## 1 Introduction
It has been established that homo- and copolymers based on 1-vinyl-1,2,4-triazole have a wide range of valuable properties, such as good solubility in water and polar organic solvents, chemical resistance and thermal stability, biocompatibility, and non-toxicity, as well as the ability of complex formation [22; 23; 24]. 1-Vinyl-1,2,4-triazole under conditions of controlled radical polymerization with reversible chain transfer by the addition-fragmentation (RAFT) mechanism can form narrowly dispersed polymers with molecular weights ranging from 11 to 61 kDa [25]. Using RAFT polymerization, amphiphilic block copolymers of various compositions containing successive block fragments of triazole and carbazole units have been obtained [18]. Polymers based on 1-vinyl-1,2,4-triazole exhibit a high stabilizing ability in the formation of polymer nanocomposites with nanoparticles of various metals (Ag, Au, Fe, and so on) [22; 26; 27]. This is because of the presence of pyridine nitrogen atoms in the triazole fragment of macromolecules, which are capable of efficiently entering into coordination interactions with metal ions. Synthesized nanocomposites with silver nanoparticles have a high antibacterial activity against Gram-positive and Gram-negative microorganisms [28; 29]. The ability of PVT for complex formation determined its high sorption capacity regarding Pd(II) and Pt(IV) ions [30]. Because of their film-forming ability, as well as electrochemical, mechanical, and thermal stability (up to 300-330 \({}^{\circ}\)C), VT (co)polymers are promising for the development of proton-conducting fuel cell membranes that are capable of providing their high ionic conductivity (up to 10\({}^{-3}\)-10\({}^{-1}\) S/cm) under anhydrous conditions at temperatures above 100 \({}^{\circ}\)C [31]. Thus, taking into account the original properties of 1-vinyl-1,2,4-triazole and \(N\)-vinylcarbazole monomers, we synthesized new copolymers based on them by radical copolymerization and obtained copolymers whose macromolecules involve hole-conducting leading carbazole fragments and triazole units with complexing and plastic properties. By varying the ratio of starting monomers, copolymers of different compositions were obtained. So, the formation of polymeric luminescent systems was performed in three main stages. In the first stage, functional triazole\(-\)carbazole copolymers, poly(VT-co-VK), of different compositions were synthesized by free-radical copolymerization. Next, a polymer complex with terbium (III) ions (Tb\({}^{3+}\)) was obtained by donor\(-\)acceptor binding. In the last stage, the MPC was introduced into an inert matrix of polymethylmethacrylate (PMMA) in order to obtain a luminescent organic\(-\)inorganic composite. The processes of the formation of metal\(-\)polymer complexes based on synthesized polymer ligands with Tb\({}^{3+}\), which can provide the material with the desired luminescent properties in the visible range (green glow), were studied. The photophysical properties of the obtained MPCs were studied, making it possible to assess the prospects and practical significance of new materials. Materials  
1-Vinyl-1,2,4-triazoleo was synthesized and characterized by the procedure described in [20]. \(N\)-Vinylcarbazole (Sigma-Aldrich, St. Louis, MO, USA) and azobisisobutyronitrile (AIBN, Merck, Rahway, NJ, USA) were used as received. Dimethylacetamide (DMA), acetone, and ethanol were distilled under reduced pressure and were purified before use according to known procedures. Other materials were used without further purification. Synthesis of poly(1-vinyl-1,2,4-triazoleo-\(co\)-\(N\)-vinylcarbazole) (poly(VT-\(co\)-VK))-general procedure: Poly(VT-\(co\)-VK) was synthesized by radical copolymerization of VT and VK monomers using AIBN as a radical initiator. Copolymerization was performed in a sealed glass ampule in solution DMA at 60 \({}^{\circ}\)C for 17 h under an argon atmosphere. After the reaction was complete, the glass ampule was left to cool to room temperature and opened.