Batch and continuous adsorption of Cu(II) and Zn(II) ions from aqueous solution on bi-functionalized sugarcane-based biosorbent

Abstract

A new one-pot synthesis method optimized by a 2³ experimental design was developed to prepare a biosorbent, sugarcane bagasse cellulose succinate pyromellitate (SBSPy), for the removal of Cu(II) and Zn(II) from single-component aqueous solutions, in batch and continuous modes. The bi-functionalization of the biosorbent with ligands of different chemical structures increased its selectivity, improving its performance for removing pollutants from contaminated water. The succinate moiety favored Cu(II) adsorption, while the pyromellitate moiety favored Zn(II) adsorption. Sugarcane bagasse (SB) and SBSPy were characterized using several techniques. Analysis by ¹³C Multi-CP SS NMR and FTIR revealed the best order of addition of each anhydride that maximized the chemical modification of SB. The maximum adsorption capacities of SBSPy for Cu(II) and Zn(II), in batch mode, were 1.19 and 0.95 mmol g^-1, respectively. Homogeneous surface diffusion, intraparticle diffusion, and Boyd models were used to determine the steps involved in the adsorption process. Isothermal titration calorimetry was used to assess changes in enthalpy of adsorption as a function of SBSPy surface coverage. Fixed-bed column adsorption of Cu(II) and Zn(II) was performed in three cycles, showing that SBSPy has potential to be used in water treatment. Breakthrough curves were well fitted by the Thomas and Bohart-Adams models.

Introduction

Water shortages have caused great concern in several countries worldwide. At the same time, water quality has worsened due to the inappropriate discharges of effluents into soils and water bodies, over the years, by industries such as ferrous and non-ferrous metal mining, metal plating, and others (Li et al. 2019). Contamination of soils, groundwater, and surface water bodies with industrial effluents containing toxic metals is a critical environmental problem, since it causes severe adverse effects in ecosystems (Kumar et al. 2019, Salomons et al. 1995, Tang et al. 2019). Although copper and zinc are among the most common potentially toxic metals contained in industrial effluents, they are also essential trace elements for humans and animals. Acute exposure to Cu(II) and Zn(II) can contribute to adverse health issues such as heart and brain diseases, high blood pressure, destruction of red blood cells, and infantilism (Araya et al. 2007, Członkowska et al. 2018, Lu et al. 2005, Taylor et al. 2020).

Biosorption is a promising technique for the removal of toxic metals from effluents, especially because biosorbents can be produced from various agroindustrial wastes. Biosorption can offer flexibility in the operation of water and wastewater treatment plants, allowing the reuse or disposal of treated water, recovery of valuable metal ions, and regeneration of the biosorbent. The ability to regenerate the biosorbent is crucial for the economic viability of water and wastewater treatment plants operating with biosorption as a polishing step (O’Connell et al. 2008, Upadhyay et al. 2021).

The chemical modification of a lignocellulosic biomass, such as sugarcane bagasse (SB) (Harripersadth et al. 2020, Homagai et al. 2010, Júnior et al. 2009, Ramos et al. 2015), to produce a biosorbent able to remove toxic metals from water and wastewater is an attractive way to add value to a byproduct from agroindustry. The bi-functionalization of the biosorbent using two organic ligands with different physicochemical properties (such as acidity constants) can increase the overall performance of the bioadsorbent in a water or wastewater treatment plant, enabling adsorption in a wider pH range, improved capacity for regeneration, and higher selectivity for the removal of toxic metals. The selectivity of the bioadsorbent can be controlled by introducing different proportions of two organic ligands in its structure.

Therefore, the aim of this study was to synthesize a mixed ester of sugarcane bagasse cellulose, using succinic and pyromellitic anhydrides, according to a new synthesis method employing a one-pot reaction. The evidence of chemical modification was provided by elemental C, H, and N analysis, thermogravimetric analysis (TGA), X-ray diffraction (XRD), and Fourier transform infrared (FTIR) spectroscopy. The use of ¹³C multiple cross-polarization solid-state nuclear magnetic resonance (¹³C Multi-CP SS NMR) enabled quantification of the number of succinyl (S) and pyromellityl (Py) units introduced into the SB structure. The performance of the synthesized biosorbent was evaluated using the adsorption of Cu(II) and Zn(II) ions from single-component spiked aqueous solutions, in batch and continuous (fixed-bed column) modes. To this end, a 2³ experimental design was used to investigate the effects of the reaction parameters temperature (T), mole fraction of succinic anhydride (χ_SA), and reaction time (t) with each carboxylic acid anhydride, on the capacity for adsorption of Cu(II) and Zn(II). The ability to regenerate and reuse the biosorbent in batch and continuous processes was also evaluated. The thermodynamics of adsorption was investigated, considering the changes in standard free energy, enthalpy, and entropy, and their individual contributions to the adsorption process. The adsorption kinetics was investigated using the homogeneous surface diffusion model (HSDM).

Materials and methods

Materials

Pyromellitic dianhydride (PyA, ≥ 97.0%, MW = 218.12 g mol^-1) and succinic anhydride (SA, MW = 100.07 g mol^-1) were purchased from Sigma-Aldrich. ZnSO₄·7H₂O, CuSO₄·5H₂O, HNO₃ (65 wt.% in water), and NaCl were purchased from Synth (Brazil). The other materials and chemicals used were the same as reported previously (Elias et al. 2019, Almeida et al. 2019). Raw SB (45.5 ± 0.3% cellulose, 30.6 ± 0.5% hemicelluloses, and 23.8 ± 0.8% lignin) (Elias et al. 2019) was kindly donated by the Jatiboca sugar and ethanol mill (Urucânia, Minas Gerais, Brazil).

Preliminary tests for chemical modification of raw SB with SA and PyA

The chemical modification of raw SB (32 mesh, 0.500 mm) with SA and PyA was performed using a one-pot reaction method. Preliminary synthesis tests were carried out to evaluate the reactivity of the two anhydrides in the presence of each other, as well as to determine the best order of addition of each anhydride into the reaction medium. To this end, SA and PyA were added separately to the reaction medium, with the former carboxylic acid anhydride added at the beginning of the reaction and the latter added during the course of the reaction, and vice-versa.

Raw SB (1.000 g), SA (χ_SA = 0.5) or PyA (χ_PyA = 0.5), anhydrous pyridine (Py, 7.5 mL), and anhydrous N,N-dimethylacetamide (DMA, 7.5 mL) were added to a 50-mL double-neck round-bottom flask fitted with a reflux condenser, containing a drying tube filled with anhydrous CaCl₂ powder, and a solids addition funnel closed with a rubber folding-skirt stopper. The flask was immersed in a canola oil bath (100 °C) placed on a heating plate (Model PC-420D, Corning^®) and was stirred at 300 rpm for 3 h, followed by addition of SA (χ_SA = 0.5) or PyA (χ_PyA = 0.5). A ratio of carboxylic acid anhydrides (SA plus PyA) to raw SB of 4.0 g g^-1 was used. After a further 3 h, the reaction was completed. The material synthesized using the addition of SA first was denoted SBSPy, while the material synthesized with the addition of PyA first was denoted SBPyS.

After cooling the flask to room temperature, the mixture was poured into a glass Büchner funnel (150 mL, porosity 1) and the solid (SBSPy or SBPyS) was rinsed, under reduced pressure, with ethyl alcohol (95%, 50 mL), distilled water (100 mL), aqueous NaOH solution (0.01 mol L^-1, 100 mL), distilled water (100 mL), aqueous HCl solution (0.01 mol L^-1, 100 mL), distilled water (100 mL), ethyl alcohol (99.8%, 50 mL), and 2-propanone (50 mL). The SBSPy or SBPyS was dried at 85 °C for 1.5 h in an oven (Model Orion-515, Fanem).

Evaluation of the synthesis of SBSPy using a 2 ³ experimental design

The best synthesis condition for SBSPy was determined using a 2³ experimental design, with T, t_SA, and χ_SA as independent variables (IVs), and the equilibrium adsorption capacities for Cu(II) (q_e,Cu) and Zn(II) (q_e,Zn) as dependent variables (DVs). The statistical analyses were performed with a confidence level of 95%, using the 2-way interaction model and residual sum of squares (RSS) to estimate the standard errors. The processing of the experimental data was performed using Statistica^® v. 12.0 software (StatSoft Inc., USA). For determination of the best SBSPy synthesis condition, SA was added before PyA, based on the results of the preliminary synthesis experiments (“Preliminary tests for chemical modification of raw SB with SA and PyA” section). The other synthesis procedures used were those described in the “Preliminary tests for chemical modification of raw SB with SA and PyA” section.

The desirability tool of the Statistica^® software was used to predict the best synthesis condition that maximized the values of both q_e,Cu and q_e,Zn. In this procedure, the values of the responses q_e,Cu and q_e,Zn were set to 1.0. Scores of 0.0 and 1.0 obtained using the desirability tool indicate undesirable and desirable values, respectively, for the responses under optimization.

Characterization of raw SB and SBSPy

Before characterization analyses of raw SB and SBSPy, the materials were rinsed under reduced pressure with 2-propanone in a glass Büchner funnel (150 mL, porosity 1), dried in an oven at 85 °C for 1 h and cooled in a desiccator. The value of the total number of carboxylic acid functions (n_T,COOH) was determined for both materials, using the method described by Teodoro et al. (2016). The methods used to characterize raw SB and SBSPy by FTIR, point of zero charge (pH_PZC), and elemental analysis of C, H, and N were the same as described by Pereira et al. (2020). The characterizations of the materials by TGA, XRD, specific surface area (Brunauer-Emmett-Teller (BET) method), and pore size distribution (Barrett-Joyner-Halenda (BJH) method) measurements were as described by Teodoro et al. (2016).

¹³ C Multiple cross-polarization solid-state nuclear magnetic resonance ( ¹³ C Multi-CP SS NMR) spectroscopy

Estimation of the numbers of succinyl (S) and pyromellityl (Py) units introduced into the SBSPy and SBPyS structures was performed using ¹³C Multi-CP SS NMR spectroscopy. NMR spectra of raw SB, SBSPy, and SBPyS were acquired with a Bruker spectrometer (Model Avance 400) equipped with a 4-mm magic angle spinning (MAS) double-resonance probe, operating at frequencies of 100.5 MHz (¹³C) and 400.0 MHz (¹H). Further information about other procedures used and the analysis conditions can be found in the studies of Elias et al. (2019) and Almeida et al. (2019).

The estimation of the numbers of succinyl and pyromellityl units introduced into the SB structure was performed by normalizing the NMR spectra of raw SB and SBSPy or SBPyS using the signal areas corresponding to the anomeric carbon atom (C-1) of the cellulose. The spectral areas corresponding to regions A (24–40 ppm) and B (120–140 ppm) were then calculated for the raw SB, SBSPy, and SBPyS spectra. Signals related to the methylene carbons of succinyl units were expected to appear in region A, while those related to aromatic carbons of pyromellityl units were expected to appear in region B, together with signals for some of the aromatic carbons of lignin. In order to obtain the spectral area corresponding to pyromellityl in region B of the SBSPy or SBPyS spectrum, without considering the lignin contribution, the area calculated for the SBSPy or SBPyS spectrum was subtracted from the corresponding area for the raw SB spectrum. With this normalization and subtraction procedure, the spectral areas obtained from the regions A and B (subtracted from the area of the raw SB spectrum) became proportional to the number of carbon atoms of succinyl and pyromellityl units, respectively, introduced into SBSPy or SBPyS, relative to the number of C-1 carbon atoms per cellobiose unit (two β-D-anhydroglucose units (AGU) linked by a β(1→4) glycosidic bond). Further procedures used for calculation of the numbers of succinyl and pyromellityl units introduced into the SB structure were those reported by Elias et al. (2019) and Almeida et al. (2019).

NMR relaxometry

The samples of raw SB and SBSPy were first dried at 80 °C for 24 h, under reduced pressure of 800 mmHg. The samples were then soaked with DMA and kept under reduced pressure overnight. The excess DMA was removed by centrifugal filtration for 1 min using a 0.45-μm nylon membrane (Spin-X, Corning^® Costar^®) and a relative centrifugal force of 200 × g.

All the measurements were performed using a Bruker Minispec MQ-20 spectrometer operating with a 0.5 T magnetic field (¹H Larmor frequency of 20 MHz), employing a CPMG (Carr-Purcell-Meiboom-Gill) sequence. The acquisition parameters were set to 25,000 echoes, echo time of 100 μs, and recycle delay of 10 s. For each sample, the T₂ distributions were obtained using a numerical inverse Laplace transform (ILT) procedure (Borgia et al. 1998, Provencher 1982). Deconvolution of the T₂ distribution with three log-Gaussian functions enabled isolation of the contribution of each component of the distribution. The experiments were carried out in duplicate and the ILT was performed on the CPMG decay given by the average of the normalized data for each measurement.

The interaction between the pore surface and the ¹H nuclear spins of a fluid speed up the relaxation of the fluid confined inside the pore, according to a phenomenon known as surface relaxation (Meng & Ragauskas 2014). This effect allows the extraction of information about the pore space geometry, since the observed transverse relaxation rate, 1/T₂, is directly proportional to the surface to volume ratio of the pore. Hence, the T₂ distribution of a fluid confined on a given porous system qualitatively reflects the pore size distribution. At the fast diffusion limit, the relation between T₂ and pore size is given by Eq. (1) (Brownstein & Tarr 1979, Capitani et al. 2012).

$$\frac{1}{{T}_{2}}=\rho \left(\frac{S}{V}\right)$$

(1)

where $\rho$ is the surface relaxivity, which depends on the porous medium and is usually unknown, and $S$ and $V$ are the pore surface area and volume, respectively. Both the pore size distribution and the differences in fluid mobility within the pores affect the T₂ distribution.

Scanning electron microscopy

The morphological aspects of the raw SB and SBSPy surfaces were examined by scanning electron microscopy (SEM), using a Tescan/Oxford scanning electron microscope (Model Vega3 SB) equipped with a tungsten filament and a secondary electron detector. Prior to analysis, the raw SB and SBSPy (32-mesh, 0.500 mm) were mounted separately on carbon graphite tapes adhered to aluminum stubs, followed by coating with a thin layer of gold using a Quorum modular high-vacuum coater (Model Q150R ES).

Batch adsorption experiments

Assays of the single-component adsorption of Cu(II) and Zn(II) on SBSPy were performed (in batch mode) to evaluate the effects of solution pH, time, and initial Cu(II) or Zn(II) concentration. Buffer solutions were used to control the solution pH during the adsorption experiments. All the buffered Cu(II) and Zn(II) solutions were prepared using deionized water from a Milli-Q system (Millipore^®). The experimental conditions used in the adsorption experiments are summarized in Table 1. Erlenmeyer flasks (250 mL) containing samples of SBSPy weighed into cylindrical glass bottles (1.8 mm H × 2.2 mm OD) were stirred at 130 rpm in an orbital shaker-incubator (Model MA-830, Marconi). All the experiments were performed in duplicate, at 25 °C.

Table 1 Conditions used in the adsorption, desorption, and re-adsorption experiments

At the end of the adsorption experiment, the spent SBSPy was separated from the liquid phase by single filtration, using JP-41 filter paper, and the concentration of Cu(II) (λ = 324.8 nm) or Zn(II) (λ = 213.9 nm) was determined using a flame atomic absorption spectrophotometer (FAAS) (Model SpectrAA 50B, Varian^®).

The q_x value of the SBSPy for each cation was obtained using Eq. (2):

$${\mathrm{q}}_{\mathrm{x}}=\frac{{\left({\left[\mathrm{M}\left(\mathrm{II}\right)\right]}_{0}-{\left[\mathrm{M}\left(\mathrm{II}\right)\right]}_{\mathrm{x}}\right)}_{\mathrm{M}\left(\mathrm{II}\right)}{\mathrm{V}}_{\mathrm{M}\left(\mathrm{II}\right)}}{{w}_{\mathrm{SBSPy}}}$$

(2)

where q_x (mmol g^-1) is the SBSPy adsorption capacity at time t (x = t) or at equilibrium (x = e), V_M(II) (L) is the volume of M(II) (M = Cu or Zn) solution, the term ([M(II)]₀ – [M(II)]_x)_M(II) (mmol L^-1) is the difference between the initial M(II) concentration and the concentration of M(II) at time t or at equilibrium e, and w_SBSPy (g) is the weight of SBSPy.

The data for adsorption as a function of time were modeled using the homogeneous surface diffusion model (HSDM) (Worch 2012), the intraparticle diffusion (IPD) model (Weber & Morris 1963), and the Boyd model (Boyd et al. 1947). The data for adsorption as a function of the initial Cu(II) or Zn(II) concentration were modeled using the Langmuir (Langmuir 1918) and Sips (Sips 1948) models. The equations used to fit the adsorption data can be found in the Online Resources.

Batch desorption and re-adsorption experiments

The potential to reuse the spent SBSPy was evaluated in desorption and re-adsorption experiments. Erlenmeyer flasks (125 mL) containing samples of SBSPy, SBSPy-Cu(II), or SBSPy-Zn(II) weighed into cylindrical glass bottles (1.8 mm H × 2.2 mm OD) were stirred at 130 rpm and 25 °C in an orbital shaker-incubator (Model MA-830, Marconi). The efficiencies of desorption (E_des) and re-adsorption (E_re-ads) were calculated from mass balance equations, as described by Almeida et al. (2016) and Teodoro et al. (2016). The conditions of the SBSPy reuse experiments are summarized in Table 1. The other procedures were those described in the “Batch adsorption experiments” section. The assays of desorption and re-adsorption were both performed in triplicate.

Evaluation of adsorption thermodynamics

The changes in the enthalpy of adsorption (∆_adsH) were determined by isothermal titration calorimetry (ITC). The values of ∆_adsH as a function of SBSPy surface coverage (θ), for adsorption of Cu(II) or Zn(II), were measured using a nanocalorimeter (Model TAM III, TA Instruments^®) equipped with two 4-mL calorimetry cells. The reference cell was filled with 2.7 mL of acetic acid/sodium acetate buffer solution (pH 5.5). The same volume was added to the sample cell containing 0.0100 ± 0.0001 g of SBSPy. The suspension in the sample cell was stirred continuously, using a propeller stirrer at 180 rpm. After thermal equilibrium had been reached and the liquid phase was degassed, injections of 15 µL of Cu(II) or Zn(II) solution (47 mmol L^-1 Cu(II) or 38 mmol L^-1 Zn(II)), prepared in the same buffer, were performed at 35-min intervals, using a 500-µL Hamilton syringe controlled by a piston pump. All the calorimetric titrations were performed at 25.00000 ± 0.00001 °C, in duplicate. The other experimental conditions were as described by Pereira et al. (2020).

The contribution of Cu(II) or Zn(II) dilution enthalpy to the overall adsorption process was determined by ITC measurements without the addition of SBSPy. The ∆_adsH values for different amounts of Cu(II) or Zn(II) adsorbed on SBSPy were calculated using Eq. (3):

$${\Delta }_{\mathrm{ads}}H=\frac{\sum_{i=1}^{N}\left({q}_{i,\mathrm{int}}-{q}_{i,\mathrm{del}}\right)}{\sum_{i=1}^{N}{n}_{i}}$$

(3)

where (q_i,int – q_i,dil) (kJ) is the difference between the absorbed or released heat due to interaction after each injection i in the sample cell, for the ITC experiments performed with SBSPy (q_i,int) or without SBSPy (q_i,dil), respectively, and n_i (mol) is the amount of Cu(II) or Zn(II) adsorbed on SBSPy. The calculation of the n_i values was as described by Pereira et al. (2020).

The calculation of the change in standard free energy (∆_adsGº) for adsorption of Cu(II) or Zn(II) on SBSPy was performed according to the approach described by Liu (2009), as shown in Eq. (4):

$${\Delta }_{\mathrm{ads}}G^\circ =-RT\mathrm{ln}\left[\frac{b}{{\gamma }_{e}}\left(1 \mathrm{mol }{\mathrm{L}}^{-1}\right)\right]$$

(4)

where T (K) is the absolute temperature, R (J mol^-1 K^-1) is the gas constant, b (L mol^-1) is the Langmuir constant, and γ_e is the activity coefficient of the Cu(II) or Zn(II) solution at equilibrium (at 25 °C).

Since the concentration of the Cu(II) or Zn(II) solution affected the γ_e value, a correction of the value was required. The extended Debye-Hückel law (Huckel & Debye 1923) (Eq. (5)) was used for this purpose, as follows:

$$\mathrm{log}{\gamma }_{e}=\frac{{-Az}^{2}\sqrt{{I}_{e}}}{1+B\alpha \sqrt{{I}_{e}}}$$

(5)

where I_e (mol L^-1) is the ionic strength of the Cu(II) or Zn(II) solution, z is the charge of Cu(II) or Zn(II), α is the effective diameter of the Cu(II) or Zn(II) ion (6 Å) (Fetter 2018), and A and B are empirical constants with values of 0.5085 and 0.3281 at 25 °C in water, respectively (Garrels & Christ 1965).

The ∆_adsGº parameter (Eq. (6)) is a result of enthalpic and entropic contributions to the adsorption system under study. The change in the standard enthalpy of adsorption, Δ_adsHº, was determined from a plot of Δ_adsH against C_e, extrapolating C_e → 0 (Figure not shown). The change in the standard entropy of adsorption, Δ_adsSº, was determined from Eq. (6).

$${\Delta }_{\mathrm{ads}}G^\circ ={\Delta }_{\mathrm{ads}}H^\circ -{T\Delta }_{\mathrm{ads}}S^\circ$$

(6)

Continuous adsorption on a fixed-bed column

The continuous adsorption experiments were performed using three adsorption-desorption cycles, according to the methods described by Almeida et al. (2019). The experimental conditions for continuous adsorption on a fixed-bed column were based on the results obtained in the batch adsorption studies of Cu(II) and Zn(II) on SBSPy (“Batch adsorption experiments” and “Batch desorption and re-adsorption experiments” sections), as well as on the results reported by Xavier et al. (2018), who optimized the continuous adsorption of Co(II), Cu(II), and Ni(II) on sugarcane bagasse chemically modified with trimellitic anhydride (TA). In the first cycle, buffered metal ion solution (1.4 mmol L^-1, pH 5.5, 25 °C) was pumped at a flow rate of 2.35 mL min^-1 for 440 min for Cu(II) and 420 min for Zn(II). The HNO₃ desorption solution (0.505 mol L^-1, 25 °C) was then percolated through the bed for 10 min, at a flow rate of 10 mL min^-1. Deionized water was percolated through the bed after the adsorption step, to eliminate all the cations not adsorbed on SBSPy, and after the desorption step, to remove excess HNO₃ solution.

Aliquots of the effluent to the column were collected at specific times, with quantification of the Cu(II) or Zn(II) concentrations by FAAS (“Batch adsorption experiments” section), in order to obtain the breakthrough curves. The adsorption capacity of SBSPy packed into the column, for a given operating time, was calculated from the area under the curve, according to Eq. (7):

$$Q/{\mathrm{mmolg}}^{-1}=\frac{{C}_{0}\dot{V}}{{1000w}_{\mathrm{SBSPy}}}\underset{0}{\overset{t}{\int }}\left(1-\frac{{C}_{t}}{{C}_{0}}\right)dt$$

(7)

where Q is the adsorption capacity of the SBSPy (mmol g^-1), C₀/C_t is the normalized Cu(II) or Zn(II) concentration, w_SBSPy is the weight of SBSPy packed into the column (g), and V̇ is the volumetric flow rate of the fluid phase (mL min^-1). The maximum adsorption capacity (Q_max) of the bed was reached when C_t was equal to C₀.

The effective use of the bed (H) was the effective height of the bed used for Cu(II) or Zn(II) adsorption until the breakthrough point. The H value was calculated using Eq. (8):

$$H/cm=\left(\frac{{q}_{{t}_{b}}}{{q}_{{t}_{e}}}\right)Z$$

(8)

where H is the effective use of the bed (cm), q_tb and q_te (mmol) are the amounts of Cu(II) or Zn(II) adsorbed on SBSPy until the breakthrough time (t_b) and until the exhaustion time (t_e), which were obtained from the breakthrough curve at C_t/C₀ = 0.05 and at C_t/C₀ = 0.95, respectively, and Z is the bed height (Z = 3.0 cm).

The efficiency of the adsorption process (EAP) in a fixed-bed column was calculated using Eq. (9):

$$EAP/\%=\left(\frac{{q}_{{\mathrm{t}}_{\mathrm{e}}}}{{q}_{\mathrm{M}\left(\mathrm{II}\right)}}\right)\times 100$$

(9)

where EAP is the efficiency of the adsorption process (%) and q_M(II) is the total amount of Cu(II) or Zn(II) fed into the column (mmol).

The length of the mass transfer zone (Z_MTZ) was calculated using Eq. (10):

$${Z}_{\mathrm{MTZ}}/cm=\left(1-\frac{{t}_{\mathrm{b}}}{{t}_{\mathrm{e}}}\right)Z$$

(10)

where Z_MTZ is the length of the mass transfer zone (cm).

The E_des value for each cycle was calculated as shown in Eq. (11):

$${E}_{\mathrm{des}}/\%=\left(\frac{\dot{V}\underset{0}{\overset{\mathrm{t}}{\int }}\left({C}_{\mathrm{t}}\right)dt}{{Q}_{\mathrm{max}}{w}_{\mathrm{SBSPy}}}\right)\times 100$$

(11)

where C_t is the metal ion concentration (mmol mL^-1) in the desorption solution at time t.

The E_re-ads value was determined considering that the first cycle had 100% of the Q_max value of the bed. The breakthrough curves were modeled using the Thomas (Thomas 1944), Bohart-Adams (Bohart & Adams 1920), and instantaneous local equilibrium (ILE) (Georgin et al. 2020) models, using a computational routine implemented in MATLAB^® 2016a (MathWorks Inc.), with a genetic algorithm function (Chu 2010, Xavier et al. 2018) employed to find the global minimum (See the Online Resources).

Results and discussion

For the introduction of both succinyl and pyromellityl units into the SB structure by a one-pot reaction, exploratory synthesis experiments were performed to assess which carboxylic acid anhydride should be added first to maximize the chemical modification of raw SB. Subsequently, having defined the best order of addition of SA and PyA, the chemical modification of raw SB with SA and PyA was evaluated employing a 2³ experimental design to investigate the effects of the synthesis parameters T, t_SA, and χ_SA on the values of q_e,Cu and q_e,Zn.

Exploratory experiments for the synthesis of SBSPy

The FTIR spectra of raw SB, SBSPy (SA added first), SBPyS (PyA added first), and raw SB modified with SA only (SBS) and with PyA only (SBPy) are presented in Figure 1a. All the chemically modified materials showed an intense band in the region of 1720–1740 cm^-1, which was related to stretching of the carbonyl ester group. A weak band related to stretching of the carbonyl ester group was also present at 1735 cm^-1 in the raw SB spectrum, attributed to the acetyl groups in hemicelluloses. The bands related to stretching of the carbonyl ester group in SBSPy, SBS, SBPyS, and SBPy are highlighted in Figure 1b. For SBPy (Figure 1b), the band related to the carbonyl ester group of the pyromellityl unit (conjugated carbonyl) appeared centered at 1729 cm^-1. As expected, conjugation of the carbonyl group with the phenyl group shifted the carbonyl band stretching to a lower frequency (Pavia et al. 2009). For SBS (Figure 1b), the band related to the carbonyl ester group of the succinyl unit (unconjugated carbonyl) appeared centered at 1738 cm^-1. In the IR spectrum of SBSPy (Figure 1b), where SA was added first, the band related to the carbonyl ester group was shifted to a lower wavenumber (1734 cm^-1), compared to its position in the spectrum of SBS (1738 cm^-1), due to the introduction of pyromellityl units in SBSPy. In addition, in the spectrum of SBPyS (Figure 1b), where PyA was added first, the band related to the carbonyl ester group was shifted to a higher wavenumber (1731 cm^-1), compared to its position in the IR spectrum of SBPy (1729 cm^-1), due to the introduction of succinyl units in SBPyS. As expected, the ratio between the pyromellityl (PyA) units and succinyl (SA) units introduced in SBPyS and SBSPy affected the position of the carbonyl ester band. These results suggested that the PyA-to-SA ratio in SBSPy (vC=O_ester shifted from 1738 cm^-1 (SBS) to 1734 cm^-1 (SBSPy)) was lower than in SBPyS (vC=O_ester shifted from 1738 cm^-1 (SBS) to 1731 cm^-1 (SBPyS)). However, FTIR analysis was unable to provide accurate information on the numbers of succinyl and pyromellityl units introduced in SBSPy and SBPyS. Therefore, the ¹³C Multi-CP SS NMR technique was used for this purpose.

Figure 1

FTIR spectra of a raw SB, SBSPy (SA added first), SBPyS (PyA added first), SBS (SA added only), and SBPy (PyA added only), from 500 to 4000 cm^-1, and b SBSPy, SBS, SBPyS, and SBPy, from 1650 to 1809 cm^-1 (1% w w^-1 of sample in KBr)

The ¹³C Multi-CP SS NMR spectra of raw SB, SBSPy (SA added first), and SBPyS (PyA added first) are presented in Figure 2. The use of the Multi-CP excitation method (Bernardinelli et al. 2015) enabled the acquisition of more quantitative ¹³C NMR spectra (Almeida et al. 2019, Elias et al. 2019). The introduction of PyA and SA into the SB structure was confirmed by the appearance of signals related to the aromatic carbons of the pyromellityl unit (region B, 120-140 ppm) and the methylene carbons of the succinyl unit (region A, 24–40 ppm) (Figure 2), respectively. Using the approach described in “¹³C Multiple cross-polarization solid-state nuclear magnetic resonance (¹³C Multi-CP SS NMR) spectroscopy” section, the numbers of succinyl and pyromellityl units grafted to each cellobiose unit were calculated for SBPyS and SBSPy. It was found that 0.21 ± 0.03 succinyl units and 0.34 ± 0.05 pyromellityl units were grafted to each cellobiose unit in SBPyS, while 0.27 ± 0.03 succinyl units and 0.35 ± 0.05 pyromellityl units were grafted to each cellobiose unit in SBSPy. In addition, these results confirmed that more succinyl units were introduced into the SB structure when SA was added first. This was in agreement with the values obtained from the FTIR spectra of SBSPy (PyA-to-SA ratio of 1.30) and SBPyS (PyA-to-SA ratio of 1.62). These results also suggested that a way to introduce more succinyl and pyromellityl units into the SB structure was to add SA to the reaction medium first. Therefore, the subsequent synthesis studies were carried out with the addition of SA first.

Figure 2

¹³C Multi-CP SS NMR spectra of raw SB, SBSPy (SA added first), and SBPyS (PyA added first).

Evaluation of the effect of synthesis conditions on the adsorption capacity of SBSPy for Cu(II) and Zn(II)

A 2³ factorial design was used to evaluate the effect of the synthesis conditions (t_SA, T, and χ_SA) on the values of q_e,Cu and q_e,Zn. The experimental conditions used in the factorial design are shown in Table 2, together with the values of q_e,Cu and q_e,Zn obtained experimentally. The levels of the independent variables were based on synthesis experiments described elsewhere (Ramos et al. 2015, 2016). Pareto charts of the standardized effects can be found in the Online Resources (Figure S1a–b). The variable T had significant positive effects on q_e,Cu (6.743) and q_e,Zn (7.337), indicating that the use of T at the higher level for the synthesis of SBSPy favored the adsorption of both metal ions. For Cu(II) adsorption, the interactions between t_SA and χ_SA (− 3.614) and between T and χ_SA (3.496) also had statistical significance. The marginal means plots for q_e,Cu are available in the Online Resources (Figure S2a–b). These plots allowed evaluation of the significant interactions for maximizing the q_e,Cu value. If the lower level of t_SA was applied, the use of χ_SA at the higher level was needed to maximize the q_e,Cu value. Regarding the interaction between T and χ_SA, the use of both variables at the higher level favored the q_e,Cu value.

Table 2 Experimental conditions and responses obtained for the synthesis of SBSPy using a 2³ experimental design

For Zn(II) adsorption, all the variables were statistically significant, with a positive effect of T (7.337) and negative effects of t_SA (− 9.656) and χ_SA (− 6.157) on the q_e,Zn value. Therefore, higher q_e,Zn values were obtained using the variables t_SA and χ_SA at the lower levels and the variable T at the higher level. The interactions of t_SA and χ_SA (4.842), T and χ_SA (− 6.965), and t_SA and χ_SA and T (− 6.090) were also statistically significant. The marginal means plots for q_e,Zn are available in the Online Resources (Figure S3a–c). For all the interactions, higher T levels led to higher q_e,Zn values. In addition, the interaction between t_SA and χ_SA indicated that the lower levels of t_SA and χ_SA favored higher q_e,Zn values.

The results suggested that the use of higher χ_SA levels increased the q_e,Cu value, while the use of lower χ_SA levels (higher amounts of PyA) favored the q_e,Zn value. This indicated possible preference of the metal ions for specific adsorption sites. This preference could be explained by the hard and soft acids and bases (HSAB) theory of Pearson (1963). The principle of the HSAB theory suggests that soft acids bind to soft bases, while hard acids bind to hard bases. The hardness and softness of acids and bases is related to the size of the species and their polarizability (Pearson 1963). Cu(II) and Zn(II) are considered borderline Lewis acids, so they can form stable complexes with both soft and hard bases (Pearson 1968). In addition, the electronegativities of Cu(II) and Zn(II) are 1.90 and 1.65, respectively, on the Pauling scale (Haynes et al. 2014). The active adsorption sites introduced on the surface of SBSPy were carboxylate groups that tend to behave as hard bases, although the negatively charged oxygen atom of the carboxylate ion has one of its lone electron pairs involved in resonance, which increases the delocalization of the negative charge (Pearson 1968). On the other hand, the negative charge of the carboxylate ion cannot be delocalized into the pyromellityl group by resonance. However, the other carboxyl functions bonded to the aromatic ring act as electron-withdrawing groups, due to both the inductive effect and the resonance effect, which increases the stability of the conjugated base (the carboxylate ion). This increases the acidity of at least two carboxylic acid groups (pK_a,1 = 1.92, pK_a,2 = 2.87, pK_a,3 = 4.49, and pK_a,4 = 5.63, in water at 25 ºC) (Dean & Lange 1999) of pyromellitic acid (a tetracarboxylic acid), compared to a saturated aliphatic dicarboxylic acid such as succinic acid (pK_a,1 = 4.21 and pK_a,2 = 5.64, in water at 25 ºC) (Dean & Lange 1999), which has the electron-withdrawing inductive effect from an adjacent carboxyl group to another separated by only two methylene groups. Therefore, metal ions classified as softer tend to bind preferentially to the carboxylate functions of the pyromellitate group, since the negative charges of the carboxylate ions are more delocalized in this group, compared to the succinate group. Consequently, Zn(II), which is slightly softer than Cu(II), would be expected to have greater affinity for the pyromellitate group, whereas Cu(II) should have greater affinity for the succinate group.

As the main objective of this study was to synthesize an adsorbent able to remove both metal ions from aqueous solutions, the results obtained using the 2³ experimental design indicated that the best synthesis condition should use the higher T level (100.0 ºC) and the lower t_SA level (1.0 h). For the variable χ_SA, the higher χ_SA level favored Cu(II) adsorption, while the lower χ_SA level favored Zn(II) adsorption. Therefore, the results suggested that the use of higher amounts of SA in the synthesis of SBSPy increased q_e,Cu, while the use of higher amounts of PyA favored q_e,Zn, indicating a possible preference of the metal ions for specific adsorption sites, as discussed previously.

The desirability tool of the Statistica^® software was used to determine the best condition for synthesis of SBSPy that provided the highest values of q_e,Cu and q_e,Zn. The profiles for the predicted values and desirability are available in the Online Resources (Figure S4). This analysis included maximization of the values of both q_e,Cu and q_e,Zn (“Evaluation of the synthesis of SBSPy using a 2³ experimental design” section). The desirability profile indicated that the chemical modification of raw SB with SA and PyA in a one-pot reaction should be carried out using the following reaction conditions: T = 100.0 ºC, t_SA = 1.0 h, and χ_SA = 0.62. A scheme for the synthesis of SBSPy using the best reaction condition is shown in Figure 3. For this synthesis condition, the predicted values for q_e,Cu and q_e,Zn were 1.281 ± 0.003 and 0.90234 ± 0.0006 mmol g^-1, respectively.

Figure 3

Scheme for the chemical modification of raw sugarcane bagasse (SB) with pyromellitic anhydride (PyA) and succinic anhydride (SA), using the best reaction condition predicted using the desirability tool of Statistica^®

The condition for synthesis of SBSPy predicted by the desirability tool of the Statistica^® software was validated experimentally, obtaining q_e,Cu and q_e,Zn values of 1.18 ± 0.06 and 0.78 ± 0.09 mmol g^-1, respectively. The relative errors for the predicted and experimental values of q_e,Cu and q_e,Zn were 7.8 and 13.3%, respectively. Therefore, these results demonstrated the robustness of the constructed model.

Characterization of raw SB and SBSPy

The following sections present the characterization of SBSPy, prepared using the desirable reaction condition, considering the parameters wg and n_T,COOH, together with the results of analyses using FTIR, ¹³C Multi-CP SS NMR, NMR relaxometry, and SEM. The characterization of SBSPy by XRD and TGA is presented in the Online Resources (Figures S5 and S6).

Results for wg , n _T,COOH , and analyses by FTIR and ¹³ C Multi-CP SS NMR

The SBSPy synthesized using the desirable reaction condition presented wg of 61.621 ± 0.002% and n_T,COOH of 4.21 ± 0.07 mmol g^-1. These values were similar to those reported by Elias et al. (2019) for the chemical modification of raw SB with SA and PA (phthalic anhydride), in a one-pot reaction to prepare SBSPh (wg = 60.52%, n_T,COOH = 3.51 mmol g^-1), and by Almeida et al. (2019) for the chemical modification of raw SB with SA and TA (trimellitic anhydride), in a one-pot reaction to prepare SBST (wg = 73.2%, n_T,COOH = 4.67 mmol g^-1). It is important to note that the synthesis methods used to prepare SBSPh and SBST were different to the procedure used here to prepare SBSPy. The different values of wg and n_T,COOH for SBSPh, SBST, and SBSPy were related to different numbers of succinyl (0.33) and phthalyl (0.40) units (Elias et al. 2019), succinyl (0.51) and trimellityl (0.59) units (Almeida et al. 2019), and succinyl (0.71) and pyromellityl (0.25) units introduced in SBSPh, SBST, and SBSPy, respectively. In addition, SBSPh and SBST were synthesized by the simultaneous addition of both carboxylic acid anhydrides at the beginning of the one-pot reaction, while in the synthesis of SBSPy, the carboxylic acid anhydrides were added separately. The use of different synthesis methods to prepare SBSPh, SBST, and SBSPy was due to the differences in molecular size and reactivity of PA, TA, and PyA. The total numbers of SA and PA, SA and TA, and SA and PyA units introduced in SBSPh, SBST, and SBSPy were 0.73, 1.1, and 0.96, respectively. It should be noted that the ratios of PA to SA, TA to SA, and PyA to SA units introduced in SBSPh, SBST, and SBSPy were 1.21, 1.16, and 0.35, respectively. Despite the differences in the synthesis conditions used to prepare SBSPh (T = 100 ºC, t = 11 h, χ_SA = 0.2) (Elias et al. 2019), SBST (T = 100 ºC, t = 11 h, χ_SA = 0.2) (Almeida et al. 2019), and SBSPy (T = 100 ºC, t_SA = 1 h, t_PyA = 5 h, χ_SA = 0.62), the results suggested that as the molecular size of the aromatic carboxylic acid anhydride increased, its introduction in the SB structure decreased. As a result, the method used to prepare SBSPy could not be the same as those used to prepare SBSPh and SBST.

The contents of C, H, and N in raw SB and SBSPy were 44.5 ± 0.8% and 47.6 ± 0.3%, 6.0 ± 0.2% and 5.1 ± 0.1%, and 0.2 ± 0.1% and 0.2 ± 0.1%, respectively. These results indicated that the chemical modification of raw SB with SA and PyA was successful, since the theoretical contents of C and H in SA and PyA are 48.01% and 55.07%, and 4.03% and 0.92%, respectively. The contents of C and H in the two carboxylic acid anhydrides could explain the decreased H content and the increased C content in SBSPy, which contained 0.71 succinyl units and 0.25 pyromellityl units.

The FTIR spectra of raw SB and SBSPy are shown in Figure 4. The main evidences of the chemical modification of raw SB with SA and PyA were the appearance of bands at 2631 and 2528 cm^-1 (vO-H_{carboxylic acid dimer}), 1733 cm^-1 (vC=O_{ester and carboxylic acid}), 1500 cm^-1 (vC=C_{aromatic ring (pyromellitic ring)}), 1257 cm^-1 (vC-O_ester), and 758 cm^-1 (vC(sp²)-H_{aromatic ring (pyromellitic ring)}) (Almeida et al. 2019, Elias et al. 2019, Pavia et al. 2009).

Figure 4

FTIR spectra of raw SB and SBSPy (1% w w^-1 of raw SB or SBSPy in KBr)

The ¹³C Multi-CP SS NMR spectra of raw SB and SBSPy are shown in Figure 5a. The characteristic signals of the major constituents of raw SB (cellulose, hemicelluloses, and lignin) were assigned as described by Rezende et al. (2011). As already discussed, in addition to the characteristic signals of raw SB, the NMR spectrum of SBSPy exhibited two particular regions associated with the chemical modification of raw SB with SA and PyA. Region A, from 24 to 40 ppm, was related to the ¹³C chemical shifts of carbon atoms of methylene groups present in the succinyl unit, while region B, from 120 to 140 ppm, was related to the ¹³C chemical shifts of carbon atoms of the aromatic ring present in the pyromellityl unit introduced into the SB structure. The area of region B increased as a result of the introduction of pyromellityl units into the SB structure. Other evidence of the chemical modification of raw SB was the increase in the area of signals in the 160–180 ppm region, related to the carbon atoms of the ester carbonyls of acetyl groups, present in hemicelluloses, and of the carboxyls of pyromellityl and succinyl units introduced into the SB structure (Melo et al. 2011). Using the approach presented in the “13C Multiple cross-polarization solid-state nuclear magnetic resonance (13C Multi-CP SS NMR) spectroscopy” section, the numbers of succinyl and pyromellityl units introduced into the SB structure, per cellobiose unit, were 0.71 ± 0.02 and 0.25 ± 0.03, respectively. These results showed that the introduction of both PyA and SA into the SB structure had been successfully accomplished. The proposed structure for SBSPy, based on the results obtained in the present study, is shown in Figure 5b.

Figure 5

a ¹³C Multi-CP SS NMR spectra of raw SB and SBSPy, and b proposed chemical structure for SBSPy based on ¹³C Multi-CP SS NMR data (n = 1 for cellobiose)

NMR relaxometry

The ¹H NMR relaxometry technique was used to assess the pore structures of raw SB and SBSPy. The T₂ values are directly related to the variation in the sizes of regions filled with a fluid, with longer T₂ values corresponding to larger pores (Mitchell et al. 2005). For lignocellulosic biomass, NMR relaxometry usually reveals different interstitial scales, which are related to different compartments of the microstructure of the plant. T₂ values of a few milliseconds are related to interstitial spaces on the surface of the cellulose microfibril structure, while the intermediate scale, with T₂ values of tens of milliseconds, is associated with pores within the lignin-hemicellulose matrix on the surface of the fibers. For T₂ values in the region of hundreds of milliseconds, the related interstitial scale is associated with the luminal pores or spaces between the fibers (Meng & Ragauskas 2014, Tsuchida et al. 2014).

The samples of raw SB and SBSPy were centrifuged to remove any DMA molecules that were not confined within the porous structures of the materials, in order to ensure the reproducibility of the measurements. However, there was no control of the mass and amount of DMA in each measurement, so only the proportions of DMA could be assessed for each interstitial scale. Figure 6 shows the T₂ distributions (normalized by the total area) obtained for raw SB and SBSPy, together with the corresponding deconvolutions. Comparing raw SB with SBSPy, the main difference was the greater access of DMA molecules to the smallest interstitial scale for the SBSPy sample, as shown by the higher relative area (Table 3). This increase was accompanied by reduction of the relative areas for the interstitial scales related to the lignocellulosic matrix (cell wall) and luminal spaces (lumen), a feature that was not observed so clearly for SBSPh and SBST (Almeida et al. 2019, Elias et al. 2019). This could have been a consequence of the differences in the synthesis methods applied for each material.

Figure 6

T₂ distributions for raw SB and SBSPy. The black lines indicate the distribution obtained from the ILT procedure. The red, green, and blue components are assigned to the inner microfibril, cell wall, and lumen interstitial spaces, respectively. The inset shows the averages of the CPMG signals for raw SB (red) and SBSPy (blue)

Table 3 Central T₂ values and relative areas for each deconvoluted component in the T₂ distributions

For all three interstitial scales, the T₂ values for SBSPy were lower than the corresponding values for raw SB (Table 3). This reduction was probably related to changes in the surface relaxivity, since the average pore diameter showed almost no difference between the samples, according to the results of the BJH and BET analyses, while the maximum pore size, here associated with the cell wall pores, decreased by 74%. This effect was more pronounced for the inner microfibril and lumen scales, with the central T₂ values decreasing by 49% and 43%, respectively, while the T₂ value for the cell wall decreased by 29%. The results indicated that introduction of the succinyl and pyromellityl units changed the surface of the pores, since the surface relaxivity effects were observed to a lesser extent for SBSPh and SBST (Almeida et al. 2019, Elias et al. 2019).

Scanning electron microscopy

Figure 7 shows SEM micrographs of raw SB (a, c, and e) and SBSPy (b, d, and f) at 60 × (a and b), 500 × (c and d), and 5000 × (e and f) magnifications. During the milling process, using a Wiley mill, the tangential shear forces led to partial disintegration of the SB fibers, producing elements with different sizes and shapes (Figure 7a). As expected, the SEM micrographs (Figure 7a–e) did not reveal significant morphological differences between raw SB and SBSPy. This showed that the chemical modification of raw SB with SA and PyA did not significantly change the plant cell structure, as also indicated by NMR relaxometry. This was an important result, since preservation of the plant cell structure, together with the rigidity of the cellulose fibers and their aggregation with the other cell wall components (hemicelluloses and lignin), was essential for the physical, chemical, and biological stability of the biosorbent material.

Figure 7

SEM micrographs of raw SB (a, c, and e) and SBSPy (b, d, and f) at 60 × (a and b), 500 × (c and d), and 5000 × (e and f) magnifications

Batch adsorption

Effect of solution pH on metal ion removal

The solution pH strongly affected the SBSPy adsorption capacities (q_e) for Cu(II) and Zn(II) (Figure 8). Since the pH_PZC of SBSPy was 3.11 (see Figure S7 in the Online Resources), the adsorption of both metal ions was favored at pH > pH_PZC, at which deprotonation of the carboxylic acid groups resulted in the surface of SBSPy becoming negative. The q_e for Cu(II) and Zn(II) adsorption on SBSPy increased as the solution pH increased, with the highest q_e value reached at pH 5.5, for both metal ions. In contrast, at pH < pH_PZC, the carboxylic acid groups on the surface of SBSPy were protonated, so there was no adsorption of either of the metal ions. Therefore, pH 5.5 was selected in the subsequent Cu(II) and Zn(II) adsorption studies. Adsorption of the metal ions at pH higher than 5.5 was not considered, in order to avoid the formation of hydrolyzed species such as M(OH)⁺ and M(OH)₂ (M = Cu or Zn).

Figure 8

Effect of solution pH on the adsorption capacity of SBSPy for Cu(II) and Zn(II) ([Cu(II)] = [Zn(II)] = 0.79 mmol L^-1, 130 rpm, 25 °C, 10 h)

Adsorption kinetics

The kinetic parameters were estimated using the IPD, Boyd, and HSDM models applied to the data for adsorption of Cu(II) and Zn(II) on SBSPy as a function of time (Table 4). The IPD plots for adsorption of Cu(II) and Zn(II) on SBSPy can be found in the Online Resources (Figure S8). The IPD plots were multilinear, exhibiting three stages. Each stage was defined based on the method of piecewise linear regression (Malash & El-Khaiary 2010). The first stage was related to film diffusion of metal ions through the boundary water layer surrounding the SBSPy particles (external mass transfer). The second stage was related to intraparticle diffusion of metal ions on the surface and in the pores of the SBSPy particles (surface and pore diffusion), and the third stage was attributed to adsorption equilibrium. Therefore, the adsorption of both metal ions was initially controlled by film diffusion, followed by a change to intraparticle diffusion (Hameed & El-Khaiary 2008). The k_d,1 values showed that film diffusion of Cu(II) was faster than that of Zn(II), while the k_d,2 values showed that intraparticle diffusion was similar for Cu(II) and Zn(II). The faster film diffusion of Cu(II) could be explained by its smaller hydrated ionic radius (r_H) (r_H,Cu = 4.19Å, r_H,Zn = 4.30 Å) (Nightingale 1959). The Boyd plots for Cu(II) and Zn(II) adsorption on SBSPy can be found in the Online Resources (Figure S9). According to Boyd et al. (1947), the plot of B_t against t should produce a straight line that crosses the origin (0,0), when intraparticle diffusion is the rate-limiting step of the adsorption. Hence, the intraparticle diffusion coefficient (D_i) can be determined by the slope (B) of the straight line. However, in the present case, the Boyd plots for both metal ions produced straight lines that did not cross the origin (Table 4). This suggested that intraparticle diffusion was not the only step controlling the overall kinetics for adsorption of Cu(II) and Zn(II) on SBSPy, which was in agreement with the IPD plots.

Table 4 Results of nonlinear regression (NLR) analysis of the kinetic data ([Cu(II)] = [Zn(II)] = 0.79 mmol L^-1), results of NLR analysis of the equilibrium data ([Cu(II)] = [Zn(II)] = 0.03–3.11 mmol L^-1), and results of modeling the breakthrough curves for adsorption of Cu(II) and Zn(II) on SBSPy in a fixed-bed column. The kinetic and equilibrium studies in batch mode employed 0.2 g L^-1 SBSPy, 130 rpm, 25 °C, and pH 5.5. The continuous adsorption studies using a fixed-bed column employed [Cu(II)] = [Zn(II)] = 1.4 mmol L^-1, pH 5.5, 25 °C, V̇ = 2.35 mL min^-1, Z = 3.0 cm, and 0.5 g SBSPy

Figure 9 shows the plots of q_t against t for adsorption of Cu(II) and Zn(II) on SBSPy, together with the curves fitted to the experimental data using the HSDM model. This model was used to describe the adsorption through the particle radius and to estimate the effective diffusion coefficient. The film mass transfer coefficient (k_f) and the surface diffusion coefficient (D_s) were used to determine the Biot number (Bi), which characterizes the ratio of the external and internal mass transfer resistances (Worch 2012). The values of k_f, D_s, and Bi obtained from HSDM model are presented in Table 4. The k_f and D_s values were similar for the two metal ions, with Cu(II) exhibiting slightly lower k_f value and higher D_s value than Zn(II) (Table 4). If Bi > 100, the overall kinetics is controlled by surface diffusion (intraparticle mass transfer), while if Bi < 1, film diffusion (external mass transfer) controls the overall kinetics. If 1 < Bi < 100, both diffusions are relevant for the overall kinetics (Guibal et al. 1998, Prasad & Srivastava 2009). Therefore, a lower Bi value is associated with greater film diffusion, relative to intraparticle diffusion (Worch 2012). Since the Bi values were higher than 1 (Bi_Cu = 17.8 and Bi_Zn = 25.3), but much lower than 100, both external and internal diffusion contributed to the overall kinetics, as suggested by the IPD model. Plots of the adsorption capacities (q_t) for Cu(II) and Zn(II) on SBSPy, as a function of time and the radial coordinate (r), are shown in Figure 10. Both metal ions were adsorbed at higher r values, because the adsorption initially occurred at the outer surface of the SBSPy particles (r = R), with a few minutes being required for adsorption to occur in the pores of the particles. This was in agreement with the first and second steps of the IPD model, as well as with the Bi values obtained.

Figure 9

Plot of q_t against t for adsorption of a Cu(II) and b Zn(II) on SBSPy ([Cu(II)] = [Zn(II)] = 0.79 mmol L^-1, 0.2 g L^-1 SBSPy, 130 rpm, 25 °C, pH 5.5)

Figure 10

Adsorption capacity (q_t) for a Cu(II) and b Zn(II), as a function of time and the radial coordinate (r)

Adsorption isotherms

The effects of the initial metal ion solution concentrations on the q_e values for adsorption of Cu(II) and Zn(II) on SBSPy are shown in Figure 11, together with the curves fitted to the adsorption data using the Langmuir and Sips models. The estimated isotherm parameters are shown in Table 4. Both isotherm models were able to describe the adsorption of Cu(II) and Zn(II) on SBSPy. The Sips model is a three-parameter model, so it can provide better fits to adsorption data, compared to the two-parameter Langmuir model. However, despite showing slightly lower R²_adj values and higher χ²_red values, the maximum adsorption capacities (Q_max) predicted by the Langmuir model were closer to the experimental Q_max values. The parameter n of the Sips model is related to the heterogeneity of the system under study (Do 1998). A value of n different from unity indicates that the adsorption system diverges from the homogeneity assumed by the Langmuir model. The Langmuir constant (b) is associated with the adsorbate-adsorbent affinity, such that the higher the b value, the greater the affinity of the metal ion for the adsorption site. Since b_Cu(II) > b_Zn(II), the affinity of the Cu(II) ions for the SBSPy adsorption sites was greater than the affinity of the Zn(II) ions for the sites. This was in agreement with the results reported by Bunting and Thong (1970), who investigated the relative stabilities of complexes formed between various divalent metal ions and carboxylate anions.

Figure 11

Isotherms for adsorption of a Cu(II) and b Zn(II) on SBSPy ([Cu(II)] = [Zn(II)] = 0.033–3.11 mmol L^-1, 0.2 g L^-1 SBSPy, pH 5.5, t_Cu(II) = 120 min, t_Zn(II) = 180 min, 25 °C)

Regeneration and reuse of SBSPy

The feasibility of regeneration and reuse of the SBSPy was evaluated in an adsorption-desorption-(re)adsorption cycle. The SBSPy showed E_des of 88.8 ± 0.6% and E_re-ads of 94 ± 2% for Cu(II), and E_des of 99 ± 1% and E_re-ads of 95 ± 2% for Zn(II). Xavier et al. (2018) demonstrated that continuous desorption in a fixed-bed column of raw SB modified with TA was able to remove metal ions (Co(II), Cu(II), and Ni(II)) not desorbed in previous cycles, because the higher concentration gradient between the non-desorbed metal ions on the adsorbent surface and the inlet desorption solution provided a higher driving force for desorption.

Evaluation of adsorption thermodynamics

Changes in enthalpy of adsorption (∆ _ads H)

A plot of ∆_adsH against SBSPy surface coverage (θ) is shown in Figure 12. The ∆_adsH values indicated that for both metal ions, adsorption on the SBSPy surface was an endothermic process. At θ < 0.3, the curves exhibited different behaviors, with the Zn(II) adsorption process becoming less endothermic, which was opposite to the behavior observed for the Cu(II) adsorption process. At θ = 0.3, the ∆_adsH values were the same for adsorption of the two metal ions, suggesting that at this surface coverage, the balance of intermolecular interactions was similar for the two adsorption systems. At θ > 0.3, the curves for the SBSPy-Cu(II) and SBSPy-Zn(II) systems exhibited similar trends, with the ∆_adsH values becoming less endothermic as SBSPy surface coverage increased. However, the ∆_adsH values for the SBSPy-Zn(II) system became less endothermic than for the SBSPy-Cu(II) system, suggesting that different subprocesses were involved in the adsorption of Cu(II) and Zn(II) on SBSPy.

Figure 12

Changes in enthalpy of adsorption of Cu(II) and Zn(II), as a function of SBSPy surface coverage (θ) (pH 5.5, 25 °C)

The ∆_adsH value (Figure 12) was the result of the contributions of three subprocesses (Eq. (12)) that occurred during adsorption of the metal ions on SBSPy, as follows:

$${\Delta }_{\mathrm{ads}}H={\Delta }_{\mathrm{desol}}{H}^{\mathrm{SBSPy site},\mathrm{ metal}}+{\Delta }_{\mathrm{int}}{H}^{\mathrm{ metal}-\mathrm{metal}}+{\Delta }_{\mathrm{int}}{H}^{\mathrm{SBSPy site}-\mathrm{ metal}}$$

(12)

where Δ_desolH^{SBSPy site, metal} is the change in enthalpy due to the desolvation of metal ions and SBSPy adsorption sites, Δ_intH^metal-metal is the change in enthalpy due to the metal-metal interaction, and Δ_intH^{SBSPy site-metal} is the change in enthalpy due to the formation of interactions between the metal ions and the SBSPy adsorption sites (Teodoro et al. 2016).

The Δ_desolH^{SBSPy site, metal} subprocess was endothermic, since desolvation of the SBSPy adsorption sites and metal ions required energy. The Δ_intH^metal-metal subprocess could be endothermic, if metal ion-metal ion interactions in solution were disrupted and/or repulsion occurred between adsorbed species on the surface of SBSPy, or exothermic, if metal ion-metal ion interactions occurred in solution and/or on the surface of SBSPy. The Δ_intH^{SBSPy site-metal} subprocess was exothermic, because the formation of interactions between two oppositely charged species releases energy (Marcus 1994, McMurray & Fay 2004).

As discussed previously, it was expected that Zn(II) ions, which are slightly softer than Cu(II) ions, would have more affinity for the carboxylate groups of pyromellitate units, while Cu(II) ions would have more affinity for the carboxylate groups of succinate units. In addition, the affinity of the SBSPy adsorption sites for Cu(II) ions (b_Cu(II) = 18 L mmol^-1) was greater than for Zn(II) ions (b_Zn(II) = 5.2 L mmol^-1). Therefore, a possible explanation for the different behaviors of the curves of ∆_adsH as a function of θ, for adsorption of Cu(II) and Zn(II) on SBSPy, was the formation of complexes with different stabilities between the SBSPy adsorption sites and the metal ions, resulting in different Δ_intH^{SBSPy site-metal} values. At low θ values, the quantity of adsorbed metal ions on the surface of SBSPy was low, so the contribution of Δ_intH^metal-metal could be neglected. However, the Δ_intH^metal-metal value probably became significant with increasing coverage of the SBSPy surface by metal ions, because the distances between the positively charged adsorbed species decreased.

For the SBSPy-Zn(II) system, Δ_adsH decreased with increasing θ, in the entire θ range studied. The same behavior was not observed for the SBSPy-Cu(II) system, where Δ_adsH only decreased at θ > 0.3. For the SBSPy-Cu(II) system, Δ_adsH increased until θ reached 0.3, indicating that endothermic contributions (Δ_desolH^{SBSPy sites, metal} and Δ_intH^metal-metal) probably dominated the adsorption enthalpy balance. Since the Δ_desolH^{SBSPy sites, metal} values changed slightly during the global adsorption process, due to energy differences of the different adsorption sites, the different contributions of Δ_intH^{SBSPy site-metal} and Δ_intH^metal-metal determined the Δ_adsH value. The differences in Δ_intH^{SBSPy site-metal} during Cu(II) and Zn(II) adsorption on SBSPy were mainly related to the presence of different adsorption sites on SBSPy, with different affinities for Cu(II) and Zn(II), namely, the carboxylate groups of succinyl (0.71) and pyromellityl (0.25) units. On the other hand, the differences in Δ_intH^metal-metal during the adsorption of Cu(II) and Zn(II) on SBSPy were mainly related to different interactions between metal ion species adsorbed on the surface of SBSPy, as the θ value increased. Therefore, the less positive ∆_adsH values for Zn(II) adsorption, compared to Cu(II) adsorption, could be mainly attributed to different balances between Δ_intH^{SBSPy site-metal} and Δ_intH^metal-metal, in the θ range studied.

Changes in free energy and adsorption entropy

The thermodynamic parameters for adsorption of Cu(II) and Zn(II), respectively, on SBSPy were Δ_adsG° = − 28 ± 1 and − 25 ± 1 kJ mol^-1, Δ_adsH° = 9.3 ± 0.2 and 14.2 ± 0.1 kJ mol^-1, and TΔ_adsS° = 37 ± 1 and 39 ± 1 kJ mol^-1. For thermodynamic processes at constant temperature and pressure, Δ_adsG is the thermodynamic potential of the process. Teodoro et al. (2016), Elias et al. (2019), and Almeida et al. (2019) reported similar adsorption energy changes for transition metals (Co(II), Cu(II), and Ni(II)) adsorbed on cellulosic and lignocellulosic materials modified with different carboxylic acid anhydrides. For both systems studied here, the Δ_adsG° values were negative, with the migration of metal ions from the liquid phase to the SBSPy surface prevailing over the free forms of adsorbent and adsorbate in solution. The Δ_adsH° and TΔ_adsS° values were positive for the two systems studied here, indicating that the adsorption of both metal ions on the surface of SBSPy was entropically favored. The entropic contribution could be mainly attributed to water molecules released from the solvation shells of metal ions and the SBSPy adsorption sites, and the corresponding balance associated with migration of the metal ions from the bulk solution to the surface of SBSPy, to form new interactions. The magnitude of the TΔ_adsS° term for adsorption of both metal ions on SBSPy suggested that water molecules from the solvation shells of the metal ions migrated to the solution after adsorption, which could be attributed to the formation of inner-sphere complexes between SBSPy adsorption sites and metal ions. Since the Δ_adsH values obtained by ITC included the contributions of three subprocesses, including Δ_intH^{SBSPy site-metal}, it was not possible to use the Δ_adsH value to distinguish between physisorption and chemisorption.

Continuous adsorption in a fixed-bed column

The amounts of adsorbed (w_ads) and desorbed (w_des) metal ions, the maximum adsorption capacity of the bed (Q_max,exp), and the desorption efficiency (E_des) for each cycle are shown in Table 5 for the two adsorption systems studied. The regeneration of SBSPy proved to be feasible, since the E_des values were close to 100% in all the cycles. The values of the operating parameters (Table 5) for the adsorption cycles indicated that there were no significant decreases of Q_max,exp for the two adsorption systems. Therefore, it was feasible to use SBSPy as an adsorbent in several cycles. These results showed the technical viability of using SBSPy as an adsorbent in a fixed-bed column to remove metal ions from contaminated water.

Table 5 Operating parameters used in three cycles of adsorption and desorption of Cu(II) and Zn(II) on SBSPy in a fixed-bed column at 25 °C

The curves obtained by fitting of the experimental data using the Thomas, Bohart-Adams, and ILE models are shown in Figure 13. The estimated model parameters obtained by the fitting are provided in Table 4. For both adsorption systems, the Thomas and Bohart-Adams provided satisfactory fits to the experimental data, with low RMSE and χ²_red values, and high R²_adj values. In addition, the Q_max values estimated by the Thomas and Bohart-Adams were close to the Q_max,exp values. According to Chu (2010), when bC₀ >> 1, the Langmuir isotherm approaches the rectangular isotherm and, consequently, the Thomas model approximates to the Bohart-Adams model, with the pseudo-second-order rate constant (k_Th) of the Thomas model approximating to the quasi-chemical rate constant (k_B-A) of the Bohart-Adams model. Therefore, since bC₀ >> 1 for both adsorption systems studied (25.2 with Cu(II) and 7.3 with Zn(II)), the Thomas and Bohart-Adams models could be used to describe the adsorption of both metal ions on SBSPy. The adsorption rate constants, k_Th and k_B-A, consider the combination of all the steps involved in the adsorption process (film diffusion, intraparticle diffusion, and adsorption). For the two adsorption systems studied, the k_Th and k_B-A values were similar, under the same operating conditions.

Figure 13

Breakthrough curves for adsorption of a Cu(II) and b Zn(II) on SBSPy in a fixed-bed column at 25 °C ([Cu(II)] = [Zn(II)] = 1.4 mmol L^-1, pH 5.5, V̇ = 2.35 mL min^-1, 0.5 g SBSPy)

The ILE model was also used to model the breakthrough curve and estimate the operating parameters of the continuous adsorption system. In order to fit the breakthrough curve, this model is fed with the physical properties of the adsorbent and the adsorption parameters obtained from single batch adsorption. To solve the ILE model, the Langmuir isotherm was used, since it provided the best description of single batch adsorption of Cu(II) and Zn(II) on SBSPy. As shown in Figure 13a–b, the ILE-Langmuir model provided a good fit to the breakthrough curve, especially for the experimental data closer to bed saturation, but with poorer prediction of the initial data points closer to the breakthrough point. This could have been related to the assumptions of the model, which uses an approximation by local and instantaneous equilibrium, assuming that the mass transfer of the solute from the fluid to the solid is relatively fast, with axial dispersion being considered relevant for the process.

The mass transfer resistance for transport of the solute from the fluid to the solid was high, as shown by the steepness of the breakthrough curve, which is directly proportional to the mass transfer resistance (Worch 2012). This high mass transfer resistance could provide an explanation for the lower Q_max values obtained for continuous adsorption in a fixed-bed column, compared to single batch adsorption. Furthermore, the mass transfer resistance for transport from the fluid to the solid phase is higher in continuous adsorption using a fixed-bed column under a non-turbulent flow regime, compared to batch adsorption (Viegas et al. 2014). Therefore, the use of an inlet flow rate different from that employed here could allow a longer contact time between metal ions in the fluid phase and SBSPy particles, resulting in higher values of Q_max, EAP, and H (Xavier et al. 2018). The high inlet flow rate employed in this study also affected the length of the mass transfer zone (Z_MTZ), as well as the EAP and H values for both adsorption systems, leading to lower performance than expected in the continuous adsorption operation (Table 4). The EAP and H values for Cu(II) adsorption in a fixed-bed column were higher than for Zn(II) adsorption. Furthermore, the Z_MTZ value was higher for Cu(II) adsorption, compared to Zn(II) adsorption. Therefore, this indicated that the mass transfer resistance was lower for Cu(II) adsorption than for Zn(II) adsorption, which was corroborated by the higher steepness of the breakthrough curve for Cu(II) adsorption.

Comparison with literature data for Cu(II) and Zn(II) adsorption on different adsorbent materials

Table 6 lists some adsorbents prepared from cellulose, lignocellulosic biomass, algae, fungal biomass, and vermiculite, used to remove Cu(II) and Zn(II) from single-component spiked aqueous solutions, employing batch and fixed-bed column systems, in the pH range from 2 to 6.3. For batch adsorption, SBSPy at low adsorbent dosage exhibited high Q_max values for Cu(II) and Zn(II), which were comparable to the values reported in the literature. The Q_max values of SBSPy for Cu(II) and Zn(II) were much higher than the values obtained using raw SB. For continuous adsorption in a fixed-bed column, SBSPy also exhibited high Q_max values for Cu(II) and Zn(II). In addition, the ability to regenerate and reuse SBSPy in both batch and continuous modes confirmed its potential as an adsorbent for metal ions, since it could enable not only the removal of pollutants from an effluent, but also the recovery of the metal ions for possible reuse.

Table 6 Compilation of different adsorbent materials reported in the literature for removal of Cu(II) and Zn(II) from single-component spiked aqueous solutions in batch and continuous (fixed-bed column) systems

Conclusions

The chemical modification of raw SB with succinic and pyromellitic anhydrides, using a one-pot reaction, was successfully accomplished, yielding an efficient, selective, and reusable adsorbent (SBSPy) possessing adsorption sites with different affinities for Cu(II) and Zn(II). The FTIR and ¹³C Multi-CP SS NMR spectra of SBSPy showed that the order of addition of the carboxylic acid anhydrides directly affected the synthesis yield and, especially, the quantities of succinyl and pyromellityl units introduced into the SB structure. Succinic anhydride should be added to the reaction medium first, in order to introduce more succinyl units into the SB structure. The results indicated selectivity of the adsorption sites, with the succinate moiety being responsible for increasing Cu(II) adsorption, while the pyromellitate moiety was responsible for increasing Zn(II) adsorption. Analyses using ¹³C Multi-CP SS NMR showed that under the optimized synthesis condition, 0.25 pyromellityl units and 0.71 succinyl units were covalently linked to each cellobiose unit. Relaxometry analyses showed that interstitial scale spaces decreased. This indicated that the succinyl and pyromellityl groups occupied previously free spaces, mainly at the inner microfibril and lumen scales. The use of diffusion kinetics models indicated that both film and intraparticle diffusion contributed to the adsorption rate. Thermodynamic data showed that the adsorption was endothermic and entropy-driven. SBSPy was successfully used in a fixed-bed column, in three cycles of adsorption-desorption. Therefore, SBSPy has potential to be used as a biodegradable adsorbent in water and wastewater treatment plants, with the advantage of being able to be regenerated and reused, enabling the safe recovery of toxic metal ions removed from contaminated water.