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Analysis of FTIRUnderstanding the functional groups involved in the biosorption of toxic metals is essential to elucidate the mechanism of this process. Groups such as carboxylic, hydroxyl and amine are among the main responsible for the absorption of metals by cellulose34 In the Fig. 1, show the FTIR of ECx.Figure 1FTIR of ECx before and after of adsorptions of Cr (VI).Full size imageAccording to13 the bandwidth at 3000–3600 cm−1 corresponds to bonds related to the -OH group. These hydrogen bonds are useful tools for cation exchange with heavy metals. This evidenced in the color spectrum (dark green) that represents an ECx sample with attached Cr (VI) after the adsorption process, where the stretching of the (OH) group lost part of its extension. The change observed in the peak from 3420 cm−1 of ECx to 3440 cm−1 in ECx-Cr indicates that these groups have a participation in the bond with the Cr (VI) ions. The variation of bands in the peak of the amines after adsorption confirms the participation of these groups in the adsorption process. This result confirmed by the ion exchange evaluation experiment discussed later in section SEM–EDX.The change in peak 3280, after Cr (VI) adsorption, indicates that EC removed Cr (VI) based on interaction with (OH), part of (OH) lost due to formation of vibrations of ascension O–Cr. Also, after Cr (VI) biosorption on ECx, the peak of the EC-S group is shifted to 590. This can be explained by surface complexation or ion exchange35.In general, comparable results reported in the literature for cellulose in the absorption of other toxic metals, as for other cellulose-derived biosorbentes in the removal of Cr (VI) ions36.One way to corroborate the information presented in the FTIR measurements is through SEM images since with these images it is possible to observe the distribution of the reagents in the ECx biomass treatment and subsequently the Cr (VI) adsorption process.SEM–EDXFigure 2 shows the micrographs obtained for the biomass before (a) the adsorption of Cr (VI), in addition to showing the distribution of the different biomass chemical modifications in (b) and in (c) it shows the distribution of chromium around all biomasses.Figure 2Biomass before (a) Cr (VI) adsorption, biomass chemical modifications in (b) and shows the distribution of chromium around the whole biomass (c).Full size imageFrom Fig. 2a, it can see that the biomass has a very irregular rough surface, with macropores and cracks. Many of these irregularities may associated with damage caused by the delignification process of E. crassipes cellulose with NaOH14. In Fig. 2b it is possible to visualize the components of the cellulose xanthogenate, coming from sodium, distributed throughout the biomass, a result like that reported in other studies35 The colored dots represent the elements in the samples, green dots represent carbon, red dots represent oxygen, and yellow dots represent the places where sodium lodged.Table 2 shows that, in addition to carbon and oxygen, the element with the greatest presence in the composition of pure waste is sodium and sulfur from the xanthogenate cellulose transformation process. Table 2 shows the physicochemical characterization of the ECx sample, through EDS.Table 2 Features of sample of ECx.Full size tableCellulose xanthogenate, is one of the cellulose transformations to improve the adsorption performance of heavy metals, this compound produced from dry and ground biomass, mixing with sodium hydroxide (NaOH) to remove lignin, creating alkaline biomass, then disulfide (CS2) added13,14. (CS2) reacts with hydratable hydroxycellulose, forming C-SNa complexes; these are responsible for the cation exchange with heavy metals. Metal ions enter the interior of E. crassipes with (CS2), exchanging with Na36,37.The SEM morphology of ECx and coupled with the high content of sulfides (7.3%) determined by the spectrum in Table 2, it further confirms that xanthate groups are successfully grafted onto the biomass of E. crassipes, and Fig. 3 represents this information based on13,36,37,38.Figure 3Prototype.Full size imageExchange biochemistry is usually identified as the main mechanism for the adsorption of metals in cellulose and its derivatives35 and through the evaluation of EDS this process could verify. Similar observations were made by36 where the adhesion of Cr (VI) in this biomass was observed. Also, in xanthogenate cellulose processes, the adhesion of Pb (II) to this type of biomass verified, concluding that this cellulose is important in the removal of heavy metals from water13.The SEM morphology of ECx with Cr (VI) coupled with the high content of sulfides determined by the spectrum in Table 3, was the determinate for the chemisorption’s of Cr (VI). The mechanism of Cr (VI) sorption by cellulose xanthate is:$$left[ {{4}left( {{text{C}}_{{6}} {text{H}}_{{{12}}} {text{O}}_{{6}} } right)} right]*{text{2CS}}_{{2}} {text{Na }} + {text{ Cr}}_{{2}} {text{O}}_{7}^{ – 2} to left{ {left[ {{4}left( {{text{C}}_{{6}} {text{H}}_{{5}} {text{O}}_{{6}} } right)} right] , *{text{2CS}}_{{2}} } right}*{mathbf{Cr}}_{{mathbf{2}}} + {text{Na}} + {text{7H}}_{{2}} {text{O}}$$where [4(C6H12O6)] *2CS2Na represents the xanthogenate biomass, and Cr2O7–2 represents the Cr (VI), that 4 parts of glucose xanthate react with the dichromate. In the Tables 3 and 4, the relationship between cellulose xanthogenate and Cr (VI), with related weights of 10.4 for Cr (VI).Table 3 Features of sample of ECx with Cr (VI).Full size tableTable 4 Researcher of process of the desorption.Full size tableMass balance in treatmentAdsorption is the phenomenon through which the removal of Cr (VI) achieved in the treatment systems; this quantified by means of the general balance equation of the treatment system as shown in Fig. 3.Adsorption is the phenomenon through which the removal of Cr (VI) achieved in treatment systems, this quantified by mass balance. Equation (1) shows the general balance of matter in the treatment system, together with the accumulation, inputs, and outputs of the system and the chemical process of adsorption.$${text{Acumulation }}upvarepsilon *frac{{partial {text{Cr}}left( {{text{VI}}} right)}}{{partial {text{t}}}} = {text{In}} frac{{partial {text{Cr}}left( {{text{VI}}} right)_{0} }}{{partial {text{t}}}} – {text{Out}}frac{{partial {text{Cr}}left( {{text{VI}}} right)}}{{partial {text{t}}}} – {text{Adsortion}},{rho b}frac{{partial {text{q}}}}{{partial {text{t}}}}$$
(1)
Accumulation represents by Eq. (1), where ∂C(VI) is the contaminant input to the treatment system, (ε) is the porosity of the bed, which calculated as the ratio between the density of the bed of treatment and the density of the microparticle of this biomass. This parameter must be above 0.548 achieved using particle diameters less than 0.212 mm, which favors contact between the contaminant and the particle49. The contaminant input to the treatment system represents by the design speed and the amount of contaminant that the system could treat. The output in the treatment system represents by the same input speed and the amount of contaminant that comes out. With these equations, the general material balance will be complete, summarized in Eq. (2), where it can see that the accumulation is equal to the input to the system, minus the output, and minus the adsorption.$$upvarepsilon *frac{{partial {text{Cr}}left( {{text{VI}}} right)}}{{partial {text{t}}}} = frac{{partial {text{Cr}} left( {{text{VI}}} right)}}{{partial {text{t}}}} – frac{{partial {text{Cr}} left( {{text{VI}}} right)}}{{partial {text{t}}}} – frac{{text{M}}}{{text{V}}}*frac{{partial {text{q}}}}{{partial {text{t}}}}$$
(2)
where V = System volume (ml), ε = Porosity, Co = Initial concentration of Cr (VI) (mg/ml), C = Final concentration Cr (VI) in the treated solution (mg/ml), Q = design flow (ml/min), Tb = Breaking time (Min), M = amount of biomass used (g), q = Adsorption capacity of the biomass used (mg/g).$${text{V}}*upvarepsilon *{text{Co}} = {text{Q}}*{text{Tb}}*{text{Co}} – {text{Q}}*{text{Tb}}*{text{C}} – {text{M}}*{text{q}}$$
(3)
Depending on the most important parameters when building a treatment system, Eq. (3) could use to model and validate the best form of treatment, for example, the necessary amount of biomass to use to treat a certain amount of contaminant, in the present investigation it used to establish the adsorption capacity in these initial treatment conditions. The remaining Eq. (4) determines the adsorption capacity.$${text{q}} = frac{{{text{QTbCo}}}}{{text{M}}} – frac{{{text{QTbCf}}}}{{text{M}}} – frac{{upvarepsilon {text{VCo}}}}{{text{M}}}$$
(4)
Adsorption capacity is generally taken through Eq. (5) for both batch and continuous experiments20,21But unlike Eqs. (5), (4) takes into account design variables such as flow rate (Q), rupture time (Tb), particle bed porosity ε, and vessel design volume (v).$${text{q}} = frac{{{text{v}}left( {{text{Co}} – {text{C}}} right)}}{{text{m }}}$$
(5)
where m: Mass used in the treatment, V: Volume, Co: Initial concentration, C: Final Concentration, Q: adsorption capacity.However, unlike Eqs. (5),  (4) considers the design variables such as flow rate (Q), rupture time (Tb), particle bed porosity ε and vessel design volume (v).When a desorption-elution process is involved for the reuse of biomass, Eq. (4) would be:$${text{q}}_{{text{T}}} = mathop sum limits_{j = 1}^{n} left[ {frac{{{text{QTbjCo}}}}{{text{M}}} – frac{{{text{QTbjCj}}}}{{text{M}}} – frac{{upvarepsilon {text{VCo}}}}{{text{M}}}} right]$$
(6)
where Q = design flow (ml/min), Tbj = Break time of use number j (Min), Co = Initial concentration of Cr (VI) (mg/ml), C = Final concentration Cr (VI) in the treated solution (mg/ml), V = System volume (ml), ε = Porosity, M = amount of biomass used (g), q_T = Total adsorption capacity of the biomass used (mg/g).This model (6) is design to determine the adsorption capacity when different elution processes have conducted, it will used to determine the new adsorption capacity and is one of the contributions of the present investigation.Result process of adsorptionsIn Fig. 4 shows the Cr (VI) adsorption process of the system.Figure 4Percentages of Cr (VI) removal the system for ECx.Full size imageVarious researchers have extensively studied the influence of factors such as bed height, flow rate and metal inlet concentration on rupture (Tb) curves. For example, the influence and similarity of the initial contaminant concentrations should be reflected as in the case of a tannery, with initial concentrations of 600 mg/l. Figure 4 shows the progress curves obtained for the study of Cr (VI) removal by the studied biomasses, reflecting the percentage of Cr (VI) removal in contrast to the treated volume, which is a very important parameter to time to scale the process.Regarding the effect of the input concentration, it can see in Fig. 5 that the breakpoint had a better performance in all the initial concentrations in the ECx biomass. comparing it with the EC-Na biomass (see Fig. 5), always obtaining breakpoints with more treated volume.Figure 5Percentages of Cr (VI) removal the system for EC-Na.Full size imageThe difference between the rupture curves between ECx and EC-Na indicates that the cellulose xanthate modification scheme should completed, although it can also elucidate that the EC-Na biomass has high yields compared to other biomass studied. for example, in Ref.34 investigate the biomass of E. crassipes without modifying, having removals below this alkaline cellulose.Adsorption capacitiesThrough Eq. (3), the adsorption capacity of ECx, using the initial concentration of 600 mg/l, since it was the maximum concentration used.The break point was around 1200 ml according to Fig. 6 and together with the flow rate of 15 ml/min; the break time obtained in 80 min.$${text{q}} = frac{{80{*}15{*}0.6}}{40} – frac{{80{*}15{*}0.04}}{40} – frac{{0.66{*}78{*}0.6}}{40}$$q: Adsorption capacity, Co: 0.6 mg/ml, C: 0.06 mg/ml, M: 40 g, Tb: rupture time 80 min, Q: 15 Flow rate ml/min, ε: 0.6649, V: Occupied volume: 70 ml.Figure 6Adsorption capacities in the different adsorption processes in the biomass ECx.Full size imageA result of 16 mg/g obtained in this continuous study for the biomass ECx. With this same equation it gives the capacity of the biomass EC-Na, with 11 mg/g.Desorption-Elution and reuseThrough Eq. (6), the sum of the Cr (VI) adsorption capacities established, after different biomass reuses due to EDTA elution. In the second treatment process, it yielded the following results under concentrations of 6 g/l of EDTA.$${text{q}}left( {text{T}} right) = frac{{60{*}15{*}0.6}}{40} – frac{{50{*}15{*}0.06}}{40} – frac{{0.66{*}68{*}0.6}}{40}$$Co: 0.6 mg/ml, C: 0.06 mg/ml, M: 45 g Biomass eluted with EDTA, Tb: rupture time: 60 min, Q: 15 Flow ml/min, ε: 0.6649, V: Occupied volume: 68 ml, q: 10 mg/g.Five Cr (VI) adsorption cycles performed using ECx and EC-Na cellulose in a continuous system to evaluate the regeneration and reuse potential. Between each biosorption cycle, a desorption cycle performed using three different concentrations of EDTA eluent.According to Figs. 6 and 7, although the adsorption capacity gradually decreases from the first adsorption process, it could consider that it is a satisfactory biomass recycling process and a design parameter for later stages of this treatment system.Figure 7Adsorption capacities in the different adsorption processes in the biomass EC-Na.Full size imageIn the experiments with concentrations of 6 g/l, five reuse processes obtained, obtaining a final sum of 52 mg/g. In concentrations of 3 g/l of EDTA, final capacities of 51 mg/g obtained lower than concentrations of 6 g/l but with half of this reagent. With concentrations of 1 g/l, final capacities of 33 mg/g obtained.The desorption processes of the EC-Na biomass with initial capacities of 11 mg/g were also evaluated and through desorption processes with EDTA of 3 g/l this biomass recycled on 5 occasions, reaching 32 mg/l in capacities of adsorption and like the EC-Na biomass, the ideal concentration in the process for desorption processes is 3 g/l, due to the considerable increase in reuse processes and low concentration compared to 6 g/l, which, although higher, does not this value is significant in the absorption capacity.Through Eq. (6) and with different bibliographic references, representative data obtained to feed this equation, determining the capacities of each of these biomasses together with the new capacities determining the desorption power of the different eluents shown and summarized in Table 4.For the EDTA eluent and with Eq. (6), satisfactory results evidenced by removing Al (II), reaching almost 150% of its adsorption capacity, corroborating what presented in the present investigation, also the EDTA reagent obtained interesting yields to recycle the cassava biomass increasing up to 40 mg/g. In Ref.39 used the biomass of Phanera vahlii to remove Cr (VI) obtaining results of 30 mg/g and with NaOH they reached capacities in the reuse process of this biomass up to 62 mg/g, reaching almost double of its total capacity41, also used NaOH for desorption processes with green synthesized nanocrystalline chlorapatite biomass, achieving results of 75% more. The eluent HCl is also a good chemical agent to use in desorption processes since it reached more than 100% in the reuse of biochar alginate for Cr (VI) but not so significant with biomass A. barbadensis Miller to remove Ni (II) and in40 significant results were also obtained to remove Pb (II) with pine cone Shell biomass. With the chemical agent HNO3, interesting contaminant recycling processes obtained, since more than 100% of the adsorption capacity of the biomasses used in this process used1,45.Mathematical models of adsorptionIn general, the models presented R2 greater than 0.95 for the adjustment of all the advance curves, which indicates a good adherence to the data, the model that best describes the behavior of the ECx system was the phenomenological model Thomas, which presented all the R2 values above 0.99.This model could use for the extension of the Cr (VI) ion biosorption system using cellulose xanthogenate, in the literature it is possible to observe that this model often tends to better adapt to the experimental data of the adsorption systems that use cellulose for the absorption of toxic metals28,30,31.With qt values remarkably close to the experimental values of Eq. (4) designed and presented in this investigation, indicating the validity of this equation where it reflects the maximum capacity obtained. Table 5 shows the adsorption constant of the Thomas model (Kt), which corresponds to the adsorption rate of Cr (VI) in the biomass49 This value was 0.048 (ml/mg*min) reflecting the speed with which Cr (VI) is chemisorbed in the biomass of ECx, in the EC-Na cellulose there was a Thomas model speed of 0.039 (ml/ mg*min) evidencing a lower adsorption rate than ECx. In the adsorption of Cr (VI) by rice biomass, the Thomas constant is 0.1 (ml/mg*min)47,50 also in the adsorption of Cr (VI) by biomass. Nanocrystalline chlorapatite biomass obtained at the Thomas constant 0.013 (ml/mg*min)49.Table 5 Summary of the experiments obtained with material ECx.Full size tableIn the Table 6, it presents summary of the experiments obtained with material EC-Na.Table 6 Summary of the experiments obtained with material EC-Na.Full size tableThe Cr (VI) adsorption process in the EC-Na biomass represented through the Bohart equation, since the sorption rate is proportional to the biomass capacity, obtaining an adsorption rate of 0.85(ml/mg*min). Having an alkalized biomass represents this model due to the homogeneity of this adsorbent.Mathematical models in desorption processesThe continuous desorption process with its fit to the Thomas model for biomass ECx always shows the fit of this model with significance, because this type of model fits representatively to desorption processes with good performance32,51 It can also verify that with values of qt it is close to the experimental values of Eq. (6) designed and presented in this research, indicating the validity of this equation again, where it reflects the maximum capacity obtained.In the Table 7. Show Summary of the experiments obtained with material ECx in process of desorption’s.Table 7 Summary of the experiments obtained with material ECx in process of desorption’s.Full size tableIn the Table 8 the EC-Na biomass had a different behavior and in its second and third cycle it adjusted to the Yoon model and later to the Bohart model.Table 8 Summary of the experiments obtained with material EC-Na in process of desorption’s.Full size tableThis behavior is due to the alkalinization of the biomass and this process makes the biomass a little more unstable. The values of qt, although a resemblance evidenced, were not so representative due to the little adjustment that there was with respect to the Thomas model. More