All of the chemicals were analytical-grade reagents and were used without further purification.

The graphene oxide (GO) sheets and copper(II) chloride dihydrate (CuCl₂·2H₂O, 99.0%, average M.W. = 170.48 g/mol) were purchased from Sigma-Aldrich Chemical Co. The N,N-dimethylformamide (DMF) (C₃H₇NO, M.W. = 73.09 g/mol), calcium chloride (CaCl₂, 85%), and sodium alginate (C₆H₉NaO₇, M.W. = 216.121 g/mol) were purchased from Daejung Chemicals & Metals Co. (South Korea). The DMF was used for the polymerization of the acrylonitrile monomer to PAN. All of the solutions were prepared with ultra-pure water (18.2 MW×cm), which was obtained from Vivagen co. Ltd. (EXL5 Analysis 16, South Korea).

The GO (0.02 g) was added to 20 mL of ultrapure water and dispersed completely using sonication (JAC-4020P, KODO Technical Research Co.) for 2 h. Sodium alginate (0.10 g) was added into the ultrasonicated GO solution and completely dissolved by stirring, followed by ultrasonic irradiation. For functionalization with PAN, the acrylonitrile monomer was added and stirred for 2 h under an N₂ atmosphere. After stirring, methanol was added in order to precipitate the slurry. To obtain a perfect solution by removing the homopolymer, the solution was washed several times with DMF. When a homogeneous solution was obtained, this was dropped into a CaCl₂·2H₂O solution (10 g/L, 200 mL) using a syringe pump (NE1000, 4science Co., USA) at 2 mL/min under continuous magnetic stirring to encapsulate the alginate beads. The hydrogels were kept in CaCl₂·2H₂O solution for stabilization, washed 2–3 times with ultrapure water, then placed in an oven and allowed to dry for 24 h for subsequent use as adsorbents.

The morphology of the sorbents was analyzed by FE-SEM (SU8220, Hitachi, Japan). The specific surface area, pore size, and pore volume were measured using a surface area and pore size analyzer (BET, Autosorb-IQ & Quadrasorb SI, Quantachrome). The functional groups were analyzed to identify the chemical combination of sorbents by FT-IR (Frontier, PerkinElmer, USA). The thermal properties of the sorbents were identified via TGA (Q600, TA-Instrument, Japan) under an N₂ atmosphere at a heating rate of 10°C/min.

As simulated wastewater, Cu²⁺ solutions were prepared with varying concentrations from 0.1 to 60 mM. All experiments were performed in a 50 mL conical tube (PE, SPL Korea) using a duplicate batch system. To carry out the adsorption isotherm experiments, 0.05 g of adsorbent was added into 55 mL of the Cu²⁺ solutions (0.1, 0.5, 1.0, 2.0, 5.0, 10, 20, 30, 40, 50 and 60 mM) and was mixed at 250 rpm for 24 h at room temperature. The samples were then centrifuged at 4,000 rpm for 10 min to separate the sorbent from the solution. The solution was filtered using 0.20 mm nitrocellulose membrane filters (Whatman) before analysis.

Adsorption kinetic experiments were conducted by sampling at various time intervals after mixing the solutions containing 0.05 g of adsorbent and 55 mL of 2mM Cu²⁺ in the tubes.

The supernatants were analyzed by inductively coupled plasma optical emission spectroscopy (ICP-OES, Optima 2100DV, PerkinElmer Co., USA) to measure the adsorption capacities. The equilibrium (q_e) value is given by Eq. (1):

where q_e is the Cu²⁺ adsorption capacity in milligrams per gram (mg/g) of adsorbent, C_o is the initial concentration of Cu²⁺ solution, C_e is the concentration of Cu²⁺ in the effluent solution after adsorption, V is the solution contact volume (mL), and m is the mass of the adsorbent (g).

The FT-IR spectra of the GO, GO/Ca-Alg₂, and GO/Ca-Alg₂-PAN in the 4000–400 cm⁻¹ region are presented in Fig. 1. Comparison of the spectra of GO (Fig. 1(a)) and GO/Ca-Alg₂ (Fig. 1(b)) reveals the appearance of four new bands at 1453 cm⁻¹, 1358 cm⁻¹, 1249 cm⁻¹, and 1074 cm⁻¹, which indicate that the graphene oxide was fully reacted with the calcium alginate during the preparation of the double-network composite [21]. The presence of the –COO stretching vibrations and the C–H stretching bands located at 1453 and 1074 cm⁻¹, the C–OH bending band at 1357 cm ⁻¹, the C–O–C asymmetric stretching band at 1249 cm⁻¹ was observed [22]. An additional new band in the spectrum of GO/Ca-Alg₂-PAN (Fig. 1(c)) indicates the successful combination of poly(acrylonitrile). Normally, nitrile-containing compounds have a sharp adsorption in the region of 2260–2200 cm⁻¹ [23, 24]. The results of the spectral analysis of functional groups thus confirmed that the double-network 3D complex GO/Ca-Alg₂-PAN was successfully synthesized.

The qualitative EDS results for the GO/Ca-Alg₂-PAN showed the presence of C, N, O, Ca and Cl, as anticipated (Fig. 2). The presence of Ca and Cl in the Ca-Alg₂ beads, along with C and O in the GO and PAN, demonstrate that the synthesized GO/Ca-Alg₂-PAN beads have sufficient adsorption sites. In addition, the transformation of Na-Alg to Ca-Alg₂ was achieved by cation-exchange as the beads formed the “egg-box” structure [13].

The surface structures of the GO/Ca-Alg₂-PAN were investigated by analysis of the physical properties and FE-SEM images presented in Fig. 3. The FE-SEM image in Fig. 3(a) indicates that the GO consists of 2D plates, while Fig. 3(b) indicates the 3D structure of the GO/Ca-Alg₂ beads after transformation of the GO/Na-Alg solution. The GO/Ca-Alg₂-PAN composites are imaged in Fig. 3(c–d), which shows a group of spheres onto which the 3D-structured polymer was functionalized. The surface area of GO is much greater than those of GO/Ca-Alg₂ and GO/Ca-Alg₂-PAN; hence, the surface area of the GO/Ca-Alg₂ is dramatically reduced to 2.466 m² per gram of alginate. However, the functionalization of GO/Ca-Alg₂ with PAN to form GO/Ca-Alg₂-PAN with the double interpenetrating polymer network (IPN) structure led to an increase in surface area. The pore-sizes were similar, while the pore volume of GO was the largest. The final composition, GO/Ca-Alg₂-PAN, had a pore volume of 0.034 cm³/g. The smaller surface area and pore volume relative to GO were due to the presence of alginate, but the resulting beads are easily separated from aqueous solution and have the advantage of high efficiency for a low surface area. [25]. As shown in Fig. 3, the PAN polymer was successfully functionalized onto the GO/Ca-Alg₂ hydrogel-forming 3D structure.

The data obtained from the Cu²⁺ adsorption experiment were fitted using two equilibrium models to confirm the adsorption behavior. The Langmuir isotherm model represents the monolayer adsorption of metal ions in accordance with Eq. (2):

where q_m (mmol/g) is the maximum sorption capacity, b (L/mmol) is the Langmuir adsorption constant related to the free energy of the sorption, and C_e is the equilibrium concentration of Cu²⁺ aqueous solution.

Alternatively, multiple-layer adsorption can be analyzed according to the Freundlich adsorption model given by Eq. (3):

where K_f [(mmol/g) (L/mmol)^1/n] and n are constants of the Freundlich model.

The kinetic behavior of Cu²⁺ adsorption was fitted using Lagergren’s pseudo first-order and pseudo second-order models, Eqs. (4) and (5), respectively:

where q_t is the concentration of Cu²⁺ ions (mmol/g) at time (t), q_e is the equilibrium concentration, k₁ is the pseudo-first-order constant (min⁻¹) and k₂ is the pseudo-second-order constant (g/mmol/min).

From the pseudo second-order model, the initial adsorption rate (h) could be calculated according to Eq. (6):

Fig. 4 shows the equilibrium isotherm nonlinear models and kinetic models for the removal of Cu²⁺ at room temperature. In the Langmuir isotherm model, the maximum adsorption capacity (q_m) value of the GO/Ca-Alg₂-PAN is 5.99 mmol/g. In the Freundlich model, however, the maximum adsorption amount increased with increasing concentration in solution. In Fig. 4(a), both kinetic models were well-fitted to the experimental data.

The constants and correlation coefficients of the isotherm and kinetic models are indicated in Table 1. When fitting the two adsorption models with the experimental data, the Freundlich isotherm model gave a better fit than the Langmuir isotherm model. In the Freundlich isotherm model, the determination coefficient (r²) was 0.980, which is closer to 1. Since the Freundlich model is well-suited to modeling Cu²⁺ removal using GO/Ca-Alg₂-PAN, we conclude that the synthesized GO/Ca-Alg₂-PAN is a double-network capable of adsorbing multiple layers of Cu²⁺ at multiple adsorption sites. In the absorption kinetics results, the kinetic behavior of the GO/Ca-Alg₂-PAN depended on the second-order model better than the first-order model through the r² value of two kinetic models for the absorption of 1 mM and 2mM of Cu²⁺. According to the pseudo first-order model, the equilibrium of adsorption was achieved within about 120 mins. Normally, powdered adsorbents reach equilibrium in a minimum of 10 mins [26]. However, the beads require time to swell in aqueous solution, so stirring for extra time was considered in order to reach equilibrium. As a result, the isotherm adsorption experiments in the present study confirmed that a stirring-time of 24 h allowed sufficient contact time for equilibrium to be reached. In addition, for the pseudo second-order model, the h value and the q_e value increase as the concentration of Cu²⁺ increases. Hence, as the concentration increases, the time to reach the adsorption equilibrium decreases and the amount absorbed increases.

Generally, the mechanism of adsorption consists of three steps, namely: (i) external mass transfer, (ii) particle pore diffusion, and (ii) adsorption reaction at a surface site [27]. It can be interpreted according to two equations relating to the intraparticle diffusion [28] and the external mass transfer rate [29]. The rate of intraparticle diffusion equation is given by Eq. (7):

where k_i is an intraparticle diffusion rate constant (mmol/g·min^0.5), t is the contact time (min) and q_t is the intraparticle diffusion rate.

From this, the diffusion coefficient (D, m²/s) is calculated using Eq. (8):

where t_1/2 is the time when the adsorption reaches one half of the equilibrium value and d is the diameter of the adsorbents (m).

The external mass transfer rate can be represented by Eq. (9):

where A is the surface area of adsorbents (m²), V is the volume of solution (m³), and the mass transfer coefficient k_s (m²/min) can be determined experimentally from a plot of −ln(C(t)/C_o) against t.

As indicated in Fig. 5, multilinearities were observed in the plots of q_t versus t_0.5 for 1 and 2 mM Cu²⁺. The graph is divided into two linear lines, indicating that the Cu²⁺ adsorption takes place in a complex process involving external mass transfer and intraparticle diffusion. The steep slope in the first step indicates the external mass transfer to the external surface, and the second shallower slope is due to the intraparticle diffusion [30, 31]. The parameters from the Figures are presented in Table 2. The k_i,1 and k_i,2 values were calculated from the two straight lines in Fig. 5, each of which has a high correlation value (r²) of 0.9 or more. Although the adsorption rate was higher for a Cu²⁺ concentration of 2 mM than for 1 mM, the values of D and k_s of the external material were decreased. This is because the adsorption rate is fast but takes a relatively long time to reach the adsorption equilibrium. These results confirm that the adsorption occurs by both internal diffusion and external mass transfer. With 1 mM Cu²⁺, the D value of the intraparticle diffusion is 3.8034 × 10⁹ and the k_s value of the external mass transfer is 12.2478. For 2 mM Cu²⁺, the corresponding values are 2.5563 ×10⁹ m²/s and 9.0247×10⁸ m/s, respectively. Therefore, intraparticle diffusion relatively dominates the total adsorption process.