Batch and Fixed-Bed Column Studies on Palladium Recovery from Acidic Solution by Modified MgSiO3

Effective recovery of palladium ions from acidic waste solutions is important due to palladium’s intensive usage as a catalyst for different industrial processes and to the high price paid for its production from natural resources. In this paper, we test the ability of a new adsorbent, MgSiO3 functionalized by impregnation with DL-cysteine (cys), for palladium ion recovery from waste solutions. The Brunauer–Emmett–Teller (BET) surface area analysis, Barrett–Joyner–Halenda (BJH) pore size and volume analysis, scanning electron microscopy (SEM), energy dispersive X-ray (EDX) spectroscopy and Fourier-Transformed Infrared (FTIR) spectroscopy have been performed to characterize this material. Firstly, the maximum adsorption capacity of the new obtained material, MgSiO3-cys, in batch, was studied. To establish the adsorption mechanism, the obtained experimental data were fitted using the Langmuir, Freundlich and Sips adsorption isotherms. Studies on the adsorption of palladium ions on the synthesized material were performed in a dynamic regime, in a fixed-bed column. The Pd(II) recovery mechanism in the dynamic column regime was established based on Bohart–Adams, Yoon–Nelson, Thomas, and Clark models. The obtained equilibrium adsorption capacity was 9.3 (mg g−1) in static regime (batch) and 3 (mg g−1) in dynamic regime (column). The models that best describe the Pd(II) recovery process for batch and column adsorption are Sips and Clark, respectively.


Introduction
The noble metals platinum, palladium and rhodium have a wide application range based on their distinct physical and chemical properties [1][2][3][4][5]. One of the first historical uses of the precious metals was as currency, internationally recognized under ISO 4217. Palladium and its alloys are currently used by the telecommunication and automotive industries (as catalytic converters), the metallurgy and chemical industries, for jewelry manufacturing and in the medical field (dental alloy production) [5][6][7][8][9].
Its growing popularity led, in 2010, to official recognition as the fourth most precious metal, after gold, silver and platinum, a statute that requires the marking of each jewel. White gold contains variable amounts of palladium (up to 20%); furthermore, dental alloys can contain up to 10% palladium [5,[10][11][12][13][14][15].
The purpose of this study was to develop an ecological strategy for Pd(II) recovery using (florisil) MgSiO3 functionalized by impregnation with DL-cysteine (cys) [49]. This new material has -SH, -NH2, and -COOH pendant groups derived from the amino acid DL-cysteine [54,55].
The first objective was to test the new MgSiO3 cys material's ability to recover palladium ions from waste solutions by adsorption. The second goal of this research was to compare the static adsorption process with the dynamic one.

Adsorbent Synthesis and Characterization
Functionalized MgSiO3 using DL-cysteine (DL-cysteine-hydrochloride monohydrate 99.0%, Fluka, Buchs, Switzerland) as extractant was obtained using 0.1 g of DL-cysteine. This amount of extractant was dissolved in 25 mL of deionized water. The obtained solution was mixed with 1 g of support (MgSiO3, 60-100 mesh, Merck, Darmstadt, Germany), corresponding to a ratio support: extractant of 1:0.1 and they were brought into contact for 24 h in stand-by (SIR, solvent impregnated resin-dry method) [49,51]. After that, the obtained material was dried in the oven (Pol-Eko SLW 53 STD, POL-EKO-APARATURA, Wodzisław Śląski, Poland) for 24 h at 323 K. The appearance of the adsorbent material can be seen in Figure 1. The specific surface area, cumulative pore volume, and pore size of the adsorbent material were measured with a Micromeritics ASAP 2020 instrument (Brunauer-Emmett-Teller, BET, surface area analysis and Barrett-Joyner-Halenda, BJH, pore size and volume analysis, at liquid nitrogen temperature, −196 °C) from Micromeritics Instrument, Norcross, GA, USA. The point of zero charge (pHPZC) and density were determined using the solid addition method and pycnometer method, respectively. Furthermore, the adsorbent was analyzed by scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) spectroscopy, using the FEI Quanta FEG 250 instrument (FEI, Eindhoven, The Netherlands), and Fourier-Transformed Infrared (FTIR) spectroscopy using a Bruker Platinum ATR-QL Diamond apparatus (Bruker Optik GmbH, Ettlingen, Germany) in the range of 4000-400 cm −1 .

Batch Adsorption Experiments
The effect of the initial concentration of Pd(II) upon the adsorption capacity of the materials was studied using Pd(II) solutions of different concentrations (5,10,20,30,40, and 50 mg L −1 ), prepared by the appropriate dilution of a stock solution of palladium (II) chloride (5 wt% in 10 wt% HCl, Sigma-Aldrich, St. Louis, MO, USA). Adsorptions were carried out at pH = 2 for one hour at 298 K. The equilibrium concentration was determined using thermostatic Julabo SW23 water bath and shaken at a rotation speed of 200 rpm. The adsorption mechanism was established by modeling the The specific surface area, cumulative pore volume, and pore size of the adsorbent material were measured with a Micromeritics ASAP 2020 instrument (Brunauer-Emmett-Teller, BET, surface area analysis and Barrett-Joyner-Halenda, BJH, pore size and volume analysis, at liquid nitrogen temperature, −196 • C) from Micromeritics Instrument, Norcross, GA, USA. The point of zero charge (pH PZC ) and density were determined using the solid addition method and pycnometer method, respectively. Furthermore, the adsorbent was analyzed by scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) spectroscopy, using the FEI Quanta FEG 250 instrument (FEI, Eindhoven, The Netherlands), and Fourier-Transformed Infrared (FTIR) spectroscopy using a Bruker Platinum ATR-QL Diamond apparatus (Bruker Optik GmbH, Ettlingen, Germany) in the range of 4000-400 cm −1 .

Batch Adsorption Experiments
The effect of the initial concentration of Pd(II) upon the adsorption capacity of the materials was studied using Pd(II) solutions of different concentrations (5,10,20,30,40, and 50 mg L −1 ), prepared by the appropriate dilution of a stock solution of palladium (II) chloride (5 wt% in 10 wt% HCl, Sigma-Aldrich, St. Louis, MO, USA). Adsorptions were carried out at pH = 2 for one hour at 298 K. The equilibrium concentration was determined using thermostatic Julabo SW23 water bath and shaken at a rotation speed of 200 rpm. The adsorption mechanism was established by modeling the experiment using three specific isotherms in non-linear form: Langmuir, Freundlich and Sips, according to equations used in scientific literature [56][57][58][59].
Langmuir q e = q m · K L · C e 1 + K L · C e (1) Sips q e = q m · K S · C 1/n S e where q e is the maximum absorption capacity (mg g −1 ), q m is maximum adsorption capacity (mg g −1 ), K L is the Langmuir constant, C e is the equilibrium concentration of Pd(II) in solution (mg L −1 ), K F is the Freundlich constant, 1/n F is the heterogeneity factor, K S is Sips constant, and 1/n S is the Sips model exponent. Three independent replicates were performed for each batch adsorption experiment.
The experimental setup was made using a glass column (diameter 20 mm and height 300 mm) loaded with three different amounts of adsorbent material (10, 5, and 3 g), corresponding to three layers' heights (70,35, and 21 mm, respectively) ( Figure 2). The Pd(II) solution was transferred in the experimental column using a peristaltic pump (Heidolph SP quick, Heidolph Instruments, Schwabach, Germany) at a flow rate of 7 (mL min −1 ). The studies were made using samples sequences of 25 mL. The retention times of the solution in the adsorption column, corresponding to the amounts of adsorbent mentioned above, were approximately 3, 1.5, and 1 min, respectively. The residual concentration of Pd(II) was measured using an atomic absorption spectrometer type Varian AAS 280 FS (Varian Inc., Mulgrave, Australia).
where qe is the maximum absorption capacity (mg g −1 ), qm is maximum adsorption capacity (mg g −1 ), KL is the Langmuir constant, Ce is the equilibrium concentration of Pd(II) in solution (mg L −1 ), KF is the Freundlich constant, 1/nF is the heterogeneity factor, KS is Sips constant, and 1/nS is the Sips model exponent.
Three independent replicates were performed for each batch adsorption experiment.

Column Adsorption Experiments
The obtained sorbent, MgSiO3 functionalized using DL-cysteine (MgSiO3-cys), was used for dynamic studies in a fixed-bed column. Pd(II) solutions' initial concentration was 60 (mg L −1 ), prepared using appropriate dilution of a stock solution of palladium (II) chloride (5 wt% in 10 wt% HCl, Sigma-Aldrich, St. Louis, MO, USA).
The experimental setup was made using a glass column (diameter 20 mm and height 300 mm) loaded with three different amounts of adsorbent material (10, 5, and 3 g), corresponding to three layers' heights (70,35, and 21 mm, respectively) ( Figure 2). The Pd(II) solution was transferred in the experimental column using a peristaltic pump (Heidolph SP quick, Heidolph Instruments, Schwabach, Germany) at a flow rate of 7 (mL min −1 ). The studies were made using samples sequences of 25 mL. The retention times of the solution in the adsorption column, corresponding to the amounts of adsorbent mentioned above, were approximately 3, 1.5, and 1 min, respectively. The residual concentration of Pd(II) was measured using an atomic absorption spectrometer type Varian AAS 280 FS (Varian Inc., Mulgrave, Australia).

Bohart-Adams ln
Clark ln where C 0 is the influent concentration (mg L −1 ); C t is the solution concentration at time t in the effluent (mg L −1 ); t is time (min); k BA is the kinetic constant of the Bohart-Adam model (L mg −1 min −1 ); F is the linear velocity calculated by dividing the flow rate by the column section area; Z is the bed depth of column (cm); N 0 is the saturation concentration (mg L −1 ); k Th is the Thomas rate constant (L mi −1 mg −1 ); q Th is the equilibrium compound uptake per g of the resin (mg g −1 ); m is the mass of sorbent resin (g); Q is the flow rate (mL min −1 ); k YN is the rate constant (min −1 ); τ is the time required for 50% adsorbate breakthrough (min); n is the Freundlich constant determined experimentally in batch; r is the Clark model constant (min −1 ); and A is the Clark model constant.

Characterization of the MgSiO 3 -Cys
BET analysis showed that the specific surface area was S BET = 166 (m 2 g −1 ). The average pore size and cumulative pore volume calculated using BJH method were 25.24 nm and 0.43 (cm 3 g −1 ), respectively. The value of pH PZC was six and the density was about 4 (g cm −3 ). Figure 3 shows the main morphological changes of the surface of the adsorbent material that appeared after impregnation. The presence of functional groups in MgSiO 3 -cys was investigated using energy dispersive X-ray spectroscopy (EDX) ( Figure 4). The EDX spectra of MgSiO 3 -cys show both magnesium silicate peaks (O, Mg, Si) and N, S, and C characteristic peaks, confirming the presence of specific peaks for functionalized sorbent.      Infrared spectroscopy (FTIR) was used to confirm the MgSiO 3 functionalization. The FTIR spectra for commercial magnesium silicate together with functionalized MgSiO 3 -cys are presented in Figure 5. Magnesium silicate-specific peaks can be observed on both spectra: a large peak at 1052 cm −1 and another peak at 600 cm −1 , corresponding to Si-O stretching vibrations, and the peak at 800 cm −1 , assigned to Si-O-Si bending vibrations. The MgSiO 3 spectrum show a band at~3500 cm −1 and a peak at 1637 cm −1 , specific to the -OH bond from H 2 O molecules.     The FTIR spectrum of magnesium silicate functionalized with DL-cysteine shows specific peaks for the -SH bond at~2620 cm −1 , the -NH 2 bond at~2245 cm −1 , the -COOH bond at~1325 cm −1 . The intensities of those peaks are lower compared to those of MgSiO 3 due to the small cysteine amount used in the functionalization process. This process leads to an attenuation of MgSiO 3 specific vibrations.

Equilibrium Adsorption Studies. Adsorption Isotherms
The maximum adsorption capacity of the MgSiO 3 -cys material was determined based on adsorption experiment data using three isotherm models: Langmuir, Freundlich, and Sips [66]. The equilibrium adsorption capacity was determined by monitoring the dependence of materials' adsorption capacity vs. initial Pd(II) concentration, illustrated in Figure 6. capacity up to an approximately constant value. The highest Pd(II) adsorption capacity (qm) on DLcysteine functionalized magnesium silicate, for a steady state concentration of 40 (mg L −1 ), was 9.23 (mg g −1 ). Figure 7 shows the equilibrium isotherms for the studied material. The parameters of the isotherm models for palladium ion adsorption on the studied functionalized material are presented in Table 1.    Augmentation of the initial Pd(II) solution concentration led to an increase in the adsorption capacity up to an approximately constant value. The highest Pd(II) adsorption capacity (q m ) on DL-cysteine functionalized magnesium silicate, for a steady state concentration of 40 (mg L −1 ), was 9.23 (mg g −1 ). Figure 7 shows the equilibrium isotherms for the studied material. The parameters of the isotherm models for palladium ion adsorption on the studied functionalized material are presented in Table 1.

Equilibrium Adsorption Studies. Adsorption Isotherms
The maximum adsorption capacity of the MgSiO3-cys material was determined based on adsorption experiment data using three isotherm models: Langmuir, Freundlich, and Sips [66]. The equilibrium adsorption capacity was determined by monitoring the dependence of materials' adsorption capacity vs. initial Pd(II) concentration, illustrated in Figure 6.
Augmentation of the initial Pd(II) solution concentration led to an increase in the adsorption capacity up to an approximately constant value. The highest Pd(II) adsorption capacity (qm) on DLcysteine functionalized magnesium silicate, for a steady state concentration of 40 (mg L −1 ), was 9.23 (mg g −1 ). Figure 7 shows the equilibrium isotherms for the studied material. The parameters of the isotherm models for palladium ion adsorption on the studied functionalized material are presented in Table 1.    The existing literature data [67] suggest that most metallic ion adsorption processes on the MgSiO 3 -cys material obtained by chemical modification are multilayer processes and the surface is heterogeneous. At the same time, the adsorption mechanism is controlled by chemisorption processes due to the strong chelation between metal ions and OH − groups or free electron pairs of S and/or N-containing pendant groups present on the surface of the chemical functionalized material.
Using the Sips isotherm to model the obtained experimental data leads to a parameter 1/n s value deviated from unity, suggesting the heterogeneity of the adsorbent surface [68]. Regardless of the extractant used for functionalization, the Sips model better describes the adsorption process, reflected by the highest correlation coefficient (R 2 ) values. In the case of Pd(III) adsorbed on DL-cysteine functionalized magnesium silicate, the correlation coefficient of the Sips isotherm, R 2 = 0.9953, is higher than those obtained using the Langmuir and Freundlich adsorption isotherms. In addition, the calculated equilibrium adsorption capacity of the Sips model (9.62 mg g −1 ) was consistent with that obtained experimentally (9.23 mg g −1 ).

Bed Height Column (BHC) Influence on the Pd(II) Breakthrough Curves
An important parameter in the sorption process is the bed depth. Pd(II) retention in a fixed-bed column depends, among other factors, on the sorbent quantity reflected by the bed depth of the column works. Three different heights of the MgSiO 3 -cys sorbent filling the fixed-bed column were used in the experiments: 2.1, 3.5, and 7.0 cm.
According to Figure 8, the column adsorption process is highlighted by establishing breakthrough curves, which represent the variation of the ratio between the residual concentration of Pd(II) and its initial concentration (C rez /C 0 ), depending on the volume of effluent passed through the column, for three distinct amounts of material. Volumes of Pd(II) of 60 (mg L −1 ) concentration were varied between 1500 and 3000 mL, depending on the amount of adsorbent material in the column. The existing literature data [67] suggest that most metallic ion adsorption processes on the MgSiO3-cys material obtained by chemical modification are multilayer processes and the surface is heterogeneous. At the same time, the adsorption mechanism is controlled by chemisorption processes due to the strong chelation between metal ions and OHgroups or free electron pairs of S and/or Ncontaining pendant groups present on the surface of the chemical functionalized material.
Using the Sips isotherm to model the obtained experimental data leads to a parameter 1/ns value deviated from unity, suggesting the heterogeneity of the adsorbent surface [68]. Regardless of the extractant used for functionalization, the Sips model better describes the adsorption process, reflected by the highest correlation coefficient (R 2 ) values. In the case of Pd(III) adsorbed on DL-cysteine functionalized magnesium silicate, the correlation coefficient of the Sips isotherm, R 2 = 0.9953, is higher than those obtained using the Langmuir and Freundlich adsorption isotherms. In addition, the calculated equilibrium adsorption capacity of the Sips model (9.62 mg g −1 ) was consistent with that obtained experimentally (9.23 mg g −1 ).

Bed Height Column (BHC) Influence on the Pd(II) Breakthrough Curves
An important parameter in the sorption process is the bed depth. Pd(II) retention in a fixed-bed column depends, among other factors, on the sorbent quantity reflected by the bed depth of the column works. Three different heights of the MgSiO3-cys sorbent filling the fixed-bed column were used in the experiments: 2.1, 3.5, and 7.0 cm.
According to Figure 8, the column adsorption process is highlighted by establishing breakthrough curves, which represent the variation of the ratio between the residual concentration of Pd (II) and its initial concentration (Crez/C0), depending on the volume of effluent passed through the column, for three distinct amounts of material. Volumes of Pd (II) of 60 (mg L −1 ) concentration were varied between 1500 and 3000 mL, depending on the amount of adsorbent material in the column. The mass transfer area is the active surface of the bed of adsorbent material where the adsorption of Pd(II) ions takes place [65]. The first part of the column adsorption process takes place rapidly, through the adsorption of Pd(II) on the surface of the material, called the primary adsorption zone. This is why, at the beginning, the collected samples do not contain Pd(II) ions. The second part of the adsorption process is slower and is characterized by the adsorption of Pd(II) ions on the adsorbent material, achieving mass transfer. The adsorption process is complete, the concentration of Pd(II) ions varies from 60 to 0 (mg L −1 ), and the saturation of the material is total.
For the three different bed depths used, as the bed depth increases (from 2.1 at 7 cm), the breakthrough point increases (from 100 to 325 min). A rational explanation of this behavior is that The mass transfer area is the active surface of the bed of adsorbent material where the adsorption of Pd(II) ions takes place [65]. The first part of the column adsorption process takes place rapidly, through the adsorption of Pd(II) on the surface of the material, called the primary adsorption zone. This is why, at the beginning, the collected samples do not contain Pd(II) ions. The second part of the adsorption process is slower and is characterized by the adsorption of Pd(II) ions on the adsorbent material, achieving mass transfer. The adsorption process is complete, the concentration of Pd(II) ions varies from 60 to 0 (mg L −1 ), and the saturation of the material is total.
For the three different bed depths used, as the bed depth increases (from 2.1 at 7 cm), the breakthrough point increases (from 100 to 325 min). A rational explanation of this behavior is that with increasing column sorbent height a greater number of binding sites become available and the quantity of the Pd(II) removed increases accordingly [69].
A higher BHC leads to a longer contact time between the waste solution and the MgSiO 3 -cys sorbent (from about 1 min to 3 min), having a positive influence on Pd(II) adsorption. Figure 8 shows an alteration of the steep concave shape to flat concave shape curves as BHC increases, which leads to an enlargement of the mass transfer area [70][71][72]. However, too high a layer of adsorbent material in the column is not recommended as it increases the flow resistance [73].

Modeling for Adsorption Behaviors of Pd(II) on MgSiO 3 -Cys
Various practical parameters such as sorbent capacity, contact time between adsorbent and adsorbed, column operating life span, regeneration time, and prediction of the time necessarily have a significant influence upon the operation of the column. Knowing these parameters is important to model the adsorption process in a fixed-bed column.
The four models tested (Bohart-Adams, Yoon-Nelson, Thomas, and Clark) provide detailed conclusions about the process mechanism. The adsorption column is subjected to axial dispersion, external film strength, and intraparticle diffusion resistance [74].
The Bohart-Adams model is used for one-component systems and provides information on the saturation concentration of the material. This model characterizes the beginning of the column penetration, gives information about the adsorbent material used, and shows the maximum concentration at which the column is instantly broken through [60]. The Yoon-Nelson model is used to model a one-component system and provides information about the time by which half of the column is broken through. It is a purely theoretical model which does not focus on the properties of the adsorbent, the type of adsorbent, or the physical characteristics of the fixed bed [74]. The Thomas model provides information on the maximum solid phase concentration of the adsorbent and on the rate constant [62], while the Clark model describes, very well, the dynamic adsorption process [74]. Figure 9 illustrates the influence of sorbent dose (10, 5, and 3 g) corresponding to the three previously mentioned BHCs (7, 3.5, and 2.1 cm) on the ln (C t /C 0 ) vs. time curves. The graphic shows a direct influence of the sorbent amount upon maximum adsorption capacity, N 0 , and the kinetic constant, k BA , which indicates that, kinetically, the process is controlled by the mass transfer in the first part of the breakthrough process. The calculated regression coefficients have relatively low values (between 0.9717 and 0.9755); therefore, one can assume that the model is not the most suitable to describe the Pd(II) adsorption mechanism on MgSiO 3 -cys in a dynamic regime. with increasing column sorbent height a greater number of binding sites become available and the quantity of the Pd(II) removed increases accordingly [69]. A higher BHC leads to a longer contact time between the waste solution and the MgSiO3-cys sorbent (from about 1 min to 3 min), having a positive influence on Pd(II) adsorption. Figure 8 shows an alteration of the steep concave shape to flat concave shape curves as BHC increases, which leads to an enlargement of the mass transfer area [70][71][72]. However, too high a layer of adsorbent material in the column is not recommended as it increases the flow resistance [73].

Modeling for Adsorption Behaviors of Pd(II) on MgSiO3-Cys
Various practical parameters such as sorbent capacity, contact time between adsorbent and adsorbed, column operating life span, regeneration time, and prediction of the time necessarily have a significant influence upon the operation of the column. Knowing these parameters is important to model the adsorption process in a fixed-bed column.
The four models tested (Bohart-Adams, Yoon-Nelson, Thomas, and Clark) provide detailed conclusions about the process mechanism. The adsorption column is subjected to axial dispersion, external film strength, and intraparticle diffusion resistance [74].
The Bohart-Adams model is used for one-component systems and provides information on the saturation concentration of the material. This model characterizes the beginning of the column penetration, gives information about the adsorbent material used, and shows the maximum concentration at which the column is instantly broken through [60]. The Yoon-Nelson model is used to model a one-component system and provides information about the time by which half of the column is broken through. It is a purely theoretical model which does not focus on the properties of the adsorbent, the type of adsorbent, or the physical characteristics of the fixed bed [74]. The Thomas model provides information on the maximum solid phase concentration of the adsorbent and on the rate constant [62], while the Clark model describes, very well, the dynamic adsorption process [74]. Figure 9 illustrates the influence of sorbent dose (10, 5, and 3 g) corresponding to the three previously mentioned BHCs (7, 3.5, and 2.1 cm) on the ln (Ct/C0) vs. time curves. The graphic shows a direct influence of the sorbent amount upon maximum adsorption capacity, N0, and the kinetic constant, kBA, which indicates that, kinetically, the process is controlled by the mass transfer in the first part of the breakthrough process. The calculated regression coefficients have relatively low values (between 0.9717 and 0.9755); therefore, one can assume that the model is not the most suitable to describe the Pd(II) adsorption mechanism on MgSiO3-cys in a dynamic regime.   Figure 10 shows the influence of sorbent dose (10, 5, and 3 g) upon the ln[(C 0 /C t ) − 1] vs. time curves. The figure illustrates that a higher sorbent amount leads to a decrease in the Thomas rate constant k Th . The reason for this behavior is the adsorption driving force given by the difference between the Pd(II) concentration in the sorbent and in the solution [75][76][77][78]. The determination coefficient R 2 values (between 0.9704 and 0.9961) indicated positive correlation, but we cannot assume that this model is best fitted for the adsorption mechanism. The adsorption capacity q Th and the kinetic constant are presented in Table 2.  Figure 10 shows the influence of sorbent dose (10, 5, and 3 g) upon the ln[(C0/Ct) − 1] vs. time curves. The figure illustrates that a higher sorbent amount leads to a decrease in the Thomas rate constant kTh. The reason for this behavior is the adsorption driving force given by the difference between the Pd(II) concentration in the sorbent and in the solution [75][76][77][78]. The determination coefficient R 2 values (between 0.9704 and 0.9961) indicated positive correlation, but we cannot assume that this model is best fitted for the adsorption mechanism. The adsorption capacity qTh and the kinetic constant are presented in Table 2.  Table 2. Pd(II) adsorption process parameters in a fixed-bed column.    Figure 11 illustrates the relationship of ln[C t /(C 0 − C t )] vs. time for the three sorbent doses. Increasing the sorbent mass leads to an increase in the breakthrough time and also in the k YN constant, as it is presented in Table 2. The determination coefficient R 2 ranged between 0.9722 and 0.9941 but we cannot assume that it best describes the adsorption process.  Figure 11 illustrates the relationship of ln[Ct/(C0 − Ct)] vs. time for the three sorbent doses. Increasing the sorbent mass leads to an increase in the breakthrough time and also in the kYN constant, as it is presented in Table 2. The determination coefficient R 2 ranged between 0.9722 and 0.9941 but we cannot assume that it best describes the adsorption process. Figure 11. Yoon-Nelson model for the adsorption of Pd(II) in a fixed-bed column at various MgSiO3cys amounts.

Clark Model
The relationship ln[(C0/Ct) n−1 − 1] vs. time for all adsorbent doses studied is shown in Figure 12, where n is the Freundlich constant, determined experimentally in batch section. The value of this parameter was 1.81. The high values of the determination coefficient R 2 (between 0.9881 and 0.9973) certify that the Clark model best describes the adsorption in a fixed-bed column. The value of r and A parameters are presented in Table 2.

Clark Model
The relationship ln[(C 0 /C t ) n−1 − 1] vs. time for all adsorbent doses studied is shown in Figure 12, where n is the Freundlich constant, determined experimentally in batch section. The value of this parameter was 1.81. The high values of the determination coefficient R 2 (between 0.9881 and 0.9973) certify that the Clark model best describes the adsorption in a fixed-bed column. The value of r and A parameters are presented in Table 2.  Figure 11 illustrates the relationship of ln[Ct/(C0 − Ct)] vs. time for the three sorbent doses. Increasing the sorbent mass leads to an increase in the breakthrough time and also in the kYN constant, as it is presented in Table 2. The determination coefficient R 2 ranged between 0.9722 and 0.9941 but we cannot assume that it best describes the adsorption process. Figure 11. Yoon-Nelson model for the adsorption of Pd(II) in a fixed-bed column at various MgSiO3cys amounts.

Clark Model
The relationship ln[(C0/Ct) n−1 − 1] vs. time for all adsorbent doses studied is shown in Figure 12, where n is the Freundlich constant, determined experimentally in batch section. The value of this parameter was 1.81. The high values of the determination coefficient R 2 (between 0.9881 and 0.9973) certify that the Clark model best describes the adsorption in a fixed-bed column. The value of r and A parameters are presented in Table 2.   Table 3 provides a comparison between the DL-cysteine functionalized magnesium silicate obtained in this study and other commonly used sorbents for Pd(II) removal in batch systems. The equilibrium adsorption capacity value is comparable to or even higher than those obtained in previous studies using various adsorbent materials. This behavior is based on the presence of the -SH and -NH 2 groups in functionalized material structures, suggesting the surface adsorption of Pd(II) by free electrons or by creating hydrogen bridges. In addition, the experimental conditions in which the adsorption studies were performed, for each material, are highlighted.

Conclusions
The current paper presents a new adsorbent, MgSiO 3 functionalized with DL-cysteine (cys), designed for palladium ion recovery from waste solutions.
SEM, EDX and FTIR analyses revealed morphological changes in the surface of the adsorbent material after impregnation and confirmed the functionalization of MgSiO 3 with DL-cysteine.
The modeling of the experimental data obtained in the batch system showed that the Sips isotherm best describes the adsorption process, because the correlation coefficient R 2 approaches 1 and the maximum calculated adsorption capacity (9.62 mg g −1 ) is close to the experimentally determined value (9.23 mg g −1 ). The obtained adsorption capacity is better than those reported in the literature for other adsorbent materials due to the presence of the -SH and -NH 2 groups in the structure of the functionalized material which allow the surface adsorption of Pd(II) by free electrons or by creating hydrogen bridges.
Palladium ion adsorption studies in a dynamic regime using a fixed-bed column are influenced by the adsorbent bed height (the output flow rate decreases as the fixed-bed height increases). The adsorption process is characterized by the Clark model for all the MgSiO 3 -cys material bed heights studied.