## 1 Introduction  
Along with the rapid industrial development, plenty of wastewaters containing heavy metals (e.g., lead, mercury, copper, cadmium, and chromium) are produced, especially in the fields of electroplating, leather-making, textile dyeing and printing, and battery production [1; 2; 3; 4]. Unlike organic pollutants, heavy metals cannot be decomposed. As a result, if the wastewaters are unable to be properly treated, heavy metals will always exist in environment or accumulate in organisms through the food cycle [5], resulting in serious damage to the environmental safety and human health because of their high toxicity and carcinogenicity. Among the heavy metals, Pb(II) pollution is now attracting considerable attention due to its high neurotoxicity and hematotoxicity. The Pb(II) ion is readily assimilated and will be chronically accumulated inside the human body, leading to neurasthenia, anemia, anorexia, stomach ache, diarrhea, and kidney damage [2; 3; 4]. Thus, it is strongly necessary to design and prepare effective materials or technologies to eliminate Pb(II) from wastewaters in prior to its discharge.  
Traditional approaches, including chemical precipitation, ion exchange, membrane filtration, electrolysis etc., were previously reported to effectively remove Pb(II) ion from water phase. However, these methods were usually limited because of their complicated operation process, potential secondary pollution, high operating cost, or difficulty in recycling [6; 7; 8]. Therefore, adsorption is now still regardedas the most popular techniques for heavy metal removal owing to its simple process, inresponsiveness, and high efficiency. So far, several types of sorbent materials, including clay minerals [9; 10], zeolite [11], carbon materials [12; 13; 14; 15], natural and synthetic polymers etc. [16; 17; 18; 19], have been reported to isolate Pb(II) from water phase. Nevertheless, extensive use of these sorbents was very restrictive due to their complex operations (such as filtering and centrifugation) in adsorbent recollection after usage. To overcome this defect, magnetic nanoparticles (MNPs) were widely applied to eliminate pollutant from wastewaters in recent years [20; 21; 22]. The MNPs were usually surface-modified with the chemical substances containing amidogen, carboxyl, hydroxyl, sulfhydryl, or phosphate groups; after surface modification, the MNPs can be easily dispersed in water phase via simple oscillation or stirring, but also exhibit higher affinity for heavy metals via the generation of complexes or chelates [23; 24]. More importantly, the well-designed MNPs are able to be magnetically recycled from wastewater facilely.  
Recently, the MNPs were also reported to be loaded onto biochar [2; 3], grapheme [23], zeolite [25], litchi peel [5], spent coffee grounds [4], chitosan, alginate beads, etc. [1; 26], and the prepared magnetic sorbents showed good performance for Pb(II) adsorption. Nonetheless, the synthetic procedure of above-mentioned magnetic adsorbents involved several steps and was relatively complex, and there remains a need to develop easy-to-synthesize MNPs for Pb(II) sorption. Consequently, in the present work, a class of polyethyleneimine (PEI)-functionalized Fe\({}_{3}\)O\({}_{4}\) MNPs was facilely prepared via a solvothermal process, and directly used for Pb(II) isolation from water environment. In our previous work [27], a series of PEI-functionalized Fe\({}_{3}\)O\({}_{4}\) MNPs were prepared at various solvothermal reaction times and applied for simultaneous separation of emulsified oil, Cr(VI), and Cu(II) from aqueous environment. As part of our ongoing research, the fabricated PEI-functionalized MNPs were further applied to isolate Pb(II) from water phase. The kinetic and thermodynamic behaviors for Pb(II) adsorption were carefully studied; meanwhile, the impacts of temperature, pH, and electrolyte on Pb(II) adsorbing capacity were examined in detail. Besides, the reusability of synthetic PEI-functionalized MNPs was further investigated.