Optimization of electric energy density in epoxy aluminium

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Optimization of electric energy density in epoxy aluminium

  1. 1. INTERNATIONAL Electrical EngineeringELECTRICAL ENGINEERING International Journal of JOURNAL OF and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME & TECHNOLOGY (IJEET)ISSN 0976 – 6545(Print)ISSN 0976 – 6553(Online)Volume 4, Issue 1, January- February (2013), pp. 36-45 IJEET© IAEME: www.iaeme.com/ijeet.aspJournal Impact Factor (2012): 3.2031 (Calculated by GISI)www.jifactor.com ©IAEME OPTIMIZATION OF ELECTRIC ENERGY DENSITY IN EPOXY-ALUMINIUM NANOCOMPOSITE AS DIELECTRIC Siny Paul1, Sindhu T.K2 1 (Department of Electrical and Electronics Engineering, Mar Athanasius College of Engineering, Kothamangalam, Kerala, India, siny_binoy@yahoo.co.in) 2 (Department of Electrical Engineering, National Institute of Technology Calicut, Kerala, India, tk_sindhu@nitc.ac.in) ABSTRACT Dielectric materials with large permittivity and high breakdown strength are required for large electric energy storage in capacitors. Polymers of high breakdown strength combined with nanoparticles of high permittivity substantially enhance the electric energy density of the resulting nanocomposites. In this paper, epoxy-aluminium nanocomposite is modeled as a three phase material and the dielectric properties of the nanocomposite are investigated using this model. Influences of aluminium particle size and filler loading on the permittivity, breakdown strength and electric energy density of the nanocomposite are evaluated. Numerical results show a drastic increase in permittivity close to the transition threshold. As the volume fraction increases, there is reduction in breakdown strength, but the net effect is a notable increment in energy density. The filler size and concentration correspond to maximum energy density are evaluated. It is found that inter particle distance controlling breakdown strength have a significant effect on the electric energy storage. Keywords : Dielectric permittivity, Energy density, Epoxy, Nanocomposite, Polarization. 1. INTRODUCTION Polymers have high breakdown strength compared to ceramics but low dielectric constant in the range of 2-5. While ceramic materials usually have large permittivity, their applications are limited by their relatively small breakdown strength. Since the electric energy density in a dielectric material is ½kEb2 where k is the dielectric constant or permittivity of the material and Eb is the breakdown strength, both large permittivity and high breakdown strength are required for large electric energy storage. Therefore, it is important to 36
  2. 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEkeep a balance between the contradictory criteria of enhancing dielectric constant whilemaintaining high breakdown strength. Numerous efforts have been made in the past fewyears to combine the polymers of high breakdown strength with ceramic particles of highpermittivity. Conductive filler - polymer composite is another approach towards high-k materials,which is a kind of conductor-insulator composite based on percolation theory [1]. Ultra-highk can be expected with conductive filler - polymer composites when the concentration of theconductive filler is approaching the percolation threshold. The minimum volume content ofthe conducting filler at which the drastic change in electrical properties begins is referred toas the percolation threshold [2]. Sometimes the effective k of the metal-insulator compositecould be three or four magnitudes higher than the k of the insulating polymer matrix. Andalso this percolative approach requires much lower volume concentration of the fillercompared to traditional approach of high-k particles in a polymer matrix [3]. Therefore, thismaterial option represents advantageous characteristics over the conventional ceramic-polymer composites [1,2]. Various conductive fillers, such as silver (Ag), aluminium (Al),nickel (Ni), carbon black, have been used to prepare the polymer-conductive filler composites[4-9]. For instance, Z. M. Dang, Y. Shen and C. W. Nan [7] and Jiongxin Lu and C.P.Wong[1] reported k value of 400 and 2000 in Ni/PVDF composite and Ag flake/epoxy compositerespectively.2. MODELING OF POLYMER NANOCOMPOSITES Polymer nanocomposites are defined as polymers in which small amounts ofnanometer size fillers are homogeneously dispersed. The small size of nanoparticles relativeto micron fillers means that there are many more particles and much more interfacial area perunit volume of filler, when the particles are well dispersed. The polymer nanocomposite ismodeled as a three-phase material, consisting of a polymer matrix (phase 1), an interfacialphase of fixed thickness l (phase 2), and nanoparticle fillers (phase 3), schematically shownin Fig.1. The interfacial phase is between polymer matrix and nanoparticles and this can beviewed as a core-shell type of structure [10]. Fig.1. Schematic diagram of a dielectric nanocomposite consisting of polymer matrix, nanoparticles, and interfacial phase. 37
  3. 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME There are large interfacial areas in a nanocomposite, which could promote interfacialexchange coupling through a dipolar interface layer and lead to enhanced polarization andpolarizability in polymer matrix near the interface [11,12]. As a result, enhanced permittivitycan be expected in the polymer matrix near the interfaces. As particle loading increases, theinteraction zones begin to overlap, leading to effective percolation of the interfacial areas atrelatively low loadings. The inclusion of nanoparticles with high dielectric constantsincreases the average dielectric constant of a composite. They also produce a highlyinhomogeneous electric field with local hot spots of increased electric field concentration andreduced dielectric strength, thus reducing the effective breakdown strength of the composite[10]. According to J.Y.Li et al. [10], the effective permittivity of the nanocomposite can beexpressed as:k * = k 1 + f 2(k 2 − k 1) a 2 + f 3( k 3 − k 1)a 3 (1) where k* is the effective relative permittivity of the nanocomposite, k1, k2, k3 are therelative permittivities of matrix, interphase and nanoparticles respectively. f2 is the volumefraction of interfacial phase which is given by: (r + l ) 3 − r 3 f2 = f3 (2) r3 The interfacial thickness l is governed by exchange constant and permittivity of polymerand thus it is reasonable to assume that the interfacial phase has fixed thickness independentof nanoparticle size. f3 is the volume fraction of nanoparticles and r is the nanoparticleradius. From Eq.(2) it is clear that the interfacial fraction f2 increases substantially when thenanoparticle size decreases. ar is the electric field concentration factor for correspondingphase r, which relates the average electric field in phase r to that applied at boundary, E0. The average electric field in phase r is given by: E r = ar E0 (3) For the core-shell type of structure, the electric field concentration factor is given by: [ar = 1 − s (kr − k * ) −1 k * + s ]−1 , r = 2,3 (4) where s is the component of the dielectric Eshelby tensor that is related to thedepolarization factor and for spherical particles s is 1/3. As k* appears on both sides ofEq.(1), a numerical solution is required. When a2 and a3 are determined from Eq.(4), theelectric field concentration factor a1 can then be determined from the normalizationcondition: 38
  4. 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME∑ 3 r =1 f r ar = 1 (5) With the addition of nanoparticles of larger permittivity, the average electric field inpolymer matrix E1 will be enhanced compared to that applied at boundary as: E1 = a1 E0 (6) When the field fluctuation is taken into account, electric field in the polymer matrix isagain enhanced to E2 which is given by Eq.(7) as: 2E2 = E1 + E12 − E1 (7) 2 1 δk * 2where E 1 = E0 (8) f1 δk1 Which is the second order moment of electric field in polymer matrix . Accordingly, thebreakdown strength of the composite will be reduced. This criterion only considers the field fluctuation in the polymer matrix due to the additionof nanoparticles and ignores the introduction of defects that could reduce breakdown strengtheven further. As such, the results can be viewed as an upper bound on the breakdown strengthof the composite.3. DIELECTRIC CONSTANT OF ALUMINIUM The present study concentrates mainly on the modeling and evaluation of thedielectric properties of aluminium–epoxy nanocomposite as a function of composition andparticle size. Relative permittivity of epoxy is around 3.6. But the concept of dielectricconstant for a conducting material is not defined. The dielectric constant is related to theelectronic susceptance in an isotropic material. The susceptance is basically the ratio ofpolarization to applied electric field. A conductor have "bound" electrons in that they cannotleave the entire material, but are free to polarize across the entire length of a conductor. Whenan external electric field is applied to a conductor, the entire conductor will be polarized, suchthat the polarization causes the electric field inside the conductor to be zero (electrostaticequilibrium). In a normal dielectric, the bound electrons cannot move as far as in a conductorand hence they have a much smaller polarization. Hence, the polarization vectors in aconductor are nearly infinite compared to the polarization vectors of a dielectric. Thesusceptance is therefore very large and so is the permittivity. It should be noted that theconcept of permittivity of conductor might be used only to express the effect of the metalfiller on the dielectric constant of the polymer matrix. For the conventional (micron sized) fillers, based on the Lichtenecker-Rother logarithmiclaw [13] of mixing applicable to chaotic or statistical mixtures, the relative permittivity ofthe microcomposite is given by: 39
  5. 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMElog kc = y p log k p + ym log k m (9)where kc is the relative permittivity of composite and yp , ym are volume fractions of the twocomponents having relative permittivities kp and km. Vishal Singh, A. R. Kulkarni and T. R. Rama Mohan [2] conducted experiments onaluminium-epoxy microcomposites and evaluated the value of composite permittivity fordifferent filler loadings. They used Eq.(9) to evaluate permittivity of aluminium (km) asfollows; for each composition point, determined the value of km such that the value ofcomposite permittivity obtained using the above equation is equal to the experimental valueand then estimated the average of the values of km found at various composition points. Theaverage value of km was found to be 1145.4. RESULTS AND DISCUSSIONS In this work, Al-epoxy nanocomposite is modeled and its permittivity, breakdownstrength and energy density are evaluated. Modeling is done on the assumption that thedispersed particles are spherical in shape and of uniform size. 3µm Relative permittivity of the composite 600 20nm 500 60nm 100nm 400 300 200 100 0 0 10 20 30 40 50 60 % volume of Nanoparticles added Fig.2. Relative permittivity of epoxy-aluminium composites. (Filler size of 3µm, 20nm, 60nm and 100nm ) Solving equations (1) to (5), substituting 3.6 for k1 and 1145 for k3 which are the relativepermittivities of epoxy and aluminium respectively, the effective permittivity of aluminium-epoxy nanocomposite for different filler concentration is evaluated and plotted as shown inFig.2. Effective permittivity of three different sizes of nanofillers such as 20nm, 60nm and100nm are evaluated and compared with that of the microcomposite. It is clear from Fig.2 that the relative permittivity of nanocomposites is very highcompared to relative permittivity of microcomposites. There is a rapid increase in effectivepermittivity beyond a threshold in volume fraction. In addition, the interfacial exchange 40
  6. 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEMEcoupling shifts the transition threshold towards lower volume fraction and higher dielectricconstants are obtained for composite with smaller nanoparticles. Nanoparticles can indeedlead to higher dielectric constant in composites compared to microscale particles. Thispermittivity enhancement is attributed to interfacial polarization also referred to as theMaxwell–Wagner–Sillars (MWS) effect, a phenomenon that appears in heterogeneous mediaconsisting of phases with different dielectric permittivity and conductivity. This may be dueto the accumulation of charges at the interfaces [2]. Electric field enhancement in polymer matrix is calculated using Eq.(6) and also theincrement in electric field due to field fluctuations is considered to evaluate the breakdownstrength of the composite. DC breakdown strength of pure epoxy is around 60kV/mm [14].The calculated breakdown strength of the composite as a function of nanoparticle volumefraction is given in Fig.3. Three cases of aluminium particle size 20nm, 60nm and 100nm areconsidered. It is observed that the breakdown strength decreases rapidly with the increase ofnanoparticle volume fraction until the percolation threshold is reached. Beyond thepercolation transition, the breakdown strength rebounds because the field fluctuation isreduced as nanoparticle fraction increases. As the inter particle distance decreases below thelimit, breakdown strength falls down rapidly. However, the calculated values are the upperbound on the breakdown strength because the agglomeration of the metal particles and otherdefects are likely to reduce the breakdown strength even further. DC Breakdown Voltage of Composite (KV/mm) 60 20nm 50 60nm 100nm 40 30 20 10 0 0 10 20 30 40 50 60 % volume of Nanoparticles added Fig.3. Breakdown strength of epoxy-aluminium nanocomposites (Filler size of 20nm, 60nm and 100nm ) The energy density of nanocomposite as a function of volume fraction of nanoparticles iscalculated. It is compared with the energy density of pure epoxy(0.0573J/cm3) and the energydensity increment ratio is plotted as shown in Fig.4. Below percolation transition, the netenergy density is smaller than that of pure polymer matrix. Beyond percolation transition,energy density rises rapidly, but depends on the reliability of breakdown strength. 41
  7. 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME The microstructure of nanocomposite must be carefully controlled to avoid defects andensure uniform dispersion to obtain expected gain in electric energy density. Energy densityattains a maximum value and then reduces due to the rapid reduction in breakdown strengthas the filler concentration increases. The energy density increment ratio plotted in Fig.4shows that energy density of the composite can be upto 15 - 25 times as that of pure epoxy. 25 20nm Energy density increment ratio 60nm 20 100nm 15 10 5 0 0 10 20 30 40 50 60 % volume of Nanoparticles added Fig. 4. Energy density increment ratio of epoxy-aluminium nanocomposites (Filler size of 20nm, 60nm and 100nm ) Maximum energy density increment ratio and corresponding percentage volume of fillersadded vs. filler size are shown in Fig.5 and Fig.6 respectively. For composites with smallernanoparticles, the maximum energy density is obtained at lower volume fractions. Maximum Energy density increment ratio 30 25 20 15 10 5 0 0 20 40 60 80 100 120 140 Filler size (nm) Fig.5. Maximum energy density increment ratio vs. filler size 42
  8. 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME 60 % volume of fillers correspond to 50 maximum energy density 40 30 20 10 0 0 20 40 60 80 100 120 140 Filler size (nm) Fig.6. Percentage volume of nanoparticles added correspond to maximum energy density vs. filler size. Uniform dispersion of nanoparticles in nanocomposite materials is required because nanoparticleagglomeration will lead to undesirable electrical or material properties. Therefore, dispersion ofnanoparticles is an extremely important contributor for achieving improved dielectric properties andelectric energy density. The inter particle distance D is calculated based on Eq.(10) assuming that the nanofillers arespherical in shape [15]. 1 π  ρ   100  wt %  ρ m   3 D=   m   wt % 1 − 100 1 − ρ   − 1 d    (10)  6  ρn     n    Where ρm is the specific gravity of matrix, ρn is the specific gravity of filler and d is the diameterof nanoparticle. 100nm 200 60nm Interparticle distance (nm) 20nm 150 100 50 0 0 10 20 30 40 50 60 % volume of Nanoparticles added Fig.7. Interparticle distance of epoxy-aluminium nanocomposite. (Filler size of 20nm, 60nm and 100nm ) 43
  9. 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME From the plot of inter particle distance (Fig.7), it is observed that maximum energydensity is obtained at the same inter particle distance for each particle size. When the interparticle distance is reduced below this, breakdown strength of the composite falls downrapidly. Thus inter particle distance plays an important role in determining the dielectricproperties of nanocomposites.5. CONCLUSION Theoretical modeling of epoxy-aluminium nanocomposite shows that the inclusion ofaluminium nanoparticles increases the effective permittivity of the composite. Thepermittivity increases rapidly when a particular volume fraction (transition point or threshold)is reached. It is observed that the breakdown strength decreases rapidly with increase ofnanoparticle volume fraction until the threshold is reached. Beyond the transition, thebreakdown strength rebounds because the field fluctuation is reduced as nanoparticle fractionincreases. But the net effect is a notable increment in energy density. The electric energydensity below transition threshold is low and the net energy density is smaller than that ofpure polymer matrix. Beyond the transition, energy density rises rapidly and reaches amaximum value and then falls down as the inter particle distance reduces. It is observed thatfiller concentration correspond to maximum energy density is shifted towards lower volumefractions as the size of nanoparticles is reduced. From the simulations it is concluded that anenergy density increment up to 25 times is possible by optimally selecting the filler size andconcentration. Modeling and evaluation of dielectric properties and energy density of thenanocomposite shows that epoxy-aluminium nanocomposite is a promising candidatematerial for high energy density capacitor applications.6. ACKNOWLEDGEMENT The authors acknowledge the financial support for this work from Department ofScience and Technology, Govt. of India.REFERENCES[1] J.Lu and C.P.Wong, Recent Advances in High – k Nanocomposite Materials forEmbedded capacitor applications, IEEE Transactions on Dielectrics and Electrical Insulation,15(5), 2008, 1322-1328.[2] Vishal Singh, A. R. Kulkarni, T. R. Rama Mohan, Dielectric Properties ofAluminum–Epoxy Composites, Journal of Applied Polymer Science, 90, 2003, 3602–3608.[3] J.Y.Li, Cheng Huang, Q Zhang, Enhanced Electromechanical properties in all-polymer percolative composites, Applied Physics Letters, 84, 2004, 3124[4] J.Xu, C.P Wong, Low loss percolative dielectric composite, Applied PhysicsLetters, 87, 2005, 082907.[5] L. Qi, B. I. Lee, S. Chen, W. D. Samuels and G. J. Exarhos, High dielectric constantsilver- epoxy composites as embedded dielectrics, Advanced Materials, 17, 2005, 1777-1781.[6] J. Lu, K. S. Moon, J. Xu and C. P. Wong, Synthesis and dielectric properties of novelhigh-K polymer composites containing in-situ formed silver nanoparticles for embeddedcapacitor applications, Journal of Material Chemistry, 16, 2006, 1543-1548. 44
  10. 10. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME[7] Z. M. Dang, Y. Shen and C. W. Nan, Dielectric behavior of three-phase percolativeNi–BaTiO3/ polyvinylidene fluoride composites, Applied Physics Letters, 81, 2002, 4814-4816.[8] H. W. Choi, Y. W. Heo, J. H. Lee, J. J. Kim, H. Y. Lee, E. T. Park and Y. K. Chung,Effects of BaTiO3 on dielectric behavior of BaTiO3-Nipolymethylmethacrylatecomposites, Applied Physics Letters, 89, 2006, 132910.[9] J. Xu and C. P. Wong, Super high dielectric constant carbon black-filled polymercomposites as integral capacitor dielectrics, Proc. 54th IEEE Conf. on Electronic Componentsand Technology, 2004, 536-541.[10] J. Y. Li, L. Zhang, and S. Ducharme, Electric energy density of dielectricnanocomposites, Applied Physics Letters, 90, 2007, 132901.[11] Ch.Chakradhar Reddy and T.S.Ramu, Polymer Nanocomposites as Insulation for HVDC Cables – Investigations on the Thermal Breakdown, IEEE Transactions onDielectrics and Electrical Insulation, 15, 2008, 221-227.[12] T. Tanaka, G. C. Montanari and R. Mulhaupt, Polymer Nanocomposites as Dielectricsand Electrical Insulation - Perspectives for processing Technologies, MaterialCharacterization and Future Applications, IEEE Transactions on Dielectrics andElectrical Insulation, 11, 2004, 763-784.[13] J Keith Nelson and John C Fothergill, Internal charge behaviour of nanocomposites,Nanotechnology, 15, 2004, 586-595.[14] P.Preetha and M.Joy Thomas, Partial Discharge Resistant Characteristics of EpoxyNanocomposites, IEEE Transactions on Dielectrics and Electrical Insulation,18, 2011,264-274.[15] T. Tanaka, M. Kozako, N. Fuse and Y. Ohki, Proposal of a multi-core model forpolymer nanocomposite dielectrics, IEEE Trans. on Dielectrics and Electrical Insulation, 12(4), 2005, 669-681.[16] Siddhant Datta , B.M. Nagabhushana and R. Harikrishna, “A New Nano-CeriaReinforced Epoxy Polymer Composite With Improved Mechanical Properties”, Internationaljournal of Advanced Research in Engineering & Technology (IJARET), Volume 3, Issue 2,2012, pp. 248 - 256, Published by IAEME.[17] Ahmed Thabet, and Youssef A. Mobarak, “Experimental Study For Dielectric StrengthOf New Nanocomposite Polyethylene Industrial Materials”, International Journal ofElectrical Engineering & Technology (IJEET), Volume 3, Issue 1, 2012, pp. 353 - 364,Published by IAEME. 45

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