## 1 Introduction  
Thermosetting polymers based on epoxy resins are widely used in the production of paints and various coatings [1, 2], high-performance adhesives [3, 4], and microelectronics [5, 6]. The most promising area of application is polymeric construction materials in the automotive and aerospace industries [7, 8]. Due to the large set of hardeners [9], it is possible to vary the curing temperature-time conditions and to obtain epoxy resins with a high strength and special properties including high adhesion to most materials. In addition, the advantage of epoxy polymer synthesis technology is low shrinkage of about 5-7% [10] and the absence of harmful and hazardous volatile compounds during synthesis. However, the modern requirements of materials are increasing, so epoxy resins should be modified. Epoxy nanocomposites are finding vast applications in various sectors such as the aerospace, defense, and automobile industries, anti-corrosive coatings, high-voltage fields, and wind energy [11, 12]. The physical and chemical properties of the epoxy systems are influenced by the processing techniques, clay modifier, and curing agents used for the preparation of nanocomposites [9]. Researchers and industries have adopted epoxy nanocomposites as suitable materials in designing the parts for use in sensors, electronics, electromagnetic interference shielding, and more [13]. To change and improve the properties, fillers of different chemical natures, shapes, and sizes, including fibers [14], nanotubes [15], and micro- and nanoparticles [16], are introduced into the epoxy matrix. Nanoscale fillers are characterized by a high specific surface area. Consequently, a very small amount of nanofillers in the matrix is enough to achieve functional properties similar to those of other types of microfillers. Composite materials based on the epoxy matrix and inorganic nanoparticles and carbon nanofillers (CNFs) provide an opportunity to improve their performances. Inorganic nanoparticles such as ZnO, TiO\({}_{2}\), SiO\({}_{2}\), and Al\({}_{2}\)O\({}_{3}\) are added to epoxy resin to improve its mechanical [17; 18; 19; 20; 21], dielectric [22; 23], and other properties. The addition of CNFs can increase the fracture toughness, flexural strength, and electrical conductivity of epoxy resin [18; 20]. The incorporation of Al\({}_{2}\)O\({}_{3}\) nanoparticles into the epoxy resin improved the flexural stiffness, flexural strength, and fracture toughness of the polymer at the same time. Moreover, the Al\({}_{2}\)O\({}_{3}\) nanoparticles improved the fatigue crack propagation resistance of epoxy [21]. The addition of graphene oxide and ZnO to epoxy resin can increase its tensile strength, flexural strength, and elasticity modulus [18]. Similarly, the addition of TiO\({}_{2}\) and SiO\({}_{2}\) nanoparticles can improve the hardness and wear resistance of epoxy resin [19]. Titanium (IV) dioxide nanoparticles (TiO\({}_{2}\)) are widely used as inorganic fillers due to the set of unique properties, such as photocatalytic [24], optical [25], electrical [26], and sensory [27] ones, as well as their chemical inertness, relatively low toxicity, low cost, etc. Titanium dioxide is widely used as a white pigment in the construction, pharmaceutical, and food industries, cosmetology, etc. [28], as a photocatalyst for purifying air and water from harmful impurities and as a component of self-cleaning [28; 29; 30] and reflective [31; 32] coatings in space technology. Epoxy nanocomposites are produced by the curing of epoxy oligomers in the presence of a filler (ex situ method) or the corresponding precursor of metal nanoparticles [33] (in situ method). These additives can affect the kinetics of the process and the properties of the resulting matrix, which was discussed in detail in the review by [PERSON] [34]. The properties of polymer nanocomposite materials are mainly determined by the size and shape of the inorganic particles, their distribution in the polymer volume, and their interaction with the organic binder [35; 36].