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Journal of Electrostatics 86 (2017) 1e11

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Journal of Electrostatics

journal homepage: www.elsevier .com/locate/elstat

Correlating the breakdown strength with electric field analysis forpolyethylene/silica nanocomposites

K.Y. Lau a, *, M.A.M. Piah a, K.Y. Ching b

a Institute of High Voltage and High Current, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysiab School of Foundation, University of Reading Malaysia, 79200 Iskandar Puteri, Malaysia

a r t i c l e i n f o

Article history:Received 4 October 2016Received in revised form22 December 2016Accepted 30 December 2016Available online 4 January 2017

Keywords:NanocompositesInterphaseFinite element modelingElectric fieldBreakdown

* Corresponding author.E-mail address: kwanyiew@utm.my (K.Y. Lau).

http://dx.doi.org/10.1016/j.elstat.2016.12.0210304-3886/© 2017 Elsevier B.V. All rights reserved.

a b s t r a c t

The experimental findings on the DC and AC breakdown strength of polyethylene/silica nanocompositesare reported and correlated with simulation results on the electric field distribution of possible nano-composite models. Specifically, the effects of interphase permittivity and interparticle distances on theelectric field intensity and the breakdown strength are discussed with the aid of the Finite ElementMethod Magnetics (FEMM) 4.2 software. The results showed that the presence of the interphase, whenassigned a unique interphase permittivity value, led to variations in electric field distributions. Theelectric field also changed as adjacent nanoparticles separated from each other with different inter-particle distances.

© 2017 Elsevier B.V. All rights reserved.

1. Introduction

Polymer nanocomposites concern polymers with nanometer-sized fillers homogeneously dispersed at just a few weight per-centage (wt%). In the dielectrics community, the term “nanometricdielectrics” [1], “nanodielectrics” [2,3], or “dielectric polymernanocomposites” [4] has been introduced to refer to nano-composites of specific interest in connection with their dielectriccharacteristics. These materials have been envisioned to be thefuture of high voltage electrical insulation, and are capable ofenhancing the dielectric performance of conventional insulationsystemswhich commonly suffer from reduced breakdown strength[5e7]. This is attributed to the presence of the much smaller size ofthe filler (nanometer-sized filler), which subsequently leads to thepresence of an extensive interphase e an interaction zone betweenthe nanofiller and the polymer [8e12].

For anticipating the presence of the interphase in nanodi-electrics, two prominent interphase models have been proposed byLewis [8] and Tanaka et al. [9] in the early 2000s. Based on Lewis'diffuse electrical double layer model [1,8,10], a Stern layer and aGouy-Chapman diffuse double layer were assumed to exist at the

interface between the filler and the polymer. The formation of theselayers was thought to change the internal charge activity and theresulting electrical potential distribution at the interphase, whichcould then influence the dielectric properties of the resultingnanodielectrics. The multi-core model proposed by Tanaka et al.[9,11], on the other hand, assumed the presence of four layers, i.e.,the bonded layer, the bound layer, the loose layer, and the Gouy-Chapman diffuse layer, within the interphase. Through the multi-core model, the interphase of a nanoparticle was permitted tooverlap with the interphase of its neighboring nanoparticle, thuscausing a far-field effect which results in a cooperative effect be-tween the nanoparticles.

In addition, many other interphase models have been proposedin an attempt to explain the phenomena at the interphase thatinfluence the dielectric behaviors of nanocomposites. For example,the multi-region structure model, the dual layer model, and thepolymer chain alignment model were suggested by Li et al. [12],Singha and Thomas [13], and Andritsch [14], respectively, byassuming that nanoparticle/polymer interactions led to the for-mation of two interphase layers around the nanoparticle. Thepresence of a single interphase layer was also proposed by Raetzkeet al. [15] and Daily et al. [16] in an attempt to clarify the electricalproperties of nanocomposites based on the distinct features at theinterphase.

Although various nanocomposite systems have been

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investigated and positive experimental results on the breakdownstrength of nanocomposites have been reported [17e20], there aremany fundamental challenges yet to be addressed for the use ofnanocomposites as electrical insulating materials [21,22]. Forexample, the experimental work of Huang et al. [23] revealed thatthe breakdown performance of polyethylene/aluminum nano-composites was not as good as the base polymer, even thoughsurface-treated nanoparticles were introduced. Also, the electricalbreakdown performance of polymers was found to be adverselyaffected by the presence of large aggregates of nanofillers [24].Although chemical means such as silane coupling agents andcompatibilizers can be used to improve the interfacial adhesionbetween the nanofiller and the polymer [23,25], the use of differentsilane coupling agents may result in entirely different dielectricbehaviors, a consequence which is closely associated with pro-cesses at the interphase. This shows that the incorporation ofnanoparticles does not always improve the breakdown strengthand that there might be subtle unidentified factors that jeopardizethe breakdown performance due to nanoinclusions.

Nevertheless, breakdown performances of polymer nano-composites have been reported to be much better than theirequivalent microcomposites [12,17]. In this regard, the size of thefiller e or the presence of the interphase e was found to criticallyinfluence the breakdown strength, where microcomposites tendedto fail at far lower applied fields as compared with nanocompositesor unfilled polymers [26]. Consequently, the relative improvementof electrical breakdown properties of nanocomposites could beresulted from a more uniform electric field distribution within thinfilms [8].

According to Wang et al. [27], finite element simulations canprovide a statistical view of the local electric field distributionwithin nanocomposites. When high dielectric constant fillers areused, the polymermatrixmay sustainmost of the electrical stressethe locally enhanced field can be linked to the electrical breakdownstrength for a short term breakdown process. Significantly, theoverall permittivity of a composite material is often related to thecompatibility of its constituents, hence electrical performance ofthe composite [28]. In oil-pressboard insulation, for example,permittivity mismatches between the two materials usually assistsflashover phenomenon at the interface [29]. This is due to the non-uniform electric field distribution results from the permittivitymismatches. This raises the electrical stress andmay act as a criticalflaw in dielectric breakdown [30]. By reducing the mismatch indielectric constant at the matrix-filler interface, the buildup of fieldconcentrations responsible for the premature breakdown eventscould be mitigated.

According to conventional mixing rules, the addition of fillersinto polymers should result in an overall permittivity according tothe constituents (fillers and polymers) with a value between theconstituents [31e33]. Nevertheless, the presence of interphases innanocomposites has resulted in a seemingly new concept ofpermittivity that defies conventional mixing rules. According toFrech�ette et al. [21] and Andritsch et al. [34], the permittivity ofnanocomposites can increase or decrease remarkably, out of thepermittivity range of the constituents, depending on the nanofiller/polymer combinations and processing methods. Considering theeffect of the interphase, the mixing rules may be generalized tohave an additional term representing the interphase [33e37].Consequently, if the volume fraction and the permittivity of theinterphase dominate, the overall permittivity will reflect thepermittivity of the interphase rather than a simple binary combi-nation of permittivity of the filler and the polymer, as in conven-tional microcomposites. This observation is not unusual and hasbeen anticipated by Lau et al. [38], where water molecules mayreside within the interphase of a nanocomposite, resulting in

higher overall permittivity of the nanocomposite due to the pres-ence of more polar dipoles (i.e. hydroxyl groups) from the waterthat can readily respond to the applied field.

Since the breakdown characteristics of an insulating materialdepends on its resistance against voltage or electric field [39], theanalysis of the electric field intensity within the insulating materialis important to understand the material's breakdown performance[40]. In this paper, we seek to correlate the experimental findingson the breakdown strength of polyethylene/silica nanocompositeswith the simulation results on the electric field distribution of ourproposed nanocomposite models. Specifically, the effects of inter-phase permittivity and interparticle distances on the electric fieldintensity and the possible breakdown strength are discussed withthe aid of the Finite Element Method Magnetics (FEMM) 4.2software.

2. Experimental

2.1. Materials and sample preparation

The polymers used in the experimental work were the lowdensity polyethylene (LDPE) grade Titanlene LDF200YZ and thehigh density polyethylene (HDPE) grade Titanzex HI2000, obtainedfrom Lotte Chemical Titan. The nanofiller used was silicon dioxide(SiO2) nanopowder (nanosilica) obtained from NanoAmor, with anaverage particle size of 80 nm.

Nanocomposite samples were prepared using a mechanicalmixing method. The desired amount of nanosilica (1 wt%, 3 wt%,and 5 wt%) was mixed with polyethylene (LDPE or HDPE) in alaboratory two-roll mill at a temperature of ~140 �C for ~30 min.Samples for breakdown measurements were then prepared using ahydraulic press at a temperature of ~160 �C. The thickness of theprepared samples was ~100 mm.

2.2. Characterization

Breakdown testing was conducted by placing a test samplebetween two opposing 6.35 mm diameter steel ball-bearing elec-trodes immersed in Hyrax Hypertrans transformer oil to preventsurface flashover. A DC voltagewith a step voltage of 2 kV every 20 sor an AC voltage with a step voltage of 1 kV every 20 s was applieduntil the sample failed. Six breakdown tests were performed oneach type of material. The voltage obtained from each measure-ment was divided by the specimen thickness at the breakdownpoint in order to obtain the breakdown field. The resulting dielec-tric breakdown data were statistically analyzed assuming two-parameter Weibull statistics [41]; the cumulative probability offailure was approximated using the median rank method [42].

3. Modeling in FEMM 4.2

The electrostatics module in FEMM 4.2 was used for electricfield analysis purposes; the use of electrostatic analysis is commonin simulating electric field distribution such as those related to highvoltage research [43,44], electromagnetics [45], materials science[46], experimental and particle physics [47,48], and medicine [49].The mesh size parameter, which defines a constraint on the largestpossible elements size allowed in the associated section, was cho-sen to be 0.001; this led to more than 1,000,000 nodes and2,000,000 elements generated. This allowed the mesh generator inFEMM 4.2 to fill the region with nearly equilateral triangles inwhich the sides were approximately the same length as the spec-ified mesh size parameter. Meanwhile, the solver precision used todetermine the single precision accuracy was set at 10�8. Never-theless, as with many other finite element methods, the boundaries

K.Y. Lau et al. / Journal of Electrostatics 86 (2017) 1e11 3

for different materials with different values for permittivity couldnot be competently resolved using FEMM 4.2, thus resulting indiscontinuities along the boundaries; solving these boundaryconditions was not of our main interest here, but it can be pursuedelsewhere in the literature [50e54].

Several assumptions were made for simulation purposes, suchas: i) the particle was spherical in size and it was enclosed in aninterphase of a constant thickness, ii) the particle distributionwithin the polyethylene was homogeneous, iii) the particle inter-acted strongly with the polymer, iv) the electric field intensity wasmainly affected by the variation in permittivity, and v) the electricfield intensity was not significantly affected by temperature orspace charge effects.

3.1. Nanocomposite models

In the current work, we propose a two-dimensional unit cellmodel based upon a polymer and a spherical nanoparticle with asurrounding interphase layer of discrete thickness that waspermitted to overlap with neighboring interphase layers. For this,three unique phases were assumed to exist within the nano-composites: the polymer, the nanoparticle, and the single-layerinterphase. The model (1 mm � 1 mm) was placed between a highvoltage electrode (þ200 V) and a ground electrode, as shown inFig. 1.

The nanocomposite models were based upon polyethylene asthe polymer and silicon dioxide as the nanoparticle (nanosilica),with assumed permittivity values of 2.3 and 3.9, respectively[38,55,56]. In all models, the size of each nanoparticle was assumed80 nm in diameter; this would somehow match the nanosilica'saverage particle size used in the experimental work. Since mostinterphase layers were assumed to have a thickness of several tenthnm [9,11,16,57], an interphase thickness of 40 nm (half the diameterof the nanoparticle) was assumed in our case. As the nanoparticlesize and the interphase thickness were fixed, changes in themodelswere determined by varying the permittivity values within theinterphase and the separation distance between neighboringnanoparticles (to determine the overlapping effect of theinterphase).

Table 1 summarizes the nanocomposite models used in theanalysis of electric field distribution. Polymer Model was used forreference purposes. The permittivity of the unfilled polymer wasfixed at ε1 ¼ 2.3 to resemble unfilled polyethylene; since no

Fig. 1. Two dimensional unit cell model (1 mm � 1 mm) of a nanocomposite composedof a polymer, a nanoparticle, and an interphase, placed between a high voltage elec-trode and a ground electrode.

nanoparticle was added, the permittivity values for the nano-particle and the interphase were not considered. For Nano Model I(see Fig. 2a), the interfacial effect of a single nanoparticle within apolymer was considered. Since our main focus was on the effect ofnanosilica, the permittivity of the nanoparticlewas fixed at ε2¼ 3.9;the permittivity of the unfilled polymer was fixed at ε1 ¼ 2.3.Meanwhile, the permittivity of the interphase was varied, withvalues of ε3 ¼ 1.5, 3.9, or 9.0. These chosen interphase permittivityvalues would take into account the possibilities that the interphasepermittivity is lower than that of the polymer and the nanoparticle,intermediate between that of the polymer and the nanoparticle, orhigher than that of the polymer and the nanoparticle.

According to the literature [9,15,16], when the nanofiller loadinglevel is relatively high, the interphases of adjacent nanoparticles arelikely to overlap, and vice versa. Therefore, NanoModels II, III, IV, V,and VI were proposed to represent various overlapping phenomenaof the interphase. For this, the interparticle distance, measuredfrom the surface of a nanoparticle to the surface of its adjacentnanoparticle, was varied. For Nano Model II and Nano Model III,adjacent nanoparticles with 0 nm (see Fig. 2b) and 40 nm (seeFig. 2c) interparticle distances were considered for representing theoverlapping interphase effects. For Nano Model IV, V, and VI,adjacent nanoparticles with 80 nm (see Fig. 2d), 120 nm (seeFig. 2e), and 240 nm (see Fig. 2f) interparticle distances wereconsidered for representing the non-overlapping interphase ef-fects. Of note, the nanoparticle and the interphase for Nano ModelII, III, IV, V, and VI were assumed similar with Nano Model I.

Lastly, Particle Size Model was introduced to determine the ef-fect of particle size distribution on the electric field distribution. Forthis, about 10% and 90% particle under-sizing was considered e theelectric field distribution for nanoparticles with 70 nm and 10 nmdiameters was analyzed and compared with that of the 80 nmdiameter. In these, the thickness of the interphase was, again,assumed half the diameter of the nanoparticle. The permittivityvalues for the polymer, nanoparticle, and interphase were fixed at2.3, 3.9, and 3.0, respectively.

Fig. 3a shows an illustrating example of the analyzed electricfield intensity in Nano Model 1. The field distribution of theanalyzed area represents the case where the permittivity of theinterphase became different from the permittivity of the polymerand the nanoparticle. The y-line and the x-line in Fig. 3a showwhere the electric field intensity datawere taken from each case forcomparison purposes. Meanwhile, Fig. 3b illustrates how theinterparticle distance between adjacent nanoparticles wasmodeled, with analyzed electric field intensity. The colors repre-senting varying electric field intensities across a sample are shownin Fig. 3c.

4. Results

4.1. Experimental breakdown strength

4.1.1. DC breakdown strengthFig. 4a compares Weibull plots of DC breakdown strength for

LDPE containing 0 wt%, 1 wt%, 3 wt%, and 5 wt% of nanosilica. TheDC breakdown strength of the unfilled LDPE was 240 kV/mm. TheDC breakdown strength of LDPE containing 1 wt% of nanosilicareduced to 131 kV/mm. As the amount of nanosilica increased from1 wt% to 3 wt%, the DC breakdown strength increased slightly to150 kV/mm. Nevertheless, considering the uncertainties in Weibullanalysis, the slight variation of the DC breakdown strength for LDPEcontaining 1 wt% and 3 wt% of nanosilica is negligible. Meanwhile,the DC breakdown strength of LDPE containing 5 wt% of nanosilicawas the lowest among all, i.e., 103 kV/mm. To confirm the behaviorof polyethylene on the addition of nanosilica, another batch of

Table 1Models and parameters.

Model Permittivity Remarks

Polymer, ε1 Nanoparticle, ε2 Interphase, ε3

Polymer Model Fixed: 2.3 e e No nanoparticleNano Model I Fixed: 2.3 Fixed: 3.9 Varied: 1.5, 3.0, or 9.0 Single nanoparticleNano Model II Fixed: 2.3 Fixed: 3.9 Varied: 1.5, 3.0, or 9.0 Interparticle distance: 0 nm

(overlapped interphase)Nano Model III Fixed: 2.3 Fixed: 3.9 Varied: 1.5, 3.0, or 9.0 Interparticle distance: 40 nm

(overlapped interphase)Nano Model IV Fixed: 2.3 Fixed: 3.9 Varied: 1.5, 3.0, or 9.0 Interparticle distance: 80 nm

(non-overlapped interphase)Nano Model V Fixed: 2.3 Fixed: 3.9 Varied: 1.5, 3.0, or 9.0 Interparticle distance: 120 nm

(non-overlapped interphase)Nano Model VI Fixed: 2.3 Fixed: 3.9 Varied: 1.5, 3.0, or 9.0 Interparticle distance: 240 nm

(non-overlapped interphase)Particle Size Model Fixed: 2.3 Fixed: 3.9 Fixed: 3.0 Single nanoparticle with varied sizes: 80 nm, 70 nm, or 10 nm

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material systems was investigated, where HDPE was used in placeof LDPE, and a similar breakdown trend was observed (see Fig. 4b).

4.1.2. AC breakdown strengthFig. 5a compares Weibull plots of AC breakdown strength for

LDPE containing 0 wt%, 1 wt%, 3 wt%, and 5 wt% of nanosilica. TheAC breakdown strength of the unfilled LDPE was 148 kV/mm. TheAC breakdown strength of LDPE containing 1 wt% of nanosilica was129 kV/mm. As the amount of nanosilica increased from 1 wt% to3 wt%, the DC breakdown strength decreased slightly to 125 kV/mm. Nevertheless, considering the uncertainties in Weibull anal-ysis, the variation of the AC breakdown strength for LDPE con-taining 0 wt%, 1 wt%, and 3 wt% of nanosilica is negligibly small.Meanwhile, the AC breakdown strength of LDPE containing 5 wt%of nanosilica was the lowest among all, i.e., 105 kV/mm. Again,HDPE was used in place of LDPE to confirm the AC breakdownbehavior of polyethylene on the addition of nanosilica, and a similarbreakdown trend was observed (see Fig. 5b).

4.2. Electric field analysis

Fig. 6 shows plots of the electric field intensity along the y-lineand the x-line, from the center of origin of the nanoparticle,extending towards the polymer region. The electric field was foundto be homogeneously distributed in the unfilled polymer (PolymerModel). The electric field intensity of the unfilled polymer wasfound to remain constant at 200 kV/mm irrespective of permittivityvalues (see the plot for “Unfilled” in Fig. 6).

With the addition of a nanoparticle without interphase having apermittivity value of ε2 ¼ 3.9, higher than that of the polymer, theelectric field intensity within the nanoparticle became lower(149 kV/mm) than that in the polymer region (see the plot for “NoInterphase” in Fig. 6b). However, the electric field intensityimmediately adjacent to the surface of the nanoparticle (along they-line) increased significantly up to 251 kV/mm. Further away fromthe nanoparticle's surface, the electric field intensity resumedslowly to that of the polymer. Meanwhile, the electric field intensityfor the regions along the x-line showed an opposite effect (seeFig. 6c) e in a dielectric, an increase in electric field intensity at alocation is compensated by a decrease in electric field intensityelsewhere. Therefore, the electric field distribution was distorted.

When an interphase was assumed to surround a nanoparticle(Nano Model I), the electric field intensity within the interphaseand at regions immediately adjacent to the interphase along the y-line became every different from that without an interphase. Forthe case where the interphase permittivity was assumed to belowered (ε3 ¼ 1.5) than that of the nanoparticle (ε2 ¼ 3.9) and the

polymer (ε1 ¼ 2.3), high electric field intensity was recorded withinthe interphase (see the plot for “Interphase 1.5” in Fig. 6b). Theintensity reduced significantly at regions immediately adjacent tothe interphase, before resuming to the value exhibited by the un-filled polymer. Meanwhile, a higher permittivity value of theinterphase (ε3¼ 9.0) compared to that of the nanoparticle (ε2 ¼ 3.9)and the polymer (ε1 ¼ 2.3) resulted in an entirely opposite fieldeffect within the interphase and at regions immediately adjacent tothe interphase (compare the plots between “Interphase 9.0” and“Interphase 1.5” in Fig. 6b). If the interphase permittivity value liesbetween (ε3 ¼ 3.0) that of the nanoparticle (ε2 ¼ 3.9) and thepolymer (ε1 ¼ 2.3), the variation in electric field intensity across thenanoparticle region, the interphase region and the polymer regionappears to be less drastic (compare the plots for “Interphase 3.0”,“Interphase 9.0”, “Interphase 1.5” and “No Interphase” in Fig. 6b).Along the x-line, the effects of permittivity on the electric fieldintensity immediately adjacent to the surface of the nanoparticleare entirely opposite to that along the y-line (compare Fig. 6c withFig. 6b). For brevity, we will focus on the electric field intensityalong the y-line from this point onwards.

Fig. 7 shows the effects of electric field distribution within amodel nanocomposite containing two adjacent nanoparticlesseparated 0 nm apart (with overlapping interphases) (Nano ModelII). If the interphase permittivity became lower (1.5) than theconstituents' permittivity (ε1 ¼ 2.3 for the polymer and ε2 ¼ 3.9 forthe nanoparticle), the electric field intensity adjacent to the nano-particles' touching surface (see line A1 in Fig. 7b) and at the inter-phase (between lines B1 and C1 in Fig. 7b) increased significantlycompared to that of the unfilled polymer. Outwards from theinterphase (see line C1 onwards in Fig. 7b), the electric field in-tensity was slightly lower than the unfilled polymer case, butresumed to that of the polymer at distances further away from theinterphase. An entirely opposite trend to the situation discussedabove can be observed for the case of nanocomposites having aninterphase permittivity higher (ε3 ¼ 9.0) than the constituents'permittivity. Meanwhile, the electric field distribution for the caseof nanocomposites having interphase permittivity between thoseof the constituents (ε3 ¼ 3.0) seems to be less distorted whencompared with the aforementioned two cases. The trend seemscomparable to the case of nanocomposites having no interphase,albeit that the variation of electric field intensity at regionsimmediately adjacent to the nanoparticle surface is greater for thecase of nanocomposites having no interphase.

When two adjacent nanoparticles became 40 nm separatedapart (with overlapping interphases), as shown in Fig. 8 (NanoModel III), the electric field distortion within the overlappedinterphase (between lines A2 and B2 in Fig. 8b) became noticeable.

Fig. 2. Nano Model with the interphase effect of a single nanoparticle within a polymer was considered in (a), the overlapping interphase effects of adjacent nanoparticles wereconsidered in (b) and (c) for 0 nm and 40 nm interparticle distances respectively, and the non-overlapping interphase effects of adjacent nanoparticles were considered in (d), (e),and (f) for 80 nm, 120 nm, and 240 nm interparticle distances, respectively.

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Again, the lower (ε3 ¼ 1.5) or higher (ε3 ¼ 9.0) interphase permit-tivity as compared with the constituents' permittivity resulted inhighly distorted electric field intensity along the analyzed regions.Meanwhile, for the case of nanocomposites having interphasepermittivity between (ε3 ¼ 3.0) those of the constituents, theelectric field intensity seems to be less distorted when comparedwith the case of nanocomposites having no interphase, and the

electric field distribution within the interphase region (betweenlines A2 and B2 and between lines C2 and D2 in Fig. 8b) of thenanocomposite was somehow comparable with the unfilledpolymer.

Fig. 9a illustrates two adjacent nanoparticles that were sepa-rated 80 nm apart such that the interphases of the nanoparticlesdid not overlap, but touched each other (Nano Model IV). In this

Fig. 3. (a) Modeling of a nanocomposite with an interphase. The y-line and the x-line show how the electric field intensity data were taken for Nano Model I. (b) Modeling of ananocomposite with adjacent nanoparticles (with interphases) separated apart (interparticle distance). (c) Colors representing varying electric field intensities across a sample. (Forinterpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Weibull plots comparing the DC breakdown strength of (a) LDPE, (b) HDPE containing 0 wt%, 1 wt%, 3 wt%, and 5 wt% of nanosilica.

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case, the advantage of having an interphase with the permittivitybetween (ε3 ¼ 3.0) those of the constituents became moreapparent. Overall, the distortion of the electric field intensity for thecase of nanocomposites having interphase permittivity between(ε3 ¼ 3.0) those of the constituents was less than the case ofnanocomposites having no interphase and having interphasepermittivity lower (ε3 ¼ 1.5) and higher (ε3 ¼ 9.0) than those of theconstituents (see Fig. 9b).

Fig. 10 shows the effects of interphase permittivity as the adja-cent nanoparticles were separated further apart (120 nm), suchthat the interphases of the adjacent nanoparticles did not toucheach other (Nano Model V). For all investigated cases with

interphases, the distortion of the electric field intensity in thepolymer region adjacent to the nanoparticle surfaces (betweenlines B4 and C4 in Fig.10b) became great. The nanocomposite havinginterphase permittivity between (ε3¼ 3.0) those of the constituentsshowed a sudden increase of electric field intensity within the re-gion encompassing lines B4 and C4. Nevertheless, the electric fieldintensity was, again, somehow comparable with the case of nano-composite having no interphase.

Similar effects as discussed in Fig. 10 can be observed in Fig. 11for the case of adjacent nanoparticles separated further apart(240 nm; Nano Model VI). However, the distortion effects of theelectric field intensity in the polymer region adjacent to the

Fig. 5. Weibull plots comparing the AC breakdown strength of (a) LDPE, (b) HDPE containing 0 wt%, 1 wt%, 3 wt%, and 5 wt% of nanosilica.

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nanoparticle surfaces (between lines B5 and C5) became mitigatedas the separation distance between the adjacent particlesincreased. Again, the electric field distortion effects for the cases ofhaving no interphase and interphase permittivity between(ε3 ¼ 3.0) those of the constituents seem to be comparable, but themaximum value of the electric field intensity was higher for thecase of having no interphase.

Fig. 12 shows that the electric field distribution is dependentupon the size e and the interphase thickness e of the nanoparticle.The much smaller-sized nanoparticle (10 nm) showed quick,momentarily changes in electric field intensity when comparedwith those with larger diameter nanoparticles (70 nm and 80 nm).

5. Discussion

From the experimental results, the DC breakdown strength ofthe unfilled LDPE and HDPE was the highest in comparison withtheir nanofilled counterparts containing 1 wt%, 3 wt%, and 5 wt% ofnanosilica. For this, the addition of nanosilica into polyethylenereduced the DC breakdown strength of the polyethylene. Mean-while, the variation of AC breakdown strength for both the LDPEand HDPE containing 1 wt% and 3wt% of nanosilicawas found to beinsignificant in comparison with their unfilled counterparts. TheseDC and AC breakdown trends are not unusual and have also beenreported elsewhere for polyethylene blend samples added with0e10 wt% of nanosilica (10e20 nm size range) [58].

The simplest explanation for the reduced DC breakdownstrength can be to attributed the effect to nanoparticles agglom-eration, which seems to be more pronounced in DC than in AC, andmore sensitive to the nanofiller loading level. Nevertheless, anotherpossible explanation for the reduced DC breakdown strength is thatthe addition of nanosilica introduces permittivity mismatches thatcould enhance the electric field intensity e an effect that as wellseems to be more critical in DC field than in AC field. We will nowdiscuss the analysis of DC electric field in detail.

If the permittivity of a nanoparticle is higher than that of a

polymer, the electric field intensity surrounding the nanoparticlewill be distorted. This resembles the electric field distribution incommonly used polymers and nanoparticles as nanocomposites ein our case, polyethylene (ε1¼ 2.3) and nanosilica (ε2¼ 3.9). Clearly,adding nanoparticles into polymers results in distorted electricfield intensity within the material.

By assuming that an interphase is present around a nano-particle, and the interphase has a unique permittivity itself, theelectric field distribution within the interphase region would bevery different from that of the nanoparticle and the polymer.Significantly, our analysis suggests that the permittivity of theinterphase needs to lie between the permittivity of the constituentsfor mitigating electric field distortion effects. Although the electricfield distribution in these cases is nowhere as homogeneous as thecase of unfilled polymer, the electric field distortion effects can bemitigated as adjacent nanoparticles separated further away fromeach other. This may help in explaining improved DC breakdownperformance of nanocomposites having low nanofiller contents incomparison with nanocomposites having high nanofiller contentsas noticed in our breakdown experiments e as the nanofilleramount is reduced, the separation distance between adjacentnanoparticles becomes greater, and the electric field becomes lessdistorted, so the breakdown strength increases.

Alternatively, if the permittivity of the interphase is higher thanthe permittivity of the constituents, a large distortion of the electricfield would occur, and this would theoretically jeopardize thedielectric performance of the resulting nanocomposites. In reality,this phenomenon resembles the presence of water within theinterphase of nanocomposites, since the interphase can be apreferred location for the aggregation of water molecules. As watermolecules couple strongly with the applied field, changes in theirenvironment will be reflected in changes in the electric field in-tensity, particularly under DC fields. Since the nanosilica used inour experiment will inevitably contain surface hydroxyl groups,water tends to create bonding with the hydroxyl groups. Conse-quently, higher permittivity values may be noticed within the

Fig. 6. Effects of (a) nanoparticle (with interphase) on the plots of electric field in-tensity along the (b) y-line, (c) x-line, from the center of origin of the nanoparticle,extending towards the polymer region (Nano Model I).

Fig. 7. Effects of (a) adjacent nanoparticles separated 0 nm apart (with interphases) onthe plots of electric field intensity along the (b) y-line, from the center of origin of ananoparticle, extending towards the polymer region (Nano Model II).

Fig. 8. Effects of (a) adjacent nanoparticles separated 40 nm apart (with interphases)on the plots of electric field intensity along the (b) y-line, from the center of origin of ananoparticle, extending towards the polymer region (Nano Model III).

K.Y. Lau et al. / Journal of Electrostatics 86 (2017) 1e118

interphase, thus distorting the electric field distribution and sub-sequently reducing the breakdown strength of thenanocomposites.

It has been reported that the overall permittivity of a nano-composite could decrease remarkably, out of the permittivity rangeof its constituents [21,34]. In this case, the lowered overallpermittivity could be attributed to the lowered interphasepermittivity than the permittivity of the constituents. While low-ered permittivity values of the interphase is thought to enhance thebreakdown performance of a nanocomposite, our analysis showedotherwise e a large distortion of the electric field would occurunder this condition, and reduced breakdown performance couldbe expected.

In addition, our analysis also showed that, with the interphasemaintained to be half the diameter of the nanoparticle, muchsmaller sized nanoparticles would theoretically lead to less electricfield distortion when compared with larger sized nanoparticles.

Therefore, provided that nanoparticles could be homogenouslydispersed in nanocomposites and the interphase within nano-composites could be properly managed, the use of nanoparticleswith small diameters would seem to be preferable over their larger

Fig. 9. Effects of (a) adjacent nanoparticles separated 80 nm apart (with interphases)on the plots of electric field intensity along the (b) y-line, from the center of origin of ananoparticle, extending towards the polymer region (Nano Model IV).

Fig. 10. Effects of (a) adjacent nanoparticles separated 120 nm apart (with interphases)on the plots of electric field intensity along the (b) y-line, from the center of origin of ananoparticle, extending towards the polymer region (Nano Model V).

Fig. 11. Effects of (a) adjacent nanoparticles separated 240 nm apart (with interphases)on the plots of electric field intensity along the (b) y-line, from the center of origin of ananoparticle, extending towards the polymer region (Nano Model IV).

K.Y. Lau et al. / Journal of Electrostatics 86 (2017) 1e11 9

diameter counterparts.It is noteworthy that our discussion thus far is mainly for the

material's breakdown behavior under DC electric fields. This isbecause, under AC electric fields, the material's response may notbe able to keep up with changes in AC frequencies when taking into

account the phase lag between AC and material responses [59].Consequently, the AC breakdown behaviors are quite different fromthe DC breakdown behaviors, as noticed in our experiments. Tofurther understand these breakdown behaviors, polarization ef-fects upon nanoinclusions can be pursued elsewhere in the litera-ture [38,60,61].

6. Conclusions

The results from our current work show that the polyethylene/silica nanocomposites' breakdown behaviors are different under DCand AC applied fields. The addition of an increasing amount ofnanosilica into the LDPE and the HDPE progressively reduces the DCbreakdown strength of the polyethylenes; such an effect is notapparent under AC applied fields. While the simplest explanation isto attribute the effect to nanoparticle agglomeration, which seemsto be more pronounced in DC than in AC, we seek to clarify the DCeffect based upon the concept of permittivity mismatch betweenthe nanofiller and the polymer. Our analysis shows that, if thepermittivity of a nanoparticle is higher than that of a polymer, theelectric field intensity is nowhere as homogeneous as the case ofthe unfilled polymer, and this may subsequently lead to reducedbreakdown strength. Meanwhile, the presence of the interphase,when assigned a unique interphase permittivity value betweenthose of the constituents, results in less distorted electric fielddistribution in comparison with the cases of nanocomposites hav-ing interphase permittivity lower or higher than the constituents'permittivity. Also, the electric field distortion effects can be miti-gated as adjacent nanoparticles separated far away from each other,a phenomenon commonly associated with nanocomposites con-taining a lower amount of nanoparticles, thus improving thebreakdown performance. It is noteworthy that our current analysisonly considers the effects of a single particle or adjacent particles inour attempt to relate the electric field distribution of our proposednanocomposite models with the observed experimental

Fig. 12. Effects of (a) nanoparticle size distribution (with interphase) on the plots ofelectric field intensity along the (b) y-line, from the center of origin of a nanoparticle,extending towards the polymer region (Nano Model VII).

K.Y. Lau et al. / Journal of Electrostatics 86 (2017) 1e1110

breakdown strength. As such, our analysis falls short of providing acomprehensive understanding on the electric field effects within apractical bulk nanocomposite system. Of note, breakdown mecha-nisms in a dielectric material is not solely affected by the permit-tivity of the material constituents or the electric field distributionwithin thematerial, and other factors such as thermal and chemicaleffects need to be considered altogether. Nevertheless, we believeour current work helps further to understand the experimentallyobserved DC and AC breakdown performances of the nano-composites from the perspective of electric field distributionwithinthe nanocomposites, based upon our proposed nanocompositemodels.

Acknowledgments

The authors acknowledge the Ministry of Higher Education,Malaysia and Universiti Teknologi Malaysia for financial sponsor-ships and the research grants 13H12 and 4F707. The authors alsothank Ms. Ku Fazilah and Ms. Nurfarhana for their help in carryingout the experimental work.

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