## 1 Introduction  
Chiral organocatalysis is one of the most attractive methods for the production of optically active medical and pharmaceutical products due to advantages such as being metal-free, exhibiting higher stability against moisture and oxygen, and facilitating experimental operation [1; 2; 3]. Among the chiral organocatalysts, chiral imidazolidinones and their salts, so-called MacMillan catalysts, have been applied to various asymmetric reactions via HOMO or LUMO activation mechanisms, such as the Diels-Alder (DA) reaction [4], 1,3-dipolar cycloaddition [5], Friedel-Crafts alkylation [6], indole alkylation [7], the \(\alpha\)-halogenation of aldehydes [8; 9], direct aldol reaction [10], intramolecular Michael reaction [11], and the epoxidation [12] of aldehydes. The MacMillan catalysts were also applied for the \(\alpha\)-alkylation, \(\alpha\)-allylation [13; 14; 15; 16; 17; 18], \(\alpha\)-benzylation [19], \(\beta\)-arylation [20], and \(\beta\)-alkylation [21] of aldehydes or ketones via the SOMO-activation mechanism [22]. Despite the efficiency of MacMillan organocatalysts in asymmetric reactions, relatively high catalyst loading (generally 5 to 20 mol %) is required to proceed with such asymmetrical reactions at reasonable reaction rates; besides, a burdensome purification method, such as column chromatography, is required to isolate a product and to separate the MacMillan catalyst from a reaction mixture. Therefore, a MacMillan catalyst is generally not reused. The covalent immobilization of MacMillan catalyst onto a heterogeneous support represents an attractive approach to solving the issues, in regard to its sustainability. Covalently immobilizedMacMillan catalysts have been developed and applied for catalytic, asymmetric reactions [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. However, conventional, polymer-immobilized MacMillan catalysts possess some drawbacks, such as elaborate multistep preparation, and the decrement of catalytic activity due to the modification of the MacMillan catalyst. Therefore, the design of a heterogeneous chiral catalyst, including the immobilization method and the support polymer, is essential for efficient asymmetric reactions. For the immobilization of method, we developed an ionic immobilization method for chiral organocatalysts, such as MacMillan catalyst and cinchonidinium, via neutralization reaction or ion-exchange reaction with sulfonated polymers [39; 40]. The ionic immobilization methodology has been applied for the synthesis of the main chain of chiral polymers, many of which were prepared by intermolecular reactions of chiral organocatalyst dimers with disulfide acid derivatives [41; 42; 43; 44; 45; 46]. Functionalized polymer microspheres have been widely used as industrial materials in various areas, such as coatings, electronics, biomedical engineering, and organic synthesis [47; 48; 49]. Interestingly, some polymer microspheres with achiral or chiral catalysts have been used as heterogeneous catalysts for organic reactions [50; 51; 52]. We first synthesized polymer microsphere-immobilized chiral 1,2-diamine ligands with uniform, core-shell, or core-corona structures, and these complexes with ruthenium were used as heterogeneous, polymeric chiral catalysts in the asymmetric transfer hydrogenation (ATH) of ketones [51]. Both the yield and enantiomeric excess (ee) of the product were greatly influenced by the introduction position of the chiral catalyst onto the polymer microsphere and the degree of crosslinking, along with the hydrophobicity of polymer microsphere. Recently, we successfully synthesized core-corona polymer microsphere-supported cinchonidinium salt and applied it as a heterogeneous polymeric catalyst for the asymmetric alkylation reaction of a glycine derivative [52].