## 3.1 Structure and morphologies

Figure 1a-1d showed FESEM images of MNPs, KH230-MNPs, PEI-MNPs and mLap/(AA-AM), respectively. Both MNPs, KH230-MNPs, PEI-MNPs have spherical shape with average size of 30–31 nm and narrow particle size distribution, indicating that surface modifications by KH230 and PEI do not destroy the structure and morphology of magnetic nanoparticles. However, mLap/(AA-AM) has rough and uneven surfaces with many porous structures, which favors the diffusion of heavy metal ions into the inside active sites of the magnetic composite hydrogels, and thus promotes the adsorption of the heavy metal ions.

As can be seen from XRD spectra(Fig. 2a), MNPs, KH230-MNPs and PEI-MNPs have characteristic diffraction peaks at 2θ = 30.2°, 35.5°, 43.4°, 53.7°, 57.1° and 62.7°, which correspond to 220, 311, 400, 422, 511 and 440 crystal faces of standard Fe3O4(JCPDS No.19-06290). As indicated in Fig. 2b, mLap/(AA-AM) has characteristic diffraction peaks of Fe3O4 attributed to 220, 311, 511 and 440 crystal faces, indicating that crystal structure of Fe3O4 is not destroyed during radical copolymerization of acrylamide and acrylic acid. However, characteristic diffraction peaks of Laponite disappear for mLap/(AA-AM). This suggests that Laponite is dispersed in the polymer matrix with amorphous structure.

As seen from FTIR spectra(Fig. 2c), MNPs, KH230-MNPs, PEI-MNPs and mLap/(AA-AM) have broad peaks around 3440 cm-1 assigned to O–H stretching vibration and 585 cm-1 ascribed to Fe-O groups(Chandra and Bhattacharya 2019; Sun et al 2019). KH230-MNPs has peaks at 2924 cm-1 and 1132 cm-1 attributed to the characteristic absorption of CH2 and Si-O bond[21], respectively, indicating that KH230 has been grafted onto the surface of magnetic nanoparticles. PEI-MNPs has peak at 1548cm-1 ascribed to N-H bending vibration[21], implying that PEI is grafted onto the surface of magnetic nanoparticles. In addition, mLap/(AA-AM) has characteristic peaks such as 1726 cm–1(carbonyl stretching vibration), 1659cm-1( amide stretching absorption), 1454 cm-1 (NH2 and OH bending vibration[21], 1399cm-1(carbonyl bending vibration absorption) and 990cm-1(Si-O stretching vibration of Laponite). Thus, FTIR results show that MNPs, KH230-MNPs, PEI-MNPs and mLap/(AA-AM) have target structures.

EDX spectrum(Fig. 2d) demonstrates that mLap/(AA-AM) have elements of C, O, N, Fe, Na, Mg and Si, where C, O, N, Na and Si are derived from polymeric matrix, Fe and O come from Fe3O4, and Si, O, Mg, Na originate from Laponite. This further demonstrates that mLap/(AA-AM) has target element composition.

## 3.2 Adsorption kinetics and thermodynamics of heavy metal ions

To investigate the mechanism of heavy metal ion adsorption, pseudo-first-order[22] and pseudo-second-order equation[23] were used to fit the experimental data of heavy metal ions adsorption. Pseudo-first- order and pseudo-second- order models are given as Eq. (1) and Eq. (2), respectively.

ln(qe−qt) = lnqe−k1t (1)

t/qt =1/( k2qe2) + t/qe (2)

where qe is the adsorbed amount at equilibrium, qt is the adsorbed amount at time t, k1 and k2 are the first order rate constant and second order rate constant, respectively.

As depicted in Fig. 3a, correlation coefficients (R2) of pseudo-first-order kinetic model are lower than (R2 < 0.989) those((R2 > 0.996) of pseudo-second-order kinetic model for heavy metal ion absorptions. Also, the calculated qe values (226.5mg/g for Cu(II), 242.8mg/g for Cd(II) and 430.9mg/g for Pb(II)) obtained from the pseudo-first-order kinetic model are much lower than experimental values (Cu(II) (238mg/g), Cd(II) (259mg/g) and Pb(II)(466mg/g)). Moreover, the calculated qe values(250.8mg/g for Cu(II), 267.3mg/g for Cd(II) and 473.9mg/g for Pb(II)) from pseudo-second-order kinetic model almost accord with the experimental data. These indicate that the adsorption of heavy metal ions belongs to the second-order kinetic model.

According to pseudo-second-order mechanism, rate determining step is chemisorption, involving valence forces through sharing or exchange of electrons between adsorbent and adsorbate[23]. Therefore, the heavy metal ions adsorption onto mLap/(AA-AM) is a chemical process in addition to physisorption.

Langmuir and Freundlich adsorption isotherm models, expressed in Eq. (3) and Eq. (4), respectively, were used to determine the appropriate isotherm for adsorption of heavy metal ions.

Ce/qe= 1/(Q0b) + Ce/Q0 (3)

lnqe = lnKF + (1/n)ln Ce (4)

where Ce is the equilibrium concentration, qe is the adsorbed amount at equilibrium, Q0 and b are Langmuir constants. KF is the Freundlich constant and n is the Freundlich exponent.

As demonstrated in Fig. 3b-3c, correlation coefficient (R2) of Langmuir adsorption model(R2 > 0.993) for heavy metal ions are higher than those of Freundlich adsorption model(R2 < 0.799). Besides, the adsorption capacities of Cu(II), Cd (II) and Pb (II) calculated by Langmuir fitting equation are 243.8 mg/g, 262.6 mg/g and 468.6 mg/g, respectively, which are in good agreement with the experimental data. The results indicate that the adsorption process of heavy metal ions for mLap/(AA-AM) is consistent with Langmuir adsorption model. As shown in Fig. 1d, mLap/(AA-AM) has porous and uneven structure, which may not meet the requirement for Langmuir isotherm model. However, the driving forces such as coordinating interaction and ion exchange for heavy metal ions adsorbed on mLap/(AA-AM) is beneficial for Langmuir isotherm model. Therefore, Langmuir isotherm model fits well the experimental data.

Adsorption thermodynamic parameters such as Gibbs free energy(ΔGΘ), enthalpy(ΔHΘ) and entropy(ΔSΘ) can be obtained by the thermodynamic equations as follows:

ΔGΘ=-RTlnK=-RTln(qe/Ce) (5)

ΔGΘ = ΔHΘ-TΔSΘ (6)

ln(qe/Ce)= ΔSΘ/R-ΔHΘ/(RT) (7)

where R is gas constant, T is the temperature and K is the equilibrium constant, qe is the adsorbed amount at equilibrium and Ce is the equilibrium concentration.

As depicted in Fig. 3d, the value of ln(qe/Ce) is positive, thus the value of ΔGΘ is negative at different temperatures according to Eq. (5). This indicates the adsorption of heavy metal ions for mLap/(AA-AM) is spontaneous process. In addition, absolute values of ΔGΘ gradually increases as the temperature increases, implying that higher temperature facilitates the adsorption of heavy metal ions. Besides, calculated adsorption enthalpy(ΔHΘ) has positive value, an indicative of endothermic process for heavy metal ions adsorption of mLap/(AA-AM). Therefore, increasing temperature enhances the adsorption of heavy metal ions.

As shown in Fig. 3d, a positive value of adsorption entropy (ΔSΘ) indicates that the adsorption of heavy metal ions by mLap/(AA-AM) is an entropy increasing process, indicating increased randomness at the solid/solution interface during heavy metal ions adsorption and high affinity of mLap/(AA-AM) for heavy metal ions[24].

## 3.3 Viscoelasticity, magnetic response and recycling performance

Figure 4a-4b showed the relationships between Laponite amount and storage modulus (*G′*) and the loss modulus (*G″*) of mLap/(AA-AM), respectively. Within the frequency range from 0.1 to 100 rad/s, storage moduli of mLap/(AA-AM) are always greater than loss moduli, an evidence of typical gel networks[25]. Both *G′* and G*″* of mLap/(AA-AM) increase with amount of Laponite, caused by the high cross-linking degree of mLap/(AA-AM) and strengthening effect of Laponite. This means that Laponite, acting as physical crosslinker, can enhance the mechanical strength of magnetic composite hydrogels, which can solve the disadvantage of insufficient gel strength of conventional hydrogels and favor the practical application of mLap/(AA-AM). Negatively charged Laponite can physically crosslink with carboxyl and amide groups of polymer matrix through hydrogen bonding, etc. Therefore, the energy consumed by deformation of hydrogels and the rigidity of resistance to external forces are increased, resulting in an increase in both storage modulus (gel strength) and loss modulus.

As shown in Fig. 4c, saturation magnetization of MNPs reaches 67.08 emu/g, while those of KH230-MNPs and PEI-MNPs decrease slightly with the saturation magnetization of 57.06 emu/g and 50.07 emu/g, respectively. Due to none-magnetic response of KH230, PEI, Laponite and polymer matrix, saturation magnetization of mLap/(AA-AM) decrease to 15.05 emu/g. In addition, hysteresis loops of all magnetic materials pass through the origin, an indicative of remanence and coercivity of zero, which is the evidence for superparamagnetic property. Such superparamagnetic performance of mLap/(AA-AM) is important for solid-liquid separation via an external magnetic field, which can solve the problems of complicated and time-consuming solid-liquid separation process of common adsorbents.

It is well known that the recyclability and stability of the adsorbent is crucial for practical applications. As seen from Fig. 4d, after five cycles, the removal efficiency of heavy metal ions decreases to 72.8%,73.9% and 74.5% for Cu(II), Cd (II) and Pb (II) as compared with those for the first absorption, respectively, indicating good reversibility and stability of mLap/(AA-AM). The decrease of removal efficiency may be caused by a few active sites not being released or inactivated.

mLap/(AA-AM) has three-dimensional networks with PEI-modified magnetic nanoparticles and Laponite entrapped within the polymeric networks. PEI and Laponite can interact with the polymeric matrix via hydrogen bond to form multi-level three-dimensional networks. Moreover, PEI chains contain many amino and imine groups which have good adsorption for heavy metal ions through coordination complexation with heavy metal ions. In addition, Laponite has negative charges on the surface, which is conducive to the adsorption of cationic heavy metal ions. Therefore, introduction of PEI magnetic nanoparticles and Laponite into the 3D network of polymer hydrogels can better the polymer networks with multi-level three-dimensional structure and enhance both adsorption capacity for heavy metal ions and mechanical strength of mLap/(AA-AM). Besides, mLap/(AA-AM) has many functional groups such as COOH, COONa and CONH2,which can adsorb heavy metal ions through coordination complexation and electrostatic interaction. Finally, mLap/(AA-AM) has uneven and porous structure, which can promote heavy metal ions to penetrate into the three-dimensional polymer networks of mLap/(AA-AM), and thus enhance the heavy metal ions adsorption for mLap/(AA-AM).