## 1 Introduction  
Modern progress in engineering and technology is characterized by the widespread use of polymer-based composite materials both in key heavy industries, including aircraft and automotive production, petrochemical and construction industries, and in biomedical technologies. Polymer materials provide a reduction of product weight, facilitate higher production rates and demonstrate increased resistance to aggressive environments [1]. The development of composite materials with improved properties and the utilization of cost-efficient and environmentally friendly technologies for their production and processing are among the most important tasks of modern polymer material science. Recent progress in the field of nanotechnologies [2, 3, 4] led to vigorous research on the utilization of various nanosized particles as fillers for polymer composites as well as on the performance of resulting materials. It was shown [5, 6, 7, 8, 9, 10, 11] that small additions of nanofillers (up to a few percent) can drastically change electrical and thermal characteristics of the polymer, and can also lead to noticeable changes in its mechanical properties. In particular, [PERSON] et al. have shown [10] that filling the polystyrene matrix with just 0.1-1 wt% of single-walled carbon nanotubes can provide an increase in electrical conductivity of the composite by 5-7 orders of magnitude reaching \(10^{-1}\) S/m at filler concentration of 1 wt%. At the same time, the composites were characterized by increased brittleness and reduced bending strength and elongation at break. In experiments by [PERSON] et al. [9] introduction of small amounts (up to 0.1 wt%) of carbon allotropes had no effect on the strength of polystyrene-based composites but caused a reduced elongation at break. An increase in the nanofiller concentration provided a significant increase in the Young's modulus of the material. However, it is known that over some threshold concentrations, the composite properties tend to decrease, which can be due to nonuniform dispersion and aggregation of filler particles. The pronounced effect of nanosized particles on the mechanical properties of polymers can be explained by the fact that, at a particle size of 10-100 nm, their surface becomes large enough to transfer almost the entire polymer into the state of an interfacial layer, even at filler concentrations of tenths of a percent. Homogeneous dispersion and strong interaction of the particles with the matrix are required for efficient reinforcement of the material. Robust bonding of filler particles to the matrix is necessary for efficient transfer of the applied stress to the filler allowing it to bear most of the load [12]. Among the high-demand materials are composites based on thermoplastics (polypypylene, polyethylene, polystyrene, etc. ), that are expected to provide required mechanical, thermal, structural, and electrical properties, see, e.g., recent papers on polystyrene-based composites intended for various applications [13; 14; 15]. Challenges arising in the fabrication of composites based on thermoplastics with different types of nanoparticles and attaining desired properties are discussed in a number of reviews (see [1; 4; 16; 17; 18]). As known, the tendency of nanosized particles to aggregate can deteriorate significantly the composite properties. Numerous publications are devoted to methods used for stabilization of nanoparticles and for their introduction into polymer matrices aimed at obtaining the required mechanical characteristics of the resulting material [19; 20; 21; 22]. Dispersion of nanofillers in a melt of the polymer matrix is considered to be one of the most efficient ways for the fabrication of nanocomposites based on thermoplastics. The low dielectric constant of the melt reduces electrostatic adhesion between particles and facilitates their dispersion in the bulk of the polymer matrix. The main advantage of the melt technology is the absence of any solvents, which eliminates harmful effluents and enables fast and rather simple processing.