CHAPTER 2 Electrical Conductivity, Percolation Theory, Electromagnetic Interference (EMI) and Its Mechanisms

Transcription

1 CHAPTER 2 Electrical Conductivity, Percolation Theory, Electromagnetic Interference (EMI) and Its Mechanisms 21

2 2.1 Introduction Demand of conductive composites use in advance applications is increasing. To know the value of these materials, it is essential to build up basic understanding of the factor that affects composite conductivity. This includes understanding basic principles of composites conductivity and how different constituent material properties could effect the conductivity values. This study helps to develop new composites for various applications. In generally, without any additives or modifiers, almost all commercial polymers are electrical insulators. Any insulating material, electrical charges deposited on a polymer surface are live longer, continuous lifetime of the charge; it causes damage to electronics that come near or into contact with it. A significant amount of time has been spent to develop ways to make insulative polymers into electrically conductive or static dissipative. Most common methods are inherently dissipative conductive polymers, chemical additives and conductive fillers. 2.2 Fundamentals of Electrical Conductivity First start with the phenomenon of electrical conduction the strictures by which it is articulated, the conduction mechanism by electrons, and how these electron energy band structures of amaterial influence its capability to conduct. These principles are further extended to metals, semi-conductors, and insulators (ceramics and polymers). Ohm s Law Electrical individuality of a solid material, how easewhich it transmits an electric current within the body. Ohm s law relates the potential difference, 'V' in volts, with the electrical resistance, 'R' in ohms and the electrical current, 'I' in amp. Equation 1 22

3 Ohm's law is valid to most but not all materials. The resistance 'R' is theresistance of the material through which the current is passing. The value of resistance is influenced by specimen configuration such as; size, shape and materials properties, etc. Equation 2 Where, R is the resistance in ohms, A is the cross-sectional area in cm 2, l is the length in cm, ρ is the resistivity or Electrical resistivity (Ohm-cm). Equation 2 can be rewritten as Equation 3 Figure 2.1 Resistivity of various materials 23

4 The main feature of the electrical conductivity of polymeric materials is an extreme difference between electric resistivity of a polymer matrix and that of the filler, which reaches a factor of 10 24, as shown in figure 2.1 no such difference is observed for any other physical property of composite ingredients. In conductive composites, current can flow through continuous chains of filler particles. Because of the small as compared with the sample volume, size of the filler particles, there are a great number of variants of their mutual arrangement, many of which are impossible to differentiate; however, only a small portion will convince the spatial structure where current flow is possible. The probability of forming such a structure depends on a variety of factors, namely: quantity of a filler, shape of filler particles and their capability of becoming combined with a polymer, method of mixing, etc. Since the influence of these factors is clear, they should be taken into consideration in creation of conducting composites. 2.3 Percolation Theory [1-5] An important theory for understanding conductivity within composite materials, especially where the polymer matrix and the fillers have very different characteristics, is the concept of percolation. Percolation procedures were developed by Flory in 1941 and Stockmayer in 1943 to describe how small branching molecules react and form very large macromolecules [6]. In mathematical literature, percolation was introduced by Hammersley and Broadbent in The percolation concept originally dealt with the spread of hypothetical fluid particles through a random medium. Figure 2.2 Schematics of percolation pathway 24

5 In a view of electrical conduction in a polymer matrix, electrons are free to flow through conductive filler particles. If these filler particles contact one another, a continuous path is formed through the polymer matrix, which is an insulating material, for electrons to travel through. This path is called a conductive network, and the material with the conductive network turns into a conducting material, as shown in figure 2.2. For the increase loading of conductive filler, there are three main district define the relationship to the conductivity of conductive filled polymer composites [7] as shown in figure 2.3 Figure 2.3 Percolation S Curve At low concentration filler loadings shown in district A, the electrical conductivity value equals zero, since there is no path exists for electron transport and the conductivity of the composite is closer to that of the neat polymer matrix. At a certain critical loading, known as the percolation threshold, enough filler has been introduced so that it begins to form a continuous conductive network path through the composite. Following the percolation threshold is a district that produces a significant increase in conductivity with very little increase in filler amount, as exhibited by district B. After this district of radical increase, the conductivity slows its increase, and approaches that of the filler material as increase happens because the conductive networkpath through the sample is complete. This is represented in area C of figure 2.3. Eventually, percolation max is reached, at which point the addition of more filler does not increase the ease of electron movement. 25

6 2.4 Factors affecting the conduction behavior of conductive composites Important factors that influence the initiation and extent of conductivity of conductive polymer composite materials are (a) intrinsic conductivity of filler, (b) Filler concentration and (c) Geometry of filler such as size, shape and aspect ratio Filler Conductivity The composite conductivity is affected by the intrinsic conductivity of the filler and matrix, and polymer-filler interactions. In systems with a high polymer filler bond, the polymer forms a thick film or coating around the conductive filler which limits the particle-particle contact; thus gives the composite has low conductivity properties. Conductive polymer composite materials formed with more conducting filler have higher conductivity. Thus, composites made with metallic fillers, which have high volume conductivity will be more conductive than those made with nonmetallic fillers such as carbon black, once enough filler has been added to form a conductive network Filler Concentration Figure 2.4 Relationship between composite resistive &loading of conductive filler It can be seen from the figure 2.4 that up to a critical filler concentration, resistivity of the composite is hardly reduced by the filler. In the region of critical concentration, resistivity drops sharply. Further increase in filler concentration continues to reduce the resistivity of the composite, but at a much lower rate. On the basis of the concept of 26

7 network formation, the behavior showed in figure 2.2 and 2.3. At 10% filler concentration, too small quantity of filler is present to form a conductive network; that is, very few of the particles are nearly or actually in contact with other conductive particles. As a result, the conductive path includes many large gaps between filler particles, where conduction across the highly resistive matrix resin is necessary. The composite resistivity is determined by insulating polymer matrix material. At the critical concentration, dependent on filler morphology and other factors, the number of interparticle contacts increases sharply over a narrow range of filler concentration. The conductive path now consists of a network of filler particles that either are touching or are separated by very small gaps and the resistivity falls sharply as a result. Once an extensive conductive network has formed, further increases in filler concentration increase the average cross section of the conductive network by increasing the number of parallel pathways and the volume resistivity gradually falls accordingly Aspect Ratio of Filler Figure 2.5. Effect of filler aspect ratio on network formation Figure 2.5 shows the effect of aspect ratio on network formation. For given conductive filler, the critical concentration is very sensitive to its aspect ratio, which is defined as the ratio of the long dimension to the short dimension of the filler particles. For example, the ratio of a cylindrical rod is equal to its length divided by its diameter. In practice, the aspect ratio can vary from 1, for spherical particles, to several hundred or more for fibers. The shape of the plot of resistivity versus filler concentration relationship remains about the same as the aspect ratio changes. However, network formation begins at lower filler concentrations as the aspect ratio increases. In each of these frames, the filler particles occupy 20 area percent and have the same randomly assigned positions and orientations, 27

8 but their aspect ratio varies from frame to frame. At an aspect ratio of 1, network formation is very short 12 order; most particles are not in contact with any other filler particles. Some additional interparticle contacts are made at an aspect ratio of 4. When the aspect ratio is increased to 64, the particles are joined into an effective network that contains multiple conduction paths. As illustrated in figure 2.3. At low filler concentrations the electrical conductivity is close to the electrical conductivity of the polymer used in the composite. Polymers usually have electrical conductivities of to S/cm, making them very electrically resistant. At a critical volume concentration, known as the percolation threshold, the electrical conductivity of the composite will increase rapidly with only asmall change in the amount of filler. After the percolation threshold has been reached the electrical conductivity will flatten and approach the electrical conductivity of the fillers used in the composite. Carbon fillers usually have electrical conductivities in the range 10 2 to 10 5 S/cm. The percolation threshold is the point where there is enough filler in the composite to start forming conductive networks. These conductive networks form a continuous path that allows electricity to pass easily through a composite, thus increasing the electrical conductivity [8-11]. Typical electrical conductivities for different carbon fillers are: carbon black 10 2 S/cm, graphite forms 10 5 S/cm, and PAN based carbon fibers 10 3 S/cm [12-14]. 2.5 Electromagnetic Interference (EMI) and its Mechanisms Figure 2.6 Electromagnetic waves [15] 28

9 Investigate in conductive composites was instigated to find a light-weight, inexpensive method to prevent medical, military, and aircraft systems from electromagnetic interference (EMI) which can result in damages ranging from data jamming to burn out of sensitive equipment. It is a basically electrical phenomenon in nature and exists in form of electromagnetic waves shown in figure 2.6 at different radio frequency (RF) figure 2.7. Figure 2.7Electromagnetic spectrum [16] Electromagnetic interference interrupts, obstructs, degrades or limits the effective performance of electronics/electrical equipment. It can be induced intentionally, as in some forms of electronic unintentionally, as a result of intermodulation products for instance. This unwanted electromagnetic emission is caused by rapid changes in voltages and currents within wires or circuits. The electromagnetic interference is transmitted in two forms: conducted (several KHz to 30 MHz) and radiated (30 MHz to 12 GHz) [17]. For radiated EMI, various shielding materials are applied to eliminate the noise; while for conducted EMI, filters have to be added when designing the circuit. For example, most power electronic equipments have grounded cabinets which shield both interna land external radiated noises. Radiated EMI is the consequence of reflection loss, transmission or absorption loss and internal reflection loss at existing interfaces of the incident electromagnetic waves in samples. As shown in Figure 2.8, in passing through a shielding material layer, an electromagnetic wave may be attenuated inthree ways [18] 1) Absorption (A) due to the thickness of the shield 2) Reflection at the surfaces (R) 29

10 3) Multiple internal reflections (B) Figure 2.8 Electromagnetic wave attenuated in three forms: reflection, absorption and multiple internal reflections The primary mechanism, reflection, requires the existence of mobile charge carriers (electrons or holes) which interact with the electromagnetic radiation. Thus the shield tends to be electrically conducting, though a high conductivity is not required for shielding. For example, a volume resistivity of the order of 1 Ωcm is typically sufficient. The reflection loss is a function of the ratio σ r /μ r where σ r isthe electrical conductivity relative to copper and μ r is the relative magnetic permeability. The reflection loss decreases with increasing frequency [18]. The second mechanism of Electromagnetic interference shielding, absorption requires both electric & magnetic dipoles which act together with the electromagnetic fields. The electric dipoles may be afforded by materials that having high magnetic permeability. Silver, copper, nickel, gold and aluminium are excellent for reflection, due to their high conductivity. Supermalloy are excellent for absorption, due to their high magnetic permeability [18] The third mechanism of attenuation is multiple reflections. This refers to the reflections at various surfaces or interfaces in the shield. This mechanism requires the presence of a 30

11 large surface area or interface area in the shield. For instance, a porousor foam material has a large surface area, and a composite material contains fillers hasa large interface area in the shield. The loss due to multiple reflections can be neglected when the distance between the reflecting surfaces or interfaces large is compared to the skin depth which is the distance that electromagnetic radiation can penetrated at certain high frequency. Electromagnetic interference shielding refers to the reflection and/or adsorption of electromagnetic radiation by a material, which thereby acts as a shield against the penetration of the radiation through the shield [18]. It is characterized by EMI shielding effectiveness (SE) which is a number that quantifies the amount of attenuation typical of a particular material so it is also called attenuation upon transmission [18] SE = (R + A + B) db Equation 4 Where, shielding effectiveness (SE) expressed in db, is the loss that represents the reduction of the level of an electromagnetic field at a point in space after a conductive barrier is inserted between that point and the source. 'R' is the sum of initial reflection losses in db from both surfaces of the shield exclusive of additional reflection losses, 'A' is the absorption or penetration loss in db within the barrier itself and 'B' is the internal reflection loss atexiting interface in db. This term may be either positive or negative and is negligiblefor A 15 db. Based on these mechanisms, a composite with high conductivity to improve reflection, suitable matrix and reinforcement with proper dipoles to advance magnetic permeability, and large surface or interface area to increase reflection and absorption can be an ideal candidate for EMI shielding material Skin Effect Skin effect is another concern for choosing a right material in EMI shielding application. Electromagnetic radiation can be divided into near field and far field regions. In near 31

12 field, the electromagnetic signal can be predominantly an electric vector or a magnetic vector depending upon the nature of the source. Electromagnetic radiation at high frequencies penetrates only the near surface region of an electrical conductor. This is known as the skin effect. The electric field of a plane wave penetrating a conductor drops exponentially with increasing depth into the conductor. The depth at which the field drops to 1/e of the incident value is called the skindepth (δ) [18], which is given by equation 2 Equation 5 Where f = frequency, μ = magnetic permeability = μ 0 μ r, μ r = relative magnetic permeability, μ 0 = 4π 10 7 Hm -1, and σ = electrical conductivity in Ω 1 m -1. Hence, the skin depth decreases with increasing frequency and with increasing conductivity or permeability. For copper, μ r = 1, σ = Ω 1 m -1, so δ is2.09 μm at a frequency of 1 GHz. For nickel of μ r = 100, σ = Ω 1 m -1, so δ is 0.47 μm at 1 GHz. The small value of δ for nickel compared to copper ismainly due to the ferromagnetic nature of nickel [18]. In order to improve EMI capability of composites, relatively low skin depth material should be choosing so that electromagnetic field can rapidly decay within the small distance Composites for EMI shielding An electromagnetic shielding material is a material that attenuates radiated electromagnetic energy. For commercial and military application, shielding effectiveness of materials must achieve >40 db and >80 db, respectively [19]. Metals are the most common materials for shielding by far, but they are heavy, expensive and tend to suffer from their poor wear or scratch resistance [18]. On the other hand, the uses of polymers for housing the electronics device arepopular due to its light weight, flexible and less expensive. In order to shield against electromagnetic interference, the technical approach, which has been considered extensively, is to incorporate electrically conductive fillers in polymer matrices. Due to the skin effect, a composite material having conductive filler 32

13 with a small unitsize is more effective than the one with a large unit size of the filler. For effective use of the entire cross-section of a filler unit for shielding, the unit size of the filler shouldbe comparable to or less than the skin depth. Therefore, a filler of unit size 1 μm or less is typically preferred [18], though such a small unit size is not commonly available for most fillers and the dispersion of the filler is more difficult when the filler unit size decreases. Thus, various carbon materials are selected for use in different microelectronics devices application depending on their SE over different frequency ranges. This report addresses and compares the composites for EMI shielding including expanded graphite, PAN carbon fibers (chopped) and nickel coated expanded graphite. 2.6 Conclusion This chapter presents the fundamentals of electrical conductivity, percolation theory and factor affecting the electrical properties of composites and complete discussion on EMI and its mechanisms. The overall study gives us a better understanding and knowledge for further work. 33

14 2.7 References 1. Clingerman, M.L., Development and Modelling of Electrically Conductive Composite Materials, in Chemical Engineering. 2001, Michigan Technological University: Michigan. p Heiser, J.A., Conductive, Shielding, Tensile, and Impact Properties of Carbonfilled Nylon 6,6 Based Resins, in Chemical Engineering. 2003, Michigan Technological University: Michigan. 3. Kovacs, J.Z., Composites Science and Technology, : p Kirkpatrick, S., Reviews of Modern Physics, (4). 5. Sahimi, Applications of Percolation Theory Tylor & Francis Ltd. 6. Stauffer, D, Introduction of Percolation Theory. 1985, London: Tylor and Francis. 7. Mali, T.J., Thermoplastic Composites for Polymer Electrolyte Membrane Fuel Cell Bipolar Plates, University of Waterloo: Waterloo, Canada 8. D. Bigg, Metal Filler Polymers: Properties and Applications, S. K. Bhattacharya (Ed), Marcel Dekker Inc, New York, 1986, Y. Agari, and T. Uno, Journal of Applied Polymer Science, 30, (1985). 10. Y. Agari, A. Ueda, and S. Nagai, Journal of Applied Polymer Science, 42, (1991). 11. M. L. Clingerman, E. H. Weber, J. A. King, K. H. Schulz. Journal of AppliedPolymer Science, 88, (2003). 12. M. L. Clingerman, Development and Modeling of Electrically Conductive Composite Materials, Ph.D. Dissertation, Michigan Technological University, Houghton, MI, A. Demain and J-P. Issi, Journal of Composite Materials, 27, (1993). 14. J.-B. Donnet, R. C. Bansal, and M.-J. Wang, Carbon Black, 2nd edition, Marcel Dekker, Inc, New York, Perez X Reinaldo. Handbook of electromagnetic compatibility: Academic Press,

15 18. Chung D.D.L, Carbon, Vol 39 PP.279 to 285, Joo.J, Lee., Journal of Applied Physics, Vol 88 pp