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Optimization of electric energy density in epoxy aluminium nanocomposite
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.asp Journal 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.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME keep a balance between the contradictory criteria of enhancing dielectric constant while maintaining high breakdown strength. Numerous efforts have been made in the past few years to combine the polymers of high breakdown strength with ceramic particles of high permittivity. 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-high k can be expected with conductive filler - polymer composites when the concentration of the conductive filler is approaching the percolation threshold. The minimum volume content of the conducting filler at which the drastic change in electrical properties begins is referred to as the percolation threshold [2]. Sometimes the effective k of the metal-insulator composite could be three or four magnitudes higher than the k of the insulating polymer matrix. And also this percolative approach requires much lower volume concentration of the filler compared to traditional approach of high-k particles in a polymer matrix [3]. Therefore, this material 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 composite respectively. 2. MODELING OF POLYMER NANOCOMPOSITES Polymer nanocomposites are defined as polymers in which small amounts of nanometer size fillers are homogeneously dispersed. The small size of nanoparticles relative to micron fillers means that there are many more particles and much more interfacial area per unit volume of filler, when the particles are well dispersed. The polymer nanocomposite is modeled as a three-phase material, consisting of a polymer matrix (phase 1), an interfacial phase of fixed thickness l (phase 2), and nanoparticle fillers (phase 3), schematically shown in Fig.1. The interfacial phase is between polymer matrix and nanoparticles and this can be viewed 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.
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 interfacial exchange coupling through a dipolar interface layer and lead to enhanced polarization and polarizability in polymer matrix near the interface [11,12]. As a result, enhanced permittivity can be expected in the polymer matrix near the interfaces. As particle loading increases, the interaction zones begin to overlap, leading to effective percolation of the interfacial areas at relatively low loadings. The inclusion of nanoparticles with high dielectric constants increases the average dielectric constant of a composite. They also produce a highly inhomogeneous electric field with local hot spots of increased electric field concentration and reduced 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 be expressed 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 the relative permittivities of matrix, interphase and nanoparticles respectively. f2 is the volume fraction 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 polymer and thus it is reasonable to assume that the interfacial phase has fixed thickness independent of nanoparticle size. f3 is the volume fraction of nanoparticles and r is the nanoparticle radius. From Eq.(2) it is clear that the interfacial fraction f2 increases substantially when the nanoparticle size decreases. ar is the electric field concentration factor for corresponding phase 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 the depolarization factor and for spherical particles s is 1/3. As k* appears on both sides of Eq.(1), a numerical solution is required. When a2 and a3 are determined from Eq.(4), the electric field concentration factor a1 can then be determined from the normalization condition: 38
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 in polymer 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 is again enhanced to E2 which is given by Eq.(7) as: 2 E2 = E1 + E12 − E1 (7) 2 1 δk * 2 where E 1 = E0 (8) f1 δk1 Which is the second order moment of electric field in polymer matrix . Accordingly, the breakdown strength of the composite will be reduced. This criterion only considers the field fluctuation in the polymer matrix due to the addition of nanoparticles and ignores the introduction of defects that could reduce breakdown strength even further. As such, the results can be viewed as an upper bound on the breakdown strength of the composite. 3. DIELECTRIC CONSTANT OF ALUMINIUM The present study concentrates mainly on the modeling and evaluation of the dielectric properties of aluminium–epoxy nanocomposite as a function of composition and particle size. Relative permittivity of epoxy is around 3.6. But the concept of dielectric constant for a conducting material is not defined. The dielectric constant is related to the electronic susceptance in an isotropic material. The susceptance is basically the ratio of polarization to applied electric field. A conductor have "bound" electrons in that they cannot leave the entire material, but are free to polarize across the entire length of a conductor. When an external electric field is applied to a conductor, the entire conductor will be polarized, such that the polarization causes the electric field inside the conductor to be zero (electrostatic equilibrium). In a normal dielectric, the bound electrons cannot move as far as in a conductor and hence they have a much smaller polarization. Hence, the polarization vectors in a conductor are nearly infinite compared to the polarization vectors of a dielectric. The susceptance is therefore very large and so is the permittivity. It should be noted that the concept of permittivity of conductor might be used only to express the effect of the metal filler on the dielectric constant of the polymer matrix. For the conventional (micron sized) fillers, based on the Lichtenecker-Rother logarithmic law [13] of mixing applicable to chaotic or statistical mixtures, the relative permittivity of the microcomposite is given by: 39
5.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME log 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 two components having relative permittivities kp and km. Vishal Singh, A. R. Kulkarni and T. R. Rama Mohan [2] conducted experiments on aluminium-epoxy microcomposites and evaluated the value of composite permittivity for different filler loadings. They used Eq.(9) to evaluate permittivity of aluminium (km) as follows; for each composition point, determined the value of km such that the value of composite permittivity obtained using the above equation is equal to the experimental value and then estimated the average of the values of km found at various composition points. The average value of km was found to be 1145. 4. RESULTS AND DISCUSSIONS In this work, Al-epoxy nanocomposite is modeled and its permittivity, breakdown strength and energy density are evaluated. Modeling is done on the assumption that the dispersed 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 relative permittivities of epoxy and aluminium respectively, the effective permittivity of aluminium- epoxy nanocomposite for different filler concentration is evaluated and plotted as shown in Fig.2. Effective permittivity of three different sizes of nanofillers such as 20nm, 60nm and 100nm are evaluated and compared with that of the microcomposite. It is clear from Fig.2 that the relative permittivity of nanocomposites is very high compared to relative permittivity of microcomposites. There is a rapid increase in effective permittivity beyond a threshold in volume fraction. In addition, the interfacial exchange 40
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International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME coupling shifts the transition threshold towards lower volume fraction and higher dielectric constants are obtained for composite with smaller nanoparticles. Nanoparticles can indeed lead to higher dielectric constant in composites compared to microscale particles. This permittivity enhancement is attributed to interfacial polarization also referred to as the Maxwell–Wagner–Sillars (MWS) effect, a phenomenon that appears in heterogeneous media consisting of phases with different dielectric permittivity and conductivity. This may be due to the accumulation of charges at the interfaces [2]. Electric field enhancement in polymer matrix is calculated using Eq.(6) and also the increment in electric field due to field fluctuations is considered to evaluate the breakdown strength 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 volume fraction is given in Fig.3. Three cases of aluminium particle size 20nm, 60nm and 100nm are considered. It is observed that the breakdown strength decreases rapidly with the increase of nanoparticle volume fraction until the percolation threshold is reached. Beyond the percolation transition, the breakdown strength rebounds because the field fluctuation is reduced as nanoparticle fraction increases. As the inter particle distance decreases below the limit, breakdown strength falls down rapidly. However, the calculated values are the upper bound on the breakdown strength because the agglomeration of the metal particles and other defects 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 is calculated. It is compared with the energy density of pure epoxy(0.0573J/cm3) and the energy density increment ratio is plotted as shown in Fig.4. Below percolation transition, the net energy 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
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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 and ensure uniform dispersion to obtain expected gain in electric energy density. Energy density attains a maximum value and then reduces due to the rapid reduction in breakdown strength as the filler concentration increases. The energy density increment ratio plotted in Fig.4 shows 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 fillers added vs. filler size are shown in Fig.5 and Fig.6 respectively. For composites with smaller nanoparticles, 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.
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 nanoparticle agglomeration will lead to undesirable electrical or material properties. Therefore, dispersion of nanoparticles is an extremely important contributor for achieving improved dielectric properties and electric energy density. The inter particle distance D is calculated based on Eq.(10) assuming that the nanofillers are spherical 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 diameter of 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.
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 energy density is obtained at the same inter particle distance for each particle size. When the inter particle distance is reduced below this, breakdown strength of the composite falls down rapidly. Thus inter particle distance plays an important role in determining the dielectric properties of nanocomposites. 5. CONCLUSION Theoretical modeling of epoxy-aluminium nanocomposite shows that the inclusion of aluminium nanoparticles increases the effective permittivity of the composite. The permittivity increases rapidly when a particular volume fraction (transition point or threshold) is reached. It is observed that the breakdown strength decreases rapidly with increase of nanoparticle volume fraction until the threshold is reached. Beyond the transition, the breakdown strength rebounds because the field fluctuation is reduced as nanoparticle fraction increases. But the net effect is a notable increment in energy density. The electric energy density below transition threshold is low and the net energy density is smaller than that of pure polymer matrix. Beyond the transition, energy density rises rapidly and reaches a maximum value and then falls down as the inter particle distance reduces. It is observed that filler concentration correspond to maximum energy density is shifted towards lower volume fractions as the size of nanoparticles is reduced. From the simulations it is concluded that an energy density increment up to 25 times is possible by optimally selecting the filler size and concentration. Modeling and evaluation of dielectric properties and energy density of the nanocomposite shows that epoxy-aluminium nanocomposite is a promising candidate material for high energy density capacitor applications. REFERENCES [1] J.Lu and C.P.Wong, Recent Advances in High – k Nanocomposite Materials for Embedded 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 of Aluminum–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 Physics Letters, 87, 2005, 082907. [5] L. Qi, B. I. Lee, S. Chen, W. D. Samuels and G. J. Exarhos, High dielectric constant silver- 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 novel high-K polymer composites containing in-situ formed silver nanoparticles for embedded capacitor applications, Journal of Material Chemistry, 16, 2006, 1543-1548. [7] Z. M. Dang, Y. Shen and C. W. Nan, Dielectric behavior of three-phase percolative Ni–BaTiO3/ polyvinylidene fluoride composites, Applied Physics Letters, 81, 2002, 4814- 4816. 44
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Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME [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-Nipolymethylmethacrylate composites, Applied Physics Letters, 89, 2006, 132910. [9] J. Xu and C. P. Wong, Super high dielectric constant carbon black-filled polymer composites as integral capacitor dielectrics, Proc. 54th IEEE Conf. on Electronic Components and Technology, 2004, 536-541. [10] J. Y. Li, L. Zhang, and S. Ducharme, Electric energy density of dielectric nanocomposites, Applied Physics Letters, 90, 2007, 132901. [11] Ch.Chakradhar Reddy and T.S.Ramu, Polymer Nanocomposites as Insulation for HV DC Cables – Investigations on the Thermal Breakdown, IEEE Transactions on Dielectrics and Electrical Insulation, 15, 2008, 221-227. [12] T. Tanaka, G. C. Montanari and R. Mulhaupt, Polymer Nanocomposites as Dielectrics and Electrical Insulation - Perspectives for processing Technologies, Material Characterization and Future Applications, IEEE Transactions on Dielectrics and Electrical 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 Epoxy Nanocomposites, 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 for polymer 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-Ceria Reinforced Epoxy Polymer Composite With Improved Mechanical Properties”, International journal 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 Strength Of New Nanocomposite Polyethylene Industrial Materials”, International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 1, 2012, pp. 353 - 364, Published by IAEME. 45
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