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In situ synthesis of epoxy nanocomposites with hierarchical surface-modified SiO2 clusters

Polymer nanocomposites are often produced using in situ approaches where an inorganic filler (as the dispersed phase) is synthesized directly in an organic matrix. Such an approach generally leads to improved dispersion and reduced agglomeration of the filler material. Epoxy-based nanocomposites have demonstrated promising properties for application as high-voltage insulation materials. In this work, a sol–gel based method has been adapted to synthesize surface-functionalized SiO2 in situ in epoxy. The synthesized SiO2 moieties were dispersed in clusters of 10–80 nm, and formed chemical bonds with the epoxy monomers via a silane coupling agent. Raman spectra show the formation of four-membered D1 rings, which may be part of a cage-like structure similar to that of polyhedral oligomeric silsesquioxanes (POSS). SAXS measurements indicate that the SiO2 clusters consist of a hierarchical structure with an increasing fractal dimension with increasing SiO2 content. The nanocomposites displayed improved thermal stability, while the glass transition behavior varied depending on the structure and content of the SiO2 moieties. While the relative permittivity showed no significant changes from that of pure epoxy, the onset of the dielectric relaxation changed with the SiO2 structure and content, similar to the behavior observed for the glass transition. The synthesis of surface-functionalized SiO2 in situ in an epoxy resin (DGEBA) resulted in a good dispersion and limited agglomeration of the SiO2 in the nanocomposite, with little deviation in the dielectric properties (i.e., complex permittivity). The SiO2 is suspected to have a hierarchical structure based on the SAXS measurements, with the primary structural level consisting of POSS-like cages, and an evolution in the structure from inorganic chains to cross-linked clusters with increasing SiO2 content. The synthesis of surface-functionalized SiO2 in situ in an epoxy resin (DGEBA) resulted in a good dispersion and limited agglomeration of the SiO2 in the nanocomposite, with little deviation in the dielectric properties (i.e., complex permittivity). The SiO2 is suspected to have a hierarchical structure based on the SAXS measurements, with the primary structural level consisting of POSS-like cages, and an evolution in the structure from inorganic chains to cross-linked clusters with increasing SiO2 content. Surface-modified SiO2 clusters of 10–80 nm synthesized in situ in epoxy using a sol–gel method. Raman spectra show the formation of four-membered SiO rings (D1 breathing mode). SAXS indicates the presence of a hierarchical structure within the SiO2 clusters. The glass transition and the dielectric relaxation varies with the structure and content of SiO2. No significant changes in relative permittivity. Surface-modified SiO2 clusters of 10–80 nm synthesized in situ in epoxy using a sol–gel method. Raman spectra show the formation of four-membered SiO rings (D1 breathing mode). SAXS indicates the presence of a hierarchical structure within the SiO2 clusters. The glass transition and the dielectric relaxation varies with the structure and content of SiO2. No significant changes in relative permittivity.


Introduction
Epoxy-based nanocomposites, containing inorganic oxide nanoparticles as filler, are often used as nanodielectrics in high-voltage insulation materials or microelectromechanical systems due to the novel properties exhibited by these hybrid materials [1][2][3]. Several studies have presented the advantages of adding nanoparticles of SiO 2 , TiO 2 , MgO, ZnO, BN, etc. to the epoxy matrix, such as higher dielectric breakdown strengths, reduced complex permittivity, decreased accumulation of space charge, greater mechanical strength and fracture toughness, increased thermal stability, and higher glass transition temperatures [4][5][6][7][8][9][10][11]. However, there is a large spread in the reported results, likely due to the difficulty in consistently achieving a homogeneous and stable dispersion of nanoparticles in epoxy. A poor dispersion quality can result in a deterioration of the desired dielectric properties [12]. The use of surface modifiers for the nanoparticles, such as silane coupling agents (SCAs) or organophosphate ligands, have been shown to improve the properties of epoxy nanocomposites [13]. These surface modifiers allow chemical bonds to form at the interfaces between the nanoparticles and the polymer chains, facilitating the dispersion of the nanoparticles [14], thereby increasing the interfacial area. The interfacial region between the nanoparticles and the polymer chains is thought to play a key role in determining the properties of these nanocomposites. Tanaka et al. [15] proposed a multicore model to describe the interfacial region, suggesting three distinct layers around the nanoparticles. The strength of the bonds between the polymer chains and the nanoparticle surface varied in each layer, thus affecting the mobility and chain conformation. Earlier studies of the dielectric properties of epoxy nanocomposites have primarily applied an ex situ blending method in the preparation of the materials, which involves mechanically mixing presynthesized nanoparticles into the uncured epoxy resin. The high viscosity of the epoxy resin makes it difficult to disperse the nanoparticles during a physical mixing procedure, which also does not always break up any existing agglomerates. The use of ultrasonication has shown to improve the dispersion quality to a certain degree [16]. However, even with the use of surface-functionalized nanoparticles, the use of ex situ techniques makes it challenging to obtain a homogeneous dispersion of nonagglomerated nanoparticles in the epoxy.
An alternative approach to improve the dispersion quality is in situ synthesis of the inorganic oxide directly in the epoxy using the sol-gel method [17]. One of the advantages of this method is the ability to control the size and morphology of the inorganic moieties formed by adjusting the synthesis parameters, e.g., precursor concentration, temperature, pH, as well as type and amount of catalyst [18]. SCAs may also be applied to form stronger interactions between the organic and inorganic components, resulting in the formation of class II hybrid materials [19]. Several studies have investigated the in situ formation of SiO 2 networks in epoxy using sol-gel methods and the resulting changes in the structure, as well as the mechanical and thermal properties of the hybrid materials. Matějka et al. [20,21] showed variations in the fractal dimension of the SiO 2 structures formed, depending on whether a singlestep procedure or a two-step procedure (with prehydrolyzed tetraethylorthosilicate (TEOS) as the SiO 2 precursor) was used in the synthesis. Nazir et al. [22] and Afzal and Siddiqi [18] reported improvements in the dispersion quality, the storage modulus, and a higher glass transition temperature (T g ) when a two-step procedure with SCAs was used. Yu et al. [23] found an improved dispersion quality and higher flexural moduli and impact strengths for in situ prepared nanocomposites. However, to the best of our knowledge, no studies have reported the dielectric properties such as the complex permittivity and dielectric breakdown strength of epoxy-SiO 2 nanocomposites synthesized using an in situ sol-gel method. These are critical properties for applications of these hybrid materials, for example as nanodielectrics in high-voltage power insulation systems and components.
Hence, the objective of this work is to develop a synthesis route to epoxy-SiO 2 nanocomposites with a homogeneous dispersion of the SiO 2 , by nucleating surfacefunctionalized SiO 2 nanoparticles in situ in silanized epoxy. The structure of the hybrid materials and their thermal stability, glass transition, and complex permittivity have been investigated and an improved understanding of the structure-property relations has been developed. This provides a solid basis for optimization of the synthesis route to tailor the functional properties of nanocomposites, and eventually improve the dielectric properties.

Materials
Diglycidyl ether of bisphenol-A (DGEBA, molar mass of 340.41 g mol −1 , epoxide equivalent weight of 170.2 g/eq epoxy) was used as the epoxy monomer. Poly(propylene glycol) bis(2-aminopropyl ether) (molar mass of 230 g mol −1 , and amine-hydrogen equivalent weight of 57.5 g/eq amine) was the curing agent for the system. TEOS was used as the precursor for the SiO 2 , and 3-(aminopropyl) triethoxysilane (APTES) was employed as the coupling agent between the SiO 2 and the epoxy chains. Distilled water, brought to pH 2 using concentrated HCl (37%), was the catalyst for the hydrolysis reaction. All chemicals were obtained from Merck.

Pure epoxy samples
As a reference, samples of pure epoxy (containing no SiO 2 or APTES) were prepared by mixing DGEBA with the curing agent (1:1 ratio of epoxide to amine-hydrogen groups) in a beaker for 15 min at room temperature using a mechanical stirrer. The mixture was degassed in vacuum (<10 mbar pressure) for 15-20 min to remove entrapped gas and air bubbles introduced during the stirring. Two different types of samples were prepared for different characterization methods. Bulk samples (30 mm diameter, thickness varying between 3 and 15 mm) were formed by pouring the resins into cylindrical Teflon molds. The walls of the molds were waxed lightly with high-vacuum silicone grease to allow the samples to be more easily ejected from the molds after curing. The samples were cured at 100°C for 5 h. Thin disc-shaped samples (10 cm in diameter, 0.5 mm thick) were also prepared by mixing the resin and curing agent, and then injecting the resin using 700 mbar of air pressure into a stainless steel mold under vacuum. Frekote NC-150 (Henkel) was used as the release agent for this mold. The mold was then kept under vacuum (<10 mbar pressure) for 30 min to remove any air bubbles remaining in the resin before curing at 100°C for 5 h.

Epoxy-SiO 2 nanocomposites
The chronological two-step procedure employed by Afzal and Siddiqi [18] is adapted in this study for the preparation of the nanocomposite samples. Table 1 shows the reactants and amounts used in the synthesis of the materials with different SiO 2 contents. The sample names in Table 1 are used to identify the different materials investigated in this work.
DGEBA was initially heated to 80°C under reflux in a round-bottomed flask on a heating mantle to reduce the viscosity and enable easier stirring. APTES was added to the DGEBA (in a weight ratio of 1:10 for APTES:DGEBA) and mixed with a magnetic stirrer for 1 h at 80°C. Afterward TEOS was added to the mixture, which was stirred for another hour at 60°C. The amount of TEOS was varied corresponding to a SiO 2 content between 0 and 5 wt% of the total mass. Water (in the ratio 2:1 for water to TEOS and 1.5:1 for water to APTES), brought to pH 2 using concentrated HCl, was then added to catalyze the hydrolysis of TEOS. The mixture was stirred for 4 h at 60°C, and then 1 h at 80°C to allow the hydrolysis and condensation reactions to be completed. The mixture was then poured into a beaker, and stirred for 15-18 h at 80°C overnight to evaporate any unreacted water or alcohol byproducts. The resin was then mixed with the curing agent, casted in the molds, and cured using the same procedures as described above. All the samples are identified based on the SiO 2 content that originated from the TEOS added. Figure 1 displays a flow chart for the preparation of the nanocomposites.

Characterization
Fourier transform infrared (FTIR) spectroscopy was performed on the thin disc samples using a Bruker Vertex 80 v spectrophotometer equipped with a Bruker Platinum attenuated total reflectance (ATR) diamond. For each sample, 32 scans were recorded at a resolution of 1 cm −1 . For the in situ measurements, a drop of the reactant mixture from each synthesis step was placed on the ATR diamond. For the measurements on the cured samples, 0.5 mm films were pressed down on top of the diamond. Raman spectroscopy was also performed on the disc samples using a WITec Alpha 300R using a monochromatic diode laser (λ = 532 nm) at 10 mW power. The spectra were measured with three accumulations collected over an integration time of 60 s for each accumulation.
Small angle X-ray scattering (SAXS) measurements were performed on a Bruker NanoSTAR instrument with a Cu microsource and Våntex-2000 detector, operating at 50 kV and 600 μA. Both the disc and the bulk samples, which were cut to 1 mm thickness using a diamond saw, were used. The scattering vector (q) range was from 0.009 to 0.3 Å −1 , and a glassy carbon standard was used to obtain an absolute scale for the scattering intensities. All the intensities were corrected for the scattering from the empty sample compartment. The measurements were analyzed using both model-independent methods (Guinier and Porod laws), and the unified exponential/power-law fitting model developed by Beaucage (for hierarchical structures) [24] to characterize the inorganic structures after subtraction of the background scattering from the pure epoxy matrix. The software SasView 4.2.0 was used to obtain the fits to the unified model.
Transmission electron microscopy (TEM) was performed using a JEOL JEM 2100F with an accelerating voltage of 200 kV. The samples were prepared from the bulk samples using an ultramicrotome to cut~50-100 nm thin slices.
Differential scanning calorimetry (DSC) was performed on a Netzsch DSC 214 Polyma instrument. Five to ten milligrams sized pieces were cut from the bulk samples and used for the measurements. The samples were cycled four times between 0 and 200°C at 10°C/min rates (both heating and cooling), with N 2 gas flow at 40 mL/min. The glass transition temperature was determined from the local maxima in the heat capacity measured in the final cycle. Thermogravimetric analysis (TGA) was carried out on a Netzsch STA 449C using an alumina crucible and synthetic air (30 mL/min gas flow). The samples were first held at 120°C for 30 min, before being heated to 900°C at 10°C/min. Dielectric spectroscopy was performed using a Novocontrol Spectrometer with an Alpha Beta dielectric analyzer and a BDS1200 sample cell. The cylindrical bulk samples were grinded with SiC paper (#800, #1200, and #2000 grade) and dried in a vacuum oven at 120°C for 2 h, before gold electrodes were sputtered onto the top and bottom surfaces. An electric field of 0.1 V/mm was used, and the spectroscopy was performed between 1 and 10 6 Hz at room temperature. Measurements were performed on four to five samples for each nanocomposite with SiO 2 and for pure epoxy.

Structure and morphology of the nanocomposites
The prepared nanocomposite and pure epoxy samples were transparent and clear. No visual indication of phase separation of the inorganic filler from the epoxy matrix was observed. The dispersion of the in situ prepared SiO 2 nanoparticles was observed from the representative TEM and STEM images in Fig. 2. The SiO 2 nanoparticles are arranged in irregularly shaped clusters varying in size  between 10 and 20 nm for the EAS2 sample, and between 20 and 50 nm with some larger clusters up to 80 nm for the EAS5 sample. Figure 3a shows the development of the FTIR spectra during the in situ synthesis. Figure 3b, c magnify the regions in which important changes occur as the reaction proceeds. The strong characteristic bands from Si-O-C bonds (1070-1105 cm −1 ) and the ethyl groups (940-970 cm −1 ), present in both APTES and TEOS, are observed [25]. These bands are strongest upon addition of TEOS, but as the reaction proceeds they become relatively weaker (compared with the band at 1036 cm −1 assigned to the aromatic C-O-C group in the DGEBA [26]). The band originating from the oxirane ring at 915 cm −1 [26] is also weaker upon reaction with APTES (shown by the dotted red lines). The broad band between 3300 and 3600 cm −1 corresponds to O-H groups, which becomes stronger at later stages of the reaction. The characteristic band from the N-H bonds in APTES at 1620 cm −1 is difficult to distinguish due to overlap with the C = C aromatic band in DGEBA [26]. The spectra of the pure epoxy (EAS0) and nanocomposite epoxy film (EAS4) after curing are shown in Fig. 4. The broad band from the O-H groups is more intense due to the opening of all the oxirane rings in DGEBA by the curing agent, which results in a significant decrease in the characteristic band at 915 cm −1 .
The O-Si-O rocking band is observed at 450 cm −1 in the nanocomposite. The more characteristic fingerprint of inorganic Si-O-Si networks is observed at 1080-1100 cm −1 [27,28] for the nanocomposite sample containing SiO 2 , shown in the inset. The pure epoxy also exhibits a band in the same range, which is attributed to the C-O stretching (1089 cm −1 ) from the curing agent [29]. A considerable Magnified spectra are shown in the (b) 800-1200 cm −1 range, and the (c) 2500-3800 cm −1 range as the reaction proceeds overlap between these two bands is observed in the cured nanocomposite samples containing SiO 2 .
In the Raman spectra, shown in Fig. 5, the band from the four-membered SiO rings is observed at 483 cm −1 (D 1 * ) in the EAS3 sample. A broad Raman peak in the range of 470-510 cm −1 is detected for samples with a larger SiO 2 content (EAS4 and EAS5). This peak can be identified as an overlap of two Raman modes, D 1 * mode at 484 cm −1 and D 1 at 493 cm −1 . For pure epoxy (EAS0) these bands are absent in this region, as expected due to the lack of any SiO 2 , while for small amounts of SiO 2 (EAS1 and EAS2) they were weaker and difficult to detect. Figure 6a displays the SAXS profiles of pure epoxy as well as nanocomposites with varying SiO 2 content. The scattering intensity increased with the amount of SiO 2 . All the materials exhibit a broad knee feature in a q range between 0.02 and 0.07 Å −1 , which shifts to lower q values with increasing SiO 2 content. The nanocomposites with higher SiO 2 content (EAS3 and EAS5) possess an additional knee at higher q values (between 0.1 and 0.2 Å −1 ) that can be attributed to inorganic domains with higher electron density [30]. These features in the scattering may be attributed to inorganic nanoparticles arranged in hierarchical structures at different size scales [31]. The scattering data for all the samples were analyzed using modelindependent methods. At low q values below 0.02 Å −1 , Guinier analysis was performed to calculate the radius of gyration, R g , for the nanoparticles. Assuming that the scattering objects are spherical, the size of the inorganic domains (d) was calculated using as The slopes of the linear regions of a log-log plot (log(I) vs log(q)) at intermediate q values (0.03 < q < 0.13), where the best linear fit for each plot could be obtained, were calculated to obtain the power-law scaling of the scattering by the inorganic structures (fractal dimension, D). Both the model-independent analysis and the fitting to the unified model were performed after subtraction of the background scattering from the pure epoxy matrix, so that the calculations represent the SiO 2 only and do not include scattering effects from the epoxy. The fits of the SAXS data with the unified model [24] using two structural levels for the EAS3 and EAS5 samples in the q range 0.015-025 Å −1 are shown in Fig. 6b. The first structural level was assumed to consist of perfectly spherical nanoparticles (with size d 1 ), which are then arranged in clusters (of size d 2 ) to form the second structural level. Acceptable fits were not obtained for the samples containing a lower amount of SiO 2 , since they do not exhibit the scattering feature at higher q. From these fits, the radius of gyration for the two structural levels (R g 1 and R g 2 ), the particle size and cluster size (d 1 and d 2 , respectively), and the fractal dimension for the clusters in the second structural level (D 2 ) were obtained. The fractal dimension for the first structural level was fixed to a value of 4, assuming that the spherical nanoparticles have perfectly smooth surfaces. Table 2 shows the calculated parameters from the modelindependent Guinier and Porod laws and from the unified model. Using both analysis methods, an increase in the SiO 2 content resulted in an increasing R g (and therefore an increasing particle or cluster size) and an increase in the fractal dimension. The increase in R g indicates the formation of larger inorganic domains. The calculated size of these structures is comparable with the sizes observed from the TEM images. The increase in the fractal dimension may also represent an evolution of the network structure of the SiO 2the samples with a lower SiO 2 content (EAS1,  . The inset shows a magnified part of the low frequency region of the spectra, exhibiting the difference in the spectra EAS2, and EAS3) are more likely to consist of inorganic chains, representing a mass fractal structure (D < 3), while for a higher SiO 2 content (EAS5) the chains are coiled up and cross-linked into a more compact structure, representing a surface fractal (3 < D < 4).

Properties of the nanocomposites
The glass transition temperatures (T g ) of the nanocomposites were determined from the local maxima in the heat capacity as shown in Fig. 7a, and the measured values are  Table 2 Calculated structural parameters of the epoxy-SiO 2 nanocomposites calculated from the model-independent Guinier and Porod laws, and from the unified model fits

Sample
Guinier and Porod laws Unified model The superscripts 1 and 2 indicate the first and second levels in the hierarchical structures shown in Table 3. The incorporation of SiO 2 in epoxy resulted in an initial decrease of T g to~73°C for 2 wt% SiO 2 , followed by an increase to 87°C for 5 wt% SiO 2 . Figure 7b shows the TGA of the nanocomposites, displaying the increased thermal stability of the nanocomposites compared with pure epoxy at temperatures above 325°C. Above 330°C, the pure epoxy experiences a rapid drop in mass as it decomposes. The nanocomposites do not degrade until 350°C. The pure epoxy is completely decomposed before 600°C, while in the nanocomposites the decomposition is delayed to 650°C. The remaining mass beyond 650°C corresponds to the amount of SiO 2 in the sample. The measured values of the temperatures for the initial decomposition (10% mass loss) from the TGA are included in Table 3. Figure 8 shows the results from the dielectric spectroscopy measurements, i.e., the relative permittivity (or dielectric constant) and the dielectric loss tangent (tan δ) of pure epoxy and epoxy-SiO 2 nanocomposites. The permittivity curves and dielectric loss tangents were averaged over at least four different samples for each composition. The addition of SiO 2 does not significantly affect the complex permittivity. The real relative permittivity differed between 0.2 and 0.4 from the values of pure epoxy across all frequencies measured. The nanocomposites exhibited a larger dielectric loss than the pure epoxy below 500 Hz, although the losses for all the samples were generally quite low (below 1%) at 50 Hz. Table 3 also contains the permittivity and loss tangent (tan δ) at 50 Hz for each material, as well as the frequency for the onset of the dielectric relaxation exhibited by all the materials. This frequency was determined by the intersection of two linear regression lines from the two regions, as demonstrated in the inset in Fig. 8.

Reaction pathway and resulting structure of the inorganic component
A schematic showing the proposed pathway for the reaction, based on the changes observed in the FTIR spectra, is shown in Fig. 9. The decrease in the band from the oxirane ring, the emergence of the O-H band, and the absence of the N-H band confirm that the DGEBA monomers have been silanized with the APTES. Upon addition of TEOS and the subsequent reaction with water, no further changes are observed in the oxirane ring band. However, the O-H band increases over time, which can be attributed to the hydrolysis of the TEOS and subsequent formation of surface O-H (silanol) groups after the SiO 2 clusters have formed. The band for the Si-O-C groups is present in the initial mixture (due to the APTES) and is seen to increase after addition of TEOS, as expected. The initial decrease in this signal over the first few hours is attributed to the  As seen in the Raman spectra (Fig. 5), the D 1 breathing mode at 495 cm −1 is shifting between 484 and 503 cm −1 depending on the organic groups that are attached to the Si [32]. The shift to D 1 * in samples containing SiO 2 can therefore be attributed to the surface functionalization, where one of the Si in the four-membered rings originates from the APTES and is connected to a carbon chain instead of oxygen. Due to the presence of the D 1 * mode only for the nanocomposite with 3 wt% of SiO 2 , it is likely that all of the SiO 2 structures formed are chemically bonded directly to the epoxy, while for higher SiO 2 contents (4 and 5 wt%) both types of four-membered rings are formed. Therefore, some of these rings are originating from the APTES (as demonstrated in Fig. 9) and the others are formed from the hydrolysis and condensation of isolated TEOS molecules with no covalent attachment to the epoxy.
In addition, the features observed by SAXS of these nanocomposites are similar to those observed for the epoxy nanocomposites containing silsesquioxanes structures [30,33,34]. The size of the primary structure level (5 nm and 7 nm for 3 wt% and 5 wt% SiO 2 , respectively) is close to that reported for polyhedral oligomeric silsesquioxanes (1-3 nm) [35,36]. Combined with the observations from Raman, it is therefore likely that the SiO 2 domains in the nanocomposites in the present work consist of particles built from oligomeric silsesquioxanes units, consisting of a cage structure with four-membered SiO rings on each face, as exemplified in Fig. 10. These structures may contain SiO rings with or without attachment to the APTES (resulting in the D 1 * and D 1 bands in the Raman spectra).
The model-independent analysis of the SAXS measurements only provides limited information from a certain q range, since Guinier's law is only applied at q < 0.02. As seen in Fig. 6a, the scattering from the samples shows more complex behavior, particularly for higher SiO 2 content, with multiple Guinier regions (represented by the broad features, or knees) separated by a power-law (Porod) region. The data for the samples with 3 and 5 wt% SiO 2 (EAS3 and EAS5) showed a reasonable fit to the unified model developed by Beaucage [24], which describes hierarchical systems that show multiple Guinier and Porod regions in the scattering. These hierarchical systems consist of multiple structure levels, where each structure level is composed by an arrangement of the previous smaller level. The model could not provide good fits for the samples with 1 and 2 wt% SiO 2 (EAS1 and EAS2). The calculated parameters (R g 2 and d 2 ) for the EAS5 sample are closer to the equivalent parameters calculated using the Guinier and Porod laws (R g and d), while for the EAS3 sample there is a larger difference between them. The unified model also predicts higher fractal dimensions than using Porod's law. However, it should be noted that while the term fractal dimension is used to describe the inorganic structure, it is not necessarily expected that the clusters demonstrate fractal organization over multiple length scales. This is because the fractal dimensions were calculated from the slope in a narrow q range, since the power-law regime displays structural limits due to the Guinier features. However, this is a still useful qualitative descriptor for the type of structure (chains in the case of mass fractals, or a cross-linked network in the case of surface fractals) present in the clusters.
The size of the SiO 2 clusters calculated from the SAXS measurements are comparable with those measured by TEM, as seen for the EAS5 sample where the SAXS calculations predict an average cluster size between 31 and A similar comparison can be made for the EAS2 sample. However, it is more difficult to determine from the TEM if the SiO 2 is organized as a mass or surface fractal network, as predicted by the SAXS.

Properties of the nanocomposites
The thermal analysis of the nanocomposites displays an interesting effect of the incorporated SiO 2 on the glass transition temperature of the epoxy, as shown in Fig. 11. The initial decrease in T g for lower SiO 2 contents may be attributed to the mass fractal structure of the SiO 2 , with polymer-like chains of silsesquioxanes, exhibiting a plasticizing effect on the surrounding resin [33]. With higher SiO 2 content, the inorganic domains form more clustered structures, as evidenced by the increase in fractal dimension from the SAXS measurements. In addition, there are more nanoparticles chemically bonded to the polymer chains for the higher SiO 2 content. The nanoparticles and the interfacial regions subsequently become more rigid, hindering the free motion of the polymer chains, thereby leading to an increase in T g . The thermal stability of the materials is also improved by the incorporation of SiO 2 . The initial degradation temperature is increased by 13-17°C compared with pure epoxy, and is independent of the amount of SiO 2 added. The plateau in the polymer decomposition was also observed by Bauer et al. [37], and was attributed to char formation where the samples are carbonized. The increased thermal stability of the nanocomposites may be explained by the inorganic nanodomains of SiO 2 acting as a barrier to the decay of the organic components, with higher temperatures needed to break the chemical bonds at the interfaces. A closer observation of the morphology of the SiO 2 remaining after the pyrolysis of the epoxy shows a skeletal SiO 2 network with a shape similar to that of the original sample but slightly smaller in size, suggesting the formation of a continuous inorganic network as the epoxy is burnt off during the degradation.
Another effect of the SiO 2 is the shift in the dielectric relaxation observed around 10 3 -10 4 Hz (Fig. 8). This is classified as a β-relaxation, which is attributed to the relaxations caused by O-H groups in the chain [5,38]. The onset of the relaxation is observed to shift to a higher frequency initially for samples with a low SiO 2 content, or to a lower frequency for samples with a higher SiO 2 content, as shown in Table 3 and in Fig. 11. This behavior mimics the changes observed for the T g in the opposite pattern, and may be explained with a similar reasoning. The samples with 1 and 2 wt% SiO 2 have polymer-like inorganic chains, where the dipoles in the O-H groups are more free to move and reorient themselves. These dipoles can therefore keep up  Fig. 11 Comparison of the changes in the glass transition temperature and the dielectric relaxation frequency with the amount of SiO 2 in the nanocomposites with the alternating electric field up to higher frequencies, delaying the dielectric relaxation. However, the inorganic domains are more compact and clustered (with higher fractal dimension) in the samples with higher SiO 2 content, and the dipoles cannot reorient themselves as quickly. The increased rigidity in the nanodomains results in the dielectric relaxation occurring at lower frequencies.
Tanaka et al. proposed that the presence of inorganic nanofillers possessing strong chemical bonds to the polymer matrix would lead to lower relative permittivity and loss factors [15]. However, despite the dispersion of the in situ grown SiO 2 nanodomains, there is no significant influence of the filler content on the permittivity or losses of the materials. Most of the studies reporting a decreased complex permittivity of epoxy nanocomposites have employed spherical nanoparticles that are dispersed. It is therefore possible that the fractal-like network structure of the inorganic nanodomains produced in the present work may be responsible for the absence of any significant changes in the relative permittivity from that of pure epoxy. Thus, it is of interest to vary the parameters of the in situ sol-gel synthesis that are known to affect the reaction kinetics in order to form different nanostructures of the inorganic oxide component.

Conclusion
The use of an adapted sol-gel method to synthesize and grow SiO 2 nanoparticles directly in the epoxy matrix is shown to be a successful approach in obtaining a well dispersed inorganic filler phase in the prepared nanocomposites. The nanoparticles were found to consist of cage-like four-membered SiO rings, which may then be arranged in fractal-like clusters (either as inorganic chains or a cross-linked network, depending on the SiO 2 content). The resulting epoxy-SiO 2 nanocomposites have improved thermal stability compared with pure epoxy, while the complex permittivity does not show significant deviation from that of pure epoxy. The presence of SiO 2 as more mobile chains causes a softening effect on the surrounding polymer, resulting in a lower glass transition and a delay in the dielectric relaxation. On the other hand, when the SiO 2 is present as a cross-linked network, it results in an increased rigidity of the surrounding polymer and an associated increase in the glass transition temperature and earlier onset of the dielectric relaxation. These findings show the influence of the inorganic filler morphology and structure on the properties of the final nanocomposite material.