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The relationship between the boundary-layer strength and filler surface structure in suspensions of carbon fibers in an epoxy-resin solution is studied using ideas of fractal analysis. An increase in the fractal dimension of the fiber surface is shown to lead to enlargement of the contact area between components of the considered suspensions. The yield stress of the suspensions depends on the filler particle size and grows as the particle size decreases. Considerable enhancement of interfacial interactions is observed for nanoparticles and is treated to be the nanoadhesion effect. The proposed model enables us to carry out estimations of interfacial adhesion in solid-phase composites based on the results obtained for the suspensions.

The basic structural factors enabling the design of high-modulus and high-strength nanocomposites (polymer/carbon-nanotube) with mechanical characteristics analogous to the corresponding parameters of steel are studied in the framework of fractal analysis and percolation theory. The main factor is the formation in the polymer matrix of carbon-nanotube tows consisting of many of them with a structural fractal dimension close to Euclidean (close to three). Such tows have an elastic modulus close to the nominal value of a separate nanotube. The proposed procedure allows the limiting mechanical characteristics of nanocomposites to be determined.

A fractal model allowing one to theoretically estimate the shearing strength of the interfacial contact in a polymer-carbon nanotube system is proposed. It takes into account the structure of carbon nanotube surface and describes experimental data accurately enough. This makes the model promising for predicting the polymer/nanofiller contact strength. As a function of nanotube diameter and contact length, this strength showed a strong scale effect.

We consider physical foundations for the realization of high-modulus and high-strength polymer/carbon nanotube nanocomposites with mechanical characteristics comparable with those for steel. We have determined two main factors that make it possible to obtain such nanocomposites, i.e., the structure of the nanofiller in the polymer matrix and a quite high concentration of the nanofiller. The fractal dimension of such a structure must be close to that of the surrounding Euclidian space (i.e., 3). It is shown that additional stretching of the nanocomposite gives two positive effects: the reduction of waviness of carbon nanotubes and the increase of the elastic modulus of the polymer matrix due to alignment of its macromolecules.

It is shown that theoretical models elaborated for polymer microcomposites are not capable to describe variation of the melt viscosity of polypropylene/globular carbon nanocomposites at change in the nanofiller contents. Then a fractal model of viscosity is proposed, which takes into account the sizes of nanofiller aggregates and their surface structure. This model shows a good agreement with experimental data. It demonstrates a fundamental difference in the behavior of melt viscosity for polymer micro- and nanocomposites.

The effect of the polymer matrix on the degree of reinforcement of nanocomposites for polymer/organoclay nanocomposites is investigated. It is shown that the elastic modulus and the structure of the nanofiller in the polymer matrix are only a function of the elastic modulus of the matrix polymer and can be either higher or lower than the nominal value of this parameter. In the case of an elastomeric matrix, the nanofiller structure has a constant fractal dimension. The proposed technique can be used to predict the degree of reinforcement of nanocomposites with any type of nanofiller.

The possibility for predicting tribological characteristics of polymer nanocomposites was studied with the example of nanocomposite poly (ether ketone)/graphene. It has been shown that the “escapement” effect of polymer matrix macromolecules by graphene surface essentially reduces (a several times) the indicated characteristics. The proposed simple structural model describes the obtained results through experiments. The fulfilled estimations indicate that the “escapement” effect of macromolecules by graphene surface results in a loss of 60–86% of the initial area of contact polymer matrix-nanofiller with a growth of graphene content up to 10 mas %. Thus, the improvement of the indicated contact (i.e., by nanofiller functionalization) likely leads to essential improvement of tribological characteristics of nanocomposite.

It was shown that the physical and/or chemical interactions of the polymer matrix and the nanofiller surface are determined by two factors: the degree of polymer adsorption by the nanofiller and its surface structure. The introduction of a binding agent enhances these interactions and increases the level of interfacial adhesion. If structural factors and physical and/or chemical interactions are known, it is possible to predict the level of interfacial adhesion.

The structure of a nanofiller in a polymer matrix determines the properties of nanocomposites and a change in the type of structure from local to spatial; for example, formation of the percolation framework of particles (particle aggregates) of a nanofiller leads to a sharp deterioration in the properties of nanocomposites. Using the example of particulate-filled polymer/nanodiamond nanocomposites, it is shown that the transition from the standard mixing mode of a nanofiller with a polymer matrix melt in an extruder to mixing in the flow “breakdown” mode leads to a significant increase in the properties of nanocomposites. It is established that this effect is caused by a change in the type of structure of the nanofiller in the polymer matrix from a continuous spatial one (chain of nanofiller particles) to a local one (formation of individual clusters of nanoparticles). Within the framework of the fractal analysis, it is demonstrated that, when the type of structure changes from one-dimensional to two-dimensional, its fractal dimension changes from 1.18 to 1.75. The quantitative estimates of the degree of reinforcement of nanocomposites carried out within the percolation model with the established increase in the fractal dimension of the structure of the nanofiller are fully confirmed by experimental data. It is also shown that the elastic modulus of the nanofiller depends on the stiffness of the polymer matrix. The experimentally observed effect of dispersion of a nanofiller when mixing components in the “breakdown” mode is described in terms of the model of irreversible aggregation.

The relationship between the effective (real) specific surface area of the nanofiller and the elastic modulus for polymer/graphene nanocomposites is studied. The process of aggregation of a graphene 2D nanofiller (the formation of its tactoids) leads to a decrease in its effective specific surface area, since the surface of graphene plates inside the tactoid, which does not interact with the polymer matrix, does not affect the formation of the properties of nanocomposites. This effect is realized only above the percolation threshold of the nanofiller. An interpretation is proposed that allows estimating the number of graphene plates in one tactoid. Further calculations allow the determination of the effective specific surface area of the nanofiller and the degree of reinforcement of the nanocomposite.

—The effect of the fractal dimension of the filler on the tribotechnical characteristics of the polyetherketone/graphene nanocomposites was assessed. It is shown that the indicated characteristics for a fixed nanofiller content are determined by the structural state of graphene in the polymer matrix, characterized by its fractal dimension. The proposed model is valid for the main classes of polymer nanocomposites.

A percolation model for the reinforcement of polymer nanocomposites is proposed which allows a quantitative evaluation of the degree of aggregation of nanofillers of arbitrary dimension. In this model, the efficiency of a nanofiller is determined not by its initial characteristics, but by its ability to generate interfacial regions.

The theoretical analysis of shearing strength of interphase layer in polymer composites (nanocomposites) was performed within the framework of fractal analysis. These theoretical estimations correspond quantitatively to known literary data, demonstrating reduction of the indicated strength at enhancement of sizes of particles (aggregates of particles) of filler, i.e. scaling effect. The structure of filler surface plays important role at this effect realization.

The paper shows that the elastic modulus of carbon nanotubes in a polymer matrix nanocomposite is lower not only than its nominal value, but also the elastic modulus of the interfacial regions. Therefore, a degree of reinforcing carbon nanotube/polydimethylsiloxane nanocomposites is completely determined by the amount of the interfacial regions, whereas the effectiveness of the nanofiller is determined by its ability to generate such regions.

In a polymer matrix, 1D and 2D nanofillers are shown to form aggregates that are fractal objects. Their dimensionality determines the degree of reinforcement of polymer nanocomposites at a fixed nanofiller volume. The theoretical estimates of the properties of these nanocomposites must use the real values of characteristics of their components.

The spectrophotometric method is widely used for the qualitative and quantitative analysis of substances, in the study of the structure and composition of various compounds. The article solved the actual problem of spectrophotometers measuring process automating. The structure of the spectrophotometer control unit based on the Arduino Uno hardware platform has been proposed, a stepper motor driver scheme, providing replacement of the manual rotation system of the spectrophotometer diffraction grating to a system using modern stepper motors has been developed. It made it possible to increase the measurement efficiency by reducing the measurement time and improving the metrological characteristics of the spectrophotometer (the limiting absolute error in setting the wavelength is reduced from ± 0.5 nm to ± 0.3 nm).

Carbon nanotubes and graphene are both promising anisotropic fillers for use in high-quality polymer nanocomposites. In the present work, their reinforcing properties are analyzed. The generalized model of reinforcement employed for nanocomposites takes account of the characteristics of the nanofiller and matrix polymer, as well as the type of filler.

In the proposed structural model of the viscosity of the melt of polymer–carbon nanotube nanocomposites, carbon nanotubes are modeled as an analog of macromolecular coils of branched polymers. This approach makes it possible to determine the real degree of anisotropy of this nanofiller. The use of the degree of anisotropy allows accurate prediction of the melt viscosity of the considered nanocomposites. The formation of such a specific structure of carbon nanotubes in a polymer matrix leads to a twofold decrease in melt viscosity in comparison with nanocomposites containing linear carbon nanotubes.

A procedure for calculating the fractal dimension of tactoid structures of a 2D-nanofiller (graphene oxide) in the polymer matrix of a nanocomposite is proposed. The fractal nature of tactoids leads to the fact that only a part of their surface (the unscreened surface) is available for the formation of interphase polymer-matrix—2D-nanofiller contacts. An increase in the unscreened surface dimensions determines the enhancement of a relative fraction of the interphase regions and, as consequence, improvement in the mechanical properties of the nanocomposites. It is suggested that the interaction of graphene-oxide tactoids has a certain influence on the indicated properties.

The structure of the nanofiller in the polymer matrix of polymer/carbon nanotube nanocomposites can be characterized by the dimension of the nanofiller network, which is a direct indicator of its aggregation level. The formation process of such a network is considered as a result of interaction of the matrix polymer and a carbon nanotube; which allows us to determine its dimension with the help of fractal analysis. It is found that the dimension of the carbon nanotube network changes both qualitatively and quantitatively at their percolation threshold, reflecting different aggregation levels. This dimension uniquely determines the degree of reinforcement of such nanocomposites and their structural state as a system.

By virtue of high degree of anisotropy and small transverse stiffness, carbon nanotubes are known to form ring-shaped annular structures (fractal objects) in the polymer matrix of nanocomposites. We used the fractal dimension for quantitative and physically strict characterization of the nanofiller structure (carbon nanotubes) in the polymer matrix of nanocomposites. Two methods of calculation based on the models of irreversible aggregation and fractal analysis are proposed. The results obtained using both approaches match each other within 6%. It has been shown that formation of the annular structures occurs according to the cluster-cluster mechanism (i.e., by combining small formations into larger ones, rather than individual nanotubes). Moreover, the method of fractal analysis takes into account the effect of the polymer matrix on the structure of ring-shaped formations and, hence, on the properties of polymer nanocomposites. The correctness of the methods thus used was proved using the percolation model, which showed good agreement between the theory and experiment when using fractal dimensions determined by both methods. This means that for a fixed nanofiller content, the properties of nanocomposites are determined only by the nanofiller structure. In other words, a significant change in the properties (for the degree of reinforcement more than by an order of magnitude) is possible even at a low content of a nanofiller, which is realized only through change in the nanofiller structure using various methods of nanofiller treatment (ultrasound, functionalization, construction of special types of nanofiller frame, etc.).

—It has been shown that the tribological characteristics of nanocomposites of polymer/carbon nanotubes are determined by the same parameters as the other properties of these nanomaterials. These parameters are the properties of the matrix polymer, structure, and nanofiller contents. In turn, the structure of nanofillers, treated as annular formations of carbon nanotubes, determines both their degree of aggregation and level of interphase interactions. This leads to a change in the control tribological characteristics of nanocomposites via a target-oriented change of the nanofiller structure, for example, by functionalization.

It has been shown that almost every theoretical model known to date allows for correctly describing the properties of polymer nanocomposites on the condition that the real not nominal characteristics of their components are used. These real characteristics are always related to the formation of the interfacial regions in the mentioned nanomaterials. This means that the efficiency of the filler in polymer nanocomposites is controlled by its ability to generate interfacial regions.

It is shown that the surface characteristics of a 2D nanofiller (boron nitride) in a polymer matrix significantly change with an increase in the filler content due to aggregation of the initial nanoparticles. At the aggregation threshold of the nanofiller, an abrupt decrease in these characteristics is observed; it leads to an extreme dependence of the elastic modulus of poly(vinyl alcohol)/boron nitride nanocomposites. The surface structure of a 2D nanofiller determines the efficiency of mechanical-stress transfer at the interface and the mechanical properties of the nanocomposites.

The methodics of characterization of 2D-nanofiller tactoids structure in polymer matrix of nanocomposite was proposed, which shown that the indicated tactoids are fractal objects with dimension of 1.75-2.16. This variation of tactoids structural state is due to interfacial interactions. It has been shown within the framework of reinforcement percolation theory, that structure of tactoids is single factor, defining reinforcement efficiency is characterized by its ability to create interfacial regions.

The structural aspects, defining reinforcement degree (enhancement of elasticity modulus) of nanocomposites polymer/carbon nanotubes with ultrasmall concentrations of nanofiller, were considered. It has been shown that the indicated parameter is controlled by two factors, namely, structure of nanocomposite and type of reinforcing component. Introduction of nanofiller in matrix polymer changes its structure in virtue of formation of interfacial regions. Hence, the efficiency of nanofiller as reinforcing element is defined by its ability to generate interfacial regions.

The structural aspects of determining the degree of reinforcement (increase in elasticity modulus) of carbon polymer–nanotube composites with ultralow concentrations of nanofiller are considered. It is shown that the specified parameter is controlled by two factors, the structure of the nanocomposite and the type of reinforcing component. The introduction of a nanofiller in the polymer matrix modifies its structure due to the formation of interfacial regions. Hence, the efficiency of nanofiller as the reinforcing element is determined by its ability to generate interfacial regions.

The paper explores the stiffness of the nanofiller particle aggregates in polymer matrix composites, such as particulate reinforced, carbon nanotube polymer and graphene polymer composites, i.e. composites reinforced with 0D, 1D and 2D nanofillers. It is shown that independently of the nanofiller, the structure of its particle aggregates is characterized by the fractal dimension as a physically accurate parameter. The true elastic modulus of the nanofiller particle aggregates is determined by two factors, namely the aggregates structure and the stiffness of the polymer matrix. The idea about the reinforcement degree control of polymer-matrix composites by the nanofiller structure is proved in this paper.

The influence of uniaxial extrusion on the structure, molecular characteristics, and properties of polymer/2D nanofiller nanocomposites is elucidated by example of polyvinyl chloride/boron nitride nanocomposites. The extrusion is found to cause a drastic (by 2.5 times) increase in statistical rigidity of polymer chains in the nanocomposite matrix determined by their characteristic ratio. The characteristic ratio for unoriented samples is less than that for a polymer precursor, but exceeds the values for oriented specimens. Nanofiller particles (or their aggregates) form a fractal network (“skeleton”) in the polymer matrix, whose dimension increases upon uniaxial extrusion. This effect leads to a linear reduction of the percolation index in the percolation model of reinforcement of nanocomposites, which significantly affects the degree of their reinforcement. When the dimension reaches its threshold of 2.8, the percolation index changes values from positive to negative values, meaning the transition from the “ant” to the “termite” limit. This yields an abrupt (to ~150) increase in the degree of reinforcement of polymer nanocomposites at low nanofiller contents. The characteristic ratio of polymer chains of the nanocomposite matrix is closely related to the aggregation level of the 2D nanofiller, which depends on the number of boron nitride slabs in a “package” (tactoid). The relative fraction of interfaces serving as reinforcing elements in a nanocomposite structure by analogy with nanofillers is also a function of statistical rigidity of polymer chains in the matrix and increases with the characteristic ratio. The theoretical estimates in the context of the percolation model of reinforcement reveal the prospects in the improvement of the properties of polymer/2D nanofiller nanocomposites.

Structural treatment of Ostwald—de Waele equation is proposed. It involves the representations of fractal analysis for describing the rheological properties of the rubber/disperse filler system. It is shown that the magnitude of viscosity and the type of system flow are determined by the filler particle structure (aggregates) characterized by their fractal dimension. In turn, this dimension is determined by the mechanism of aggregate formation. The model proposed makes it possible to predict the viscosity of the rubber/disperse filler systems for different filler contents and shear rates.

—The effect of changing structural characteristics of a particulate nanofiller during its aggregation on the degree of transfer of the mechanical stress applied to the sample from the polymer matrix to the nanofiller has been studied. The properties of particulate-filled nanocomposites are controlled by the quality of the stress transfer rather than the characteristics of the starting nanofiller. The stress transfer is sharply reduced because of the aggregation of nanofiller particles.

The estimations made within the fractal analysis have shown that 2D-nanofiller sheets in polymer medium form clusters (tactoids) that are fractal objects. This conclusion is confirmed by means of the irreversible aggregation model. The major factor determining the dimension of these clusters is the dimension of the random walk of initial nanoparticles. The structure of the 2D-nanofiller tactoids definitely determines the elastic modulus of the nanocomposite at the fixed nanofiller content.

Experimental data on the phenomenon of nozzle choking at diffusion combustion of a high-speed hydrogen microjet at its ignition close to the nozzle are presented. As is found, such a phenomenon is due to the nozzle heating by the «bottleneck flame region» which is generated at the origin of microjet. This flow region persists up to transonic velocities of the microjet preventing from cooling of the nozzle and the transition to supersonic speed. In the case of hydrogen ignition far from the nozzle exit in supersonic conditions, the «bottleneck flame region» is suppressed, the flame becomes detached from the nozzle which is no longer heated so that the supersonic range is attained. The subsonic combustion of hydrogen microjet is stabilized by the «bottleneck flame region» while the supersonic one becomes more stable at the generation of shock cells. The results of the present study provide new details on the combustion of hydrogen microjets and could by useful for the operation of different burners.