A response surface modelling study for sorption of Cu 2+,Ni 2+,Zn 2+ and Cd 2+ using chemically modified poly(vinylpyrrolidone) and poly(vinylpyrrolidone- co -methylacrylate) hydrogels

Abstract

In this present study, response surface methodology was applied for the optimization and evaluation of different heavy-metal sorption processes. Poly(vinylpyrrolidone) and poly(vinylpyrrolidone-co-methylacrylate) hydrogels were used as pH-responsive adsorbents to investigate their efficiency in the uptake of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions from aqueous solution in a batch reactor system. The effect of operational parameters such as initial pH and contact time were studied using central composite design. Analysis of variance depicted the central composite design model was significant for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions removal by the investigated hydrogels. A comparison between the model results and experimental data showed that poly(vinylpyrrolidone-co-methylacrylate) possessed higher metal ions binding affinity than poly(vinylpyrrolidone) hydrogel. The heavy-metal ions sorption kinetic well fitted the pseudo second-order kinetic model. Evaluation of the intraparticle diffusion model suggested the sorption process occurred in two phases: surface sorption and intraparticle diffusion. Isothermic results revealed that Freundlich and Temkin isotherms best described the adsorbate–adsorbent interactions. Maximum sorption capacities were observed for Cu²⁺ ion and were determined as 86.66 mg/g and 98.53 mg/g for poly(vinylpyrrolidone) and poly(vinylpyrrolidone-co-methylacrylate) hydrogels, respectively.

Keywords

Hydrogel pH responsive response surface methodology sorption. vinylpyrrolidone

Introduction

High effluent discharge by the industrial sector such as metal finishing, welding, alloy manufacturing, plating and mining serves as vital pollutant sources of heavy metals in the soil and water. This has remarkably contributed to the increase in the concentration of toxic heavy-metal ions in waters which represent a potential source of several hazardous disadvantages on aquatic flora, animals and even on humans (Gonzalez-Gomez et al., 2014; Jadhav et al., 2014). Unlike some other organic pollutants, heavy metals are nonbiodegradable, highly toxic and carcinogenic. In addition, due to their high solubility, they can easily accumulate in the food chain thus causing serious health-threatening problems. Heavy-metal ions such as Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ classified as toxic metals have demonstrated to be associated with several health problems. For example, nausea and stomach ache which are gastrointestinal diseases are caused by Cu ion poisoning. Also, consumption of high levels of Ni ion in water may cause significant harm to the kidneys, lungs and the skin (Jamnongkan et al., 2014; Kalantari et al., 2014). Therefore, great attention towards the treatment of industrial effluents is eminent. Various treatment techniques have been investigated for the removal of heavy-metal ions from aqueous solutions. Among these techniques, sorption method has proven to be the most widely applied due to its simplicity, less time consuming and cost effective (Mahmoud, 2013). This method of treatment has demonstrated significant benefits attributed to the high-level loading capacity of heavy-metal ions for the used adsorbent. In the midst of used adsorbents, hydrogels have been classified as one of the most suitable material for the removal of heavy-metal ions from aqueous solutions (Antic et al., 2015; Soto et al., 2015; Wang and Li, 2015). Hydrogels, as previously defined in the literature, are 3D crosslinked polymeric material with the ability to retain high level of water and remain insoluble due to the existence of physical or chemical crosslinking in the material’s network structure (Erdem et al., 2016; Kamal et al., 2016; Yildiz et al., 2010). Stimuli-responsive hydrogels have shown great applicability in different areas of research such as sensors materials, drug delivery, tissue engineering and wastewater treatments. This is due to their unique capability to change in volume or shape in response to surrounding environmental signals. This stimuli response can either be physical or chemical such as temperature, pH, electric field and enzymes or light (Eswaramma et al., 2016; Koetting et al., 2016; Ozay, 2014).

Response surface methodology (RSM) is an assembly of mathematical and statistical analysis used to evaluate the relative significance of different experimental factors by approximating the shape of the response surface and determining optimum conditions within a limited number of experiments (Daneshvar et al., 2015; Xu et al., 2015). As one of the practical RSM models, central composite design (CCD), a second-order model, is widely used to estimate the true response surface (Alslaibi et al., 2014a). This second-order model minimizes the experimental points and maintains high accuracy and precision of prediction compared to the one factorial design. This methodology is favourable and widely applied in the optimization of sorption processes (Ghosh et al., 2014; Soleymani et al., 2015).

The objective of the present study was to optimize and evaluate the effect of initial pH and contact time on the sorption of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions by RSM modelling using two types of pH-responsive hydrogels composed of poly(vinylpyrrolidone) (PVP) and poly(vinylpyrrolidone-co-methylacrylate) (P(VP-co-MA)). The optimum conditions for elimination of the heavy-metal ions were determined with RSM using CCD modelling. A comparison between the hydrogels as adsorbents in heavy-metal ions sorption was performed for estimating their performance by determining the best fit for the sorption system using different sorption kinetic and isotherm models.

Materials and methods

Materials

Vinylpyrrolidone (VP) and methylacrylate (MA) were purchased from Merck. Analytical grade 4,4′-dicyano-4,4′-azovaleric acid (Fluka), poly(ethylene glycol) (Merck) and 4-vinylbenzyl chloride (Sigma–Aldrich) were used as monomers for synthesizing the macroinimer (MIM) (Yildiz et al., 2010). Chemicals of Cd(NO₃)₂·4H₂O, CuCl₂·2H₂O, ZnCl₂·2H₂O, NiCl₂·2H₂O, NaOH and HCl were supplied by Merck and used without further purification.

Synthesis of hydrogels

Preparations of PVP and P(VP-co-MA) hydrogels (Figure 1) were performed based on the detailed described procedure in previous study (Yildiz et al., 2010). Via bulk polymerization at 70℃, 2 g of VP was mixed with varying ratios of MIM (Table 1). The mixture was then allowed to stir for 5 min under argon gas and after 3 h, the tubes containing the different samples were then immersed in distilled water for 24 h. The obtained PVP samples were then dried under vacuum at 50℃ until constant weight. Synthesis of different P(VP-co-MA) samples was also performed as described above. Varying amounts of VP and MA (Table 1) were mixed in the presence of same MIM (0.30 g) amount and then the obtained hydrogel samples were dried. The prepared PVP and P(VP-co-MA) hydrogels were then characterized accordingly using various techniques as reported by our previous study (Yildiz et al., 2010), and then used for further applications and optimization.

Figure 1.

Depicting structural formation of (a) MIM-initiated PVP and (b) MIM-initiated P(VP-co-MA) hydrogel. MIM: macroinimer; PVP: poly(vinylpyrrolidone); P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate).

Table 1.

Synthesis composition of monomers.

	PVP			P(VP-co-MA)
Sample code	VP(g)	MIM(g)	Sample code	VP(g)	MA(g)	MIM(g)
PV1	2.00	0.10	PVM1	0.25	1.75	0.30
PV2	2.00	0.30	PVM2	0.50	1.50	0.30
PV3	2.00	0.50	PVM3	0.75	1.25	0.30
PV4	2.00	0.80	PVM4	1.00	1.00	0.30
PV5	2.00	1.20	PVM5	1.25	0.75	0.30

MA: methylacrylate; MIM: macroinimer; PVP: poly(vinylpyrrolidone); VP: vinylpyrrolidone; PV: poly(vinylpyrrolidone) hydrogel sample; PVM: poly(vinylpyrrolidone-co-methylacrylate) hydrogel sample.

Preparation of aqueous metal ions solutions

Stock solutions of 1000 ppm concentration for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions were prepared using CuCl₂·2H₂O, NiCl₂·2H₂O, ZnCl₂·2H₂O and Cd(NO₃)₂·4H₂O, respectively. The sorption properties of PVP and P(VP-co-MA) hydrogels for the different metal ions were then tested under non-competitive conditions by immersing the hydrogels in the different metal ions solutions. The sorption experiments were performed by agitating a given amount of hydrogel in 50 mL of solution containing a metal-ion concentration of 5 ppm at varying pH of 2, 5 and 8 for a time period of 24 h. The pH value of each solution was adjusted by either 0.1 M HCl or 0.1 M NaOH. The metal-ion concentrations in the solutions were quantified before and after the hydrogel immersion by dilution to an appropriate concentration with distilled water and measured with atomic absorption spectrometer (Perkin-Elmer Analyst 800). Readings were conducted at wavelengths of 324, 232, 213.9 and 228.8 nm for copper, nickel, zinc and cadmium ions, respectively. Absorption readings were collected in duplicates, and the average value was determined as the final value.

Batch sorption investigations

Binding capacities of PVP and P(VP-co-MA) hydrogels for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions were investigated under agitation at 200 r/min in 50 mL of varying metal-ion concentrations solutions (5–15 ppm), pH (2–8) and contact time (1–24 h) to reach sorption equilibrium. In order to minimize error, experimental runs were performed in duplicates, and then average results were obtained. The equilibrium sorption uptake for the heavy metal ions was calculated using the equation below:

q_{e} = (C_{o} - C_{e}) \frac{V}{M}

(1)

where C_o = initial concentration (ppm) of the metal ions, C_e = equilibrium concentration (ppm), M = mass of hydrogels (g), V = volume of metal ion solutions (L) and q_e = equilibrium amount of metal ions adsorbed (mg/g) (Alslaibi et al., 2014b; Azari et al., 2015).

Design experiment and optimization of sorption

Experimental optimization of the different PVP and P(VP-co-MA) hydrogels was analyzed using Design-Expert 9.0 software. In the present investigation, RSM, a useful statistical technique for optimizing complex processes, was used to reduce the number of experimental trials which require evaluating several parameters and their interactions. RSM is less strenuous and time consuming than other approaches. Factors such as initial pH of solution and contact time greatly affected the removal capacity of the metals. Therefore, the second-order RSM CCD model was applied as empirical for investigating the correlation between the response function (equilibrium sorption capacity) and the process parameters of initial pH and contact time with experimental levels of the independent parameters shown in Table 2. In this optimization process, the response was related to selected factors of a quadratic model which is given as:

Y = b_{o} + \sum_{i = 1}^{k} b_{i} x_{i} + \sum_{i = 1}^{k} b_{ii} x_{i}^{2} + \sum_{i = 1}^{k} \sum_{j = 1}^{k} b_{ij} x_{i} x_{j} \dots

(2)

where Y is the predicted response (heavy-metal sorption capacity); b_o is constant; x_i and x_j are the coded values of the parameters; and b_i, b_ii and b_ij are the linear coefficient, quadratic coefficient and interaction effect coefficient, respectively (Bingöl, 2011; Khodadoust et al., 2014; Soleymani et al., 2015).

Table 2.

Independent parameters and their levels used in the CCD experimental design.

Variable	Factor name	Low (−)	High (+)	−α	+α
X ₁	pH	2	8	0.75	9.24
X ₂	Contact time (h)	2	6	1.17	6.83
		Level 1		Level 2
Type of adsorbent		PVP		P(VP-co-MA)

CCD: central composite design; P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate); PVP: poly(vnylpyrrolidone).

Results and discussion

Batch sorption optimization

In order to determine the most efficient of PVP and P(VP-co-MA) varying hydrogel samples, batch sorption investigations were carried out at predetermined conditions of pH 8, 5 ppm initial metal concentration, 50 mg hydrogel dosage, 25℃ temperature and contact time 6 h. The results obtained as represented in Figure 2 showed that maximum sorption capacities were observed in PV3 and PVM5 samples of PVP and P(VP-co-MA) hydrogels, respectively. On the other hand, P(VP-co-MA) hydrogels demonstrated greater efficiency in the removal of the metal ions compared to PVP hydrogels. This was attributed to the additional binding affinity via the incorporation of the methacrylate monomer in the hydrogel network structure. The removal efficiency of the metal ions by PVP and P(VP-co-MA) hydrogels, respectively, was observed to be in the magnitude of Cu²⁺> Zn²⁺> Ni²⁺> Cd²⁺ and Cu²⁺> Ni²⁺> Zn²⁺> Cd²⁺.

Figure 2.

Equilibrium sorption capacities of different (a) PVP and (b) P(VP-co-MA) hydrogels for the sorption of varying metal ions. P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate); PVP: poly(vinylpyrrolidone).

RSM model and analysis

Table 3 represents the results for the full-factorial CCD with two factors in two levels, alongside the experimental and predicted responses for the different heavy metal ions investigated. Based on the obtained results, second-order polynomial equations for the various heavy metals were obtained as given in Table 4 for which X₁ and X₂ represents pH and contact time, respectively. The equations in Table 4 demonstrate how the studied factors and the interaction between two factors affect the sorption of selected heavy metals by PVP and P(VP-co-MA) hydrogels. In addition, the negative and positive coefficients in the equations depict the negative and positive effect on the heavy-metal ions removal.

Table 3.

Obtained results of response-surface CCD.

	Independent factors		Experimental (mg/g)				Predicted (mg/g)
Run no.	X ₁	X ₂	Y₁ (Cu²⁺)	Y₂ (Ni²⁺)	Y₃ (Zn²⁺)	Y₄ (Cd²⁺)	Y₁ (Cu²⁺)	Y₂ (Ni²⁺)	Y₃ (Zn²⁺)	Y₄ (Cd²⁺)
PVP hydrogel
1	0	0	58.33	10.75	31.05	8.17	68.59	9.13	30.61	12.10
2	+1	−1	84.96	18.49	30.67	13.90	80.65	15.35	27.89	13.39
3	−1	−1	15.72	8.76	14.22	2.62	22.71	7.71	17.65	4.06
4	−1	+1	10.04	2.17	14.80	2.81	15.65	1.63	18.73	4.42
5	0	0	67.60	10.58	33.70	14.81	68.59	9.13	30.61	12.10
6	+α	0	81.69	14.00	19.82	11.14	89.04	17.31	23.65	11.98
7	0	−α	61.38	9.25	31.29	11.62	59.76	11.45	31.06	11.19
8	+1	+1	92.35	16.05	34.49	12.13	86.66	13.43	32.20	11.79
9	0	0	67.27	7.49	29.11	11.38	68.59	9.13	30.61	12.10
10	0	0	74.87	9.60	32.32	11.35	68.59	9.13	30.61	12.10
11	0	+α	58.69	4.32	35.79	10.98	59.02	5.80	34.87	10.31
12	0	0	74.85	7.25	26.89	14.77	68.59	9.13	30.61	12.10
13	−α	0	6.49	3.19	11.86	2.10	2.15	3.56	6.89	0.17
P(VP-co-MA) hydrogel
1	0	0	93.84	66.21	44.38	19.97	85.59	69.82	46.05	22.73
2	+1	−1	102.28	75.41	59.78	41.40	97.04	67.95	54.03	34.05
3	−1	−1	31.97	38.37	34.02	17.24	36.40	40.41	34.00	16.40
4	−1	+1	36.45	38.37	31.65	18.78	43.47	43.28	31.29	18.65
5	0	0	89.45	68.56	45.82	23.18	85.59	69.82	46.05	22.73
6	+α	0	86.03	60.35	52.89	29.61	91.99	68.34	60.01	37.97
7	0	−α	82.67	57.37	43.90	21.88	83.61	60.68	46.71	26.12
8	+1	+1	101.19	76.10	68.04	43.94	98.53	71.52	61.94	37.29
9	0	0	86.84	72.28	45.66	26.84	85.59	69.82	46.05	22.73
10	0	0	78.10	76.89	46.90	23.18	85.59	69.82	46.05	22.73
11	0	+α	92.38	65.99	47.07	26.77	89.67	65.23	50.38	30.01
12	0	0	79.74	65.18	47.50	20.46	85.59	69.82	46.05	22.73
13	−α	0	17.90	34.35	25.17	13.18	10.17	28.90	24.17	12.31

CCD: central composite design; P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate); PVP: poly(vinylpyrrolidone).

Table 4.

Second-order polynomial equations for the investigated heavy metals.

Predicted response (mg/g)	PVP	P(VP-co-MA)
Y₁ (Cu²⁺)	= 68.59 + 32.24 X₁ − 0.26 X₂ + 3.2 X₁X₂ − 12.57 X₁²− 4.60 X₂²	= 85.59 + 28.93 X₁ + 2.14 X₂ − 1.39 X₁X₂ − 17.26 X₁²+ 0.52 X₂²
Y₂ (Ni²⁺)	= 9.13 + 4.86 X₁ − 2.00 X₂ + 1.04 X₁X₂ + 0.65 X₁²− 0.25 X₂²	= 69.82 + 13.94 X₁ + 1.61 X₂ + 0.17X₁X₂ − 10.60 X₁²− 3.43 X₂²
Y₃ (Zn²⁺)	= 30.61 + 5.93 X₁ − 1.35 X₂ + 0.81 X₁X₂ − 7.67 X₁²− 1.18 X₂²	= 46.05 + 12.67 X₁ + 1.30 X₂ + 2.66 X₁X₂ − 1.98 X₁²+ 1.25 X₂²
Y₄ (Cd²⁺)	= 12.10 + 4.17 X₁ − 0.31 X₂ − 0.49 X₁X₂ − 3.01 X₁²− 0.67 X₂²	= 22.73 + 9.07 X₁ + 1.37 X₂ + 0.25 X₁X₂ + 1.21 X₁²+ 2.67 X₂²

P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate); PVP: poly(vinylpyrrolidone).

A negative effect of a factor indicates that the response is not significantly affected when the factor level increases and vice versa for a positive effect (Bajpai et al., 2012; Bingöl, 2011).

Therefore, from the obtained equations, X₁ for both PVP and P(VP-co-MA) hydrogels has a positive effect on the heavy metals sorption. On the other hand, X₂ negatively affects the sorption of the heavy-metal ions using PVP hydrogel while a positive effect is observed for P(VP-co-MA) hydrogel. In other words, increasing initial pH increased sorption efficiency while increase in contact time respectively decreased and increased sorption efficiency of PVP and P(VP-co-MA) hydrogels.

Statistical analysis of the model

The validity and effectiveness of the obtained sorption data were assessed using analysis of variance. Variance evaluation for the RSM quadratic model was performed and the obtained results are represented in Table 5. The correlation coefficients (R²) for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metals ions sorption onto PVP and P(VP-co-MA) hydrogels were also determined and are given in Table 5. The obtained R² values indicated that more than 82% for PVP and 86% for P(VP-co-MA) hydrogel sorption total variability can be elucidated by the quadratic model for all the investigated metal ions. A difference of <0.2 was observed for the obtained predicted R² values to the adjusted R² values (Table 5) for the different heavy-metal ions. This indicates a good correlation between the response and the investigated variables. In addition, the adjusted R² confirmed the significance of the quadratic model for the sorption process of the metal ions using PVP and P(VP-co-MA) hydrogels. The obtained p values for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions were < 0.05 implying that the model terms were significant at a confidence level of 95% or more. Low values of coefficient of variance of the model for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions sorption were <10%, indicating the precision and reliability of the experiments. The adequate precision ratio of the model for all heavy-metal ions were >4, which indicated an appropriate signal for the model (Ngwabebhoh et al., 2016; Shaker and Yakout, 2016; Thirugnanasambandham et al., 2014).

Table 5.

Analysis of variance (ANOVA) for RSM quadratic model.

Model parameter	PVP hydrogel				P(VP-co-MA) hydrogel
Model parameter	Cu²⁺	Ni²⁺	Zn²⁺	Cd²⁺	Cu²⁺	Ni²⁺	Zn²⁺	Cd²⁺
Sum of square	9518.89	229.03	741.07	204.72	8864.09	2387.95	1369.58	728.33
df	5	5	5	5	5	5	5	5
Mean square	1903.78	45.81	148.21	40.94	1772.82	477.59	273.92	145.67
F-value	29.68	6.76	9.48	6.97	32.52	11.06	13.07	4.47
P-value	0.0001	0.0131	0.0051	0.0121	0.0001	0.0032	0.0019	0.0378
R ²	0.955	0.829	0.871	0.833	0.959	0.888	0.903	0.862
Adjusted R²	0.923	0.806	0.880	0.813	0.929	0.807	0.834	0.891
Predicted R²	0.983	0.849	0.873	0.811	0.911	0.891	0.833	0.821
Adeq precision	16.757	8.867	10.420	8.024	17.615	9.546	12.144	6.615
CV%	8.01	2.60	3.95	2.42	7.38	6.57	4.58	5.71

CV: coefficient of variance; P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate); PVP: poly(vinylpyrrolidone); RSM: response surface methodology.

The acceptability of the applied mathematical model was analyzed by establishing diagnostic plots of normal probability versus studentized residuals for the uptake of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions on PVP and P(VP-co-MA) hydrogels. Figure 3 depicts normal probability plot of the studentized residuals for the heavy metal ions sorption. From Figure 3, it was observed that the residual behaviours of the various metal ions adsorbed by PVP and P(VP-co-MA) hydrogels followed a linear and normal distribution. This demonstrates that the model was adequate for the removal Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions.

Figure 3.

Normal probability plots of studentized residuals. (a) PVP and (b) P(VP-co-MA) hydrogels for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions sorption process.

Effect of initial pH and contact time on heavy-metal ions sorption

To best describe the interactive effect of two variables on the responses, three-dimensional response surface plots were constructed to analyze the effects of initial pH and contact time on the efficacy of sorption using PVP and P(VP-co-MA) hydrogels at initial metals concentration of 5 ppm, adsorbent dosage of 50 mg and temperature of 25℃. Figure 4 shows the response surface plots of initial pH and contact time on metal ions sorption. As observed from Figure 4, the metal ions sorption efficiency increased by increasing contact time from 1 to 6 h for PVP and P(VP-co-MA) hydrogels. This is explained based on the binding of the adsorbates with increasing contact time and finally saturation of adsorbent sorption active site (Bajpai et al., 2012). The effect of initial pH is an important parameter for evaluating the potency of sorption capacity of an adsorbent due to its influence on the adsorbent functional groups. Figure 4(a) illustrates the sorption efficiency of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions using PVP hydrogel. It was observed that increasing the pH from 2 to 8 enhanced the binding of the metal ions, and maximum metal ions uptake was obtained at solution pH 8. This was attributed to the behaviour of the N-atoms on the PVP hydrogel surface. At low pH, protonation of the N-atoms occurs which leads to electrostatic repulsion with the existing metal ions in solution. However, increasing solution pH leads to ionization of the N-atoms, which induces an increase in sorption of the metal ions (Faisal, 2016; Li et al., 2008). The binding capacities of the PVP hydrogels were observed in the magnitude of Cu²⁺> Zn²⁺> Ni²⁺> Cd²⁺ with obtained maximum sorption capacities of 86.44, 32.04, 13.12 and 12.90 mg/g, respectively. The sorption capacity of P(VP-co-MA) hydrogel for the different metal ions was also investigated and the obtained plots represented in Figure 4(b). Based on theoretical concept, addition of MA in the PVP matrix increases metal-ion binding efficiency of the hydrogel. Comparatively, the obtained sorption capacities of the copolymer hydrogel for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions were significantly higher than that of the homopolymer hydrogel. This was due to the presence of additional oxygen atoms from methylacrylate which coordinated more metal ions thereby increasing the metal ion binding capacities (Milosavljevic et al., 2011). The sorption capacity of P(VP-co-MA) hydrogel for the different metal ions was in the order of Cu²⁺> Ni²⁺> Zn²⁺> Cd²⁺ with obtained maximum sorption capacities of 98.84, 73.21, 61.28 and 36.88 mg/g, respectively. However, the higher sorption capacities of Cu²⁺ metal ion obtained using PVP and P(VP-co-MA) hydrogels was attributed to the Jahn–Teller effect which states ‘For any non-linear molecule in an electronically degenerate state, distortion must occur to lower the symmetry, remove the degeneracy and lower the energy’ (Justi et al., 2005; Yildiz et al., 2010). In addition, Cu²⁺ is known as one of the easiest metal ions to form complexes with ligands containing nitrogen and oxygen atoms.

Figure 4.

3D plots showing effect of pH and contact time using (a) PVP and (b) P(VP-co-MA) hydrogels for the sorption of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions.

Optimization of sorption conditions

Optimal values of the investigated variables for the sorption of the different metal ions using PVP and P(VP-co-MA) hydrogels were determined from the RSM model using obtained experimental data. In this investigation, the desirability function approach was applied for optimizing the combination of sorption process parameters (pH and contact time). The aim of the optimization was to enhance the sorption conditions in the batch system. The optimum values of the sorption parameters for the maximum sorption efficiency are given in Table 6. According to CCD results, the maximum sorption for investigated Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions were obtained at pH 8.0 and contact time 6 h for PVP and P(VP-co-MA) hydrogels with a 1.00 desirability. As illustrated in Table 6, the sorption capacities for all responses obtained from experiments and predicted values from the CCD quadratic model are in close agreement, confirming the accuracy and validity of the model approach. The obtained results affirmed that the RSM model used was a suitable tool for optimizing the operational conditions of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions sorption onto PVP and P(VP-co-MA) hydrogels.

Table 6.

Optimum values of the sorption parameters for the sorption of metal ions onto PVP and P(VP-co-MA) hydrogels.

		Responses
	Optimum	Experimental (mg/g)				Predicted (mg/g)
Factors	values	Cu²⁺	Ni²⁺	Zn²⁺	Cd²⁺	Cu²⁺	Ni²⁺	Zn²⁺	Cd²⁺	Desirability
PVP hydrogel
pH	8.00	92.35	18.49	35.79	14.81	86.66	13.43	32.20	11.79	1.00
Contact time	6.00	92.35	18.49	35.79	14.81	86.66	13.43	32.20	11.79	1.00
P(VP-co-MA) hydrogel
pH	8.00	102.28	76.89	68.05	43.94	98.53	71.52	61.941	37.29	1.00
Contact time	6.00	102.28	76.89	68.05	43.94	98.53	71.52	61.941	37.29	1.00

Validation of the regression model

In order to validate the prediction of the investigated polynomial model, some additional random batch experiments were performed within the experimental range of the CCD model and the derived results were compared with predicted values, as represented in Table 7. Comparison between experimental observed and predicted data shows close agreement for all heavy-metal ion sorption with acceptable percentage errors for the developed models.

Table 7.

Parametric values for statistical model validation.

	Independent factors		Experimental (mg/g)				Predicted (mg/g)
Run no.	pH	Time (h)	Y₁ (Cu²⁺)	Y₂ (Ni²⁺)	Y₃ (Zn²⁺)	Y₄ (Cd²⁺)	Y₁ (Cu²⁺)	Y₂ (Ni²⁺)	Y₃ (Zn²⁺)	Y₄ (Cd²⁺)
PVP hydrogel
1	4	2	44.97	5.30	22.67	6.54	46.12	8.90	25.32	9.34
2	8	3	92.05	24.78	39.24	16.21	91.30	19.56	37.59	14.56
3	5.5	3	59.72	7.04	28.90	11.88	57.45	7.91	25.78	7.09
R² values			0.935	0.819	0.841	0.803	0.903	0.839	0.850	0.817
P(VP-co-MA) hydrogel
1	3	4	34.75	7.89	10.12	5.44	35.06	8.60	13.34	9.98
2	6	2	56.38	9.80	26.40	9.38	58.89	11.67	20.76	14.83
3	7.5	5	97.65	17.28	37.09	15.10	98.90	15.03	34.35	19.84
R² values			0.973	0.858	0.863	0.842	0.995	0.901	0.898	0.877

P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate); PVP: poly(vinylpyrrolidone).

Error functions

Error analyses for sum of squared errors (SSE) and mean of squared errors (MSE) were employed to minimize errors for the different metal ions investigated and to validate the kinetic models utilized. The representation of the different error functions applied is given in equations (3) and (4) below.

SSE = \sum_{i = 1}^{n} (q_{e, cal} - q_{e, exp})^{2}

(3)

MSE = \frac{1}{n} \sum_{i = 1}^{n} (q_{e, cal} - q_{e, exp})^{2}

(4)

where n is the number of experimental data used. The values of the two error functions for the sorption of the different metal ions using PVP and P(VP-co-MA) hydrogels were calculated and presented in Table 8 for the different investigated kinetic models.

Table 8.

Kinetic parameters for the sorption of metal ions onto PVP and P(VP-co-MA) hydrogels.

	PVP hydrogel				P(VP-co-MA) hydrogel
Models	Cu²⁺	Ni²⁺	Zn²⁺	Cd²⁺	Cu²⁺	Ni²⁺	Zn²⁺	Cd²⁺
Pseudo first order
K₁ (min⁻¹) × 10⁻³	3.41	12.73	3.80	5.83	3.65	3.83	5.03	13.98
q_e,_exp (mg/g)	91.42	13.99	33.37	13.63	96.03	73.35	62.89	31.61
q_e,_cal (mg/g)	85.82	18.67	30.48	13.36	104.99	73.57	62.78	44.96
R²	0.912	0.926	0.917	0.927	0.999	0.999	0.999	0.994
SSE	0.013	0.092	0.039	0.026	0.027	0.085	0.093	0.011
MSE	0.056	0.038	0.013	0.082	0.099	0.025	0.031	0.048
Pseudo second order
K₂ (min⁻¹) × 10⁻²	15.74	11.76	9.64	8.21	41.60	39.62	37.40	35.99
q_e_, exp (mg/g)	91.42	13.99	33.37	13.63	96.03	73.35	62.89	31.61
q_e_, cal (mg/g)	91.83	13.69	33.78	13.64	95.24	73.21	62.93	30.71
R²	0.999	0.998	0.996	0.997	0.951	0.933	0.932	0.939
SSE	0.003	0.001	0.014	0.003	0.001	0.005	0.009	0.008
MSE × 10⁻⁴	1.44	4.49	2.70	11.50	0.39	0.32	0.86	0.53
Intraparticle diffusion
K_IP (mg/g min^0.5)	2.23	1.36	0.67	0.45	2.14	0.46	0.31	2.97
C	82.69	20.30	29.93	13.35	107.32	72.76	62.36	47.84
R²	0.926	0.963	0.932	0.964	0.974	0.921	0.915	0.857
SSE	0.428	0.313	0.045	0.726	0.739	0.527	0.444	0.744
MSE	0.143	0.437	0.015	0.575	0.579	0.175	0.148	0.914

MSE: mean standard error; P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate); PVP: poly(vinylpyrrolidone); SSE: sum of squared errors.

Sorption kinetic models

To investigate the transport behaviour of the adsorbate molecules in relation to time and controlling mechanism of the sorption process, the reaction-based and diffusion-based models were employed to test the experimental data obtained for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions sorption onto PVP and P(VP-co-MA) hydrogels. The three models applied were pseudo first-order, pseudo second-order and intraparticle diffusion kinetic models.

The pseudo first-order kinetic model was first suggested by Lagergren for the sorption of solid–liquid systems (Evren et al., 2014). The model is expressed using the equation below.

\ln (q_{e -} q_{t}) = \ln q_{e} - K_{1} t

(5)

where q_e is the amount of metal ions adsorbed on the hydrogels at equilibrium (mg/g), q_t is the amount of metal ions adsorbed at time t (mg/g) and K₁ is the rate constant of first-order sorption (min⁻¹).

The pseudo second-order kinetic model was suggested by Ho and McKay. This model is mostly applicable in predicting the sorption behaviour over the whole range and is in agreement with chemical sorption occurring as the rate-controlling step (Karadağ et al., 2015). The model is represented using the formulation below.

\frac{t}{q_{e}} = \frac{1}{K_{2} q_{e}^{2}} + \frac{t}{q_{e}}

(6)

where K₂ is the rate constant of second-order sorption (g/mg min).

Table 8 shows the values of the kinetic models parameters of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions sorption onto PVP and P(VP-co-MA) hydrogels. The validity of the investigated models was examined by the regression correlation coefficient (R²) and close agreement between q_e_,exp and q_e_,cal values. Based on the regression coefficient, the pseudo second-order kinetic model best described the overall sorption process of the metal ions onto the studied hydrogels, which confirmed chemical sorption occurred as the rate-controlling step. Also, the close agreement between the obtained q_e_,exp and q_e_,cal values_, and low values of SSE and MSE determined for the different metal ions as represented in Table 8 confirmed the pseudo second-order best fitted the sorption process.

The sorption mechanism of the metal ions onto the hydrogels follows three steps which are film diffusion, pore diffusion, and intraparticle diffusion (Shoueir et al., 2016). The effect of intraparticle diffusion on sorption is determined based on the relation of sorption capacity and time, which is represented by the formulation below.

q_{t} = K_{IP} t^{0.5} + C

(7)

where K_IP is the intraparticle diffusion rate constant (mg/g min^0.5) and C the boundary layer effect which contributes to the thickness of sorption surface (mg/g).

Figure 5 represents the intraparticle diffusion plots for different metal ions sorption onto PVP and P(VP-co-MA). As observed in Figure 5, the sorption process followed two phases with the resulting fitting passing through the origin. The existence of two phases in the intraparticle diffusion plot suggests that the sorption process occurred by surface sorption and the intraparticle diffusion. On the other hand, the intercept C of the plots reflected the boundary layer effect which occurred to be higher for P(VP-co-MA) compared to PVP hydrogel (Table 8). And the high R² values (≥0.9) depict the suitability of this model for expressing the experimental data which may confirm that the rate-limiting step is the intraparticle diffusion process.

Figure 5.

Intraparticle diffusion kinetic plots for Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ sorption onto (a) PVP and (b) P(VP-co-MA) hydrogel.

Sorption equilibrium isotherms

Several studies (Kumar et al., 2008; Paulino et al., 2011) have reported drawbacks involved with linearization of isotherm models, which may affect the normality assumptions of the curves thereby violating the theories behind the isotherms. So to avoid such hitches, non-linear regression equations were employed in this study for two-parameter isothermic models of Langmuir, Freundlich and Temkin, which enabled the comparison study of isotherm more reliable. These models are the most commonly used in the investigation of sorption of heavy metal species onto hydrogels because they described the adsorbate–adsorbent interaction but also reflects thermodynamic data providing information about sorption spontaneity and stability towards sorption affinity of the metal ion molecules (Piccin et al., 2011). The Langmuir isotherm theory is based on the assumption that adsorption occurs at specific homogeneous sites inside and sorption sites possess equal sorption affinity for adsorbate. In addition, once a metal ion molecule resides a site, no additional sorption can take place there (Kamal et al. 2016; Ngwabebhoh et al., 2016). The isotherm is represented be the formulation below.

q_{e} = \frac{Q_{m} K_{L} C_{e}}{1 + K_{L} C_{e}}

(8)

where q_e is the amount of metal ion adsorbed at equilibrium (mg/g), C_e is the concentration of metal ion in aqueous solution at equilibrium (ppm), Q_m is the maximum metal ion adsorbed (mg/g) and K_L is the Langmuir constant related to sorption capacity and the energy of sorption (g/mg). The Freundlich isotherm model is based on the equilibrium sorption on heterogeneous surface energy systems and describes multilayer sorption sites distributed exponentially on the adsorbent (Abdel-Aziz, 2011; Lu et al., 2011). The model is represented by the formulation below.

q_{e} = K_{F} C_{e}^{1 / n}

(9)

where K_F (mg/g (L/g)^1/ ⁿ ) and n are the Freundlich constants related to sorption capacity and sorption intensity, respectively. The Temkin isotherm model is based on the assumption that the heat of sorption of all molecules decreases linearly with the sorption coverage of the adsorbent–adsorbate interactions and that sorption is depicted by a uniform distribution of binding energies upto a maximum binding energy (Ngwabebhoh et al., 2016; Reddy et al., 2016). The isotherm formulation is represented as follows:

q_{e} = \frac{RT}{b_{T}} {InK}_{T} C_{e}

(10)

where K_T (L/g) is the Temkin isotherm constant, b_T (J/mol) is a constant related to heat of sorption, R is the ideal gas constant (8.314 J/mol K) and T is the absolute temperature (K).

Based on the regression correlation coefficient (R²) parameter, the best-fitted isotherm model was established to describe the sorption process. The sorption process favourability was assessed using the dimensionless parameter, R_L from Langmuir model. The sorption is favourable for R_L values in the range of 0 < R_L > 1 and if greater than 1 indicates the process is unfavourable (Afkhami et al., 2010; Ngwabebhoh et al., 2016). The three models examined in this study and isotherm parametric values obtained for the sorption of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions are shown in Table 9. It was observed that the sorption of metal ions onto the hydrogels was best described by Freundlich and Temkin models. This confirmed that the sorption of the metal ions onto PVP and P(VP-co-MA) occurred on multilayered surface with heterogeneous sorption active sites (Li et al., 2015; Ramirez et al., 2011). As observed in Table 9, the obtained values of R_L parameter for all the metal ions were between 0 and 1, demonstrating that Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions have desirable affinity for sorption onto PVP and P(VP-co-MA) hydrogels (Antic et al., 2015; Milosavljevic et al., 2011; Panic et al., 2013).

Table 9.

Isothermic parameters of metal ions sorption onto PVP and P(VP-co-MA) hydrogels.

	PVP hydrogel				P(VP-co-MA) hydrogel
Isotherms	Cu²⁺	Ni²⁺	Zn²⁺	Cd²⁺	Cu²⁺	Ni²⁺	Zn²⁺	Cd²⁺
Langmuir
K_L (L/mg)	2.33	1.19	1.52	1.95	3.47	2.94	3.92	3.71
Q_m (mg/g)	63.69	7.52	26.78	4.35	76.67	60.15	48.92	29.82
R_L	0.027	0.053	0.042	0.033	0.018	0.022	0.016	0.017
R²	0.870	0.803	0.868	0.816	0.895	0.856	0.821	0.813
Freundlich
K_F (mg/g (L/g)^1/ ⁿ )	2.16	0.09	1.89	0.60	7.35	5.88	4.92	2.96
n	1.57	1.17	1.49	1.30	2.92	2.01	1.92	1.96
R²	0.984	0.915	0.958	0.935	0.997	0.983	0.976	0.966
Temkin
K_T (L/g)	0.17	0.24	0.43	0.28	0.39	1.67	0.42	0.37
b_T	21.67	8.21	18.65	7.50	37.01	29.73	17.83	14.33
R²	0.954	0.907	0.929	0.906	0.991	0.963	0.993	0.953

P(VP-co-MA): poly(vinylpyrrolidone-co-methylacrylate); PVP: poly(vinylpyrrolidone).

Conclusions

This study aimed at a comparative optimization and evaluation of the sorption efficiency of synthesized homopolymer PVP and copolymer P(VP-co-MA) hydrogels for the uptake of Cu²⁺, Ni²⁺, Zn²⁺ and Cd²⁺ metal ions from aqueous solution in a batch reactor system. The obtained sorption experimental data revealed that P(VP-co-MA) hydrogel possessed greater binding capacity for investigated metal ions compared to PVP hydrogel. CCD proved to be a valuable tool for the determination of the optimal conditions for the sorption process via response surface analysis. The results showed that the sorption capacity increased with increasing the initial pH of solution and contact time. Optimum operational condition were determined at pH 8 and contact time of 6 h. Highest binding capacity was obtained for Cu²⁺ metal ion for PVP and P(VP-co-MA) hydrogels. The validation experiments affirmed the CCD model was suitable for optimizing the sorption process. The experimental data for the metal ions sorption well fitted the pseudo second-order kinetic model which predicts that chemical sorption occurred. The sorption process was best described by Freundlich model which suggested heterogeneity at the sorption sites of the hydrogels. The results of this study demonstrates that P(VP-co-MA) hydrogels were most suitable for the sorption of the heavy metals from aqueous environments due to high binding capacity and ease of separation.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflict of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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