Isotherms, kinetics, and thermodynamics of boron adsorption on fibrous polymeric chelator containing glycidol moiety optimized with response surface method

2.1 Synthesis of PE/PP-g-PVAm-G chelator

Radiation induced grafting was used to modify PE/PP non-woven sheet by placing the samples in PE zipped bags containing N₂ gas and sealed thermally. After that, the sample-containing bags were placed on dry ice before being irradiated with an electron beam accelerator (EPS 3000, Nissin High Voltage, Japan) at 25 kGy/pass with an absorbed dose of 300 kGy. The beam current was 10 mA, and the acceleration energy was 2 MeV. The samples irradiated were transferred into evacuated ampoules, and later filled with oxygen-free grafting solutions containing 20 vol% diluted NVF/toluene solution homogenized by bubbling. The ampoules were immersed in a thermostatic bath for a period of 3 h and reaction temperature of 70 °C for the grafting process. The grafted samples were taken from the ampoules and rinsed with methanol after the process a few times before being dried overnight under vacuum at 60 °C. The degree of grafting (DG) was gravimetrically estimated as 120 %. More details on RIG of NVF onto irradiated PE/PP non-woven sheets under various conditions can be found elsewhere in our previous publication (Afolabi et al., 2021a).

The grafted fibrous poly(N-vinyl formamide) (PNVF) chains in PE/PP sheets were hydrolyzed to polyvinylamine (PVAm) under reflux with 2 M solution of NaOH at 80 °C for 4 h in an oil bath. After the reaction, the treated sample was washed and dried at 60 °C under a vacuum oven. The amine content of the PVAm sample was determined by placing 0.5 g of the samples in 10 mL of 1 M HCl for 24 h. 2.5 mL from the residual acidic solution was titrated against 0.1 M NaOH solution in the presence of phenolphthalein (Senkal and Bicak, 2003). The total amine density was estimated as 5.13 mmol·g⁻¹.

2.2 Experimental design for glycidol immobilization

The PVAm chelator precursors were functionalized by dispersing the samples in DI water under stirring. Dropwise additions of glycidol were added to the mixture at room temperature along with continuous stirring before transferring to an oil bath heated at predetermined temperature and reaction time under reflux. The various reaction parameters were varied according to the experimental design for the purpose of optimization to determine the reaction condition with the best response. After the reaction, the samples were washed with an excess amount of DI water and oven-dried at 60 °C in a vacuum to constant weight. Fig. 2 shows a scheme for the grafting of NVF onto PE/PP non-woven sheet, followed by base hydrolysis and the immobilization of glycidol moiety into the PVAm chelator precursor.

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Fig. 2

Synthesis scheme for the grafting of NVF onto PE/PP non-woven fiber sheet, base hydrolysis, and the immobilization of glycidol.

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Three variable process parameters viz; concentration of glycidol, reaction time and temperature were optimized using BBD with Design Expert software (Version 10.0.1.0, Stat-Ease, Inc., Minneapolis, USA) for statistical model formation. The yield which is referred to as the glycidol functional group density was set as the system response (dependent variable). The total number of experimental runs was 17 with three-coded levels -1, 0 and + 1 involving three independent variables used for the prediction of optimum yield. Table 2 shows the ranges of the experimental values of independent variables. The glycidol functional group density in PE/PP-g-PVAm-G was calculated with Eq. (1):

The experimental ranges selected for the independent variables were 5−15 vol% of glycidol concentration, 60−80 °C for reaction temperature and 1−2 h of reaction time. The independent variables and experiment data from response surface analysis are presented in Table 3. The application of the p-value test to experimental results was used for the establishment of whether the parameter is significant to a 95% level of confidence. The predicted and corresponding experimental values of glycidol functional group density were compared. For the purpose of validating the model adequacy with the experimental data, the analysis of variance (ANOVA) was used. The determination coefficients R², adjusted R² and predicted R² from the analysis were estimated to check the model developed. Consequently, the values predicted by the equation developed from the model were compared with the verification experiments performed at optimum conditions. The independent variables interactions and their corresponding influence on the glycidol functional group density were examined using three-dimensional (3D) response surface plots.

2.3 Characterization of PE/PP-g-PVAm-G chelator

The crystallinity and structural properties of PE/PP-g-PVAm-G were analyzed using a Malvern PANalytical X'Pert3 powder diffractometer at 40 mA with a Cu anode material (Kα1 = 1.5406 A°, Kα2 = 1.5444 A°) in the Bragg's angle range of 5−50°. The chemical compositions of PE/PP-g-PVAm-G chelator samples were characterized using Fourier transform infrared (FTIR) spectrophotometer (Nicolet Magna IR-750 spectrometer) composed of diamond ATR with a wavelength ranging from 650 to 4000 cm⁻¹. Field emission scanning electron microscopy (FESEM) was used to determine the morphology using Zeiss Supra 55 VP instrument and energy dispersive x-ray (EDX) spectrometer by Zeiss model EVO LS15 VPSEM was used to provide evidence of the distribution of various elements in the chelator at 15 kV. Thermogravimetric analysis (TGA) was used to test the thermal stability of the chelator using the Mettler Toledo TGA/SDTA 851e analyzer at a heating temperature range of 30–700 °C and a heating rate of 10 °C.

2.4 Batch adsorption experiment, isotherms, and kinetics studies

The adsorption properties of PE/PP-g-PVAm-G chelator were studied to assess its performance. A stock solution of boric acid was prepared in a plastic container by dissolving 5.716 g of H₃BO₃ in DI water and diluted to 1000 mL. Further solutions of desired concentrations (10−100 mgL⁻¹) were later freshly prepared for each experimental work. The effect of different pH of the solution on the adsorption of boron was evaluated in the range of 2−11 using 0.5 g of the adsorbent in 150 mL of 100 mg/L boric acid solution in plastic Erlenmeyer flasks and the solution is continuously shaken at 30 °C with a speed of 210 rpm. The adsorption isotherms and kinetics study were investigated with different concentrations of boron (10−100 mgL⁻¹) at a fixed fibrous chelator dose of 0.5 g in an Erlenmeyer flask containing 150 mL boric acid solution. The flask was shaken continuously at 210 rpm for 3 h in an incubator shaker. Few aliquots were withdrawn at predetermined time intervals and analyzed. The thermodynamic was studied in a similar condition at various temperatures (298 K, 303 K and 313 K). At the end of each experiment, the residual concentration of boron was spectrophotometrically determined at a wavelength of 610 nm using Shimadzu UV-2600 uv–visible spectrophotometer.

2.5 Analytical method

The boron concentration at equilibrium was measured using the carmine method. The procedure involves the addition of a BoroVer®3 reagent powder pillow into a 75 mL concentrated H₂SO₄ aqueous solution. The mixture was swirl for 5 min until the powder dissolves completely. 2 mL of the specimen and DI water were accurately pipetted into different 125 mL Erlenmeyer plastic flasks. In each flask, 35 mL of the prepared BoroVer®3/H₂SO₄ solution was added, swirled, and allowed to react for 30 min. The sample prepared was inserted into the cell holder of the UV–Vis spectrophotometer (Shimadzu UV-2600) at the wavelength of 610 nm. Eq. (2) was used for the estimation of the boron quantity at equilibrium $q_e$ (mg/g).

2.6 Boron adsorption in the presence of foreign ions

The effect of foreign ions on the adsorption properties of the boron fibrous chelator coexisting in a solution of Na⁺, Ca²⁺, Cl^- and SO₄^2- were studied. Aqueous solutions containing 300 mgL⁻¹ of each ion and 0.5 g of PE/PP-g-PVAm-G chelator were added to 100 mgL⁻¹ boric acids. The adsorption process was carried out for 3 h at 210 rpm. The quantity of boron adsorbed at equilibrium was then determined.

2.7 Re-usability of PE/PP-g-PVAm-G

The PE/PP-g-PVAm-G chelator was recovered by solvent desorption technique after the adsorption process. It was removed after the adsorption process from the solution and dipped into 1 M HCl solution to strip boron from the chelator, neutralized with 1 M NaOH and water washed. The regenerated PE/PP-g-PVAm-G was then re-applied for the adsorption process. The re-usability efficiency (RE%) was determined according to Eq. (3):

3.1 Fitness of experimental data to model

A mathematical model was developed and analyzed from the experimental data fitted in the software. The BBD analysis used for testing the fitness of the model indicated that the quadratic and linear models were statistically significant with the p-value<0.0001 while the cubic model was found to be aliased and could not be used for modeling as shown in Table 4. Hence, in this study the quadratic model was selected due to its good R² values (R² = 0.9954, adjusted R² = 0.9895 and predicted R² = 0.9573) suggested. The final equation of the model explaining the mathematical interaction between the three independent variables: A, B and C with the response in the range of the experimental data is represented by Eq. (4).

3.2 Statistical analysis

The application of the ANOVA analysis was carried out to evaluate the response surface of the quadratic model and for the determination of the model significance as well as the individual term involved with respect to their p-values. The F-value of the model (169.28) suggests that the model is significant, with only a 0.01 percent chance of this F-value could occur due to noise. Consequently, the high F-value and low Prob > F value 0.0001 give an indication of Fisher’s variance ratio significance as well as confirmation of the quadratic model with a high degree of fitness. Table 5 shows that the various terms A, B, C, AB, AC, BC, A², B², and C² from the model were significant because their Prob > F is <0.0500. The “lack of fit” F-value (1.56) implies that this factor is not significant. There is a good correlation between the predicted and adjusted R² value while the Adeq precision for measuring the signal to noise ratio of the model is 49.442, suggesting that it can be utilized for navigation of the design space. Thus, these results show that the quadratic model predicted is in good agreement with the responses from the experimental and can therefore be adopted.

The ANOVA data was used to check the normality of the residuals as well as the predicted and actual responses as illustrated in Fig. 3. The plot of normal probability against the studentized residuals in Fig. 3a shows a linear trend which indicates the error distribution. As such, the model can be said to adequately predict the responses based on the reaction parameters. On the other hand with Fig. 3b showing the plot of predicted value indicate the appropriateness of the model and proper data dispersion (Nallappan et al., 2018).

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Fig. 3

Plot of (a) normal probability vs. studentized residuals and (b) predicted vs. actual numbers of response.

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3.3 Effects of independent variables and analysis of response surfaces

The interactions between the independent variables (concentration of glycidol, temperature, and reaction time) and glycidol’s functional density in the fibrous chelator are represented by Fig. 4 as established by the ANOVA analysis. The numerical optimization technique of RSM was used to optimize the variables. The 3D plot of the response surface in Fig. 4a shows the variation of glycidol density with the concentration of glycidol and temperature at a constant reaction time of 90 min. An increase in the concentration of glycidol and reaction temperature results in an increase in glycidol density. A maximum glycidol density was achieved at a concentration of 12.85 vol% and a temperature of 80 °C, respectively. This observation can be ascribed to the temperature-enhanced diffusion of the glycidol moiety into the PVAm fibrous chelator precursor. The 3D surface plot for glycidol density versus reaction time and concentration at a constant temperature of 80 °C is presented in Fig. 4b. Similarly, the glycidol density increased with an increase in both reaction time and concentration. The maximum glycidol density was recorded at a reaction time of 107.36 min and concentration of 14.02 vol% after which there was no further increment achieved because of reaching full functionalization. Fig. 4c shows the 3D plot interaction between the temperature and reaction time at a constant concentration of 12.85 vol%, in which the glycidol density increases with a rise in temperature and reaction time. It can be observed that a maximum glycidol density was achieved when the temperature and reaction time is 77.46 °C and 114.14 min, respectively.

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Fig. 4

Response surface plots for the effects of: (a) temperature vs. glycidol concentration, (b) reaction time vs. glycidol concentration (c) reaction time vs. temperature on the glycidol density in the chelator.

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3.4 Experimental validation of glycidol density

The predicted value of glycidol density from the numerical optimization (model) was validated under a chosen optimum parameter of 11.8 vol%, 78.9 °C and 109.4 min for glycidol concentration, temperature, and reaction time, respectively in triplicate runs. It is worth mentioning that the desirability of the response for the selected parameters is 1, as such the validation experiment performed was found to be 4.98 mmol·g⁻¹. This value agrees well with the 4.97 mmol·g⁻¹ glycidol density predicted with negligible deviation. Thus, this confirms a successful optimization of the glycidol density in the fibrous chelator using BBD despite the use of three levels for the independent parameters’ values in this study.

3.5 Properties of PE/PP-g-PVAm-G

The diffraction pattern of the PE/PP-g-PVAm-G chelator is shown in Fig. 5a. Five major crystalline peaks from the PE and PP substrate were observed to agree with previous studies (Afolabi et al., 2021a; Furukawa et al., 2006). This indicates that the chelator maintained its structural integrity required for the boron adsorption. The infra-red spectrum of the PE/PP-g-PVAm-G is presented in Fig. 5b. The band at 1032 cm⁻¹ depicts the C—O stretching vibration of glycidol epoxy ring-opened linkage while the peak at 1244 cm⁻¹ can be ascribed to amine's C—N stretching vibration. The peaks located at 2849 and 2916 cm⁻¹ are associated with CH₂ antisymmetric and symmetric stretching of the PE/PP skeletal structure (Hayashi et al., 2018). The very broad and strong peak around 3323 cm⁻¹ shows the presence of the O—H group for chelation in the material. These characteristics peaks are associated with chelating chelator for boron (Hoshina et al., 2021). Results of chemical changes resulting from grafting and hydrolysis were discussed in our previous publication (Afolabi et al., 2021a). The PE/PP-g-PVAm-G chelator's thermal stability is revealed by TGA. Fig. 5c depicts three stages of weight loss. The first weight loss in the temperature range of 32−140 °C is corresponding to the dehydration of the bound water molecules caused by the imparted hydrophilic character resulting from incorporation of glycidol moiety. The second weight loss was at approximately 220−385 °C which can be ascribed to the PVAm grafts depolymerization. The third weight loss (385−480 °C) denotes a typical PE/PP substrate thermal decomposition transition (Xu et al., 2019). The FESEM image (Fig. 5d) corresponds to the structure of the PE/PP-g-PVAm-G with no apparent damage in the PE/PP non-woven fibrous sheet. The EDX mapping of PE/PP-g-PVAm-G results indicates that the fibrous chelator mainly contains C (76.9%), O (18.3%) and N (4.8%) elements. The rich distribution of O indicates a random functionalization and excellent dispersion of functional groups throughout the polymeric structure, thereby making it suitable for the adsorption of boron.

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Fig. 5

(a) XRD pattern, (b) FTIR spectrum, (c) TGA thermogram and (d) FESEM-EDX mapping of PE/PP-g-PVAm-G.

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3.6 Exploring the factors influencing the experiment

3.6.1

3.6.1 Effect of pH

The distribution and quantity of each boron anion in the aqueous solution varies at different pH levels, likewise the forms at which they exist is complex. As a result, investigating boron-adsorbent complexation in various acid-base conditions is crucial. The influence of different pH solution ranges on the adsorption capacity of boron was investigated to determine the optimum pH value. The adsorption capacity of the chelator was found to initially increase from pH 2 until pH 7 beyond which it decreases as depicted from Fig. 6 illustrating the variation of adsorption capacity with pH of the treated solution. The increase in adsorption capacity with the increase in pH value can be attributed to the fact that fewer protons become available in the solution to compete with the boron ion for binding sites (glycidol) on the adsorbent surface as the pH increases (Oladipo and Gazi, 2016). At neutral pH, the adsorption capacity reaches its maximum value (21.4 mg·g⁻¹) in which formation of bis-chelate ester complex is predominant. Further increase in pH values (pH great than 7) leads to a decrease in adsorption capacity due to competition between borate ions and the growing amount of hydroxyl groups in the solution. This behaviour can be explained by the fact that boric acid, B(OH)₃ is an extremely weak, monobasic acid (pKa = 9.23) that acts as a Lewis acid by accepting hydroxyl groups in water to form B(OH)₄⁻ species, rather than donating proton (Sanfeliu et al., 2012). Similar result was reported for adsorption of boron by boron-selective adsorbent with low-cost materials (Sanfeliu et al., 2012), and N-methylglucamine-type cellulose derivatives (Inukai et al., 2004). A comparison of the chelator in this study with different boron-selective adsorbents and commercial resins performance reported in literature are summarized in Table 6.

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Fig. 6

Adsorption of boron by PE/PP-g-PVAm-G chelator as a function of pH.

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Table 6 Comparison of adsorption properties of the PE/PP-g-PVAm-G chelator in this study with previous studies for adsorbents containing vicinal diols.

Adsorbents material	Morphology	Ligands	Te (min)	qe (mg·g−1)	pH	References
Nylon-6 based adsorbent	Fibrous	NMDG	120	12.4	7	(Ikeda et al., 2011)
Terpolymer-based	Bead	Glycidol	30	17.3	6.5	(Gazi & Bicak, 2007)
Cellulose	Fibrous	NMDG	> 60	12.1	8.7	(Inukai et al., 2004)
Diaion CRB −03	Granules	NMDG	> 60	11.6	7	(Ting et al., 2016)
Chitosan	Bead	NMDG	400	20.4	7	(Wu et al., 2019)
Terpolymer-based	Bead	Glycidol	80	32.4	6.6	(Senkal & Bicak, 2003)
Nylon-6 based adsorbent	Fibrous	NMDG	30	13.8	7	(Ting et al., 2016)
Polyacrylonitrile	Nanofibrous	NMDG	100	5.5	6–7	(J. Wang et al. (2014b))
PP/PE based adsorbent	Fibrous	Glycidol	60	21.4	7	This study

T_e = Equilibrium time.

3.6.2

3.6.2 Adsorption equilibrium isotherms

Adsorption isotherm relates the quantity of adsorbate adsorbed onto the fibrous chelator to the quantity of adsorbate remaining in the solution once the adsorption process has reached equilibrium. The isotherm parameter values provide information about the chelator surface characteristic, as well as its affinity for the adsorbate, and are crucial for optimizing the chelator usage (Asare et al., 2021). Here, the adsorption isotherms examination is to demonstrate how the PE/PP-g-PVAm-G and the boron adsorbate are behaving when in contact with the solution. The fitting of adsorption isotherm data to various adsorption isotherm models is a critical step in determining the most appropriate adsorption isotherm model for design purposes. The amount of boron adsorbed onto PE/PP-g-PVAm-G was studied using six different adsorption isotherms including two parameters (Langmuir, Freundlich, and Temkin) and three parameters (Redlich-Peterson, Toth, and Sips) equations. Although linear isotherms have been utilized to describe adsorption systems in many studies, however, non-linear isotherms were used in this work for more accuracy. The adsorption isotherms were established based on certain assumptions. As a result, linearizing them would undermine the assumptions that influence their development and could lead to an erroneous solution. The non-linear form of the isotherms, despite its complexity, gives a remarkable and precise mathematical approach to compute the isotherm parameters. Hence, to prevent inaccuracy caused by linearization, the parameters of the various isotherms in this study were obtained with the non-linear technique.

The Langmuir isotherm model is representing the monolayer coverage of boron on the chelator surface at a constant temperature. It hints towards the homogeneity of the surface and assumes that the application of intermolecular forces by the chemical surface of unsaturated atoms does not extend furthermore than the adsorbed molecule diameter (Jin et al., 2019). This model also assumes that all adsorption sites have the same energy properties, and that adsorption takes place on a structurally homogeneous surface. The Langmuir equation has the following expression:

(5)

$$q_e=\frac{q_m{K}_L{C}_e}{1+K_L{C}_e}$$

(6)

$$R_L=\text{1/}{{(1+K}_{L}C}_0)$$ where $C_e$ and C_o are the liquid phase equilibrium concentration and initial concentration of boron. The equilibrium adsorption capacity is represented by $q_e$ (mg·g⁻¹), while the maximum amount of adsorbed boron per unit weight of the chelator is denoted by $q_m$ (mg·g⁻¹). The K_L (L·mg⁻¹) is related to the Langmuir equilibrium constant with binding sites affinity indicating adsorption reaction bond energy between boron and chelator (Chen et al., 2019). The separation factor of Langmuir (R_L) indicates whether the adsorption is: favorable when R_L value is between 0 and 1, unfavorable when > 1; Irreversible when = 0 and linear when = 1.

The Freundlich adsorption isotherm model portrays the heterogeneity of the surface and the adsorbed molecule’s multilayer adsorption. Therefore, it is generally used for heterogeneous systems, and the amount of adsorbed molecule is the aggregation of all the adsorption sites (each having bond energy) (Luo et al., 2020b). The equation of Freundlich isotherm can be expressed in Eq. (7).

(7)

$$q_e=K_F{C}_e^{1/n}$$ where $C_e$ (mgL⁻¹) represents the liquid phase equilibrium concentration and $q_e$ (mg·g⁻¹) is the adsorption capacity of boron at equilibrium, while $K_F$ (mg·g⁻¹)(L·mg⁻¹)^1/n and 1/n represent the Freundlich constant as well as heterogeneity factor which indicates the intensity of adsorption, respectively.

The Temkin isotherm is derived on the assumption that the decrease in adsorption heat is linear rather than logarithmic and that the adsorption process is characterized by a uniform distribution of binding energies at the chelator surface. The non-linear equation of Temkin isotherm can be represented by:

(8)

$$q_e=\frac{\mathit{RT}}{b_T}In(A_T{C}_e)$$ where b_T and A_T are Temkin isotherm constants, RT/b_T is a constant related to the heat of adsorption. The absolute temperature and the universal gas constant (8.314 J mol⁻¹ K⁻¹) are respectively denoted by T and R.

The Sips isotherm eliminates the limiting deficiencies associated with both Langmuir and Freundlich isotherms by combining them into a single equation (Asare et al., 2021). The Sips isotherm is expressed as:

(9)

$$q_e=\frac{q_s{K}_s{C}_e^{1/ns}}{1+K_s{C}_e^{1/ns}}$$ where q_s (mg·g⁻¹) is the Sips isotherm maximum adsorption capacity, while Ks (Lg⁻¹) is the Sips constant, and 1/ns is the Sips exponent. If 1/ns = 1, it denotes the process takes on a homogenous surface.

The Toth isotherm is a three-parameter isotherm that can be used for describing the adsorption behavior on a heterogeneous surface. The isotherm can describe how heterogeneous surface adsorption at low and high concentration boundaries of a particular adsorbate behaves. The Toth isotherm is written as follows:

(10)

$$q_e=\frac{q_t{K}_t{C}_e}{{\left[1+{(K_t{C}_e)}^t\right]}^{1/t}}$$ where q_t (mg·g⁻¹) represents the Toth maximal adsorption capacity, while K_t is the Toth isotherm constant, and the Toth exponent is 1/t. The isotherm simplifies to the Langmuir isotherm equation as t approaches unity (Asare et al., 2021).

Redlich-Peterson isotherm can be referred to as hybrid isotherm which features both Langmuir and Freundlich isotherms, with the existence of three parameters in the empirical equation (Foo and Hameed, 2010). Thus, due to its versatility, this model is applied for both homogenous and heterogeneous systems. The Redlich-Peterson isotherm can be expressed using Eq. (11).

(11)

$$q_e=\frac{K_R{C}_e}{1+A_R{C}_e^g}$$

where $C_e$ (mg/L) is the concentration at equilibrium in the liquid phase, and $q_e$ (mg·g⁻¹) is the adsorption capacity of boron at equilibrium, while $A_R$ (mg⁻¹) and $K_R$ (Lg⁻¹) are Redlich-Peterson adsorption isotherm constants. The isotherm exponent (g) values are ranging between 0 and 1. Different studies have proven Redlich-Peterson isotherm to be more accurate when compared with Langmuir and Freundlich isotherms due to the three unknown parameters involved in it and thus, both isotherms’ derivations can be achieved from Eq. (11) (Foo and Hameed, 2010).

Fig. 7 represents the boron adsorption equilibrium isotherms for the PE/PP-g-PVAm-G chelator. The values of various constants and fitting data including the correlation coefficient R², and χ² are also listed in Table 7. According to the estimated data from the various models of the two-parameter isotherms, the Langmuir correlation coefficient R² is 0.9799, which is greater than the values for the other two isotherms. Moreover, it shows the least χ² (0.0092) value. This data suggests that monolayer adsorption occurred on a homogeneous surface during the adsorption process. The monolayer saturation capacity (q_m) for boron on PE/PP-g-PVAm-G was estimated as 25.7 mg·g⁻¹ while the R_L values estimated were found to fall between 0 and 1 which gives an indication that the adsorption of boron is favorable (Kipçak and Özdemir, 2012; Oladipo and Gazi, 2016). Consequently, in the Freundlich isotherm model, the 1/n value obtained is below one. This suggests that the adsorption process followed a favorable normal Langmuir isotherm as indicated by the R_L values. The adsorption process is not represented by Temkin isotherm due to its correlation coefficient value, however, the heat of adsorption RT/b_T was estimated as 11 kJ mol⁻¹. The typical range of bonding energy for ion-exchange mechanisms has been reported in the range of 8–16 kJ mol⁻¹ (Baker, 2009; Wei et al., 2011).

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Fig. 7

Plots of: (a) two-parameter and (b) three-parameter isotherms of boron adsorption by PE/PP-g-PVAm-G.

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Table 7 Two-parameter isotherms for boron adsorption onto PE/PP-g-PVAm-G.

Langmuir	Freundlich	Temkin
KL = 0.203	KF = 5.18	AT = 3.68
qm = 25.7	1/n = 0.403	RT/bT = 11
R2 = 0.9799	R2 = 0.9528	R2 = 0.9659
χ2 = 0.0092	χ2 = 0.191	χ2 = 2.423

From Table 8, the correlation coefficient R² of the three-parameter isotherms is higher than all the two-parameter isotherms. This is suggesting the applicability of three-parameter isotherm models to represent the adsorption equilibrium of boron by PE/PP-g-PVAm-G chelator. The correlation coefficients in Redlich-Peterson, Toth and Sips are 0.9953, 0.9951 and 0.9858, respectively. The Redlich-Peterson and Toth adsorption model showed the highest R² value and leads to the best regression coefficients. Similar result was observed by Benzaoui et al. (2018). More so, both the Redlich-Peterson and Toth isotherm constant values i.e., g and t are not far from unity, indicating that it is approaching the Langmuir isotherm but not the Freundlich isotherm. Thus, Langmuir is a special case of Redlich-Peterson when the constant g approaches unity (Ayawei et al., 2017; Ding et al., 2017). The value of the Sips isotherm constant (1/ns) also approaches unity too, suggesting that boron uptake by PE/PP-g-PVAm-G occurs on a homogenous surface. This finding is consistent with the two-parameter isotherm analysis. Comparable results were reported for nanofibrous chelator containing NMDG counterpart for boron removal (Nallappan et al., 2019).

Table 8 Three-parameter isotherms for boron adsorption onto PE/PP-g-PVAm-G.

Redlich-Peterson	Toth	Sips
KR = 11.57	Kt = 1.29	Ks = 5.52
AR = 1.21	qt = 6.63	qs = 24.85
g = 0.74	t = 0.97	1/ns = 1.103
R2 = 0.9953	R2 = 0.9951	R2 = 0.9858
χ2 = 0.0003	χ2 = 0.477	χ2 = 1.429

3.6.3

3.6.3 Adsorption kinetics

The adsorption kinetics show how the adsorption process changes over time. Thus, the latter is a critical variable that must be considered. The pseudo-first-order, pseudo-second-order, and intraparticle diffusion models were considered for the determination of the suitable model as well as for the explanation of the experimental data mechanism. The pseudo-first-order adsorption model theorized that the rate is proportional to the number of the unoccupied adsorption sites and is expressed as:

(12)

$$q_t=q_e(1-e^{-k_{1}t})$$ where $q_e$ (mg·g⁻¹) is the adsorption capacity of boron at equilibrium and $q_t$ is the adsorption capacity of boron at any given time t (min). The k₁ (min⁻¹) represents the equilibrium rate constant for the pseudo-first-order model.

The pseudo-second-order rate expression is used to explain the chemisorption that involves valence forces through the exchange or sharing of electron as ion exchange and covalent forces between the adsorbent and adsorbate. The second-order rate expression is given below:

(13)

$$q_t=\frac{q_e^2{k}_{2}t}{1+k_2{q}_{e}t}$$ where $q_e$ (mg·g⁻¹) is the boron adsorption capacity at equilibrium and $q_t$ is the adsorption capacity of boron at any given time t (min). k₂ (min⁻¹) represents the pseudo-second-order equilibrium rate constant.

Fig. 8 shows the kinetic models with the impact of contact time on the removal of boron by PE/PP-g-PVAm-G at different concentrations and contact time. During the process of adsorption, the chelator was able to adsorb 70–85% of the saturated adsorption capacity within 30 min, and the chelator reaches the saturated adsorption capacity within 60 min because PE/PP-g-PVAm-G is rich in polyols. Henceforth, a substantial amount of boron diffused to the surface of the chelator at the start of the adsorption reaction, and the polyols and boron were continually complexed. As boron continuously occupies the adsorption sites, the adsorption rate is reduced until all of the adsorption sites are filled up, and the amount adsorbed tended to become saturated and constant (Luo et al., 2020b). Table 9 shows the data for pseudo-first-order rate constants k₁, pseudo-second-order rate constants k₂, calculated equilibrium adsorption capacity $q_e$ _(cal), R², and χ² for better understanding of the adsorption mechanism such as mass transfer and chemical reaction. The kinetics fitting results for the models indicate that the process does not follow pseudo-first-order kinetics. The pseudo-second-order kinetic best fit the experimental data as it provides the highest R², and lowest χ² values at different initial concentrations than the pseudo-first-order kinetic. This is because the pseudo-second-order kinetic $q_e$ values calculated corroborate more with the experimental results. Thus, the consistency of the ion exchange adsorption process with pseudo-second-order kinetic model further shows that the complexation between B(OH)₃ and the polyol groups from the chelator is controlled by chemical interaction (Lyu et al., 2017; Uba et al., 2020).

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Fig. 8

The Kinetic models plots for boron adsorption by the PE/PP-g-PVAm-G.

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Table 9 The adsorption kinetic parameters for boron adsorption by PE/PP-g-PVAm-G.

Kinetic models	Parameters	10 mg/L	20 mg/L	30 mg/L	50 mg/L	100 mg/L
Pseudo-first order	qe,(calc) (mg·g−1)	2.51	5.18	7.38	11.23	20.03
	k1 (min−1)	0.050	0.103	0.073	0.064	0.12
	R2	0.9811	0.9776	0.9936	0.9488	0.9872
	χ2	0.022	0.077	0.053	0.972	0.759
Pseudo-second order	qe,(calc) (mg·g−1)	3.05	5.77	8.90	13.82	22.76
	k2 (g·mg−1·min−1)	0.019	0.025	0.011	0.064	0.0081
	R2	0.9945	0.9932	0.9959	0.9872	0.9964
	χ2	0.007	0.0231	0.0337	0.243	0.190
Intraparticle diffusion	kp (mg·g−1·min1/2)	0.190	0.26	0.399	0.659	0.732
	C (mg·g−1)	0.94	2.83	3.89	5.33	13.94
	R2	0.7066	0.7477	0.7298	0.796	0.6607
	χ2	0.407	0.509	0.823	1.133	1.80

3.6.4

3.6.4 Mechanism of boron removal by PE/PP-g-PVAm-G

The mechanism involved in the boron removal by PE/PP-g-PVAm-G was evaluated with Eq. (14). The intraparticle diffusion model was adopted in this context. It is based on the theory that the fraction of boron removed depends on the chelating diffusivity of PE/PP-g-PVAm-G and the radius of boron. The intra-particle diffusion model expression is given as:

(14)

$$q_t=k_p{t}^{1/2}+C$$ where k_p (mg⁻¹·g⁻¹·min⁻²) is determined from the plot of $q_t$ versus t^1/2 as the intra-particle diffusion rate constant and C (mg·g_ad⁻¹) represents the boundary layer thickness and intercept. It is worth noting that the plot of $q_t$ versus t^1/2 provides a straight line through the origin for an adsorption process where intraparticle diffusion is the rate controlling step (Yao and Chen, 2017). However, the plot in Fig. 9 does not generate a straight line passing through the origin. This implies the presence of boundary layer, suggesting that intraparticle diffusion was not the sole mechanism controlling the removal process but other mechanisms were involved which has a chemisorption nature (Asare et al., 2021; Nallappan et al., 2019). Two major stages could be seen in the plot from Fig. 9. The first stage is faster and depicts the intraparticle diffusion where boron got transported from the surface of PE/PP-g-PVAm-G to its interior pores. The second stage is relatively slower and can be attributed to the attachment of boron to the active adsorption sites on the interior surface of PE/PP-g-PVAm-G through chemisorption. The external surface adsorption was less apparent, and this could be attributed to the fast boron diffusion onto the external surface of PE/PP-g-PVAm-G. This suggests that the first stage of diffusion is very fast and almost very instantaneous for this polymeric fibrous chelator when compared with granular adsorbents. This can be ascribed to the chelator's decreased in size and subsequent increase in the surface area coupled with the rise in the number of functional groups caused by higher glycidol density leading to a larger number of sorption sites which fastened the adsorption rate. The intercept is an indicator of the boundary layer thickness, suggesting a greater boundary layer effect on the adsorption process at high initial boron ion concentrations. This result is consistent with previous study on nanofibrous adsorbents for boron removal (Ting et al., 2016).

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Fig. 9

The intra-particle diffusion plots of boron adsorption by the PE/PP-g-PVAm-G.

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3.6.6

3.6.6 Boron adsorption in the presence of foreign ions

The presence of a large number of inorganic salts which are ionizable into various ions in aqueous solutions can reduce the chelator's adsorption capacity in surface water, industrial wastewater, and subsurface water sources. As a result, studying the selectivity properties of PE/PP-g-PVAm-G towards anions and cations in solutions is important. The adsorption selectivity study was conducted in the presence of foreign ions such as Na⁺, Ca²⁺, Cl^- and SO₄^2-. The sources of the various ions used in this study were NaCl, CaCl₂, KCl, and Na₂SO₄. The experiments revealed that, in the presence of boric acid, these foreign ions are also absorbed. The highest loading is observed for Ca²⁺ ions (1.67 mg·g⁻¹) as shown in Fig. 10. The foreign ion adsorption observed could be due to the precipitation of their hydroxides and the weak basicity of the tertiary amino group from the polymeric substrate (Gazi and Shahmohammadi, 2012). Fortunately, adsorption of those coexisting ions does not show a significant decrease in the boron loading capacity of PE/PP-g-PVAm-G. This may be due to the coordination capability of the polyol of the chelator. Not only that but may also be due to the influence of the inorganic salt ions occupying some of PE/PP-g-PVAm-G active sites, resulting in a modest reduction in boron adsorption capacity. Therefore, the chelator can be said to have good boron selectivity as well as anti-interference properties.

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Fig. 10

Adsorption capacities of the PE/PP-g-PVAm-G for boron and coexisting ions in simulated water.

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3.7 Re-usability study

The regeneration cycle result for the elution process is presented in Fig. 11. The result showed a trivial increase in capacity loss with a decrease in adsorptive efficiency after five adsorption/desorption cycles as evidenced by Fig. 11. This observation can be attributed to the fact that there is a decrease in active sites of PE/PP-g-PVAm-G. The decline in efficiency is <3% which indicates that the PE/PP-g-PVAm-G has a high recyclability and nearly maintains a constant regeneration efficiency after 5 cycles. The result implied that PE/PP-g-PVAm-G could be successfully regenerated as an effective adsorbing material for removing boron from contaminated solutions.

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Fig. 11

Re-usability of PE/PP-g-PVAm-G for boron adsorption.

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After the PE/PP-g-PVAm-G chelator is subjected to 5 cycles of adsorption–desorption, the changes in mass before and after adsorption was observed to be negligible. The infrared spectroscopy comparison of PE/PP-g-PVAm-G before and after the 5 cycles is displayed (Fig. 12). The results reveal that the PE/PP-g-PVAm-G functional groups remained unaltered after the 5 cycles of adsorption–desorption. This gives an indication that the fibrous chelator has a promising regeneration stability. To make the process green, the recovery of boron and the acid used to strip it should be considered to reach the pure water discharge. The recovered acid and boron can be further used.

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Fig. 12

IR of PE/PP-g-PVAm-G before and after 5 cycles.

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