## 1 Introduction
Most of the published works are related to the study of the photocatalytic properties of composites with titanium dioxide [32; 37; 38], and a much smaller number of publications are related to the studies of the physical and mechanical properties. The dependence of the mechanical properties on concentration and particle size was investigated by [PERSON] et al. [39] and [PERSON] [40]. The authors synthesized epoxy-matrix-based nanocomposites containing TiO\({}_{2}\) of 1%, 3%, 5%, and 10% in weight, of 17 nm and 50 nm. Improved mechanical properties were found: tensile strain increments of 3% and 5% were shown for particles of 17 nm and 50 nm in size, respectively. It is assumed that the number of nanoparticles and their size affect the quality of the interface in the composite, which in turn affects the deformation properties of the matrix. A comparative study of the TiO\({}_{2}\) particle size effect between \(\sim\)50 nm and \(\sim\)50 \(\upmu\)m on the mechanical properties of epoxy nanocomposites (ENC) was carried out by [PERSON] et al. [41]. The improvement of the mechanical properties up to the content of 4 vol. % TiO\({}_{2}\) and their subsequent decrease due to TiO\({}_{2}\) agglomeration were shown for ENC. In the case of microparticles, with an increase in their concentration, the modulus of elasticity increases and the strength characteristics, on the contrary, decrease. The article [21] describes the physical and mechanical properties of epoxy nanocomposites based on the diglycidyl ester of bisphenol A and cycloaliphatic amine with commercial surface-functionalized TiO\({}_{2}\) particles of 300 nm size, Kronos 2310 type, and specific surface area equal to 5 m\({}^{2}\)/g at concentrations up to 10 vol. %. The nanoparticles were dispersed in epoxy resin using a high shear energy device and a bead mill. The elasticity modulus and flexural strength were shown to increase by more than 30% and 10%, respectively, and strain reduction by 35%. A significant, up to 70%, increase in impact toughness was found. The mechanisms of hardening and cracking have been considered. In [42; 43; 44; 45], an analysis of the dispersing conditions of commercial TiO\({}_{2}\) of 10-50 nm in size was shown for large volumes of suspensions and high (up to 20 wt. %) concentrations of TiO\({}_{2}\) in a solution of bisphenol-A-based epoxy oligomer in methyl ethyl ketone. The effectiveness of double dispersing (ultrasonic) and mechanical high speed--up to 2000 rpm--is demonstrated. The optimal time of the ultrasonic dispersion was 15-20 min [37]. The extreme dependences of strength characteristics at concentrations up to 20 wt. % of TiO\({}_{2}\) in composites based on bisphenol A diglycidyl ether and diamines--such as aliphatic, cycloaliphatic, and aromatic ones--are found. The mechanisms of fracture formation (cracking) in epoxy nanocomposites are discussed. In some papers, the authors do not specify the hardeners used in the synthesis process, only indicating their structure (aliphatic, amine, cycloaliphatic, etc.) [45; 46; 47]. Perhaps the authors use hardeners from well-known manufacturers, and therefore the authors cannot disclose the synthesis completely. Unfortunately, this fact does not allow for a full assessment of the obtained results, since the use of different hardeners affects the final properties of the nanocomposite, including the physical and mechanical ones. Despite the great interest in the photocatalytic properties of epoxy nanocomposites filled with TiO\({}_{2}\), the physical and mechanical properties of the polymer matrix after the introduction of an inorganic nanofiller have not been sufficiently studied due to the large range of epoxy oligomers and hardeners. The aim of this work was to investigate the structural characteristics, and the mechanical and thermal properties of epoxy composites based on nanocrystalline titanium dioxide (TiO\({}_{2}\)/EP) with varying composition, content, and dispersity.