Optimizing the Biosorption Behavior of Ludwigia stolonifera in the Removal of Lead and Chromium Metal Ions from Synthetic Wastewater

: In this study, a natural low-coast, efﬁcient, and eco- bio-sorbent plant material ( Ludwigia stolonifera ), with both parts of the root and shoot, were studied for the removal of the cationic metal ions, lead Pb 2+ and chromium Cr 6+ , via batch mode experiments to evaluate their maximum adsorption capacity, and held a comparison between the used bio-sorbent roots and shoots, based on the highest bio-sorption potential. Optimization of the bio-sorption parameters, such as contact time, pH, bio-sorbent (root and shoot) dosage, and initial ion concentration was conducted. The results indicated that 1.6 g of the used bio-sorbent shoot material removed 81.4% of Pb 2+ , and 77% of Cr 6+ metal ions from liquid media under the conditions of 100 ppm of initial metal ions concentration at room temperature for 60 min of contact time with the static condition. Different isotherms and kinetic models were ﬁt to the experimental data to understand the nature of the bio-sorption process. The experimental data were best ﬁt by the pseudo-second-order kinetic model with a high correlation coefﬁcient (R 2 = 0.999), which reveals the chemisorption nature of the bio-sorption process. The chemical and structural analysis of the used bio-sorbent, before and after Cr 6+ and Pb 2+ bio-sorption, were performed using different techniques of characterization, such as Scanning Electron Microscopy (SEM) and Fourier-transform infrared spectroscopy (FTIR). The used bio-sorbent proved to be a low-cost, efﬁcient, and eco-friendly material to remove heavy metal ions from aqueous solutions.


Introduction
Freshwater is essential to all living organisms' survival as it is the main source of health, food, and energy. The whole world is facing a water crisis nowadays, due to the rapid growth of population and the consumption of large quantities of water by many industries, household, and agriculture activities. The effluent wastewater from some industries such as paper and pulp production, ceramics, smelting, and battery production is considered to be the main source of toxic heavy metals to the environment [1,2] This issue is of increasing concern, due to the adverse health effects of these effluents contaminated with various types of heavy metals types, such as; Cr 6+ , Pb 2+ , Cd 2+ , Zn 2+ , Ni 2+ , As 3+ and  50.97" E) in plastic bags. The plant samples were washed by tap water and distilled water to remove dust and then separated into shoots and roots. The samples were dried completely at 65 • C in an oven and ground into a powder with an electric grinder. Nomenclature and identification of the plant species were carried out according to Tackholm [23] and Boulos [24].

Preparation of Pb (II) and Cr (VI) Metal Ions Standard Solutions
Stock solutions of Pb 2+ and Cr 6+ metal ions were prepared by dissolving a known weight of K 2 Cr 2 O 7 , and Pb (C 2 H 3 O 2 ). 3H 2 O in Double-Distilled Water (DDW), standards of 1000 mg/L. A series of working solutions were prepared with different concentrations varying between 100 and 1000 ppm. Solution pH 2-10 was adjusted by using diluted solutions of 0.1 N HCl and 0.1 N NaOH. All chemicals are pure and analytical reagent grade acquired from Sigma Aldrich, Cairo, Egypt.

The Used Bio-Sorbent (L. stolonifera) Characterization
The surface morphology and topography of the used bio-sorbent (L. stolonifera) root and shoot before and after their bio-sorption of Pb 2+ and Cr 6+ metal ions were observed using scanning electron microscopy (SEM) (JSM-6510, JEOL/EO, Tokyo, Japan) at an accelerated voltage of 30 kV. Additionally, their chemical structure and functional group were analyzed using Fourier transform Infrared (FTIR) spectroscopic analysis. Pellets were formed through mixing samples with KBr, and then they were compressed into disks to be able to enter the FTIR instrument. The spectra were recorded in the wavenumber range from 400-4000 cm −1 and 32 scans per sample with a resolution of 8.000 from 400.1737 to 3999.8091. FTIR spectra were estimated with an FTIR spectrometer (FTIR-8400 S, Shimadzu, Kyoto, Japan).

Batch Bio-Sorption Studies
Bio-sorption of Pb 2+ and Cr 6+ metal ions onto the used bio-sorbents were performed through batch-mode experiments at room temperature. 50 mL of the prepared working metal solutions (100 ppm) was added to a defined weight of roots and shoots of the used bio-sorbent (L. stolonifera) in 250 mL Erlenmeyer flasks, then they were shaken on a mechanical shaker at 200 rpm for a specified bio-sorption contact time of 60-180 min, then, the adsorbate-adsorbent solutions were centrifuged (at 15.000 rpm for 15 min followed by filtration. The filtrates were collected, and their Pb 2+ and Cr 6+ metal ion concentration differences were measured using atomic absorption spectroscopy (Buck Scientific Accusys 211 Atomic Absorption Spectrophotometer, East Norwalk, CT, USA) with air-acetylene flame at the wavelength of 357.87 and 283.31. The conducted batch experiments include: contact time (10-300 min), pH (2-10), bio sorbent (root and shoot) dosage (0.2-1.6 g), and initial metal ion concentration (50-700 ppm) were studied and optimized to find out the maximum bio sorption capacity of the selected metal ions onto the used bio-sorbent (L. stolonifera) root and shoot. The heavy metal removal percentage and bio-sorption capacity (represent the amount of metal ion uptake) were calculated using Equations (1) and (2).
where C i and C e are the initial and final (equilibrium) metal ions concentration (ppm); m is the mass of the used bio-sorbent (L. stolonifera) (g), and V is the volume of used metal ion solution. All tests were performed in triplicate. The equilibrium studies of Pb 2+ and Cr 6+ metal ions bio-sorption onto the used bio-sorbent (L. stolonifera) root and shoot were conducted, and the obtained data were fit to three isotherms models. However, the kinetic studies were carried as a function of contact time. We observed the surface morphology, topography, and dimensions of the used biosorbent (root and shoot), before and after their bio-sorption of Cr 6+ and Pb 2+ metal ions, using SEM instrument. As can be seen in Figure 1, the used bio-sorbent root (A) and shoot (D) cells, before the bio-sorption process, almost have the same outfit and morphological structure, as the cellular structure of both cells might be the same or relatively similar from the morphological point of view. The root and shoot of the used bio-sorbent have smooth surfaces with a lack of pores. Moreover, from the figure (B,C) which represent the bio-sorption process of Cr 6+ and Pb 2+ , respectively, onto the used bio-sorbent root and (E,F), which point out the used bio-sorbent shoot after the bio-sorption process of Cr 6+ and Pb 2+ , respectively, that the surface topography of the used bio-sorbent (L. stolonifera) was different from the native cells through increasing the surface roughness. The bio-sorbed Cr 6+ and Pb 2+ ions were clearly aggregated on the used bio-sorbent surface, which approve the bio-sorption process.

Results and Discussion
ion solution. All tests were performed in triplicate. The equilibrium studies of Pb 2+ an Cr 6+ metal ions bio-sorption onto the used bio-sorbent (L. stolonifera) root and shoot wer conducted, and the obtained data were fit to three isotherms models. However, the kineti studies were carried as a function of contact time.

Scanning Electron Microscopy (SEM)
We observed the surface morphology, topography, and dimensions of the used bio sorbent (root and shoot), before and after their bio-sorption of Cr 6+ and Pb 2+ metal ion using SEM instrument. As can be seen in Figure 1, the used bio-sorbent root (A) and shoo (D) cells, before the bio-sorption process, almost have the same outfit and morphologica structure, as the cellular structure of both cells might be the same or relatively similar from the morphological point of view. The root and shoot of the used bio-sorbent have smoot surfaces with a lack of pores. Moreover, from the figure (B,C) which represent the bio sorption process of Cr 6+ and Pb 2+ , respectively, onto the used bio-sorbent root and (E,F which point out the used bio-sorbent shoot after the bio-sorption process of Cr 6+ and P 2+ , respectively, that the surface topography of the used bio-sorbent (L. stolonifera) was di ferent from the native cells through increasing the surface roughness. The bio-sorbed Cr and Pb 2+ ions were clearly aggregated on the used bio-sorbent surface, which approve th bio-sorption process.

FTIR Analysis
The used bio-sorbent, L. stolonifera (root and shoot), adsorption capacity relay on po rosity and chemical reactivity of their surface functional groups [25]. The chemical struc ture of the used bio-sorbent material (root and shoot), before and after the bio-sorption o Pb 2+ and Cr 6+ metal ions, were analyzed using the FTIR technique to figure out the differ ence in the spectra due to the reaction of the used bio-sorbent functional groups with th chosen metal ions and to understand their possible bio-sorptive interactions.
The spectra of root and shoot of the used bio-sorbent in this study are quite simila which shows that they have similar functional groups on their surfaces. It was pretty clea from Figure 2 that there were clear shifts in the wavenumber, between the used bio

FTIR Analysis
The used bio-sorbent, L. stolonifera (root and shoot), adsorption capacity relay on porosity and chemical reactivity of their surface functional groups [25]. The chemical structure of the used bio-sorbent material (root and shoot), before and after the bio-sorption of Pb 2+ and Cr 6+ metal ions, were analyzed using the FTIR technique to figure out the difference in the spectra due to the reaction of the used bio-sorbent functional groups with the chosen metal ions and to understand their possible bio-sorptive interactions.
The spectra of root and shoot of the used bio-sorbent in this study are quite similar which shows that they have similar functional groups on their surfaces. It was pretty clear from Figure 2 that there were clear shifts in the wavenumber, between the used bio-sorbent (root and shoot) sample, before and after the bio-sorption of Cr 6+ and Pb 2+ metal ions, which approved the binding process of the metals onto the used bio-sorbent surfaces [25]. As in the Figure, there was a clear shift from wavenumber at 1043 cm −1 in the root sample to 1057 cm −1 in Cr bio-sorbed root, which attributed to lignin's -OCH 3 group stretching vibration appearing in cellulose [26]. there is a broad absorption peak at 3448 cm −1 , which indicates the presence of intermolecular, free O-H groups and bands of carboxylic acids [19].
There is no remarkable shifting of this peak because we didn't make any chemical treatment to the used bio-sorbent. The presence of an intensive peak at 1645 cm −1 might be attributed to the absorption of water molecules linked with cellulose fibers [29]. The peak at 1524 cm −1 in root and shoot samples is due to stretching vibrations of C=C in the aromatic ring of lignin.  There were some peaks in the root sample that disappeared after the binding mechanism with Cr metal ions such as at 3805 and 3906 cm −1 due to the adsorption of Cr onto the (N-H) group of the used bio-sorbent. While, for root samples bio-sorbed with Pb 2+ metal ions, there was also shifting from wavenumber of 1056 cm −1 in the root sample to 1043 cm −1 in Pb bio-sorbed root, 1654 cm −1 in root sample to 1634 cm −1 in (Pb bio-sorbed root), and 3425 cm −1 to 3448 cm −1 , this might be because of Pb binding with C-O, C=O, and O-H groups of the root adsorbent material. Moreover, some peaks were absent from the root sample, including 1232, 1325, and 1722 cm −1 due to the adsorption mechanism of Pb onto C-C, C-N, and C=O groups of the adsorbent. The presence of peak at 1378 cm −1 attributed to C-H vibrations in cellulose and at 2925 cm −1 attributed to C-H bond of CH 3 and CH 2 in hemicellulose, cellulose, and lignin [27]. Additionally, the presence of (-COOH), and (-OH) functional groups, at the used bio-sorbents surfaces, can provide metal ions complexation sites. Moreover, the functional groups of nitrogen and oxygen atoms form a coordinate bond with metal cations, and that's the reason behind the high affinity to bio-sorb Pb 2+ metal ions more than Cr 6+ [28].
As for the shoot IR spectra, there was shifting from wavenumber 1440, in the shoot sample, to 1423 cm −1 in the Cr bio-sorbed shoot, due to the adsorption of Cr on C-O-H of the shoot surface. As for the adsorption of Pb ions on the shoot surface, there was a clear shift from 1379 cm −1 to 1440 cm −1 , and from 3426 cm −1 to 3448 cm −1 because of the binding of Pb metal ions with C-O-H and O-H groups of the adsorbent surface. In all samples, there is a broad absorption peak at 3448 cm −1 , which indicates the presence of intermolecular, free O-H groups and bands of carboxylic acids [19].
There is no remarkable shifting of this peak because we didn't make any chemical treatment to the used bio-sorbent. The presence of an intensive peak at 1645 cm −1 might be attributed to the absorption of water molecules linked with cellulose fibers [29]. The peak at 1524 cm −1 in root and shoot samples is due to stretching vibrations of C=C in the aromatic ring of lignin.

Effect of Bio-Sorption Contact Time
The contact time between the bio-sorbent and bio-sorbate is a critical parameter affecting the bio-sorption process kinetics [30]. The equilibrium time for the bio-sorption of Pb 2+ , and Cr 6+ metal ions onto the used bio-sorbent root and shoot was obtained through studying their time-dependent behavior in a time range of 10-300 min with keeping other parameters constant as in Figure 3a, which prevail that the bio-sorption rate was fast in the first period of contacting between the bio-sorbent and bio-sorbate, then it slowed down till near stability. Equilibria of Pb 2+ metal ions onto the used bio-sorbent root and shoot were 120, and 60 min, respectively, while they were 120 and 180 for Cr 6+ ions bio-sorbed onto root and shoot. The contact time between the bio-sorbent and bio-sorbate is a critical parameter affecting the bio-sorption process kinetics [30]. The equilibrium time for the bio-sorption of Pb 2+ , and Cr 6+ metal ions onto the used bio-sorbent root and shoot was obtained through studying their time-dependent behavior in a time range of 10-300 min with keeping other parameters constant as in Figure 3a, which prevail that the bio-sorption rate was fast in the first period of contacting between the bio-sorbent and bio-sorbate, then it slowed down till near stability. Equilibria of Pb 2+ metal ions onto the used bio-sorbent root and shoot were 120, and 60 min, respectively, while they were 120 and 180 for Cr 6+ ions biosorbed onto root and shoot.

Effect of Solution pH
Solution pH plays a vital role in changing the availability of metal ions in this solution besides, the functional groups and chemical status of the bio-sorbent, which are responsible for the bio-sorption process [31]. Variation of solution pH was studied in the range of

Effect of Solution pH
Solution pH plays a vital role in changing the availability of metal ions in this solution besides, the functional groups and chemical status of the bio-sorbent, which are responsible for the bio-sorption process [31]. Variation of solution pH was studied in the range of 2.0 up to 10.0 for Pb 2+ and Cr 6+ metal ions bio-sorption onto the used bio-sorbent. The removal efficiencies and bio-sorption capacity increase with increasing the pH in the acidic medium until it reached neutral and without a significant increase in the bio-sorption capacity, in the case of Pb 2+ ions, while they both decreased in neutral and basic solutions in case of Cr 6+ metal ions, as in Figure 3b, which illustrates that the percentage of removal increased from 21.4 up to 38.19%, from 18.93 to 28.71% for the bio-sorption of Cr 6+ onto the used bio-sorbent shoot and root, respectively, when the solution pH increased from 2 up to 7, and from 20.5 up to 35.35%, 30.98 to 41.77% for the bio-sorption of Pb 2+ ions onto the used bio-sorbent shoot and root, respectively when the solution pH increase from 2 up to 7, while they decreased with the increase in pH in case of Cr 6+ .
The bio-sorption capacity increase with increasing solution pH, as the increase in pH value, increases the negative charge on the used bio-sorbent surface which leads to a decrease in the competition between protons and metal ions. Moreover, at higher pH values (4-7), the used bio-sorbent surface possesses a negative charge which attracts the positively charged Pb 2+ ions by electrostatic attraction. Furthermore, the maximum biosorption capacity of Cr 6+ was in acidic medium and decreased in the neutral and basic medium due to the presence of excessive -OH groups in the alkaline medium hindered Cr 6+ bio-sorption [15,32].
According to the figure, the % of removal of Pb 2+ and Cr 6+ metal ions, by using the bio-sorbent material shoot, was higher than roots due to the affinity of the shoot cells to certain heavy metal ions. Figure 3c,d illustrates the effect of metal ions concentration variation on the biosorption process. The increase in Pb 2+ and Cr 6+ metal ions concentrations lead to a decrease in their removal efficiencies and increment in the bio-sorption capacities. As the percent of removal of Pb 2+ decreased from 89.32 to 41.84%, and from 81.840 to 34.46% when the initial concentration of Pb 2+ increased from 50 up to 700 ppm, while, the bio-sorption capacities increased from 3.722 to 24.407 mg/g, and from 3.410 to 20.103 mg/g when the Pb 2+ concentrations raised from 50 to 700 ppm.

Effect of Initial Metal Ion Concentration
The same trend was also observed with the removal percentage efficiencies and biosorption capacities of Cr 6+ metal ions, onto the used bio-sorbent root and shoot, as the removal percentage decreased from 82.70 to 24.16% and from 91.820 to 13.069% and from 91.820 to 13.069% and from 91.820 to 13.069% (for root and shoot respectively) with the increment of Cr 6+ initial concentration from 50 up to 700 ppm, while the bio-sorption capacities were increased from 10.338 to 70 and from 11.478 up to 45 mg/g. This behavior might be attributed to that, above a certain metal ion concentration, all available active sites became saturated, which leads to a decrease in the removal efficiency, and the number of Pb 2+ , and Cr 6+ metal ions in the liquid phase is larger than the active bio-sorption sites numbers located on the used bio-sorbents surfaces, moreover, the higher absorption rate causes increment in the bio-sorption capacities of the both used metal ions [33,34]. Samra [35], reported similar results, as the bio-sorption capacities of the used bio-sorbent increased with increasing metal ions concentrations because of the increasing metals diffusions rate in the boundary layer.

Effect of Bio-Sorbent Dosage
The effect of biomass amount on the bio-sorption of Cr 6+ and Pb 2+ metal ions was studied by varying the dosage of the used bio-sorbent root and shoot, from 0.2 up to 1.6 g, as illustrated in Figure 3e,f. The removal efficiencies of the selected metal ions increase with the increase in the used bio-sorbent material dosage, while their bio-sorption capacities decrease with the increment doses, as percent of removal increased from 29.062 up to 67.644%, and from 38.622 to 77.645% for the bio-sorption of Cr 6+ onto the used bio-sorbent root and shoot, respectively.
The biomass dosage increased from 0.2 to 1.6 g, from 32.767 to 71.342%, from 42.32 up to 81.343% for the bio-sorption of Pb 2+ ions onto the used bio-sorbent root and shoot respectively with the same dosage used with Cr 6+ ions. This is can be due to the availability of more active sites on the used bio-sorbent surface, which are responsible for the biosorption process, which increases the adhesion forces between metal ions and the bio-sorbent material. However, the bio-sorption capacity decreases with the increase in the used bio-sorbent dose [36].

Equilibrium Modeling
Models of bio-sorption isotherms give up information about bio-sorbates distributions between the solid and liquid phases at the equilibrium state. We fit the obtained experimental equilibrium data of Pb 2+ , and Cr 6+ metal ions onto the used bio-sorbent root and shoot to Langmuir, Freundlich, and Temkin isotherm models [37] to find out the best-fit model, which described the bio-sorption process well. The used bio-sorption isotherms model linear forms are showed in Table 1, their bio-sorption parameters, and their constants, are illustrated in Table 2 and Figure 4. Table 1. Adsorption equilibrium models applied in the present study.

Bio-Sorption Models Equation Parameters
Langmuir C e /q e = 1/q m K + C e /q m C e q e = 1 q m Kl + C e q m q e is the bio-sorbate amount in the bio-sorbent at equilibrium (mg/g), q m is the maximum monolayer coverage capacities (mg/g), K l is the Langmuir constant (L/mg), and C e is the equilibrium concentration (mg/L).

Freundlich
ln q e = ln K F + 1/n f ln c e lnq e = lnK F + 1 n f lnC e q e is the of bio-sorbed ions amount at equilibrium (mg/g); Ce is the bio-sorbate equilibrium ions concentration (mg/L); K F and n f are Freundlich constants related to the bio-sorption capacity and bio-sorption intensity, respectively Temkin q e = B ln KT + B ln C e KT is the Temkin constant refer to equilibrium maximum binding energy and B is the Temkin constant related to bio-sorption heat. The Langmuir model assumes monolayer coverage with a homogeneous surface bio-sorption without transmigration of the bio-sorbate molecules to the inner layers of the used bio-sorbent, and subsequently uniform, energies of bio-sorption on its surfaces. The Freundlich model means a heterogeneous and multi-layer of the bio-sorption process [38]. constant (L/mg), and Ce is the equilibrium concentration (mg/L).

Freundlich
Ln qe = ln kf + 1/nf ln ce e f F e C n K q ln 1 ln ln + = qe is the of bio-sorbed ions amount at equilibrium (mg/g); Ce is the biosorbate equilibrium ions concentration (mg/L); KF and nf are Freundlich constants related to the bio-sorption capacity and bio-sorption intensity, respectively Temkin q e = B ln KT + B ln Ce KT is the Temkin constant refer to equilibrium maximum binding energy and B is the Temkin constant related to bio-sorption heat.   High R 2 (0.975 and 0.944 for the bio-sorption of Cr 6+ onto the used bio-sorbent root and shoot, respectively, and it was equal to 0.988 and 0.992 for the bio-sorption of Pb 2+ onto the used material root and shoot, respectively) values illustrate a good curve fitting to the Langmuir model. Almost in all the fit bio-sorption isotherms models, the bio-sorption capacities of Cr 6+ were lower than Pb 2+ , which might be because of the heavy metals' complexation abilities, related to their functional groups, and solution pH. Nickel and copper can form such complexes, meanwhile, cadmium and lead possess higher biosorption capacities via ion exchange [39]. The obtained q m (mg g −1 ), which represent the maximum monolayer coverage capacities and calculated from the slope of (Figure 4a), were 43.478 and 25.641 mg/g for the bio-sorption of Cr 6+ onto the used bio-sorbent root and shoot, respectively, while they were 80.796 and 65.519 for Pb 2+ bio-sorption onto the used root and shoot bio-sorbent material. Furthermore, Kl represent the bio-sorption energy (L/mg), and their values were obtained from the intercept of (Figure 4a), as they were (0.056 and 0.045 for bio-sorption of Cr 6+ and 0.018, and 0.017 (L/mg) for Pb 2+ bio-sorption onto the used bio-sorbent root and shoot, respectively, which means that the used bio-sorbent material possesses high bio-sorption ability with low bio-sorption energy.
The Temkin isotherm deals with the indirect effects between bio-sorbent and biosorbate interactions on the bio-sorption process. The bio-sorption heat of all layer molecules decreases linearly with coverage due to bio-sorbent, and bio-sorbate reactions [40].
Finally, higher R 2 values for Langmuir than Freundlich for the bio-sorption of Cr 6+ onto the used bio-sorbent material root and shoot, suggesting a monolayer coverage of the bio-sorption process. While, their values were smaller for Langmuir than Freundlich, for the bio-sorption of Pb 2+ onto the used bio-sorbent material root and shoot, suggesting that the chemisorption is not the only the bio-sorption mechanism in this process, both chemisorption and physisorption must be taken into consideration under studied condi-tions [41]. A comparison of the calculated maximum monolayer adsorption capacity for different adsorbent materials and the used material illustrated in Table 3.

Bio-Sorption Kinetic Models
It very important for the bio-sorption process to study the kinetic models, as it points out the uptake rate of the used bio-sorbent material. The bio-sorption kinetics of Pb 2+ and Cr 6+ metal ions onto the used bio-sorbent root and shoot were evaluated using four kinetic models (pseudo-first-order [42], pseudo-second-order, Elovich, and intra-particle Diffusion). The non-linearized equations of these models are tabulated in Table 4, and their bio-sorption Parameters were illustrated in Figure 5 and Table 5.  Table 4. Bio-sorption kinetic models equations.

Bio-Sorption Kinetic Models Equation Parameters
Pseudo-First-Order Ln (q e -q t ) =ln q e -K 1 t q t is the bio-sorbed metal ions amount at time t, q e , is the bio-sorbed metal ions amount at equilibrium (mg/g). k 1 (min −1 ) is the first-order reaction rate constant Pseudo-Second-Order t/q t = (1/K 2 q e 2 ) q t is the bio-sorbed metal ions amount at time t q e , the bio-sorbed metal ions amount at equilibrium (mg/g), k 2 is the second-order reaction rate equilibrium constant (g/mg min).
Elovich q t = à +ß ln t à is the initial sorption rate (mg/g min) and ß is the extent of surface coverage and activation energy for chemisorption (g/mg) Intra-particle Diffusion q t = k id t 1/2 + I kid is the intra-particle diffusion rate constant, and I give prediction about the boundary layer thickness Pseudo-Second-Order t/qt = (1/K2qe 2 ) qt is the bio-sorbed metal ions amount at time t qe, the bio-sorbed metal ions amount at equilibrium (mg/g), k2 is the second-order reaction rate equilibrium constant (g/mg min).
Elovich qt = ὰ +ß ln t ὰ is the initial sorption rate (mg/g min) and ß is the extent of surface coverage and activation energy for chemisorption (g/mg) Intra-particle Diffusion qt = kidt 1/2 + I kid is the intra-particle diffusion rate constant, and I give prediction about the boundary layer thickness Figure 5. First-order plots (a), Second-order plots (b), Elovich plots (c), and Intra-particle diffusion plots (d) for bio-sorption of Cr 6+ , and Pb 2+ onto the used bio-sorbent (L. stolonifera) roots and shoots. , Elovich plots (c), and Intra-particle diffusion plots (d) for bio-sorption of Cr 6+ , and Pb 2+ onto the used bio-sorbent (L. stolonifera) roots and shoots. For the first-kinetic model, the q e calculated values differed from their experimental ones, which means that this model was not good enough to describe this bio-sorption process. The pseudo-second order kinetic model R 2 values obtained from the linear relationship between t/qt versus t were 0.999, 0.991, and 0.998 for the bio-sorption of Pb 2+ and Cr 6+ metal ions onto the used bio-sorbent material root and shoot, respectively, meaning that this model describes the bio-sorption process well and, subsequently, the chemisorption rate-limiting step is dominant in this process with sharing electrons between bio-sorbent and bio-sorbate [40,49].
The calculated q e (16.944 and 16.313 mg/g for the bio-sorption of Cr 6+ onto the used bio-sorbent root and shoot, while they were 16.807 and 15.625 mg/g for Pb 2+ bio-sorption onto the used material) values were compared with their experimental values (14.784 and 14.523 for Cr 6+ sorption onto bio-sorbent root and shoot and 15.838 and 16.625 mg/g for Pb 2+ sorption onto bio-sorbent root and shoot) and we found that they were so close, which shows that the gained data fit the second-order rate model. K represents the reaction rate equilibrium constant (g/mg min) of the second-order and it can be calculated from (Figure 5b) intercept. The obtained K values were 0.038 and 0.044 for the bio-sorption of Cr 6+ root and shoot, while they were 0.081 and 0.247 for Pb 2+ bio-sorption onto the used bio-material root and shoot.
The obtained K values of the second-order kinetic model indicate a fast bio-sorption rate of Cr 6+ , and Pb 2+ metal ions onto the used bio-sorbent (L. stolonifera) root and shoot.
Moreover, according to the above-mentioned results, which cleared the chemisorption attitude of the bio-sorption process, the simple Elovich model is used, which describes the chemisorption kinetics [50]. According to Table 4, it was pretty clear that the experimental data fit well with the Elovich equation with high R 2 values, which confirms the abovementioned conclusion about the chemisorption nature of the bio-sorption process utilizing the used bio-sorbent material.
Finally, we fit the obtained data with the intra-particle diffusion model. There is a multi-stage process that controls the bio-sorption of metal ions from liquid to solid phase: in the first step, metal ions transport from the liquid to the solid phase surface (bulk diffusion), followed by diffusion of the metal ions through the boundary layer of the used bio-sorbate surface (film diffusion), and finally, their transmigration from the solid bio-sorbate surface to its inner layers (intra-particle diffusion). From the intra-particle diffusion equation, the intercept represents the boundary layer thickness, so, the increment of the intercept value leads to increasing the boundary layer effect. If the linear relationship between q t against t 1/2 , results in a line that passes through the origin, in this case, the intra-particle diffusion is the controlling step [51]. In this study, no line passed through the origin for both metal ions' bio-sorption, so this shifting of lines might be due to the mass transfer rates in the first and last diffusion stages not being stable [52].

Conclusions
Phytoremediation technologies are considered an effective, eco-friendly, and cheap way to clean up water contaminated with hazardous pollutants, such as the heavy metals (Cr 6+ , and Pb 2+ ). Many factors affect the bio-sorption of metal ions onto the bio-sorbent L. stolonifera, such as metal ion content, medium pH-value, biomass dosage, and contact time between the bio-sorbent and bio-sorbate and were evaluated through a series of benchscale experiments which revealed that the maximum removal uptake percentage of Pb 2+ (81.34%) was achieved with the used bio-sorbent shoot, while it was 77.64% for Cr 6+ onto the used bio-sorbent shoot, with a maximum bio-sorption capacity of 80.79 mg/g at room temperature, according to the Langmuir isotherm. The Langmuir isotherm model was the best fit model among the three tested models, which suggested monolayer coverage of the bio-sorption of Cr 6+ and Pb 2+ metal ions onto the used bio-sorbent with a maximum biosorption capacity of 43.5 and 80.79 mg/g, respectively, at room temperature. The kinetics of the Cr 6+ and P 2+ bio-sorption rate were best explained by the pseudo-second-order kinetic equation and the simple Elovich and intraparticle diffusion models as the bio-sorption kinetics can be explained by many independent processes. According to the gained data, the % of removal of Pb 2+ and Cr 6+ metal ions by using the bio-sorbent material shoot was higher than roots, due to the affinity of the shoot cells to certain heavy metal ions, moreover, its affinity to adsorb Pb 2+ is higher than Cr 6+ due to the same reason.