Tailored functionalized polymer nanoparticles using gamma radiation for selected adsorption of barium and strontium in oilfield wastewater

2.1 Materials

Styrene-butadiene rubber (SBR) (Synaprene-1502, Styrene content 25%) and acrylonitrile monomer (AN) were obtained from Sigma-Aldrich (USA). All other chemical reagents of analytical grade were obtained from Fluka Company. Sodium salts of sulfate, sulfite, phosphite, hydrogen phosphate dihydrate and hydroxide (all from Merck) were used without further purification.

2.2 Methods

2.2.2

2.2.2 Synthesis of nanopolymers SAB and SASB

The nanopolymer blend of SBR/AN was prepared by mixing the two rubber/monomer solutions in a ratio of 50:50 vol%. The total solid loading was adjusted to 20–35 vol%. The obtained blend was mixed for 5 min at ambient conditions. After homogenization, the blend was exposed to γ-radiation at a dose of 20 kGy in order to crosslink the two polymers (Ghobashy and Abdeen, 2016). Back bone nano-sized white powder of SAB structure was obtained, see Fig. 1A.

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Fig. 1

(A) The back-bone structure of styrene butadiene blended with acrylonitrile (SAB) where (a) is buta-1,3-diene, (b) (acrylonitrile) is added to the double bond on the butadiene unit, (c) poly styrene, and (d) polyacrylonitrile (B) The back-bone structure of modified styrene butadiene blended with acrylonitrile (SASB) (c) sulphonated polystyrene (d) modified COOH groups from CN groups.

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Carboxylation: The carboxylic group was introduced by suspending 15 g of SAB (1 equiv) in 50 ml (Methanol: H₂O = 5:1) for 1 h. The suspended solution was allowed to reflux and then mixed with sodium hydroxide (5 equiv) drop-wise while stirring for 30 min. The mixture was then kept at 90 °C for 9 h to convert the nitrile (CN) groups into sod salt of carboxylate (COONa). Upon completion, the mixture was acidified with 2 N HCl to obtaine carboxylic acid groups. The product was extracted and purified with ethyl acetate. A pale yellow powder of nanosized [(SBR/AN-COOH)] was formed and separated by filtration. The obtained product was dried at 40 °C for 24 h.

Sulphonation: in the first step, a stoichiometric ratio of 98% sulphuric acid was carefully added to 15 ml acetic anhydride pre-cooled at 0 ^oC (adjusted by ice- crystals). The mixture was stirred for 10 min until the reaction mixture became yellowish viscous solution, resulting from the formed acetyl sulphate, as sulphonation agent (CH₃COOSO₃H). In the second step, 13 g of dry blend [(SBR/AN-COOH)] was added into a jacketed glass reactor containing 100 ml of dichloromethane and equipped with a condenser and mechanical stirring. Under nitrogen protection, the sulphonation agent (CH₃COOSO₃H) was add dropwise to the suspension [(SBR/AN-COOH) in dichloromethan] and stirred vigorously (200 rpm) with reflux condensation at temperature of 40 ^oC for 40 min. The desired theoretical amount of sulphonation agent (CH₃COOSO₃H) was introduced to the reaction mixture and stirred for further 30 min. The reaction was stopped by addition of cold distilled water. The sulfonated blend [SASB] was obtained as a dark yellow powder and washed several times with distilled water. The structure of SASB is illustrated in Fig. 1B.

2.3 Adsorption of Ba²⁺ and Sr²⁺

A stock aqueous solution of 1000 mg/L of selected metal ions Ba²⁺ and Sr²⁺ were prepared in deionized water. Different concentrations of total dissolved solids (TDS), up to 30 g/L, were added to simulate the real composition of sea water with composition ratios of 40% Na⁺ + K⁺, 10% Ca²⁺ + Mg²⁺, 45% Cl⁻ and 5% (HCO₃⁻ and SO₄²⁻). All batch adsorption runs were conducted in 125 ml closed shaking flasks that were agitated for 24 h at 150 rpm fixed shaking speed. Five independent variables (pH of solution ( $X_{\mathit{pH}}$  = 3 − 9), adsorbent dose (( $X_d$  = 1 − 3 g/L), initial metal ions’ concentrations ( $X_{\mathit{Co}}$  = 10 − 500 mg/L), TDS ( $X_{\mathit{TDS}}$  = 0 − 30 g/L) and solution temperature ( $X_t$  = 20 − 50°C) were examined to determine optimum conditions for the adsorption experiments. The Plackett–Burman factorial design (PBD) for the selected variables (Table 1) in conjunction with software MINITAB 17 (USA) was used to investigate the significant effect of each variable on adsorption responses (removal percentages and adsorption capacities, mg/g). Duplicate repeatability for central and factorial points of each variable in the PBD design were introduced to calculate the systematic error affecting optimization. Kinetic and thermodynamic studies were conducted at optimum conditions obtained from the Plackett–Burman design (PBD). These studies were carried out at $X_{\mathit{Co}}=$ 500 mg/L initial metals concentrations and temperatures of 20 − 50 °C for every 10 min time intervals up to 24 h.

2.4 Analytical procedure and statistical analysis

After the adsorption processes, the residual metal ions’ concentrations (Ba²⁺ and Sr²⁺) were determined by Ion Exchange Chromatography (IC, model Dionex ICS-2100 Series, USA) and checked by atomic absorption spectroscopy (AAS, model ZEEnit 700P Series, Analytica, Jena, Germany). The removal percentage (Y%) and metals adsorption capacities (mg/g) were calculated using equations (1) and (2).

Analysis of variance (ANOVA) and error statistics were used to evaluate the adequacy of the developed models by the PBD factorial design to simulate the adsorption experimental responses by both the nano-sorbents. The validation was also assessed using a parametric t-test at a probability level of 0.05 in accordance with the average absolute value of relative error, AARE (Eq. (3)), so to compare the predicted results with the experimental data (Ghaemi et al., 2011). The statistical validation and error studies were checked by using the solver add-in with Microsoft Excel@2013, MINITAB (v.17) and IBM-SPSS (v. 21) statistical package for verification of the results obtained.

3.1 Tailored-to-the-purpose polymer blend

By γ-irradiation at dose 20 kGy, an aqueous dispersion containing blend nano-polymer of AN/SBR was prepared, coded as (SAB) where S and A refer to Styrene and Acrylonitrile moieties, respectively and B refers to Blank sample. The obtained blend nano-polymer was chemically modified by introducing the functional groups (-SO₃H and -COOH) to investigate the adsorption selectivity for Sr²⁺ and Ba²⁺ ions from highly salty aqueous solutions and was coded as (SASB) where the additional S and B letters refer to Surface modified Bulk solids for selective adsorption of metal (Ba + Sr) ions from aqueous solutions. The resultant nano-blend [(SBR-SO₃H/AN-COOH)] was a dark yellow powder (SASB) (Fig. 1).

3.2 Structure characterization of the SAB and SASB nano-adsorbent

The results from the ATR-FTIR of acrylonitrile /styrene-butadiene rubber copolymer and its chemically modified SASB are presented in Fig. 2. The FTIR spectrum of functional SASB nano-adsorbent rubber/polymer blend (curve (b) in Fig. 2) showed similar characteristic features to curve (a) in Fig. 2 for the acrylonitrile /styrene-butadiene rubber copolymer (SAB), but with a slight shift and the presence of additional new peaks at lower wavenumbers. The FTIR bands corresponding to the trans >C=CH– (969 cm⁻¹) and the vinyl >C=CH₂ (916 cm⁻¹) were assigned to the trans-2-butene-1,4-diyl, 1607 cm⁻¹ (styrene) and 2240 cm⁻¹ (nitrile group) fragments of the SAB co-polymer (Peydro Rasero et al., 2013). The vibrations at 1448 and 1491 cm⁻¹ corresponding to the presence of an aromatic ring were observed. In Fig. 2b, the chemically modified copolymer blend SASB showed a minor FTIR peak at 851 cm⁻¹, suggesting bonding of -SO₃H groups to the aromatic ring of polystyrene. In addition, the band at 1027 cm⁻¹ was a result of the symmetric stretching vibration of -SO₃H groups, and the FTIR at 1159 cm⁻¹ results from a sulfonate anion attached to a phenyl ring (Lebovka, 2012). This depicts the appearance of a broad stretching band found between 1560 and 1815 cm⁻¹. Moreover, the FTIR peak at 1762 cm⁻¹ was due to carbonyl stretching characteristic for the carbonyl (–C⚌O) groups. A complete analytical picture of the spectra confirms that (SASB) contains -SO₃H and -COOH groups.

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Fig. 2

FTIR spectra for (a) SAB and (b) SASB nano-adsorbents based on acrylonitrile /styrene-butadiene rubber copolymer blend.

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Fig. 3(a) shows the TEM image of SASB. Obviously, TEM image indicates the successful formation of spherical shape nanoparticle of SASB sorbent with average diameter of 40 nm. In contrast, the charged ions or polyelectrolytes with the new functional groups (-COOH and -SO₃H) introduced by chemical modification were able to bridge the particles by electrostatic attraction causing coalescence (Sperling and Parak, 2010). Some coalescence of neighboring SASB nanoparticles can be seen in Fig. 3. Based on experimental DLS analysis (inset Fig. 3), the hydrated nanoparticles diameters of the SAB co-polymer are in the range of ≈24.4 to 55.7 nm, which are lower than the calculated diameters for functionalized SASB co-polymer (≈43.8 to 58.7 nm). Comparable to the unmodified SAB, it is also seen that SASB polymer showed extended increase in the diameter size up to 295 nm but it represents minor distribution (<22%) of total count particles. The increase of hydrated SASB particle sizes further confirms the coalescence effect of the functionalized surface with negative carboxylic and sulphonic charge groups. The Zeta-potential analysis verify that the functionalized SASB have higher negative surface charge of −12.8 mV relative to 4.0 mV of SAB (unmodified), which results from the SO₃H and -COOH -based functionalities as confirmed earlier by ATR-FTIR. CHNS(O) elemental composition is also used to confirm the successful functionalization of SASB sorbent with the bifunctional groups. Accordingly, the measured (calc.) percentage ratio of S content was found to be 1.8 wt% with increased of an oxygen content from 9.8% (in pristine SAB blend) to 24.2% in SASB sorbent, confirming successful functionalization process. Furthermore, the calculated C/N ratio was also to be reduced from 3.76 in SAB to 1.57 wt% in SASB.

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Fig. 3

(a) TEM image of SASB nanopolymer blend (inset histogram is the distriburted size diameters by DLS for the SASB (blue) vs. SAB (red) sorbents in nanoscale); (b) TGA curvatures of SAB and SASB polymer blends.

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Interestingly, their TGA results in Fig. 3b showed approximately similar thermal decomposition patterns with higher stability up to 283 °C for both SAB and SASB materials. As seen, both polymer blends were gradual decomposed after with increasing temperature over 283 °C and recording 21% weight loss at 402 °C. With increasing the temperature up to 489 ^oC, both blends were fastly decomposed to achieve a total 71% weight loss due to the carbonization of polymer chains into carbonaceous chare. The N₂ adsorption isotherm estimated that both of the prepared polymer blends have mesoporous surfaces with pore diameters around 4.61 nm and 3.92 nm for SAB and SASB sorbents, respectively. Results are consistent with the decrease in total pore volume from 0.015 cc/g SAB to 0.01 cc/g SASB at relative sorption pressure of p/po = 0.987. The decreased pore diameter in SASB may resulted from the lateral functionalized groups in the SASB blend polymer, which may talk part for the pore size (i.e., filling on phenomena). In contrast, the calculated Langmuir surface area were respectively recorded 38.2 m²/g and 20.7 m²/g for SASB and SAB polymer relative to multipoint BET specific area (S_BET) of 4.28 m²/g and 5.86 m²/g, respectively.

3.3 Screening of adsorption variables by Plackett–Burman design (PBD)

Barium and strontium metal ions are often found together with basic alkaline/earth metal ions in water environments. Hence, a 38 full factorial two-level PBD matrix was conducted in this application to evaluate the potential variables that significantly affect the adsorption of total Ba²⁺ and Sr²⁺ ions from water solutions. In addition, effect of different concentration of alkaline/earth metal ions with TDS ranging from zero to 30 g/L in solution on the adsorption responses were studied. Table 1 outlines the input variable levels in PBD and their corresponding adsorption responses by both SAB and SASB nano-adsorbents. The adsorption results showed a wide efficiency (sorption capacities) variation from 1.6% to 43.7% (0.7 to 120.4 mg/g) and from 55.4% to 99.1% (1.9 to 417.7 mg/g) when using SAB and SASB nano-sorbents, respectively.

3.3.1

3.3.1 Main and interaction effects of the adsorption variables on the adsorption performances

For better optimization of the adsorption process, it was important to investigate and optimize the adsorption capacity rather than adsorption percentages response (Behbahani et al., 2018; Younis et al., 2016). Because the adsorption capacity data (Eq. (2)) depend amount on both adsorbent dose and initial adsorbate concentration, and thus reduce comparison errors by using percentage values. Graphical representations of the polynomial regression models by MINITAB 17 software are presented in Fig. 4 and Fig A1 (Appendix A).

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Fig. 4

Interactive effects of adsorption parameters on the total Ba²⁺ + Sr²⁺ adsorption responses (mg/g) using (a) SAB and (b) SASB nano-sorbents.

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The described nanoscale blend polymer possesses a number of different properties such as high electron density and high metal ions adsorption. There are various possible interactions between different ions in aqueous solutions (adsorbate) and the surface of functionalized polymer (adsorbent) depending on the removal mechanism. Factors that affect the preferences for an adsorbate may be related to characteristics of the binding sites (e.g. functional groups, structure, surface properties) and properties of the adsorbent (e.g. concentration, ionic size, ionic weight, ionic charge, molecular structure, ionic nature or standard redox potential) and solution specifications (e.g. pH, ionic strength) (Ho, 2003; Saeed et al., 2005). As shown, Fig. A1 (Appendix A) presents the main effects of each variables and their corresponding interaction plots on the total Ba²⁺ and Sr²⁺ adsorption capacity (mg/g) responses by SAB and SASB nano-adsorbents. Interestingly, from Fig. A1 it can be seen that the maximum adsorption capacity (mg/g) by both nano-adsorbents were obtained at high levels of $X_{\mathit{Co}}$ at 500 mg/L and $X_T$ at 45°C, and 1 g/L $X_D$ of adsorbents and zero $X_{\mathit{TDS}}$ level. For instance, both SAB and SASB nanosorbents can be effectively used to capture almost all Ba²⁺ and Sr²⁺ metal cations efficiently from deionized water even over a high initial concentration ( $X_{\mathit{Co}}$ ) range for both Ba²⁺ and Sr²⁺ ions and low adsorbent dose ( $X_D$ ). In addition, variable in term of X_TDS at its zero level, along with X_T and X _pH variables are at median to high levels, were attributed to low competitive effect between alkaline earth metal ions and the enhancement of Ba²⁺ and Sr²⁺ ions diffusion rate in the bulk solution, and this is directly proportional to the temperature effect on the adsorption performances (Appendix A for details). In multi-components solutions of Ba²⁺ and Sr²⁺ along with alkaline/earth metal ions, low Ba²⁺ and Sr²⁺ adsorption capacities were recorded. However, the regression results showed lower significant effect of alkaline earth metals (i.e., Na⁺, K⁺, Ca²⁺, Mg²⁺) on the sorption performance of SASB compared to the original SAB blend even at highest $X_{\mathit{TDS}}$ of 30 g/L (details are given in Appendix A). Interestingly it is evident that the presence of low alkali ions up to 10 g/L has no apparent (negligible) effect on the sorption of Ba²⁺ and Sr²⁺ onto SASB. Results were confirmed by statistical regression analysis in Table 2, which showed lower significance effect of TDS on Ba²⁺ and Sr²⁺ adsorption capacities by SASB compared to SAB sorbent (F-values of 4.21 and 7.61 at p ≈ 0.05 and 0.01 with the percent contribution (PC%) of 1.09 and 17.12 and 1.09, respectively). However, sorption deviations at higher TDS of > 10 g/L seem to be attributed to: (1) cation complexation due to larger volume specie(s), which decreases the diffusion rate towards the adsorbent surface, and/or (2) competitive adsorption between Ba²⁺ and Sr²⁺ ions and alkaline earth metal species (TDS) present in solution (Visa et al., 2010).

Table 2 Regression coefficients and statistical analysis of the Plackett-Burman design (PBD) on the experimental adsorption responses.

Response	Effect on Percentage removal response						Effect on Adsorption capacity response
Term	Effect		t-value		F-value		Effect		t-value		F-value
	SAB	SASB	SAB	SASB	SAB	SASB	SAB	SASB	SAB	SASB	SAB	SASB
$X_{\mathit{pH}}$	−1.86	−6.268	−2.93	−5.99	8.57a	35.87a	5.81	−8.8	0.94	−0.44	0.89b	0.19b
$X_D$	12.927	13.969	20.34	13.35	413.64a	178.14a	−11.99	−115.1	−1.95	−5.74	3.79b	32.93a
$X_{\mathit{Co}}$	−8.875	9.297	−13.96	8.88	194.97a	78.92a	53.07	249	8.62	12.42	74.29a	154.19a
$X_{\mathit{TDS}}$	−18.082	−19.158	−28.45	−18.31	809.23a	335.09a	−29.8	−31.2	−4.77	−1.55	22.77a	2.42b
$X_T$	4.86	11.273	7.65	10.77	58.55a	116.01a	−2.99	−5.5	−0.49	−0.27	0.24b	0.08b

a At p < 0.001.

b At p > 0.05.

Using SASB blend nano-sorbent showed favorable Ba²⁺ and Sr²⁺ adsorption capacities for acidic or alkaline pH solutions with insignificant statistical response difference (PC% = 0.09%) compared to SAB that attained the highest adsorption at acidic pH ( $X_{\mathit{pH}}$ , PC % = 0.67%) only. As such observations might be because of the displacement of the Ba²⁺ and Sr²⁺ ions from their salts in both alkali and acidic solutions. Accordingly, it is suggested that both Ba²⁺ and Sr²⁺ should have a considerably prominent affinity for the -SO₃H group containing SASB adsorbent through a complexation mechanism (Ba-SO₃H and Sr-SO₃H)) rather than other alkali metal ions (Holmes, 1962). These observations were confirmed by statistical regression results in Table 2 which showed that $X_{\mathit{pH}}$ can be ignored when adsorption proceed by SASB compared to SAB adsorbent with F-values of 0.19 and 1.88, respectively, at p > 0.05 (Table 2). Furthermore, the analytical results showed that the affinity and adsorption capacity of SASB adsorbent were following the order of Ba²⁺ (210.5 mg/g) > Sr²⁺ (175.3 mg/g) (See Table 1). This can be explained based on the ionic radii of hydrated Br²⁺ and Sr²⁺ ions and their stability order of complexes formation (Malati and Estefan, 1966).

In this work it was found that the SASB adsorption capacity decreased in the reverse order of the hydration radii of the metal ions. The calculated hydration radii for Sr²⁺ and Ba²⁺ were found to be 2.77 Å and 2.69 Å, respectively (Tewari, 1981), and therefore Ba²⁺ ions with lower hydrated ionic radii have higher adsorptive power.

A comparison between interactive effects of adsorption variables on adsorption capacity responses (mg/g) by SAB and SASB nano-adsorbents was investigated and shown in Fig. 4. Fig. 4a shows that there were high interactions between either sorbent amount or initial metals concentrations with TDS ( $X_D\ast X_{\mathit{TDS}}$ and $X_{\mathrm{C}\mathrm{o}}\ast X_{\mathrm{T}\mathrm{D}\mathrm{S}}$ ) on the adsorption performance (mg/g) by SAB sorbent. Comparatively, three interaction effects were found between the studied parameters in terms of ( $X_{\mathrm{D}}\ast X_{\mathrm{C}\mathrm{o}}$ ), ( $X_{\mathrm{C}\mathrm{o}}\ast X_{\mathrm{T}\mathrm{D}\mathrm{S}}$ ) and ( $X_{\mathrm{C}\mathrm{o}}\ast X_{\mathrm{T}}$ ) that had the highest significant effect on Ba²⁺ and Sr²⁺ adsorption ( $Y_{\mathrm{m}\mathrm{g}/\mathrm{g}}$ ) responses using SASB blend nano-sorbent (Fig. 4b). As such, a weak to insignificant interactions effects were observed by other studied combinations between variables on Br²⁺ and Sr²⁺ adsorption responses when using SAB or SASB sorbents, and such observations were confirmed by ANOVA results (Table 3 and details are given in Appendix A).

Table 3 Multiple regression and PBD-DOE coefficients results for the quadratic polynomial regression models developed using SAB and SASB nano-sorbents.

Model components	Model terms	Estimated coefficient				t-value				PC%
		Removal %		Sorption performance		Removal %		Sorption performance		Removal %		Sorption performance
		SAB	SASB	SAB	SASB	SAB	SASB	SAB	SASB	SAB	SASB	SAB	SASB
Intercept	${\beta }_o$	27.170	45.940	14.00	94.30	0.000	6.320	0.88	4.050	–	–	–	–
$X_{\mathit{pH}}$	${\beta }_1$	−2.220	1.900	−0.69	−42.93	0.086	0.740	−0.37	−5.220	0.56	4.62	0.67	0.09
$X_D$	${\beta }_2$	6.513	9.490	−1.31	2.50	0.000	5.800	−0.220	0.480	27.28	22.95	2.85	14.88
$X_{\mathit{Co}}$	${\beta }_3$	−0.024	0.024	0.188	0.964	0.000	3.320	7.080	41.570	12.86	10.17	55.86	69.67
$X_{\mathit{TDS}}$	${\beta }_4$	−0.656	−0.690	−1.206	−0.785	0.000	−5.780	−2.760	−2.050	53.36	43.17	17.12	1.09
$X_T$	${\beta }_5$	0.160	0.521	0.031	0.380	0.004	5.090	0.080	1.160	3.86	14.94	0.18	0.03
$X_{\mathit{pH}}{X}_D$	${\beta }_{12}$	0.142	0.119	−0.540	−0.051	0.063	0.790	−0.980	−0.110	0.14	0.01	0.004	0.01
$X_{\mathit{pH}}{X}_{\mathit{Co}}$	${\beta }_{13}$	0.0002	0.001	−0.001	−0.002	0.442	1.540	−0.450	−1.090	0.02	0.19	0.09	0.04
$X_{\mathit{pH}}{X}_{\mathit{TDS}}$	${\beta }_{14}$	−0.011	0.0001	0.026	0.037	0.043	0.030	0.640	1.050	0.25	0.003	0.36	0.30
$X_{\mathit{pH}}{X}_T$	${\beta }_{15}$	0.012	0.004	0.019	0.01	0.025	0.420	0.510	0.310	0.28	0.01	0.54	0.07
$X_D{X}_{\mathit{Co}}$	${\beta }_{23}$	0.003	−0.004	−0.015	−0.223	0.002	−2.080	−2.180	−37.600	0.24	0.37	1.35	12.87
$X_D{X}_{\mathit{TDS}}$	${\beta }_{24}$	0.025	−0.018	0.468	0.296	0.112	−0.580	4.000	2.900	0.05	0.003	1.91	0.03
$X_D{X}_T$	${\beta }_{25}$	−0.050	−0.060	−0.08	−0.191	0.004	−1.840	−0.670	−1.850	0.22	0.56	0.16	0.00
$X_{\mathit{Co}}{X}_{\mathit{TDS}}$	${\beta }_{34}$	0.0001	0.0001	−0.004	−0.003	0.032	2.820	−8.560	−6.920	0.12	0.65	14.39	0.39
$X_{\mathit{Co}}{X}_T$	${\beta }_{35}$	0.0002	0.0004	0.0005	0.001	0.271	−1.980	1.080	3.610	0.04	0.35	0.24	0.11
$X_{\mathit{TDS}}{X}_T$	${\beta }_{45}$	0.002	0.000	0.005	−0.002	0.059	−0.040	0.620	−0.240	0.11	0.002	0.08	0.004

3.4 Adsorption kinetic mechanism

The kinetic studies at optimum operating conditions were carried out to identify a possible mechanism involved in the Ba²⁺ and Sr²⁺ adsorption uptake. Two non-linear kinetic models namely; pseudo-first (PFOM) and pseudo-second (PSOM) kinetic regression models (Younis and Moustafa, 2017; Matouq et al., 2015) were tested using IBM SPSS 21 software incorporating 200 iterations. A non-linear form of the kinetic equation and their corresponding calculated kinetic constants are given in Table 4.

The relationship between adsorption time and ions uptake by the SAB and SASB is presented in Fig. 5 at $X_{\mathit{Co}}$ of 500 mg/L for equal concentrations of Ba²⁺ and Sr²⁺. The adsorption equilibrium was divided into two regimes characterized by fast adsorption stage (exponential stage) of Ba²⁺ and Sr²⁺ ions to the functional adsorbent surfaces followed by a second slower stage indicating equilibrium.

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Fig. 5

Effect of contact time on the adsorption of Ba⁺² and Sr⁺² by SAB and SASB sorbents and kinetic fitting by (a) PFOM and PSOM, and (b) WMM theories.

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The second equilibrium stage evolved after approx. 8 h and 6 h for the SAB and SASB nanoparticles, respectively. The diffusion rate and adsorption uptake were slower due to the maximum saturation level of adsorbent surface functional vacant sites with adsorbates ions. Thereafter, the remaining unoccupied sites were difficult to attach by the metal ions due to steric hindrance that results between the adsorbed solute ions and solute in the bulk aqueous environment (Jin et al., 2011).

Experimental kinetic results depict a higher affinity of SASB NPs sorbent with a rapid of Ba⁺² uptake ( $q_e$ ≈ 210.4 mg/g) compared to Sr⁺² ions ( $q_e$ ≈ 175.3 mg/g) (Fig. 5a). Table 4 depicts also a rapid Ba⁺² uptake over a considerably lower period of time compared to Sr⁺² with the value of initial sorption rate values of ‘ $h_o$ ’ of 53.46 and 72.73 mg/(g h), and 8.49 and 52.06 mg/(g h) by both SAB and SASB adsorbents, respectively. To mathematically and quantitatively demonstrate the Ba⁺² or Sr⁺² selectivity, the KD distribution coefficient (Behbahani et al., 2017) was calculated to indicate the selectivity of metal ions adsorption onto the fabricated sorbents. As listed in Table 4, the KD sequence was in the order of Ba (II) > Sr (II) with the highest selectivity of the SASB NPs for barium than strontium uptake (KD ≈ 5308.35 and 2345.38 mg/mL), which is in a good agreement with the optimized data obtained above. This can be explained based on (1) The lower ionic radii of hydrated Br²⁺ (2.69 Å) than Sr²⁺ (2.77 Å) ions; (2) The higher SASB [(HSO₃-SBR/AN-COOH)] negativity charges that promote affinity and selectivity to adsorb Ba ions with lower electronegativity (0.97) comparable to Sr ions of higher electronegativity (0.99) (Fard et al., 2017); and (3) The higher tendency of Ba (II) than Sr (II) for SASB functional groups to form stable complexes formation [(Ba-SO₃-SBR/AN-COO-Ba)], which plays a role too (Malati and Estefan, 1966; Tewari, 1981). The present work thus proves that the SASB NPs preferences the accumulation of Ba (II) ions on their surface functionalities, leading to electrostatic neutrality as well as the adsorptive power decreased in the reverse order of electronegativity and the hydration radii of the metal ions.

The overall kinetic results in Table 4 revealed that the sorption of Ba²⁺ and Sr²⁺ ions by SAB and SASB nano-adsorbents were likely represented by both PFOM and PSOM as confirmed from Fig. 5a. Comparing the results of the correlation coefficients ( $R^2$ ) and AARE error values in Table 4, PFOM was found to be the superior model for Ba²⁺ and Sr²⁺ ions adsorption by SAB and SASB sorbents with high $R^2$ value and very low AARE error statistics. Such adsorption behavior of Ba⁺² and Sr⁺² by SAB and SASB adsorbents was in agreement with physical and chemical adsorption processes. Thus, the prevalent mechanism was the PFOM sorption and the overall rate constant of each adsorbent seem to be governed by the predominant physical sorption mechanism assisted by chemisorption process (Sajih et al., 2014). The kinetic data was further tested by Weber and Morris (WMM) theory (Weber and Morris, 1962) in order to quantify the pore diffusion rate-controlling step involved in adsorption (Table 4). According to the WMM theory, the Ba⁺² and Sr⁺² uptake varies with $t^{0.5}$ and $K_d$ (mg/ (g. $h^{0.5}$ )), which was the rate constant of stage i. From the results shown in Table 4, it can be seen that the $K_d$ values were in the order of Ba⁺² > Sr⁺² and their values increased with SASB adsorbent rather than with SAB sorbent. The Ba⁺² diffusion mechanism on SAB sites depended on one of the rate-controlling adsorption mechanisms until reaching equilibrium, see Fig. 5b. The deviation from zero origin or near saturation on SASB adsorbent might be due to the high desirability of chemical adsorption mechanism located between the surface functionalities (i.e., complexation and/or electrostatic chelation with (N≡C-SAB) and SASB [(HSO₃-SBR /AN-COOH) functional group) and Ba⁺² and Sr⁺² metal ions rather than the pre-diffusion mechanism. With time, almost of the surface active sites are exhausted with Ba⁺² and Sr⁺² ions, and thus the multilayer coverage take place followed by a lower uptake rate until it ultimately reaches an equilibrium plateau. As such, the physical sorption involving valence forces for sharing or exchanging electrons without formation of complexity due to complete surface active sites occupation, forming a chemical bond. Hence, one can assume that the tailored-to-purpose of co-existence of -COOH and -SO₃H groups on the functionalized surface of SASB might be a promising tool to promote selectively removed of divalent barium and strontium ions compared to other reported sorbents (Table 5) from a complex oilfield water sample or produced formation water to prevent scale formation.