Fractal-like kinetics for adsorption of Pb (II) on graphene oxide/hydrous zirconium oxide/crosslinked starch bio-composite: Application of Taguchi approach for optimization

2.1 Materials and method

Graphite fine powder (CDH, India), sodium nitrate (Merck, India), lead (II) nitrate (Merck, India), starch (SRL, India), zirconium oxychloride (Otto, India), N,N'-methylene bis-acrylamide (MBA) (Otto, India), potassium persulfate (Fisher Scientific, India), sodium hydroxide (Fisher Scientific, India), potassium permanganate (Merck, India), hydrogen peroxide (30%, Fisher Scientific, India) were used in this study.

2.2 Synthesis of graphene oxide (GO)

GO was prepared by our previously reported method (Rahman and Raheem, 2022a).

2.3 Synthesis of graphene oxide/hydrous zirconium oxide (GZ)

GO (0.5 g) was dispersed in distilled water (100 mL) and stirred for 30 min. Then 50 mL of 0.5 M ZrOCl₂·8H₂O was added in GO suspension in drop-wise manner followed by stirring. After complete addition, the pH was brought to ∼ 10 by adding NaOH (2.5 M) and magnetically stirred for 8 h at 80 °C. Finally, the material was obtained after filtration and dried in an oven at 60 °C. The same procedure was also adopted for the synthesis of hydrous zirconium oxide (HZO) without addition of GO.

2.4 Synthesis of graphene oxide/hydrous zirconium oxide/crosslinked starch bio-composite (GZS-BC)

Starch (4.5 g) was hydrolyzed in 100 mL of sodium hydroxide solution (0.15 M) by stirring at 60 °C for 1 h. The prepared GZ (1.5 g) was sonicated in distilled water for 30 min and then added to hydrolyzed starch. The reaction mixture was stirred for 1 h at 60 °C. In a separate beaker, 2.25 g potassium persulfate was dissolved in distilled water at 70 °C. In another beaker, 675 mg MBA was dissolved in distilled water at 40 °C. The solutions of potassium persulfate and MBA were added to the reaction mixture containing GZ and starch and stirred continuously at 70 °C for 3 h. After sonication for 1 h, the material was collected by filtration and dried at 60 °C.

2.5 Characterization of the GZS-BC.

The instrumentation details are presented in supplementary file (Text S1).

2.6 Taguchi method for optimization

Taguchi method was adopted for obtaining the optimum conditions for Pb (II) removal by adsorption. The effect of three factors, each at five levels, on the percent removal of Pb (II) was investigated. The selected factors (A: adsorbent dose, B: contact time and C: initial Pb (II) concentration) and their levels (1, 2, 3, 4 and 5) are given in Table S1.

[L₂₅ (5⁴)] orthogonal array (OA) for three factors, each at five different levels, are given in Table 1. The experiments were conducted according to [L₂₅ (5⁴)] design. Experimental results were analyzed using signal to noise $\left(S/N\right)$ ratio. Three types of $\left(S/N\right)$ ratio (nominal-the-better, smaller-the-better, and larger-the-better) were utilized for data evaluation. In this study maximum response (% removal) is required and thus, larger-the-better category was adopted to probe the experimental data. The larger the better $\left(S/N\right)$ ratio is presented as:

where n and y represent the replicating number of experiment and Pb (II) removal (%R), respectively. The analysis of variance (ANOVA) was adopted to reveal the impact of process variables on Pb (II) removal.

2.7 Adsorption studies

For adsorption isotherm studies, the optimum value of adsorbent (40 mg) was added to different conical flasks holding 25 mL of Pb (II) solution of varying concentrations (30–200 mg/L, pH 6) and agitated on a water shaker for 180 min at 303, 313 and 323 K. After separation of adsorbent, Pb (II) concentration was determined in the solution phase. The amount of Pb (II) adsorbed per unit mass of GZS-BC ( $q_e,$ mg/g) and removal (%) were quantified as:

Where C₀ and C_e denote initial and equilibrium concentration (mg/L), respectively. V and m are solution volume (L) and mass of GZS-BC (g).

For kinetic studies, adsorbent (40 mg) was added to Pb (II) solution (25 mL, 50 mg/L; pH 6) and stirred for different time intervals at three temperatures (303, 313 and 323 K). After filtration, Pb (II) concentration was determined in aqueous phase and capacity was calculated at different time intervals.

2.8 Error analysis

Values of Chi-square ( ${\chi }^2$ ) and average percentage error (APE) were estimated using Eqs. (4) and (5) to judge the fitness of isotherm and kinetic models.

where $q_{e,exp}$ and $q_{e,cal}$ are measured capacity and capacity (simulated) from the model, respectively.

3.1 Synthesis of bio-composite

To increase the chemical stability of the bio-composite in an aqueous solution, it was cross-linked using MBA as a cross-linking agent and potassium persulfate as radical initiator. The synthesis procedure is shown in Scheme 1.

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Scheme 1

Systematic procedure for the synthesis of GZS-BC.

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3.2 FTIR studies

Fig. 1a represents the FTIR spectra of MBA, GO, HZO, GZ, starch and GZS-BC. FTIR spectrum of GO gives a broad peak centered at 3399 cm⁻¹ which represented the O–H stretching vibration. The peak at 1174 cm⁻¹ indicated the C-O-C (epoxy) vibration. Further, the bands at 1722 cm⁻¹, 1624 cm⁻¹ and 1068 cm⁻¹ are designated to the stretching of C = O (carboxylic acid), C = C (aromatic) and C-OH, respectively (Huang, et al., 2016). In the FTIR spectrum of HZO, a broad band (3300–3600 cm⁻¹) centered at 3410 cm⁻¹ represents the stretching mode of O–H vibration of coordinated water on hydrated zirconium oxide (Cho, et al., 2016). Band at 1630 cm⁻¹ and 1576 cm⁻¹ are due to O–H vibration of water molecule (Pérez, et al., 2016; Mohammadi and Fray, 2011). Further, lattice vibration of Zr-O was identified by the peaks at 850 cm⁻¹ and 484 cm⁻¹ (Rahman and Nasir, 2018). The band at 1341 cm⁻¹ was due to bending mode of Zr-OH (Wang, et al., 2019). However, in the FTIR spectrum of GZ, the peak at 1722 cm⁻¹ (C = O) disappeared which may be due to incorporation of zirconium oxide on the GO surface. Other peaks of GO were weakened which further illustrated the formation of GZ. In the FTIR spectrum of starch, band at 1650 cm⁻¹ is associated with bending vibration of water molecule (Kibar and Us, 2014). In case of GZS-BC, the intensity of the band in the range 3300–3600 cm⁻¹ increases as compared to GZ, and shifting in peak was observed from 3408 cm⁻¹ to 3371 cm⁻¹ which may be due to H-bond formation of starch molecule with GZ. A new peak at 1456 cm⁻¹ appears in bio composite which confirmed the C-N linkage (Nesic, et al., 2016; Anirudhan and Rejeena, 2014). These results indicated the successful formation of bio composite GZS-BC.

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Fig. 1

(a) FTIR spectra of MBA, GO, HZO, GZ, starch and GZS-BC, and (b) XRD spectra of GO, HZO, GZ and GZS-BC biocomposite.

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3.3 XRD data

XRD patterns of GO, HZO, GZ and GZS-BC are shown in Fig. 1b. In the case of GO, a sharp peak is obtained at 2θ = 12.12° which is the characteristic peak of GO (Rahman and Raheem, 2022a). In case of HZO, a broad peak was observed from 20°-40° confirming its amorphous nature (Luo, et al., 2013). The GO peak disappeared in the GZ which may be because of incorporation of HZO on the GO surface. There is no change in XRD pattern of GZS-BC except sharpness of peak nearly at 30° which may be due to linkage of starch molecules with HZO.

3.4 Morphological study

SEM images of GZ and GZS-BC are shown in Fig. 2a and 2b, respectively. In the SEM image of GZ (Fig. 2a), the surface of GO sheet is covered with HZO particles which makes the surface irregular shaped. The SEM image of GZS-BC shows small pores which suggested the incorporation of starch molecules on GZ. The EDX spectrum of the bio-composite (Fig. 2c) indicated the presence of Zr (38.02%), O (31.89%), C (24.67%) and N (5.42%). The SEM results confirm that the starch molecules are successfully incorporated on the GZ surface. TEM images of bio-composite are shown in Fig. 2d, which clearly shows the amorphous nature of the material and successful synthesis of bio-composite.

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Fig. 2

SEM images of (a) GZ (b) GZS-BC (c) EDX spectrum of GZS-BC, and (d) TEM image of GZS-BC.

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3.5 Taguchi design for optimization

Experiments were conducted according to [L₂₅ (5⁴)] orthogonal array and percent removal as well as the $\left(S/N\right)$ ratio are presented in Table 1. Optimum value of controlling factor was determined based on the highest $\left(S/N\right)$ ratio (Fig. 3a). Estimated value of max–min (Δ) was used to address the impact of controlling factor on the removal efficiency (Table S2). The optimum combination was obtained as A4-B4-C2 with corresponding $\left(S/N\right)$ ratio as 39.13, 38.90 and 38.99 for Pb (II), respectively.

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Fig. 3

(a) Plot of controlling factors for $\left(S/N\right)$ ratios utilizing larger is better category through Taguchi model, and (b, c, d) Non-linear isotherm plots for adsorption of Pb (II) onto GZS-BC.

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ANOVA was performed to validate the design model using F-value, p-value, predicted $R^2$ and adjusted $R^2$ values (Table 2). The chosen factors i.e., adsorbent dose, contact time and initial concentration influence the removal efficiency because F-value of the controlling factors > critical value $F_{0.05}\left(1,12\right)=4.75$ . All controlling factors are statistically significant since their p-values were < 0.05.

Percent contribution of each controlling factor to the removal efficiency was assessed using Eq. (6) (Rahman et al., 2021).

Where ${\mathit{SS}}_{\mathit{adj}}$ and ${\mathit{SS}}_{\mathit{Tadj}}$ are individual sum of square and overall sum of square values, respectively. The order of percent contribution (Table 2) was obtained as: adsorbent dose (62.96%) > contact time (27.59%) > initial concentration (9.42%). The controlling factors i.e. A: adsorbent dose, B: contact time and C: initial concentration at the selected levels 4, 4, and 2, respectively, are significant and the optimum combination is: adsorbent dose-40 mg, contact time-180 min and initial concentration-50 mg/L for obtaining the highest removal efficiency.

3.6 Effect of pH

Solution pH played the dominant role for Pb (II) adsorption on adsorbent surfaces. The impact of pH was studied in the pH range 3–7 using the optimal values of other factors (A: adsorbent dose, B: contact time and C: initial Pb (II) concentration) obtained from Taguchi method. It was noticed that the removal efficiency increases with increasing pH and maximum removal of Pb (II) was obtained at pH 6. Beyond pH 6, decreasing trend in removal efficiency was noticed (Fig. S1). Further, adsorption experiments were carried out at pH 6.

3.7 Adsorption isotherm

The adsorption data were assessed by Langmuir, Freundlich, Temkin, Khan, and Toth isotherm models and Table S3 shows their non-linear equations The non-linear regression analysis using Origin 2023 software yielded the isotherm parameters (Table 3). The plots of $q_e$ (mg/g; experimental and estimated from isotherm models)) against the Ce (mg/L) of Pb (II) at 303, 313 and 323 K for the studied isotherm models are displayed in Fig. 3 (b, c and d). The best fitting of isotherm model was judged based on highest R² and lowest χ² and APE values (Table 3). Based on R², χ² and APE values, the fitting of isotherm models with measured data followed the sequence: Freundlich > Temkin > Langmuir > Toth > Khan. Thus, the Freundlich isotherm model was able to explain more accurately the measured data as it provided highest R² (0.9977–0.9983) and lowest χ² (0.01 – 0.02) and APE (0.90–1.14) values. The adsorption capacity of GZS-BC for Pb (II) was found to be 112.52 mg/g at 303 K. The best fitting of Freundlich isotherm model demonstrated that multi-layer adsorption took place on heterogeneous surface of GZS-BC. The Freundlich constant (n) is referred as heterogeneity factor. The value of n > 1 is indicative of favourable adsorption and the adsorption intensity increases with increase in n value (Rahman and Haseen, 2014). Herein, the values of n were 2.53, 2.56, and 2.61 at 303, 313 and 323 K, respectively, which illustrated the uptake of Pb (II) onto GZS-BC is favourable. The increase in heterogeneity factor (n) with the rising temperature suggested the improvement in adsorption intensity and endothermic nature of uptake of Pb (II) onto GZS-BC.

3.8 Adsorption kinetics

3.8.2

3.8.2 Fractal-like kinetic modeling

The fractal-like approach is utilized to describe the adsorption of Pb (II) on GZS-BC/solution interface. The rate coefficient with temporal “memories” is defined as:

(11)

$$k_f=\mathrm{k}\prime t^{-h}0\le \mathrm{h}\le 1,\mathrm{t}\ge 1$$

where $k_f$ and $\mathrm{k}\prime$ are the instantaneous and time independent rate coefficients, respectively. h is the fractal exponent determining the heterogeneity of adsorbent surface and is related to fractional time index α as:

(12)

$$\alpha =1-h$$

According to Eq. (11), the concept of fractal dependence for the adsorption coefficient has permitted to develop rate equations for fractal-like kinetic models which are expressed as:

(13)

$$q_t=q_e\left[{1-\mathrm{e}\mathrm{x}\mathrm{p}(-k}_{1,0}^{\text{'}}{t}^{\alpha }\right)]\mathrm{f}-\mathrm{P}\mathrm{F}\mathrm{O}$$

(14)

$$q_t=\frac{k_{2,0}^{\text{'}}{q}_e^2{t}^{\alpha }}{1+k_{2,0}^{\text{'}}{q}_e{t}^{\alpha }}\mathrm{f}-\mathrm{P}\mathrm{S}\mathrm{O}$$

(15)

$$q_t=q_e\frac{{1-\mathrm{e}\mathrm{x}\mathrm{p}(-k}_{1,0}^{\text{'}}{t}^{\alpha })}{1-f_2{\mathrm{e}\mathrm{x}\mathrm{p}(-k}_{1,0}^{\text{'}}{t}^{\alpha })}\mathrm{f}-\mathrm{M}\mathrm{O}$$

(16)

$$q_t=q_e\mathrm{l}\mathrm{n}\left[{2.72-1.72\mathrm{e}\mathrm{x}\mathrm{p}(-k}_{\mathit{Exp},0}^{\text{'}\text{'}}{t}^{\alpha }\right)]\mathrm{f}-\mathrm{E}\mathrm{x}\mathrm{p}$$

Where $k_{1,0}^{\text{'}},k_{2,0}^{\text{'}},and{k}_{\mathit{Exp},0}^{\text{'}\text{'}}$ are the rate coefficients of f- PFO, f- PSO, and f- exponential equations; where $k_{n,0}^{\prime }\left(n=1,2\right)=k_{n,0}/\alpha$ ,. $k_{\mathit{Exp},0}^{″}=k_{\mathit{Exp},0}^{\prime }/\alpha$

The modeling of kinetic data for adsorption of Pb (II) onto GZS-BC was carried out by non-linear regression of $q_t$ profiles according to classical kinetic (Eq. (7), 8, 9 and 10) and fractal-like kinetic equations (Eq. (13), 14, 15 and 16). The kinetic plot of classical and fractal kinetic models are shown in Fig. 4 (a, c, e) and Fig. 4 (b, d, f), respectively and their parameters are listed in Table 4. When classical kinetic models are considered, the PSO model gives best data fitting as compared to PFO, MO and Exp models because it is associated with high R² values, and low χ² value with respect to MO model. For PSO model, the value of time independent rate coefficient ( $k_2)$ was 0.12 g mg⁻¹ hour^-1 at the studied temperatures (303–323 K). On the other hand, each fractal kinetic model provides improved adsorption dynamics prediction in comparison to its classical model because of higher R² values. When fractal-like kinetic models are taken into account, the f-MO model fits best to the kinetic data with high R² values (0.9906–0.9911) and low χ² value (0.01) and thus, it is the appropriate model for narrating the Pb (II) uptake at all temperatures studied. For f-MO model, the values of $k_1^{\prime }$ were found in the range 1.76–1.78 hour^-(1-h) (1-h = 0.60 to 0.61). At initial stage (t < 2 hour), the adsorption of Pb (II) mainly takes place on the external surface and therefore, the hypothesis of uniform adsorbate concentration is reasonably valid. In this stage, both the classical and fractal-like kinetic models would be suitable to explain the uptake of Pb (II). At later stage (t > 2 hour), intraparticle diffusion occurred where uniform distribution of adsorbate concentration in inner pore with blind and open spaces is not possible which is responsible for fractal-like behaviour.

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Fig. 4

Classical and fractal- like PFO, PSO, MO and Exp kinetic models for adsorption of Pb (II) onto GZS-BC.

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Table 4 Kinetic parameters for adsorption of Pb (II) onto GZS-BC.

Kinetic model	303 K	313 K	323 K		Kinetic model	303 K	313 K	323 K
PFO					f-PFO
$q_e$ (mg/g)	29.48	29.52	29.55		$q_e$ (mg/g)	31.47	31.48	31.53
$k_1$	2.71	2.72	2.73		$k_{1,0}^{\prime }$	1.76	1.78	1.78
R2	0.9194	0.9205	0.9197		α	0.60	0.61	0.60
χ2	0.05	0.05	0.05		R2	0.9906	0.9911	0.9911
APE	4.21	4.18	4.21		χ2	0.02	0.01	0.01
					APE	2.23	2.19	2.19
PSO					f- PSO
$q_e$ (mg/g)	34.01	34.01	34.04		$q_e$ (mg/g)	33.74	33.73	33.77
$k_2$	0.12	0.12	0.12		$k_{2,0}^{\prime }$	0.09	0.09	0.09
R2	0.9858	0.9866	0.9865		α	0.85	0.86	0.86
χ2	0.34	0.33	0.33		R2	0.9884	0.9889	0.9889
APE	10.49	10.40	10.33		χ2	0.28	0.28	0.28
					APE	9.62	9.48	9.48
MO					f- MO
$q_e$ (mg/g)	34.52	34.49	34.52		$q_e$ (mg/g)	31.37	31.45	31.49
$k_1$	0.09	0.09	0.09		$k_{1,0}^{\prime }$	1.76	1.78	1.78
$f_2$	0.98	0.98	0.98		$f_2$	3.32 × 10-13	1 × 10-14	9.20 × 10-16
R2	0.9858	0.9865	0.9865		α	0.60	0.61	0.60
χ2	0.45	0.44	0.44		R2	0.9906	0.9911	0.9911
APE	12.14	11.98	11.90		χ2	0.01	0.01	0.01
					APE	1.90	2.07	2.06
Exp					f- Exp
$q_e$ (mg/g)	29.93	29.96	29.99		$q_e$ (mg/g)	32.81	32.76	32.80
$k_{\mathit{Exp}}^{\prime }$	1.95	1.97	1.97		$k_{\mathit{Exp},0}^{″}$	1.39	1.40	1.40
R2	0.9571	0.9580	0.9575		α	0.70	0.70	0.70
χ2	0.02	0.02	0.02		R2	0.9904	0.9909	0.9909
APE	3.00	2.76	2.79		χ2	0.13	0.12	0.12
					APE	6.61	6.34	6.34

Experimental adsorption capacities were obtained as 30.78 mg/g, 30.81 mg/g and 30.85 mg/g at 303 K, 313 K and 323 K, respectively.

3.9 Thermodynamic studies

The uptake of Pb (II) by GZS-BC was investigated at 303, 313 and 323 K and thermodynamic parameters (ΔG^o, ΔH^o and ΔS^o) were assessed using Eqs. (17) and (18) (Rahman and Haseen, 2014):

The value of $k_c$ , equilibrium constant as a dimensionless quantity, was obtained as (Milonjić, S.K., 2007):

Where R and T are known as universal gas constant (J K⁻¹ mol⁻¹) and temperature (Kelvin), respectively. The values of ΔH^o and ΔS^o were assessed from the plot of $\mathit{ln}{K}_c$ versus $\frac{1}{T}$ (Fig. S2). The values of Δ G⁰ (-26.76, −27.82 and −28.96 kJ mol⁻¹ at 303, 313 and 323 K, respectively) elucidated the spontaneity in the uptake of Pb (II) on GZS-BC. Based on ΔG° values, the nature of sorption can be predicted. ΔG° values falling in the range of −20 to 0 kJ mol⁻¹ pointed towards physisorption whereas −20 to −80 kJ⁻¹ mol suggested the involvement of both physisorption and chemisorption (Kumar, et al., 2014). On the basis of Δ G⁰ values, it is suggested that both physisorption and chemisorption processes are involved in the uptake of Pb (II) onto GZS-BC. Positive values of ΔH^o (6.53 kJ mol⁻¹) and ΔS^o (109.84 J mol⁻¹ K⁻¹) are indicative of endothermic nature of Pb (II) sorption and randomness at solution/GZS-BC interface, respectively.

3.10 Application of GZS-BC for removal of Pb (II) from natural water

For the removal of Pb (II) from natural water samples (surface water and municipal wastewater), a fixed concentration of Pb (II) was added (50 mg/L) and sorption experiment was conducted in batch mode using GZS-BC as adsorbent. The percentage removal of Pb (II) was obtained as 97.85% and 98.02% from surface water and municipal wastewater, respectively. Therefore, the prepared material is a potential adsorbent for removal of Pb (II) from natural water samples.