ea, ΔH#ass, ΔS#, ΔH#dis and ΔHth) for the transition state of the rate-determining step (diffusion of the substrate through the membrane phase), related to the mechanism of studied process. The original values of these parameters allow two main interpretations: firstly, the process studied is a process much more oriented by the structures of substrate and extractive agent, and not by the energy of the reaction medium. The second interpretation is very important: the structure of the unstable intermediate entity (ST) necessary for the migration of the substrate through the membrane phase is the same whatever the type of membrane adopted. The oriented processes of the facilitated extraction of Nickel (II) ions through the three examined membranes, made it possible to compare their performances in order to determine the optimal experimental and structural conditions for the realization of these facilitated transport processes through these different developed membranes. Thus, the results show that the interaction sites of the NTA agent in the PVA polymer matrix are more favorable for transporting Nickel (II) ions through the membrane phase, therefore this membrane shows a better performance as compared to its counterparts with TREN and EDTA extractive agents.