## 1 Introduction  
Rare Earth Elements (REEs) are the collection of 17 special elements which are usually divided into heavy rare earth elements (HREE) and light rare earth elements (LREE). REEs could be widely used in many fields based on their excellent properties. For instance, the chemical, electrical, magnetic, and optical characteristics make them suitable for fields, including the nuclear industry, metallurgy, and luminescence [1]. Moreover, REEs can be combined with other element or compounds and then can be used as alloys, catalysts, ceramics, etc. Therefore, these strategic usages of REEs have been attracting much attention in recent years. However, due to the limited availability, the shortage of REEs resources and the necessity of a stable supply of these metals have been concerned over the past years. Therefore, the development of a recovery method for these trace metals is important from the viewpoint of environmental protection [2; 3]. Metallic ions in aqueous solution can interact in various ways with a solid surface, including precipitation, adsorption, and ion exchange. Among these methods, adsorption has been regarded as an efficient way to remove metallic ion in aqueous solution [4; 5; 6]. For ecofriendly purposes, biological materials as an adsorbent for water purification have used by a number of researchers. The biological adsorbent has the advantages of recyclable, low cost, easy operation, and little possibility of secondary pollution. From above-mentioned, the laboratory model experiments for biosorption of REEs using seaweed biomasses [7] and shell biomass [8] have been carried out in our previous work. It was found that seaweed and shell biomass show excellent sorption capacity for lanthanides even under the presence of common cations (refer to Figure S1). In addition, surface modification of activated carbon has been recognized as an attractive approach to improve and/or enhance the removal of heavy metals [9] or lanthanides [10]. On the other hand, layered double hydroxides (LDH) are a kind of lamellar ionic compound containing positively charged brucite-like layers and exchangeable anions in the interlayer. Their abundance in nature, low cost, and high specific surface area make them suitable for adsorption of metal ions. The general formula of an LDH is \(\left[\mathrm{M}_{1-\mathrm{x}}^{\mathrm{II}}\mathrm{M}_{\mathrm{x}}^{ \mathrm{III}}(\mathrm{OH})_{2}\right]\)\(\left(\mathrm{A}^{n-}\right)_{\frac{n}{n}}\cdot\mathrm{mH}_{2}\mathrm{O}\), where cationic \(\mathrm{M}^{\mathrm{II}}\) and \(\mathrm{M}^{\mathrm{III}}\) are divalent and trivalent metals, and occupy the center of octahedral in the brucite-like layer. \(\mathrm{A}^{n-}\) is the interlayer anion of charge \(n\) that leads to the electric neutrality of the LDH, and the coefficient \(x\) is the molar ratio of \(\mathrm{M}^{\mathrm{II}}\)/(\(\mathrm{M}^{\mathrm{II}}\) + \(\mathrm{M}^{\mathrm{III}}\)). The structure of LDH suggests that these materials can be intercalated easily with other anions. Various types of anions can be intercalated in its interlayer space. It has been extensively reported by both inorganic [11; 12] and organic [13; 14] chemistry researchers. The ability of LDH to intercalate anions makes them useful as catalysts, anion exchangers, and adsorbents. We note that several physicochemical models were proposed to rationalize the anion-exchange constants [15]. Some formalisms were derived by relating the activity of an anion to the anion-exchange constant [16], while geometric features of atoms, such as charge radii of the anions were taken into account to investigate the anion-exchange ability of halide anions on LDH [17]. Moreover, LDHs modified with hybrids have also been studied as potential adsorbents of heavy metals from aqueous solution [18; 19; 20]. Chelation is a type of bonding of ions or molecules to metallic ions. It involves the formation of coordinate bonds between a single central atom and ligand within multiple separate binding sites.