Dielectric characterisation of epoxy nanocomposite with barium titanate fillers

: High permittivity materials are currently in use for mitigation of electrical stress in high-voltage apparatus and energy storage systems. In this work, epoxy-based high permittivity nanocomposites with Barium titanate (BaTiO 3 ) nanofillers are considered, for the purpose of stress mitigation. Uniform dispersion of the fillers in the polymer up to 10% by volume is achieved. Apart from the use of as-received fillers, the effect of using surface-functionalised nanoparticles (with 3-glycidoxypropyltrimethoxy-silane) before use is also investigated. The nanocomposite is characterised in terms of its complex permittivity, DC conductivity, short-term AC breakdown strength and space charge accumulation, to gauge its suitability for use in high-voltage insulation. Complex permittivity is measured using broadband dielectric spectroscopy over a broad frequency range of 1 mHz to 1 MHz. DC conductivity is studied from polarisation–depolarisation current measurements. Short-term AC breakdown strength tests are performed at power frequency (50 Hz). Space charge density along the sample thickness is obtained using pulsed electro-acoustic technique. A computational case-study is presented to show the feasibility of using the high permittivity nanocomposite for electric stress control in high-voltage equipment (viz., at mounting flanges of 69 kV bushings).


Introduction
Polymer nanocomposites with a high dielectric constant have potential applications in energy storage systems and in grading or relieving stress in high-voltage electrical insulation [1][2][3][4][5][6]. For electric stress mitigation, high permittivity materials find use at the mounting flanges of transformers [2], high-voltage cable terminations [3] and high-voltage motor and generator coils [5]. In this work, we fabricate and characterise epoxy-based nanocomposites with improved dielectric constant for use in stress control in high-voltage insulation.
Erstwhile research has reported significant improvement in properties like resistance to surface degradation, tree growth, dielectric breakdown strength, space charge accumulation, tracking and erosion resistance and DC conductivity, on adding even small amounts of nanofillers to polymer dielectrics [7][8][9][10][11]. However, improvement in complex permittivity does not usually happen. In fact, addition of very small amounts (<1% by volume) of nanofillers viz., Al 2 O 3 , TiO 2 , SiO 2 , MgO and ZnO into the polymer matrix has shown a reduction in composite permittivity [7][8][9]. However, enhancement in the complex permittivity of polymeric dielectrics is reportedly achievable with the addition of nanofillers with high permittivity (e.g. BaTiO 3 ) [1,4,11].
Polymeric materials stressed under high DC field accumulate charge within the volume of material. Accumulated space charge causes local field intensification, leading to aging, and/or premature failure of insulation. A considerable body of literature on space charge behaviour of nanocomposites with various nanofillers, e.g. Al 2 O 3 , ZnO, SiO 2 , MgO, TiO 2 is available [7][8][9] but lacks consensus in understanding charge transport and trapping [7]. Reports are limited to composites with low filler loading (<2% by volume fraction) and is lacking in studies on BaTiO 3 -filled composites. Hence, understanding of space charge behaviour in this high permittivity nanocomposite is crucial, which is done in this paper. Other than the space charge characteristics, the fabricated barium titanate (BaTiO 3 or BT) nanocomposite is characterised in terms of complex permittivity, conductivity and breakdown strength which are crucial properties of a dielectric material. A study of the effect of BT filler loading and surface functionalisation of BT particles before incorporation into the nanocomposite is also done. Moreover, a theoretical case study is also undertaken to evaluate the efficacy of high permittivity nanocomposite in mitigating local electric stress.

Functionalisation of nanoparticles
In order to achieve uniform dispersion of nanoparticles in the epoxy matrix, a protocol is established for surface functionalisation of the particles with silane. Hydrogen peroxide (H 2 O 2 ) treatment of the particles is necessary to improve the reactivity of the BaTiO 3 (BT) particles. 2 g of as-received BT powder is taken and 5 mL of H 2 O 2 added to it. The mixture is sonicated for 30 min at room  The optimum amount of GPS for surface functionalisation of BaTiO 3 nanoparticle is calculated based on criteria discussed in [12]. Accordingly, 1.937 g of hydrolysed BT particles are added to 5 mL of toluene and sonicated for 30 min at room temperature. 30 mL toluene is added to 0.457 mL silane and sonicated for 30 min. The particle solution is added to the GPS solution and stirred at 100°C for 24 h in a nitrogen environment. The functionalised nanoparticles are washed in toluene as before and vacuum-dried.
Fourier transform infra-red (FTIR) spectra of as-received and surface-functionalised BT nanopowder are shown in Fig. 2. The appearance of a new peak at 1099.33 cm −1 , after functionalisation, signifies the presence of Si-OH, Si-O-Si and Si-O-Ti bonds [11]. The peak at 1458.40 cm −1 is related to the bending vibration of -OCH 3 in silane. The appearance of these two new peaks indicates that the BT nanofillers have been successfully modified with silane, through covalent bonding between silane (GPS) with barium titanate (BaTiO 3 ) nanoparticle.

Preparation of nanocomposite specimens
As-received and surface-functionalised nanofillers are taken in required amounts (determined by the desired filler loading) and dispersed in toluene using an ultrasonic processor for 2 h. After the addition of epoxy resin to the solvent, sonication is required for another 2 h. The solution is magnetically stirred for 48 h at 1000 rpm and simultaneously heated to 60°C. The solution is then mixed with the curing agent for 3-4 min, and the mixture is poured into glass moulds lined with thin mylar sheets. The sample thickness is of the order of 250-300 µm. The specimens are dried in an oven at 60°C for 3 h, followed by post-curing at a temperature of 150°C for 3 h in a vacuum.
Field emission scanning electron microscopy (FESEM) is used to confirm that the nanofillers are uniformly dispersed in the polymer matrix. Typical FESEM images of nanocomposites with a filler loading of 10% by volume with as-received and surfacefunctionalised BaTiO 3 particles are shown in Figs. 3a and b, respectively. Nanocomposites with surface-functionalised particles are observed to be more uniformly distributed in the specimen with surface-functionalised particles (shown in Fig. 3b).

Permittivity
Alpha-A frequency response analyser (Novocontrol Technologies, GmbH & Co., Germany) is used to measure the complex permittivity [13]. The sample used is a circular specimen, 250-300 µm thick, of 30 mm diameter. Measurements are made at frequencies from 10 −3 to 10 +6 Hz, at 25°C and 50% relative humidity (RH) with an applied voltage of 1 V rms . The test specimens are placed between gold-plated brass electrodes of 20 mm diameter for measurement. All samples are pre-conditioned for 48 h at 100°C in a vacuum oven before measurement.

DC conductivity
DC conductivity is measured using an electrometer (Keithley 6517B, an accuracy of ∼10 −14 A). The three-electrode system as per ASTM D 257-14 is used [14]. A high-voltage DC source (0-30 kV, Glassmann High Voltage Inc. Japan) is used to energise the test specimen. Aluminum foils (65 µm thickness), are pasted on both sides of the specimen to eliminate air gaps. The test specimen is polarised for 3 h and depolarised for 2 h. The polarisation time was chosen such that all polarisation processes including the slow processes are complete and the current attains a steady value. Similarly, the depolarisation time was chosen such that the current becomes almost zero. At steady state, the conduction current I c (t) is calculated from where I p (t) and I d (t) are polarisation and depolarisation currents at time t after switch on or switch off, respectively. The DC conductivity (σ dc ) is calculated from where d, I c , A and V are specimen thickness, steady-state conduction current, effective electrode area and applied DC voltage.

Space charge density
Space charge measurements are carried out using a pulsed electroacoustic (PEA) system supplied by TechImp Italy. The working principle of the PEA system for a flat specimen is discussed elsewhere [15]. When a dielectric material is subjected to a uniform DC field, space charge accumulates in the volume through either injection at the interface or internal generation processes. Above a certain critical field, the current-field relation is no longer linear and begins to be dominated by the space charge accumulated in the bulk of the material (space charge limited current). The electric field at which this transition occurs is regarded as the threshold electric field for space charge accumulation. This can be estimated through different techniques viz., conduction current measurements, space charge mapping and electroluminescence measurements [16]. In this work, the threshold electric field for space charge accumulation of various samples is measured by conduction current method [17].
Before starting new measurements, the test specimen is grounded for 10,000 s to completely deplete any residual space charge. The test specimen is placed between two electrodes and energised with DC voltage such that the applied field is above the threshold electric field for space charge accumulation. An electric pulse of short duration is applied to the test specimen via a decoupling capacitor. This perturbs the charge, resulting in the generation of an acoustic wave at the space charge location. Acoustic waves travel through the test specimen and earth electrode. A piezoelectric sensor placed at the earth electrode converts the acoustic wave into an electrical signal. The amplitude of this signal is proportional to the space charge density of the test specimen. To obtain the space charge profile, a deconvolution technique is necessary. A calibration process is adopted to map the corresponding voltage signal at the oscilloscope to a spatial map of the space charge within the specimen. The calibration is based on a known charge distribution at the earth electrode. The deconvolution and calibration procedures are discussed in detail elsewhere [18][19][20][21].
For calibration and deconvolution, prior knowledge of the acoustic impedance of the test specimen is required. The acoustic velocities in neat epoxy and its nanocomposites are measured using the Panametrics (35 DL) ultrasonic precision thickness gauge (OLYMPUS). The acoustic impedance 'Z' (kg/m 2 s) of a material is calculated as where δ and υ are mass density (kg/m 3 ) of the material and speed of sound (m/s) in the material medium, respectively [18]. The acoustic impedances of epoxy and its nanocomposites are seen to be close. A marginal increase in acoustic impedance with filler concentration is seen in Table 1.
Both epoxy and its nanocomposite samples are polarised for 10,000 s and depolarised for 4000 s. The polarisation time (10,000 s) is chosen such that all polarisation processes including the slow processes are complete. Similarly, the depolarisation time (4000 s) is chosen such that the current becomes almost zero. While this is adequate for nanocomposites with low filler loadings (up to 2 vol. %), longer depolarisation times (at least 72 h) are required at 5 and 10 vol. %.
The mean magnitude of the accumulated volume charge density in the sample at time t of depolarisation, q(t;E p ), is calculated by using the following expression [21] q(t; E p ) = 1 where E p and L represent polarisation field and specimen thickness, respectively. The space charge measurement of epoxy and its nanocomposites are performed at a field of 20 kV/mm.

Short-term AC dielectric strength
The electrode assembly as per ASTM-D149 is used for short-term dielectric breakdown strength measurements [22]. The electrodes are made of brass. The test specimen and the electrode assembly are immersed in transformer oil during the test to avoid surface flashover. More than 20 samples are chosen from each batch of neat epoxy and its nanocomposites. Measurements are made at room temperature (25°C) and RH of 40-45%. Weibull distributions are used to characterise the breakdown data. The cumulative failure probability P(E), is expressed as where E, α and β are breakdown field, scale parameter and shape parameter, respectively. α and β values are positive and finite. The parameter α is denoted as the nominal field strength corresponding to a failure probability of 63.2% and the parameter β is a measure of the spread of the data.

Permittivity
The real and imaginary components of complex permittivity of epoxy and its nanocomposites (prepared from as-received BaTiO 3 fillers) are shown in Fig. 4. It is seen that complex permittivity (both real and imaginary components) increases with filler loading. The increase is significant beyond 2 vol. % as shown in Fig. 4. A similar increase with filler loading has been reported in the literature [1,4,11].
In nanocomposites with 1 vol. % loading, nanofillers are welldispersed when prepared with as-received fillers. Hence, there is no significant difference observed in real and imaginary relative permittivity of composites prepared with as-received and surfacefunctionalised nanofillers. However, in the case of nanocomposites with as-received nanofillers, at higher loadings viz., 5 and 10 vol. %, nanofillers tend to agglomerate. Improvement of dispersion is achieved by using surface-functionalised nanofillers. This manifests in a significant difference in the real relative permittivity of nanocomposites with as-received and surface-functionalised fillers at a filler loading of 5 vol. %, and above as shown in Fig. 5a.
Surface-functionalising the particles before use results in a greater increase in the real permittivity of the nanocomposites (Fig. 5a). At higher filler loadings viz., 5 and 10 vol. %, the imaginary relative permittivity of the nanocomposites shows a shift in the peak frequency and a change in peak shape as we go from an as-received nanocomposite to a surface-functionalised one (shown in Fig. 5b). This may be attributed to better uniformity of dispersion (and consequently, greater interfacial volume) and/or better bonding of particle to matrix. Existing literature is divided on the effect of incorporation of fillers on the composite permittivity. Addition of fractional wt. % of nanofillers viz., SiO 2, TiO 2 into polyvinyl chloride (PVC), was reported to show a reduction in relative permittivity [23,24]. However, significant improvement in permittivity of nanocomposites were observed with functionalised nanoparticles at higher filler loading. Maity et al. [25] found that incorporation of 1 vol. % of alumina (Al 2 O 3 ) nanofillers (with relative permittivity ≃ 10) in an epoxy, yields a composite which has a relative permittivity less than that of the base epoxy.
More importantly, several groups have documented [7,25] that the conventional mixing rules (viz., Lichtenker formula, Wiener's bound, Maxwell-Garnett equations) which have traditionally been applied to polymer composites do not necessarily provide meaningful results when used in nanocomposites. This anomaly has led researchers to believe that the nanocomposite is a three component material with the third component being the interphase/ interface/interfacial region around each nanoparticle. The interface may have properties (e.g. relative permittivity) which are different from the properties of polymer and nanofillers and significantly influence the overall properties of nanocomposites.

DC conductivity
The typical polarisation and depolarisation currents in neat epoxy resin at an electric field of 2 kV/mm are shown in Fig. 6. Similarly, measurements are repeated for nanocomposites with different filler concentrations (1 to 10 vol. %). Measurements are conducted with applied electric fields of 1-5 kV/mm to study the field-dependent DC Conductivity. Field-dependent DC conductivity of neat epoxy and its nanocomposites prepared with as-received BaTiO 3 fillers at different filler concentrations is shown in Fig. 7. It is seen that up to a filler loading of 2 vol. %, addition of nanofillers reduces DC conductivity. A decrease in conductivity was similarly observed in the epoxy filled with Al 2 O 3 nanofillers (up to 1 vol. %) by Pandey and Gupta [26]. Several groups have studied [7] the mechanism of DC conductivity of polymeric materials like LDPE, EP, PVC, filled with different nanofillers viz., TiO 2 , SiO 2 , ZnO and observed a reduction in DC conductivity due to addition of nanofillers. On an   increase in filler concentrations to 5 vol. % and higher, conductivity increase beyond that of neat epoxy (shown in Fig. 7). The significant increase in conductivity at higher filler loading may be attributed to percolation. If we assume that there is an interfacial region with conductivity higher than the base matrix around each nanoparticle [7,8], then in highly filled nanocomposites (i.e. 5 and 10 vol. %), there are a large number of overlapping interfaces through which a continuous path might be obtainable for easy movement of charges (shown in Fig. 8).
Usage of surface-functionalised fillers results in a smaller increase in conductivity, especially at high loading. In composites with surface-functionalised fillers, better uniformity in dispersion possibly reduces the area of overlap and therefore limits the increase in conductivity with filler loading as shown in Fig. 9.

Estimation of threshold electric field for space charge accumulation:
Space charge threshold characteristics for neat epoxy and its nanocomposites (1 vol. %) are shown in Fig. 10. The threshold electric field for epoxy and its nanocomposites are found to be 18 and 16 kV/mm, respectively. The estimated threshold fields for nanocomposites with different filler loadings are listed in Table 2.
It is seen that the threshold electric field decreases with increase in filler concentration. This fact may be explained as follows. During synthesis of the nanocomposites, some physical and chemical defects might be introduced in the weakly bonded regions of the interface around each nanoparticle, and these would encourage charge trapping thereby reducing the threshold electric field [27].

Space charge density
Space charge measurements on epoxy and its nanocomposites are performed at an electric field of 20 kV/mm (higher than the threshold electric field, to ensure space-charge accumulation). Fig. 11a shows the space charge profile of neat epoxy and its nanocomposites prepared with as-received BaTiO 3 nanofillers at 1 vol. % loading. It is seen that the accumulated space charge density in a nanocomposite with low filler loadings (viz., 1 vol. %) is lower than that in neat epoxy. The space charge accumulated near the electrodes is homopolar in nature as in epoxy. Reduction in space charge due to addition of nanofillers has been reported by other researchers [7]. Pandey and Gupta [26] observed that the space charge density in epoxy filled with 1 vol. % Al 2 O 3 nanofillers is less than in neat epoxy. Lower space charge density in nanocomposites is attributable to the lower charge injection at the electrodes and lower mobility of charge carriers within the volume.  For higher filler concentrations viz., 2-10 vol. %, the space charge density is higher than in neat epoxy, and increases with filler concentrations as shown in Fig. 11b. It is seen that the accumulated space charge is predominantly negative at both the electrodes.
During depolarisation, when the electric field is removed and electrodes are short-circuited, space charge is depleted. At higher filler loadings viz., 5 and 10 vol. %, depletion of charge accumulated may take considerably more time than at lower concentrations (approximately, 20 h for 5 vol. % and 72 h for 10 vol. % loading). This would indicate that the charges are trapped in deeper trap levels.
The space charge profiles of nanocomposites filled with both as-received and surface-functionalised nanofillers at different concentrations (2 and 10 vol. %) are shown in Fig. 12. At 2 vol. % loading, composites with surface-functionalised nanofillers show homopolar charges, whereas heterocharge is observed in composites with as-received filler (shown in Fig. 12). At higher loading viz., 5 and 10 vol. % space charge is predominantly negative at both the electrodes in nanocomposites (prepared with as-received and surface-functionalised fillers).
The average accumulated space charge density of epoxy and its nanocomposites (prepared with both as-received and surfacefunctionalised nanofillers) with different filler loadings are shown in Fig. 13. It is seen that average space charge density is lower in composites prepared with surface-functionalised nanofillers than with as-received. This may be attributed to local chain conformation at polymer-filler interfaces [7,8].
The charge polarity in the different nanocomposites might be explained in terms of its DC conductivity. In nanocomposites with lower filler loadings, DC conductivity is lower than in neat epoxy (shown in Figs. 7 and 9). Due to low mobility, injected charge is trapped close to the electrodes [26]. In highly filled nanocomposites (viz., 5 and 10 vol. %), DC conductivity is higher than in neat epoxy and the accumulated space charge is predominantly negative as shown in Figs. 11 and 12. Due to higher conductivity at higher filler loadings, charges do not accumulate before travelling to the opposite electrode, leading to negative charge accumulation [7].

Short-term AC dielectric strength
The Weibull probability distribution of the short-term AC dielectric strength data of epoxy and its nanocomposites with different filler concentrations is shown in Figs. 14a and b. Comparison of AC breakdown strength is made on the basis of filler loading and preprocessing of nanofillers. The scale and the shape parameters for neat epoxy and its nanocomposites prepared with as-received and pre-processed BaTiO 3 nanofillers are listed in Table 3.
It is seen that the addition of 1 vol. % of as-received BaTiO 3 nanofillers into neat epoxy reduces dielectric strength. Reduction in breakdown strength on an addition of nanofillers has earlier been reported in the literature [7,8,10]. This might be attributed to the local field intensification due to the difference in large permittivity contrast between BaTiO 3 nanoparticles, i.e. 150 and epoxy, i.e. 3.5, [28] at a frequency of 50 Hz. Such a reduction has also been reported with even a small disparity between the bulk and filler, e.g. Nelson et al. in epoxy-TiO 2 [7,8] and Patel et al. [10] in epoxy filled with Al 2 O 3 nanofillers. A further decrease in dielectric strength is observed when filler loading is increased to 2 vol. % and beyond. It is worth noting that the reduction in dielectric strength is mitigated by the use of surface-modified nanoparticles at the same filler concentration. A similar improvement in dielectric strength was observed by Abdel-Gawad et al. [23,24] in PVC-TiO 2 and PVC-SiO 2 nanocomposites with surface-modified particles. An increase in Weibull shape parameter β with surface functionalisation signifies greater predictability of the breakdown strength value. The shape parameter also increases with filler loading (up to 5 vol. %), signifying an improvement in homogeneity and reliability of composites when prepared with surface-functionalised nanofillers. This might be attributed to a better dispersion of nanoparticles on surface functionalisation.
The dielectric properties (viz., permittivity, DC conductivity, space charge density, and breakdown strength) of epoxy and its nanocomposites prepared with as-received and surfacefunctionalised BaTiO 3 nanofillers are summarised in Table 4.

Application of high permittivity dielectric material for electric stress control
In this section, we explore the feasibility of using epoxy-based BaTiO 3 nanocomposites to relieve electric stress in a composite bushing on the mounting flanges of transformer [2]. Fig. 15a shows the schematic diagram of a 69 kV bushing with a layer (10 mm thickness) of high permittivity material placed on the mounting flange. The bushing is modelled in COMSOL to obtain the electrostatic field distribution along the surface of bushing (shown in Fig. 15b). The dielectric constant of the epoxy-nanocomposite with 10 vol. % loading of BaTiO 3 nanofillers (surface-functionalised) measured at 50 Hz (obtained from the data in Fig. 5) is used in computation. It is seen that the addition of BaTiO 3 nanofillers can effectively result in a composite with high permittivity of 5.0.
The electric field is highest near the mounting flange. In Fig. 16, the solid line shows the variation of the electric field along the surface of the flange. The dotted line shows the corresponding stress profile when the nanocomposite is used instead. It is clearly seen that the stress in the critical region (first 40 mm from the ground flange) is relieved. At 25 cm, the high permittivity shield on the bushing ends (as shown in Fig. 15), due to which a discontinuity is seen in the electric field stress at this point. The field efficiency factor, which is a measure of the electric stress uniformity (defined as average electric field/maximum electric field), reduces from 55.14 to 32.05%.

Conclusions
The nanocomposite synthesised in this work shows improved permittivity, and at power frequency is theoretically shown to be employable in electric stress mitigation in regions of high local field enhancement in high-voltage insulation. The dielectric is also characterised in terms of other relevant properties. The modified dielectric properties of nanocomposites show that surfacefunctionalisation of nanofillers plays an important role in controlling the morphological structure of the surrounding polymer and improved particle dispersion in nanocomposites, thus influencing its dielectric properties to a certain extent.

Acknowledgment
The work was carried out with funds received from the Department of Science and Technology, Government of India, under Project no. SERB/EE/2015012.