Kinetic features of the formation of epoxy nanocomposites with carbon (nanotubes, graphene, and graphite), metal-containing, and aluminosilicate (montmorillonite and halloysite) fillers are considered. In contrast to linear polymers, epoxy nanocomposites are obtained only via the curing of epoxy oligomers in the presence of filler or the corresponding precursor. These additives may affect the kinetics of the process and the properties of the resulting matrix. A high reactivity of epoxy groups and a thermodynamic miscibility of epoxy oligomers with many substances make it possible to use diverse curing agents and to accomplish curing reactions under various technological conditions. The mutual effect of both a matrix and nanoparticles on the kinetics of the composite formation is discussed.
- polymer nanocomposites
- epoxy matrices
- synthesis of composites
- epoxy oligomers
Since around the mid-1990s, polymer nanocomposites have become the subject of considerable attention, as evidenced by monographs, and a great number of reviews . The application of nanocomposites is associated with their unique properties related to a huge specific surface and high surface energy of nanoparticles. Nanosized particles, as opposed to microinclusions and coarser inclusions, are not stress concentrators, and this circumstance facilitates a marked improvement in the mechanical properties of nanocomposites. Compared with the respective polymers, the transparency of nanocomposites does not decrease, because nanoparticles do not scatter light because of their small sizes. Depending on the type of nanoparticles introduced in polymeric materials even at a low concentration, nanocomposites acquire remarkable chemical (primarily catalytic), electrophysical, and biomedical properties, thereby opening wide potential for their use .
Among polymer nanocomposites, it would appear that composites based on an epoxy matrix occupy an insignificant place—nearly 10% as to the number of publications—but an ever-increasing number of papers appear annually. Moreover, the interest in them grows almost exponentially, as evidenced by the number of citations .
Epoxy polymers in terms of a set of properties stand out among other polymeric materials and play an important role in aerospace, automotive, shipbuilding, and other industries. Their wide application in engineering is associated, firstly, with a high processability of epoxy resins and, secondly, with the unique combination of performance characteristics of their curing products [3, 4, 5].
A high reactivity of epoxy groups and a thermodynamic miscibility of epoxy oligomers with many substances make it possible to use diverse curing agents and to accomplish curing reactions under various technological conditions [6, 7, 8]. Of no small importance are the features of synthesis processes, such as the absence of volatile products and low level of shrinkage.
Epoxy polymers have high values of static and shock strength, hardness, and wear resistance. They possess marked thermal stability and heat resistance. Many solid surfaces form strong adhesive bonds with epoxy polymers [2, 3]. This circumstance determines their use as compounds, glues, paint and lacquer materials, and coatings, including in aerospace engineering. Epoxy nanocomposites are designed to realize the unique functional properties of nanoparticles: electric, magnetic, optical, chemical, and biological.
Information about epoxy nanocomposites is contained most completely in . Reviews [9, 10] are devoted to epoxy nanocomposites with carbon nanotubes (CNTs). Some aspects of epoxy nanocomposites containing graphene were covered in .
Taking into consideration the urgency of the issue and the presence of recent studies not covered in the mentioned reviews, author took a chance to consider epoxy nanocomposites containing metal and mineral nanoparticles, graphene, and CNTs and to discuss kinetic features of the processes of their formation.
2. Feature of synthesis of epoxy nanocomposites
The generally accepted scheme of the amino-epoxy cure involves two main reactions of the glycidyl ether:
Epoxy-amine cure reactions scheme.
In principle, a reaction of esterification is possible—the resulting hydroxyls with epoxy groups.
The ratio of the rate constant of the secondary amine in addition to the corresponding constant of the primary one depends on electron-donating properties of an amine and may vary with temperature. Normally this ratio varies within 0.1–0.6. It is because of accumulation of hydroxyl groups during the reaction that the process of curing epoxy oligomers under the action of amines has autocatalytic character. Kinetics is often analyzed using empirical Eq. (1):
where α is the degree of conversion of epoxy groups; the sum of exponents m + n defines the overall reaction order, which is usually two. Sometimes it is assumed that m = 1 (Eq. (2)). Constants k1 and k2 reflect the autocatalytic character of the process.
From the standpoint of formation of epoxy nanocomposites, there are two types of fillers: fillers belonging to the first type are chemically unchanged and should be reduced to the desired size in one way or another. An example is provided by CNTs, diverse minerals, and graphene. Compounds whose chemical nature changes during composite formation belong to the second type. These are, in particular, metal salts, in which cations should be reduced to the zero-valence state.
In contrast to linear polymers, epoxy nanocomposites are obtained only via the curing of epoxy oligomers in the presence of filler or the corresponding precursor. It is evident that these additives may affect the kinetics of the process and the properties of the resulting matrix. The mechanism of curing of epoxy resins is fairly complicated, because many reactions occur simultaneously and depend on such phenomena as gelation and glass transition [6, 7]. After incorporation of nanoparticles into the epoxy resin, the process of its curing becomes even more complicated. A considerable number of papers concern the kinetics of curing of epoxy systems with various types of nanoparticles.
Most of kinetic studies are using DSC. DSC analysis has shown that etherification occurs at elevated temperatures once all the primary amines are exhausted. In this case, the data are analyzed as a rule in terms of the generalized formula:
For nonisothermal conditions the temperature varies with time with a constant heating rate, β = dT/dt.
Isoconversional kinetic analysis has shown that the reaction rate at constant conversion depends only on the temperature. In other words,
where Eα is the effective activation energy at a given conversion. The energy of activation was determined by varying the rate of scanning. Multistage processes show the dependence of Eα on α, the analysis of which helps not only to reveal the complexity of the process but also to identify its kinetic scheme. So, for example, starting from Eq. (1), we get 
The analysis performed in  showed that the calculation can be reconciled with the experiment by specifying the values of E2 and m. Thus, we can assume that Eq. (1) adequately describes the experimental data. Namely, this approach is used to study the effect of various additives on the kinetics of epoxy nanocomposites’ formation.
3. Influence of the fillers on the nanocomposite synthesis process
3.1 Carbon fillers: CNTs, graphene, graphite, and carbon fiber
Taking into consideration the molecular structure of carbon nanoparticles, in particular, graphene and CNTs [13, 14, 15, 16, 17], it may be stated that their influence on the kinetics of the process of curing of epoxy oligomers will be similar. Indeed, graphene, CNTs, and other compounds with the sp2-hybridized carbon can catalyze diverse organic reactions [18, 19, 20]. Their surface energy is fairly high; therefore, the adsorption of various molecules is typical of them [21, 22, 23, 24]. The components of epoxy binders are not exceptional in this respect. Adsorbed molecules may be involved in the process of matrix formation in a certain manner.
In work  the high-temperature isothermal curing of tetraglycidyl-4,4′-diamino-diphenylmethane with 4,4′-diaminodiphenyl sulfone (DDS) in the presence of multi-wall CNTs was investigated.
The typical technique used to prepare the reaction mixture for kinetic studies of the process will be described below, and the techniques described in other papers may differ from the typical one only in some details.
A mixture of an epoxy resin with preliminarily purified multi-wall CNTs was sonificated for 2 h and placed in an oil bath at temperature of 120°С, and the stoichiometric amount of a curing agent was slowly added under continuous mechanical stirring until formation of a homogeneous mixture. This process took nearly 10 min.
The kinetics was analyzed using Eq. (1). It was found that with the increase in concentration of CNTs, constant k1, which defines the initial rate of reaction, grows, while the corresponding activation energy drops. The autocatalytic constant k2 is practically unaffected by the presence of tubes. Xie et al.  believe that these effects may be attributed to the catalytic effect of surface hydroxyl groups that arise as a result of oxidation during the purification of CNTs.
The initial acceleration of the reaction under the action of single-wall CNTs was also observed , but the magnitude of this effect was insignificant. At the same time, the glass-transition temperature Tg decreased, thus suggesting a reduction in the degree of cross-linking of the matrix .
The effect of concentration and type of CNTs (single-, double-, and multi-wall) on the kinetics of reaction between low-viscosity mixture of epoxy oligomers and amine curing agents was studied by Esmizadeh et al. . The analysis was conducted in terms of the equation:
It was shown that the type of CNTs exerts almost no effect on kinetic parameters possibly because of their low concentration (0.01%). At a concentration of 0.1, 0.2, and 0.5%, the rate constant changes nonmonotonically, but on the whole it is lower than that in the absence of CNTs. The energy of activation increases from ∼6 to ∼9 kJ/mol. The heat of reaction decreases, indicating the incompletion of the process. This is also evidenced by a decrease in the high-elasticity modulus, i.e., matrix network density. In accordance with , the observed effects may be explained by the increase in the viscosity and thermal conductivity of the system in the presence of CNTs, although these properties were not estimated.
Multi-wall CNTs, when taken at low concentrations (0.5%), slightly accelerate the reaction of amine curing of bisphenol F diglycidyl ether, while at higher concentrations (1.5%) decelerate this reaction as shown by Visco et al. . They believe that the rate of the process is controlled by viscosity of the system.
The curing of an epoxy resin is regarded as a heterogeneous phase formation process, and the role of multi-wall CNTs is discussed from this viewpoint by Susin et al. . They believe that the tubes restrict the local free volume and assist in the development of the heterogeneous morphology in resin, especially at high content of multi-wall CNTs. At the same time, with the increase in their concentration (to 1%), the ultimate heat of reaction increases, while the energy of activation decreases.
Most of kinetic studies are aimed at gaining insight into the effect of functionalized CNTs using DSC. Rahaman and Mohanty  presented the data of the influence of multi-wall CNTs carrying СООН groups on the process of curing of epoxy resin EPOLAM with anhydride of 1,2,3,6-tetrahydroxymethyl-1,3,6-methanephthalic acid. According to these authors, this dependence provides evidence that in the presence of multi-wall CNTs, the degree of cross-linking increases; as a result, the mobility of unreacted groups declines. The closeness of the curves at the beginning of the curing process indicates that the addition of CNTs does not affect the value of E1. From the form of the divergence of the curves in the course of the reaction, it follows that the entrainment of the filler leads to an increase in E2.
Note that methods using the dependence of a change in the exothermal peak on the rate of heating cannot provide reasonable isothermal predictions for the kinetics of curing of epoxy compounds because of the autocatalytic character of the process [6, 7]. The presence of at least two kinetic constants, as in Eq. (1), should be taken into account.
In this context, deserve attention other methods, which, depending on the type of study or the nature of epoxy resins, can be successfully used . Among them, for example, the method of luminescence spectroscopy makes it possible to determine the degree of conversion with high accuracy at the final stage of reaction. This is hardly achievable by other methods. Analysis with the aid of a rheometer provides information about the time of gelation which cannot be obtained by another method.
The DSC studies  showed that multi-wall CNT with COOH functionalization act as catalysts, stimulating the initial stage of curing of bisphenol A diglycidyl ether (BADGE). This accelerating effect is noticeable even at a 1% content of multi-wall CNTs. Nonfunctionalized multi-wall CNTs decrease the degree of cross-linking, as evidenced by a lower overall heat of reaction and lower glass-transition temperatures of the nanocomposites compared with the neat epoxy resin. At the same time, the functionalization of multi-wall CNTs increases the degree of cross-linking.
Compared with the neat epoxy resin, 1% of carboxylated multi-wall CNTs decreases the heat of reaction and increases the energy of activation . Fluorinated tubes insignificantly influence the value of Еа but lower the ultimate degree of conversion Qlim.
The grafting of butylamine onto plasma- and CF4-treated single-wall CNTs markedly improves the ultimate conversion, whereas clean tubes, when the reaction is accomplished in the nonisothermal regime, have no effect on this parameter, while in the case of the isothermal regime (30°C), they decrease it .
There was another conclusion  that clean and aminated single-wall CNTs reduce the ultimate heat of reaction. Tubes with the grafted epoxy groups give almost the same value of heat as that obtained in the curing of resin without any filler: 355 versus 362 J/g. It is possible that different results may be attributed to different concentrations of single-wall CNTs.
The kinetic analysis of the curing process in terms of Eq. (1) does not reveal marked differences in the values of constants and exponents for the systems of interest. However, it was shown  that the introduction of 3% of clean multi-wall CNTs does not influence the kinetics of reaction, but tubes with grafted amino groups decrease the constant k1 by factor of almost 2.5, increase k2 by factor of 3, and decrease exponent m from 0.53 to 0.27.
Multi-wall CNTs with amino groups decelerate the curing of BADGE with 2-ethyl-4-methylimidazole at concentrations of 0.5 and 1 wt % , but the deceleration effect vanishes at a concentration of nanoparticles of 3%. However, in this case, the value of ultimate reaction heat decreases as well. Note that clean multi-wall CNTs accelerate curing of the same reaction system .
The impact of multi-wall CNTs carrying acidic and amino groups on the process of curing was studied by Raman and luminescence spectroscopy . Throughout the reaction conducted in the presence of nanoparticles, the rates were higher than the neat resin. The difference in the rates of curing was explained by homogeneity of the sample and the presence of chemical groups.
The kinetics of the amine curing of BADGE in the presence of multi-wall CNTs functionalized by oxygen-containing groups using viscometry and transmission electron microscopy along with calorimetry was analyzed . The samples of multi-wall CNTs had different values of specific surface S. This factor was found to be decisive in the kinetic study of reaction: if at the onset the rates were equal, then, by the time of attaining the maximum rate Wmax, the higher the value of S, the more pronounced the deceleration of the process, so that the time of attaining Wmax increased. Afterward, the inverse effect was observed, namely, acceleration, so that the higher the value of S, the more pronounced the final heat release. The rheokinetic study demonstrated that the time of a sharp gain in viscosity of the system (the gel point) also shifts to longer times with an increase in S. However, variation in the concentration of multi-wall CNTs (to 5%) insignificantly influences the kinetics of reaction.
The kinetic features of the process may become understandable if the micrograph of the epoxy composition which is measured at the initial stage of curing performed in the presence of multi-wall CNTs is examined (Figure 1). It is seen that compact polymer structures grow along the tube. Evidently, hydroxyl groups grafted on the surface catalyze the reaction of epoxy groups with amine  to give rise to new hydroxyl groups accelerating this reaction. In doing so, the process of polymer formation is localized, and the reaction assumes the frontal character. The natural consequence of the localization process is the formation of ineffective cross-links. Therefore, the value of critical conversion increases, and correlation is observed between the time of a sharp gain in viscosity and the specific surface of multi-wall CNTs.
It was shown that graphene oxide (GO) accelerates the curing of tetraglycidyl-4,4′-diaminodiphenylmethane with 4,4′-diaminodiphenyl sulfone . According to this work, this effect is related to the presence of hydroxyl and carboxyl groups on the surface of GO.
The kinetics of the nonisothermal curing of BADGE with liquid poly(amido- amine) in the presence of amine-functionalized GO using Eq. (6) was investigated . It is seen that for the systems without any filler and in the presence of GO containing NH2 groups, the parameters of this equation are similar. At the same time, GO slightly decelerates the process.
The mixture of BADGE and 1,1,2,2-tetra(p-hydroxyphenyl)ethane tetraglycidyl ether with diethyltoluenediamine in the presence of graphene was cured . It was shown that the latter somewhat accelerates the reaction and increases Тg by 15–25°C. Previously, the same authors showed using Eq. (1) that this effect is associated with an increase in constant k1 and the functionalization of graphene by amine enhances the effect of the filler .
The IR spectral analysis of the curing of BADGE with 4,4'-diaminodiphenylmethane in the presence of GO permitted to obtain kinetic curves for both epoxy groups and primary, secondary, and tertiary amino groups . These studies made a considerable contribution to gaining insight into the mechanism of reaction. It was shown that the original GO has no effect on the overall kinetics of the process and even decelerates the consumption of primary amino groups. But after autoclave purification, GO increases the rate of reaction of epoxy groups by more than factor of 2 and the rate of reaction of primary amino groups by factor of 1.8. As was shown by X-ray photoelectron spectroscopy, purification leads to a marked reduction in the amount of oxygen-containing groups on the surface of GO. The glass-transition temperature of a nanocomposite based on the crude GO is much lower than that of the epoxy matrix, whereas the purification of GO causes an increase in this parameter, although Tg does not attain the Tg value of the matrix.
The influence of various graphite fillers (graphite with a high surface area, graphite oxide, and exfoliated graphite oxide) on the reaction of epoxy ring opening of BADGE by amines—primary (benzylamine and cyclohexylamine) and secondary (dibenzylamine)—and hydroxyl (benzyl alcohol) was studied . These data indicate the strong catalytic effect of fillers on the reaction with amines. This effect is the most pronounced for the exfoliated graphite oxide. In the case of benzyl alcohol, interaction with epoxy groups was observed only for graphite oxide. A similar effect was caused by fillers on the process of matrix formation: in the presence of graphite fillers, the rate and heat effect of the reaction grow, and the gel point shifts to smaller times.
In essence, analogous data were reported by Mauro et al. . These authors believe that a marked rise in the Tg of nanocomposites compared with the neat matrix is an evidence of the catalytic effect of graphite with a high surface area (308 m2/g) and graphite oxide. The catalytic effect of graphite was confirmed using the reaction of epoxystyrene with benzylamine.
On the other hand, it was found that the samples of graphite oxide with carboxyl or amino groups have almost no effect on the kinetics of nonisothermal curing of BADGE with 4,4'-diaminodiphenylmethane . Possibly, this is related to a low concentration of the fillers (0.5%).
The effect of carbon nanofibers (diameter of 100–200 nm and length of 30–100 μm) oxidized in a solution of nitric acid and then treated with 3-glycidoxypropyltrimethoxysilanе on the kinetics of curing of epoxy resin Cycom 977 described by Eq. (1) was studied . It was shown that all kinds of fibers exert a catalytic effect which manifests itself as an increase in ultimate conversion and growth of kinetic constants k1 and k2. Note that Еа1 decreases, while Еа2 increases. In terms of catalytic efficiency growth, the fibers may be arranged in the following sequence: untreated, oxidized (СООН groups on the surface), and treated with silane (epoxy groups on the surface).
The catalytic effect of a carbon nanofiber was observed: the ultimate conversion and the kinetic constants in Eq. (1) increase, while the respective activation energies decrease . The higher activity is exhibited by fiber whose surface is modified through the oxidative polymerization of aniline (in accordance with the authors, the “nanograssy” coating).
The above results are rather contradictory, which is probably caused by ambiguity in the concentration of the filler, uncertainty in the degree of dispersion, and the magnitude and structure of its surface.
3.2 Noncarbon fillers: oxides of metals and silicon
The effect of Al2O3 nanoparticles on the kinetics of polycondensation of BADGE under the action of diethylenetriamine using modulated DSC was explored . As a result, not only the rate of the process was registered, but also variation in the heat capacity of the system during the process was monitored. It was shown that the filler increases the rate of reaction but decreases the ultimate heat. Viscosity measurements confirmed that the formation of the polymer network accelerates in the presence of nanoparticles, and the gel point shifts not only with time but also with conversion. This implies that nanoparticles are directly involved in the formation of intermolecular bonds. At the same time, experiments with water additives revealed that nanoparticles affect the kinetics of the curing reaction in qualitatively the same manner as Al2O3 nanoparticle . The authors inferred that water adsorbed by nanoparticles is responsible for the catalytic effect.
DSC was used to examine the effect of additives of Al2O3 and ZnO nanoparticles on the curing of BADGE with о-tolylbiguanidine . Both oxides decelerate the reaction but increase the ultimate limiting degree of conversion. Exponents m and n in Eq. (6) remain almost unchanged, whereas the activation energy decreases. Note that in the case of ZnO, this decrease is considerable.
At a fairly low concentration (1 and 5%), ZnO nanoparticles accelerate the reaction of BADGE with 2,2'-diamino-1,1'-binaphthyl; at concentration of 10%, their catalytic efficiency declines, while at content of 15%, retardation is observed . Compared with the neat matrix, nanocomposites feature higher values of ultimate heat and glass-transition temperature with the maximum values corresponding to 5% content of nanoparticles. Probably, reduction in the catalytic activity of nanoparticles with increasing concentration may be attributed to their aggregation; as a result, the effective surface decreases.
Ghaffari et al.  studied how the size of ZnO nanoparticles affects the kinetics of BADGE curing with poly(aminoamide). Nanoparticles were sheets with a thickness of nearly 20–40 nm, while microparticles were rods with a length of ∼1 μm. Analysis was performed using Eq. (5). It was found that the autocatalysis of reaction is absent; that is, т = 0 and п is somewhat above unity. For both composites, compared with the neat matrix, the energy of activation decreases, but the rate constant slightly grows in the case of the microcomposite and declines in the case of the nanocomposite.
BADGE with the propylenimine dendrimer carrying eight end groups -NH2 in the presence of Fe2O3 nanoparticles was cured . The latter manifested the catalytic effect. The higher the concentration of nanoparticles, the more pronounced the increase in ultimate conversion and glass-transition temperature. It is shown that the kinetics of formation of the nanocomposite containing 10% Fe2O3 is adequately described by Eq. (2). No data are available for other systems, including the neat matrix. A similar result was reported in . It was shown that the kinetics of curing of glycerol diglycidyl ether with 3,3'-dimethylglutaric anhydride in the presence of Al2O3 obeys Eq. (2).
Nanoparticles of metal oxides are able to adsorb components of the reaction system to one extent or another . Possibly, their kinetic role is associated with this property.
Direct measurements of the complex specific heat capacity demonstrated that the interaction of SiO2 nanoparticles and BADGE molecules is very weak . At all stages of polymer network formation, the interaction of nanoparticles and matrix is of a physical origin. The effect of the filler on the kinetics of curing was insignificant.
In contrast, acceleration of the process was observed [59, 60]. The kinetic studies revealed that the catalytic effect of SiO2 nanoparticles is related to the presence of hydroxyl groups on their surface . When the latter groups are changed for epoxy groups, the effect of nanoparticles on the kinetics of BADGE reaction with m-phenylenediamine is eliminated.
For polymer nanocomposites, the most popular fillers from the class of minerals are layered silicates , which are sometimes called nanoclays, in particular, montmorillonite (MMT). The structure of its crystal lattice is such that it can adsorb various ions (mostly cations) and swell in polar liquids owing to their penetration into the interlayer space [63, 64].
At the nanometer scale, MMT is composed of three-layer stacks ∼0.7 nm in thickness and several hundred nanometers in length and width. At micron level, these stacks are united into primary particles with interlayer distance of about 1.35 nm. At higher level, they form aggregates. During formation of nanocomposites, stacks should be exfoliated in order to reach a high area of contact with the matrix. In order to facilitate exfoliation, the surface of stacks should be treated for the purpose of changing their hydrophilic nature to hydrophobic, because the hydrophilic character of the silicate surface hampers the dispersion of MMT. Neutral organic compounds may form complexes with interlayer cations; for example, alkylamines are transformed into alkylammonium cations. These properties of MMT govern the kinetic features of formation of epoxy nanocomposites.
In the absence of the curing agent (1,3-phenylenediamine), the modified MMT and even the unmodified MMT promote the homopolymerization of BADGE at a high temperature . Depending on the nature of the intercalated modifier (octadecyl-, trimethylstearyl-, methyldihydroxyethylammonium), MMT may either catalyze the reaction of the epoxy oligomer or react with a prepolymer or a curing agent.
At the same time, it was found that MMTs modified with alkylamines weakly accelerate [66, 67, 68], retard , or do not affect at all  the kinetics of curing of epoxy oligomers with amines. A weak acceleration was also observed for the unmodified MMT and MMT with intercalated 3-aminopropylethoxysilane .
Thus, it should be stated that the rate of curing of epoxy oligomers is almost insensitive to the presence of MMT. However, the kinetics of formation of polymers is not reduced only to a change in the concentration of reactants: structure formation should be taken into account. Even to a higher extent, this applies to a nanocomposite, whose properties are determined not only by structural levels of polymer matrix but also by the structure of nanoparticles and the character of their distribution in the material bulk.
As was noted above, MMT requires exfoliation. Namely, this process occurs during the chemical reaction, and its efficiency depends on the reaction conditions. For example, it was shown  that the cationic polymerization of triglycidyl-p-aminophenol occurs within the interlayer space, which entails the exfoliation of MMT, whereas with DDS the epoxy oligomer reacts outside the interlayer cavity. An increase in temperature is favorable for the former reaction: ultimate conversions inside and outside the cavity are 0.19 and 0.74, respectively, at 120°C or 0.76 and 0.77 at 180°C.
The optimum structure of epoxy composites was achieved when BADGE was cured with poly(ester diamine) in the nonisothermal regime at low rise in temperature (2.5 and 5 K/min) . Small-angle X-ray scattering studies revealed the exfoliation of MMT in the matrix. The authors of  used hyperbranched polyethylenimine with end amino groups as a curing agent and attained effective exfoliation. A comparison of three systems, such as triglycidyl-p-aminophenol + DDS, BADGE + poly(ester diamine), and BADGE + hyperbranched polyethylenimine, showed  that the exfoliation ability of MMT decreases in the mentioned sequence.
As was reported in , the nonisothermal curing of epoxy oligomers with amines in the presence of MMT includes four different reactions: formation of the matrix via the interaction of epoxy groups with the diamine curing agent, intracavity homopolymerization, and two homopolymerization reactions outside MMT which are catalyzed by onium ions of organically modified clay and tertiary amines.
X-ray diffraction was used to probe the exfoliation of MMT intercalated by octadecylammonium during the isothermal curing of BADGE with DDS . It was shown that this process may be divided into three different stages (Figure 2).
The first stage is related to the penetration of BADGE into the interlayer space of MMT; at the second stage, the cationic polymerization of the epoxy resin catalyzed by ammonium takes place; and at the third stage, BADGE sorbed by MMT is cured with amine.
In order to identify the intracavity polymerization, mixture of MMT and triglycidyl-p-aminophenol was held at various temperatures for tens of days in the absence of the amine curing agent. Afterward, DDS was added and the curing process was conducted in the nonisothermal regime . A similar procedure was employed for the system BADGE-MMT-poly(ester diamine) . At the first stage, the epoxy equivalent and the glass-transition temperature increased. This technology makes it possible to improve both the degree of dispersion of MMT in the epoxy resin and the subsequent exfoliation of the clay during formation of epoxy nanocomposites. The period of the intracavity polymerization was reduced to tens of minutes by the use of complex BF3·C2H5NH2 as a catalyst .
An attempt to accomplish the intracavity polycondensation was made by Jagtap et al. . In contrast to the commonly used MMT modifiers, i.e., polyalkylamines, they used half-neutralized salt of poly(ester diamine), which was intercalated via ionic exchange in an aqueous-organic solution, assuming that these macromolecules, when fixed by the ionic end on the walls of the cavity, will react with epoxy groups of the binder via its free amine end. However, no direct evidence for this reaction is available .
3.4 Metal-containing nanoparticles synthesized in situ
The synthesis of metal-containing nanoparticles for producing nanocomposites may be accomplished by various physical processes on the preformed matrix containing molecules of appropriate precursors [82, 83, 84, 85, 86, 87]. Physical methods of obtaining metal-containing nanoparticles (photolysis, radiolysis, and thermolysis) are as a rule accompanied by chemical reactions leading to their formation. An important factor is the diffusion of preformed substances (metal atoms): the glassy state of the matrix provides a considerable obstacle to diffusion. For example, N-cetylpyridinium tetrachloroaurate was dissolved in methyl methacrylate and, after polymerization of the latter, was subjected to UV radiation. However, the formation of gold nanoparticles was registered only at temperatures above Тg of the polymer .
A substantially different method involves the combination of processes of formation of matrix and metal-containing nanoparticles, i.e., formation of nanocomposites in situ.
The main chemical method used at moderate temperatures includes the reduction of chemically bound metal atoms in nonpolar media. These methods of chemical reduction are the subject of most publications [83, 87, 89, 90, 91, 92, 93]. Mechanisms controlling formation of metal-containing nanoparticles in situ are highlighted in the review .
The transformation of the resulting single-valence atoms, or monomers, into nanoparticles includes nucleation stages with formation of primary clusters or stable particles, their growth by addition of monomers, possible subsequent coagulation, and/or Ostwald ripening. The kinetics of all these stages determines the size distribution function which strongly affects the ways and possibilities of the nanoparticles and corresponding nanocomposites’ application. An important role in this is played by a polymer medium in which chemical reactions take place, including the ability of its components or fragments of macromolecules to be adsorbed on the particles, as well as the possibility of formation of micelle-type structures.
With rapid decay of the precursor, there will be a supersaturation of the system with a monomer. In this case, in the first approximation, nucleation will be described by Gibbs-Volmer-Frenkel thermodynamic theory [95, 96], according to which the radius of the critical nucleus is determined by the formula:
where rc, σ, and Vm are radius, surface tension, and molar volume of the critical nucleus, R is the gas constant, T is temperature, and S is the supersaturation. In this case, the nucleus will be unstable if r < rc, and it stabilizes when r ≥ rc.
Rapid increase in the concentration of monomer will lead to the achievement of the critical value of Cmin (region I, the stage of prenucleation) and then overcome Cmin. Exceeding this value gives rise to proper nucleation. Because of the balance between the rate of formation of the monomer and its expenditure consumption on nucleation and growth of the generated nuclei, the concentration will reach a peak, Cmax, and then begin to decrease due to an increase in consumption for growth and again reach the critical level of Cmin, marking the end of the nucleation stage (region II). After that, the concentration of the monomer will continue to decrease to the equilibrium value of C0, expending on the growth of nucleus without renucleation, due to the fact that the supersaturation is below the critical level (region III).
Although short spatial and temporal scales of the nucleation stage hamper the direct observation of the classic process, to trace the time-resolved formation of silver CNs using small-angle X-ray scattering in situ was managed . Silver perchlorate was reduced with sodium boron hydride in an aqueous solution. As shown in Figure 4, the nanoparticles’ nucleation kinetics corresponds to the LaMer pattern: the number of particles initially grows without any appreciable change in their sizes, attaining a maximum in fractions of a second. Further, the number of nanoparticles descends, and their radius increases. This corresponds to stage III in the pattern, and nanoparticles interact with each other alongside with their simple growth via the reaction with monomers, i.e., the aggregation mechanism is engaged.
However, under conditions of formation of composites, it is hardly possible to implement such a mechanism. An alternative variant was obtained in . When studying the synthesis of gold by reducing HAuCl4 with sodium citrate, it was shown that rapid nucleation is not observed; on the contrary, the kinetic curve of accumulation of critical nuclei is S-shaped with a more or less extended induction period. The authors suggested that such features of the process are due to redox reactions leading to the conversion of gold cations to a zero-valent atom and citrate ion to acetone dicarboxylic acid. In this case, the supersaturation of the system by the monomer, Au(0), is absent. Obviously, in this case the concept of a critical nucleus becomes meaningless.
Later it was established that S-shaped kinetics is inherent in many metals with variable valence (see, e.g., the review ). To describe such processes, a rather simple two-step scheme was proposed by Watzky and Finke :
The first stage is the slow nucleation of “kinetically efficient” clusters В from precursor А, and the second stage is the particle’s fast growth reaction. In the original studies, in particular in , А represented complex [(n-С4Н9)4N]
5Na3[(1,5-cyclooctadiene)Ir・P2W15Nb3O62], and В was the catalytic surface of a Irn(0) nanocluster.
Studies of a wide range of systems show (see ) that the value depends on the number of catalytic active nuclei, namely, their ratio with increasing ratios k2A0/k1 for practically unchanged diameters of the order of 2 nm. These factors—the medium, active additives, and temperature—make it possible to achieve the formation of an almost monodisperse distribution (width not exceeding 15%) of the nanoparticles with a size determined, as a rule, by a “magic number” (number of atoms in the outer filled nanoparticle shell: 13, 55, 147, 309, etc.).
The processes of formation of zero-valence atoms or other monomers inevitably lead to their clustering. To stabilize clusters in a nonpolar solution, it is necessary to have amphiphilic molecules capable of forming adsorption layers and thereby form inverse micelles from the nanoparticles.
At the same time, when the epoxy nanocomposite films are stored under light for a while, the optical density Dmax in the region of the surface plasmon resonance of silver nanoparticles decreases. Similar changes are observed in the spectra and at storage of films in the dark  (Figure 5). The kinetic curves are described by the first-order equation (Figure 5a, straightening in Figure 5b)
in which Dlim = 0.534 (in the dark) and 0.42 (in the light).
Accordingly, the value of the limiting conversion of nanoparticles under light is higher than in dark: the conversion under light is 0.29, while in dark, the conversion is 0.11.
The decrease in Dmax in time means a drop in the total concentration of metallic silver, apparently due to its “dissolution.” The relatively recent discovery of digestive ripening (DR), which represents the transfer of atoms from large metal nanoparticles to smaller ones [94, 103], indicates the possibility of such a process.
Although the mechanism of the DR process is not fully understood, there are grounds to believe that the equation proposed in [104, 105] for describing the kinetics of Ostwald ripening (OR) is applicable to DR. The latter is one of the options for the growth of the nanoparticles, when large particles grow at the expense of small particles. According to the theory, the change in the radius r of a spherical particle in time will obey the equation:
where , D is diffusion coefficient, V is molar volume, and C0 is solubility of the monomer; R is the gas constant and T is temperature; rc is determined by equation (7).
As can be seen, the particles grow if r ≥ rc, and their dimensions decrease otherwise. This is the physical meaning of the phenomenon of OR.
A vivid example of reversible OR and DR was demonstrated by Xin and Zheng . They observed fluctuating growth of bismuth nanoparticles in the absence of precursor at 180°C. The reaction system consisted of a limited number of large Bi nanoparticles (80–150 nm in diameter) in a solution of oleylamine (surfactant) and dichlorobenzene. The Bi nanoparticles served as a source of monomeric Bi(0).
The process includes formation and growth of small particles due to large ones (DR) with simultaneous OR. The total number of particles increased for a while and then changed to the fluctuation mode. The total volume of content fluctuated near a certain level evidently given by the total volume of initial Bi nanoparticles. The size of each of the observed particles and their assemblies experienced similar fluctuations.
Obviously, the first stage of the DR process is the disassembly of small nanoparticles on zero-valence atoms and metal clusters. Under normal conditions, they subsequently lead to formation of nanoparticles, which require their diffusion displacement. But under the conditions of a glassy matrix, diffusion is difficult, if not forbidden at all. Therefore, the entire process is reduced to the first stage, i.e., “dissolution” of large nanoparticles with the formation of zero-valence atoms and silver clusters. The presence of a limit, apparently, is due to the saturation of the boundary zone surrounding the particle by the zero-valence atoms and clusters of silver formed.
As precursors soluble in organics, complexes of univalent gold [O(AuPR3)3](CF3SO3) (R = Ph or СН3) , [RN(CH3)3][Au(SC12H25)2] (R = C8H17, C12H25, and C14H29), and [(C18H37)2N(CH3)2][Au(SC12H25)2] were proposed by Nakamoto et al. ; salts of organic acids with a fairly bulky (even high-molecular-mass [109, 110, 111]) radical, such as silver myristate С13Н27СООAg, copper oleate (C18H33СОО)2Cu, silver oleate, silver octanoate C7H15COOAg, silver stearate C17H35COOAg, silver 2-hexyldecanoate p-C8H17CH(n-C6H13)COOAg, cis9-octadecanoate p-C8H17CH=CH(CH2)7COOAg, and silver neodecanoate CH3(CH2)3C(CH3)2COOAg, have enjoyed popularity [107, 112, 113, 114, 115, 116, 117].
However, the nonideal state of solutions of these compounds should be taken into account. This implies that, when a certain concentration is exceeded, precursors in solution are united into associates, i.e., are clustered. Evidently, this circumstance cannot be disregarded when considering feasible mechanisms governing formation of metal-containing nanoparticles.
The silver nanoparticles by the reduction of alkyl carboxylates in trimethylamine at 78°C were synthesized [118, 119]. It was found that the induction period grows and the maximum rate decreases in the following sequence: decanoate, myristate, and stearate. But in this sequence, the length of the hydrocarbon radical of carboxylates (С9, С13, and С17) increases. It is reasonable to assume that solubility grows in the same sequence and, hence, the possibility of formation of clusters decreases. Thus, there is a direct relationship between the rate of formation of nanoparticles and the concentration of precursor clusters.
This idea underlies the theory of formation of metal-containing nanoparticles from precursors of the silver carboxylate type via their reduction which was put forth .
The model adopted for the formation of metal-containing nanoparticles may be presented as follows. Carboxylates reversibly form triangular and tetrahedral clusters. The development of larger clusters is not allowed because of steric reasons. The reduction of cation in them occurs. As a result, the adsorption of new salt molecules becomes possible. Indeed, if for carboxylates the tetrahedral structure is limiting, then the metal atom in the limit may be surrounded by 12 molecules (the icosahedron structure). It is assumed that the concentration of the reducing agent is high, so that the corresponding reaction is pseudo first order. Thus, the kinetic scheme may be written as follows:
where (i = 0, 1, 2, …; j = 3, 4,…).
Here Rji denotes clusters composed of i carboxylate molecules and j atoms of the zero-valence metal. Accordingly, R01 is the initial carboxylate, R03 is the cluster of the triangular carboxylate, and R04 is the cluster of the tetrahedral carboxylate. Reactions with constants k1 and k2 are responsible for the formation and dissociation of associates consisting of three carboxylate molecules, and reactions with constants k3 and k4 correspond to the addition of one molecule to cluster Rji and its detachment. The reaction with constant k5 involves reduction of the bound metal in a cluster.
A system of equations corresponding to scheme (11) was analyzed with a wide variation in kinetic constants. It was shown that the values of k2, k4, and k5 have a slight effect on kinetics of the process. The decisive role is played by constants k1 and k3, that is, those constants that determine reactions giving rise to clusters, including mixed clusters.
The kinetics of the process is characterized by the existence of the induction period in the reaction of carboxylate consumption and an almost linear growth of average sizes of metal-containing nanoparticles with conversion. With the increase in constant k1, the maximum rate increases, the induction period shortens, and the sizes of resulting particles decrease. After a certain period of growth, the number of particles reaches a limiting value which is lower than the greater the value of k1 (Figure 6). At the same time, the mass of nanoparticles varies in proportion to conversion, irrespective of the constant (insert in Figure 6). At the same time, the narrow size distribution is typical of these particles.
Papers addressing methods of in situ obtainment of epoxy nanocomposites with metal nanoparticles are scarce.
Under UV radiation, 2,2'-dimethoxy-2-phenylacetophenone decomposes into radicals. A dimethoxyphenyl-carbonium radical reacts with AgSbF6 and reduces a silver cation to Ag(0) via the transfer of electron, and then the radical transforms into the carbonium cation able to initiate the polymerization of diepoxide. Hence, silver nanoparticles and network matrix are formed simultaneously . With increasing concentration of silver salt, the rate of polymerization and the ultimate conversion decrease, but the glass-transition temperature increases.
The silver nanoparticles with the same precursor, AgSbF6, were obtained but in the presence of degradable under irradiation with visible light 3,5-bis(4-methoxyphenyl)-dithieno[3,2-b;2,3d]-thiophene . A similar technique was employed to synthesize epoxy nanocomposites with nanoparticles of silver  and gold , but 2,3-bornadione (camphorquinone) was used as a source of radicals; in the case of gold, the precursor was HAuCl4.
The silver nanoparticles in situ via the reduction of AgNO3 in the epoxy resin by Triton-100, which simultaneously functioned as a stabilizer of nanoparticles, were synthesized . A cycloaliphatic epoxy resin, hexahydro-4-methylphthalic anhydride as a curing agent, a reducing agent, and a precursor were dissolved in acetonitrile and exposed to UV radiation. After completion of the process, the solvent was removed at a reduced pressure.
A complex of silver acetate and 2-ethyl-4-methylimidazole was synthesized in an epoxy resin, and during its curing Ag+ was reduced to Ag(0) as a result of thermal decomposition of the complex . In such a manner, silver nanoparticles were generated in situ. The imidazole product of complex decomposition served as a curing agent.
The epoxy resin ED-20 with triethylamine in the presence of silver myristate was cured [127, 128, 129]. The reduction of the latter and the formation of silver nanoparticles occurred simultaneously during polymerization. Reduction agents were both amine and the epoxy group. Carboxylate groups compatible with the medium functioned as stabilizers of particles.
It has been shown that, regardless of whether a filler is introduced in the reaction system or is formed in situ during the process of matrix formation, its structure changes to a greater or lesser extent than the unfilled cured epoxy binder. In addition, the matrix influences the character of distribution of nanoparticles over volume. This effect is especially important in the case of graphene and MMT, when exfoliation is the case in point. The matrix governs the size and shape of the resulting nanoparticles. They interact with the epoxy matrix through the resulting interfacial layers. There is no doubt that all these factors affect the properties of the epoxy nanocomposites.
The application areas of composites are defined by both the physicomechanical parameters of the epoxy matrix, its strength, thermomechanical stability, and adhesion ability and the unique properties of nanoparticles.
Nanoparticles of gold, silver, copper, TiO2, ZnO, fullerene, and CNTs demonstrate effective antibacterial properties; therefore, composites containing these nanoparticles may be used for the microbiological control and purification of water, disinfection of surfaces, and creation of germicidal coatings, protective films, etc. Silver shows anti-inflammatory behavior and features antiviral and antifungal abilities. Its application in the form of nanoparticles (compared with the ionic form) decreases the cellular toxicity rather than the antibacterial efficiency .
Dielectric and magnetic epoxy nanocomposites have found wide use in such fields as Fourier spectroscopy, NMR, data storage, and absorption of electromagnetic radiation from other objects. The role of nanoparticles shows itself as improvement of electric strength and stress durability, suppression of space charge, and increase in the stability of dielectric discharge. For example, in the case of built-in planar capacitors, the insertion of dielectric films between copper sheets makes it possible to efficiently reduce the number of assembly devices. This not only leads to the miniaturization of circuit boards and electric wiring but also improves the characteristics of devices (e.g., promotes reduction in electromagnetic interference and switching noises) [131, 132, 133].
Epoxy resins are often employed in anti-wear applications. The use of such fillers as graphene oxide  or complexes MMT + SiO2 , even at their very low content, decreases the rate of material wear by almost an order of magnitude.
The epoxy binders modified with carboxylated carbon nanotubes are more resistant to the action of aging factors. The presence of aggregates of carboxylated carbon nanotubes in the epoxy matrix positively influences the preservation of physicomechanical properties of the composite subjected to heat and humidity aging. Microscopic examination revealed structural features of the epoxy nanocomposite and their effect on the resistance of the composite to the heat and humidity aging .
As for the use of epoxy nanocomposites in aerospace science and technology, this important problem, in author view, should be devoted to a special work. In short, it can be formulated as follows: structural nanocomposites, which are reinforcement structures based on carbon or glass fibers embedded in a polymer matrix modified with nanofillers, are the most important application of nanocomposites in the aerospace field , laminates, and sandwich structures. In addition, they can be used as anti-lightning , anti-radar  protection devices, flame retardant, and heat-resistant paints , ameliorating anti-corrosion performances .