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Analysis of correlation between percolation concentration and elongation at break in filled electroconductive epoxy-based adhesives
European Polymer Journal 39 (2003) 585–592 www.elsevier.com/locate/europolj
Analysis of correlation between percolation concentration and elongation at break in filled electroconductive epoxy-based adhesives Igor Nov ak *, Igor Krupa, Ivan Chod ak Polymer Institute of the Slovak Academy of Sciences, D ubravsk a cesta 9, Bratislava 84236, Slovakia Received 21 March 2002; received in revised form 30 August 2002; accepted 25 September 2002
Abstract Electrical conductivity and elongation at break of epoxy filled with electroconductive carbon black, graphite or with silver-coated basalt particles or fibres were investigated in this paper. Percolation concentrations were determined to be 14 vol% for epoxy/carbon black composites, 22 vol% for epoxy/graphite composites, 28–29 vol% for both epoxy/silvercoated basalt particles and fibres. The steepest increase in electrical conductivity and the most pronounced decrease in elongation at break occurs at similar filler concentration range for all investigated systems. A good correlation between phenomenological model, introduced in [J. Mater. Sci. Lett. 18 (1998) 1457] and experimental data for all investigated systems was observed. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Adhesives; Electrical conductivity; Elongation; Epoxy resin; Silver; Carbon black
1. Introduction Electrically conductive adhesives have attracted great attention because of their adhesive and electrical properties and numerous potential applications [1,2]. It is well known that polymers filled with electrically conductive particles, exhibit a distinctive dependence of conductivity on the concentration of filler [3,4]. A growing interest is observed in the potential of electrically conductive metal-loaded polymer adhesives for solder replacement in surface mount technology and other microelectronic application. A growing interest is observed in the potential of electrically conductive metal-loaded polymer adhesives for solder replacement in surface mount technology and other microelectronic application [5,6] in cases when soldering is difficult or impossible because of low ther-
*
Corresponding author. E-mail address: [email protected] (I. Novak).
mal stability. An adhesive joining has to have either better properties or more simple technology compared to a traditional soldering. When an adhesive is loaded with a critical or higher concentration of electrically conductive filler, e.g. carbon black, graphite or metallic powder, known as the percolation threshold, transition of the composite adhesive from insulator to electrical conductor is observed [7–9]. The filler, e.g. silver-based particles and/or carbonbased filler, e.g. graphite or electrically conductive carbon black, form the electroconductive paths between the surfaces of the joint parts. Electrically conductive adhesives are also applicable for a formation of surface electroconductive shielding layer and for partially flexible electroconductive connections [10]. Two-component epoxy-based electrically conductive adhesives were developed for a broad application in many areas for both industry and household. Continuing technological development have enabled electrically conductive adhesives to be used not only as solder replacement, but also in many assembly applications such
0014-3057/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 4 - 3 0 5 7 ( 0 2 ) 0 0 2 7 1 - 9
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I. Novak et al. / European Polymer Journal 39 (2003) 585–592
as electromagnetic shielding, printed circuit manufacture, electronics packaging and surface mount technology [11–13]. Electrical and mechanical properties of epoxy-based electrically conductive adhesives containing graphite or metallized filler are investigated in this paper. The correlation between electrical conductivity and elongation at break has been investigated in all electrically conductive adhesive systems, related to the previously described correlation of the two parameters observed for thermoplastic matrices [14–17].
spective filler using a lab-scale mixer (Koba, SR) for 20 min at the mixing speed 20 rpm. The components of the composite adhesive were mixed together in the weight ratio 2:1. The dog-bone specimens with a working area 35 3:6 1 mm (mechanical experiments) and/or a circles with a diameter 30 mm and a thickness about 0.5 mm (measurements of electrical properties) were prepared by casting in the silicone rubber forms. The samples were tested after seven days of adhesive hardening. All procedures have been carried out at ambient temperature.
2. Experimental
2.2.3. Measurement of mechanical and electrical properties The elongation at break was measured at ambient temperature using an universal testing machine Instron 4301 (Instron, England) equipped with the 5 kN measuring cell and the software Serie IX at deformation rate 10 mm/min. The volume electrical conductivity of adhesives was measured according to ASTM D-257. Three-electrode electrometer arrangement was used for the DC measurement of the resistivity. The voltage level varied in the range 0.1–500 V.
2.1. Materials Two-component epoxy adhesive consisting of epoxy oligomer (bisphenol-A-diglycidylether) ChS Epoxy 531 (produced by Spolchemie, Czech Republic) modified by reactive solvent (1,6-hexanediol-diglycidylether) (Sachem, USA), viscosity at 25 °C ¼ 2:2 Pa s and a curing agent (diethylene triamine-based) Aminoamid DE 400 (Bohemiachem, Czech Republic) was used as a polymer matrix. Four kinds of filler were investigated, namely homemade silver-coated basalt particles prepared by a chemical method having diameter <15 lm and density 2.28 g cm3 , a thickness of metallic layer 1 lm, silver-coated basalt fibres with average aspect ratio approximately 5 and density 2.28 g cm3 , and a special grade of graphite with a carbon content >99.9%, size of particles being <15 m (KS 15), density 2.25 g cm3 (produced by Lonza, Switzerland). The special kind of carbon black Vulcan XC-72 R (Cabot, USA) having particle size approximately 30 nm, a specific area 254 m2 g1 and density 1.8 g cm3 was used. 2.2. Methods 2.2.1. Preparation of metallized particles The metal-coated particles were prepared using a method of electroless metallization. Two solutions have been prepared, namely solution A consisting of silver nitride (30 g) dissolved in 1000 ml of distilled water and solution B obtained by dissolving natrium–potassium tartrate (50 g) in distilled water (900 ml). Mixing 100 ml solution A and 20 ml solution B together at ambient temperature the bath for metallization was prepared. The particles were metallized in the bath at ambient temperature during 20 min, then washed thoroughly by distilled water and dried at 60 °C. 2.2.2. Preparation of adhesives and samples The electrically conductive adhesives were prepared by mixing both components of epoxy having the re-
3. Results and discussion 3.1. Electrical conductivity The dependencies of electrical conductivity of epoxy filled with electroconductive carbon black, graphite, silver-coated particles and fibres on the volume portion of the filler are shown in Figs. 1–4. In all cases, a dramatical increase in electrical conductivity was observed around a particular concentration of the filler. This concentration is generally called percolation concentration, i.e. the filler concentration at which the steep change in conductivity occurs and it is a basic characteristics of a conductive composite. The value of the percolation concentration was determined by fitting the experimental data using Eq. (1) and fitting parameters n and a were used to estimate the percolation concentration in terms of Eq. (2): logðrc =rm Þ ¼ Bð1 ea/f Þn
ð1Þ
/i /c ¼ lnðnÞ=a
ð2Þ
where B, a, n are adjustable parameters, rc is the electrical conductivity of composites, rm is the electrical conductivity of polymeric matrix and /f is the volume portion of the filler [14,15]. The percolation concentration /c was determined as the inflexion point /i of the dependency, given by Eq. (1). The percolation concentration was
I. Novak et al. / European Polymer Journal 39 (2003) 585–592
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Fig. 1. Squares: relative electrical conductivity (rc =rm ) and circles: relative elongation at break (eb;c =eb;m ) of the carbon black filled epoxy on the volume filler content. Short-dashed line: curve fitting (Eq. (1)) (plot a), dashed line: model given by Eq. (7) (plot b), dotted line: NielsenÕs model (plot c), solid line: curve fitting by Eq. (4) (plot d).
Fig. 2. Squares: relative electrical conductivity (rc =rm ) and circles: relative elongation at break (eback =ebum ) of the graphite filled epoxy on the volume filler content. Short-dashed line: curve fitting (Eq. (1)) (plot a), dashed line: model given by Eq. (7) (plot b), dotted line: NielsenÕs model (plot c), solid line: curve fitting line by Eq. (4) (plot d).
found to be 14 vol% for epoxy/carbon black composites, 22 vol% for epoxy/graphite composites, 28 vol% for
epoxy/silver-coated fibres composites and 29 vol% for epoxy/silver-coated particles composites.
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Fig. 3. Squares: relative electrical conductivity (rc =rm ) and circles: relative elongation at break (eb;c =eb;m ) of the silver-coated particles filled epoxy on the volume filler content. Short dashed line: curve fitting (Eq. (1)) (plot a), dashed line: model given by Eq. (7) (plot b), dotted line: NielsenÕs model (plot c), solid line: curve fitting by Eq. (4) (plot d).
Fig. 4. Squares: relative electrical conductivity (rc =rm ) and circles: relative elongation at break (eb;c =eb;m ) of the silver-coated fibres filled epoxy on the volume filler content. Short dashed line: curve fitting (Eq. (1)) (plot a), dashed line: model given by Eq. (7) (plot b), dotted line: NielsenÕs model (plot c), solid line: curve fitting by Eq. (4) (plot d).
It is generally known that percolation concentration strongly depends on a shape of particles and its ability to
form network within a matrix [19]. Electrically conductive carbon black consists of very fine particles
I. Novak et al. / European Polymer Journal 39 (2003) 585–592
(10–50 nm) linked together to form aggregates [10,20]. Aggregates have a tendency to form network structures at low concentration of the filler, in dependence on the rheology of the polymers during the mixing process and in post-processing step, the wettability of particles by the polymer, solidification rates after mixing, degree of crystalline of polymeric matrix, polymer–carbon black interactions, etc. [20,21]. Graphite particles are irregularly shaped and display a significant anisotropy [22]. However, if particles are randomly oriented in the matrix, an average value of the electrical conductivity can be considered. We determined the average value of 1:4 104 S/m for dry, compressed graphite. The silver-coated particles are also irregularly shaped, but to in lower extent compared to the graphite particles. Since continuous silver layer is deposited on the surface of all particles, their electrical conductivity is similar to the electrical conductivity of pure silver (6:3 107 S/m), since electrical conductivity of core-mineral is negligible. Their main advantage, comparing to silver is significantly lower density and price. The same is true for silver-coated fibres. The lowest percolation concentration was found for epoxy/carbon black composites, higher for epoxy/graphite composites and the highest for epoxy/silver-coated particles or fibres. No significant difference in percolation concentration was observed comparing epoxy/silver-coated particles with fibres composites. On the other hand, much higher electrical conductivity was observed for epoxy filled with silver-coated particles and fibres than in the case of epoxy filled with graphite, especially at higher concentrations. For instance, electrical conductivity of epoxy filled with 51 vol% of the silver-coated fibres is 3:2 104 S/m, whereas electrical conductivity of epoxy filled with the same volume portion of graphite is only 4 102 S/m. The reason for this behaviour consists in a significantly higher electrical conductivity of silver compared to that of graphite.
589
crease in electrical conductivity as a consequence of formation of an internal network within a matrix. The investigation on low-density polyethylene/carbon black and high density polyethylene/carbon black composites revealed that the steepest decrease in elongation at breaks corresponds to the steepest increase of electrical conductivity on the dependence of the given parameter on the filler content. For more exact description of experimental dependencies new concept was suggested, which links percolation concentration with the decrease in elongation at break of the composite. In this paper more mathematical details as well as boundaries of validity are discussed. On the base of formal similarity, the exponential function ðf Þ, given by Eq. (4) was suggested for description of dependence of elongation at break on volume portion of the filler: eb;c f ¼ ¼ expðb/f Þ ð4Þ eb;m where eb;c , eb;m is elongation at break of composite or matrix, /f is volume fraction of the filler and b is adjustable parameter. We defined the ‘‘pseudopercolation’’ threshold determined as the intersection /x of the tangents of the dependence in the beginning and in the end of the curve, given by Eq. (4). Exact expression, for calculating the intersection x can be found in the following form: /x ¼
f ð0Þ f ð/f;max Þ þ k2 /f;max k2 k1
ð5Þ
where f ð0Þ is relative elongation at break for zero concentration of the filler (it equals 1), f ð/max Þ is relative elongation at break for maximally used concentration of the filler and k1 and k2 are derivations of the function in the beginning (k1 ) and in the end (k2 ) of the function, given as follows: k1 ¼ b and k2 ¼ b expðb/f;max Þ. As seen from Eq. (5), /x depends also on /f;max . This fact is not desirable for general application of the model. On the other hand, if:
3.2. Elongation at break The elongation at break of the investigated composites is shown in Figs. 1–4. Elongation at break of composites decreases with an increase in the filler content in all cases. Experimental data are compared with the most commonly used NielsenÕs model [18], given by Eq. (3): eb;c 1=3 ¼ 1 /f ð3Þ eb;m where eb;c , eb;m is elongation at break of composite or matrix and /f is volume portion of filler. It is seen that the agreement between experimental data and the model is not very good. In previous paper [14] we discussed a correlation between the decrease in elongation at break and the in-
i(i) jk1 j jk2 j and (ii) f ð0Þ f ð/f;max Þ, Eq. (5) can be rewritten to the form: 1 /x ffi b
ð6Þ
The parameters k1 , k2 and f ð/max Þ are shown in Table 1. As seen, the condition f ð0Þ ¼ 1 f ð/f;max Þ is reasonable in all cases. On the other hand, the condition jk1 j jk2 j is valid only roughly. As can be proved after some algebraical manipulation, the condition jk1 j jk2 j is valid, if /x /f;max . This fact was observed for both composites polyethylene/carbon black and high-density polyethylene/carbon black [14].
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Table 1 Percolation concentration of epoxy/electrically conductive filler composites Composite
/c
b
/x
Epoxy/carbon black Epoxy/graphite Epoxy/silver-coated particles Epoxy/silver-coated fibres
0.14 0.22 0.28 0.29
8.58 1.16 4.27 0.19 3.92 0.39 3.41 0.26
0.12 0.02 0.23 0.01 0.26 0.03 0.29 0.02
Percolation concentration (/c ) determined according to Eq. (2), parameter (b) determined from curve fitting of experimental data by Eq. (4), ‘‘pseudopercolation’’ concentration (/x ) determined according to Eq. (6).
The comparison of the accuracy of NielsenÕs model [18] and models given by Eqs. (4 and 7) is done in Table 2. Relative deviation (Di ) between experimental data and values predicted from the above-mentioned models was defined as follows:
The experimental data are compared with the model, given by Eq. (4) in Figs. 1–4. Good agreement between experimental results and the model for epoxy/graphite composites is observed. In the case of epoxy/silvercoated particles and fibres the agreement worst agreement between the model and experimental data is observed for epoxy/carbon black composites. This fact can be caused by higher agglomeration of the carbon black as well as with insufficient wetting of particles. On the other hand, if fitting parameter b was used for calculation of the ‘‘pseudopercolation’’ parameter x, these values were found to be close to the percolation concentration determined from electrical conductivity measurement in all investigated cases. This fact, as well as our previous experiments allows introducing the new function, which connects percolation concentration with elongation at break of electroconductive composites. This function is given by Eq. (4): eb;c ¼ exp eb;m
/f /c
Di ¼
: model jeexp b;c ð/f;i Þ eb;c ð/f;i Þj exp : eb;c ð/f;i Þ
Pn D¼
i¼1
ð8aÞ
Di
ð8bÞ
n
: where eexp b;c is experimentally determined elongation at break of composites, emodel are elongations at break deb;c termined according to Eqs. (3, 4 and 7), /f;i is the ith concentration of the filler and n is the number of experimental points. These results confirmed the suggestion that the clusters formed by the electroconductive particles form a path not only for the fast electron transfer but also for mechanical fracture along the formed micro-crack which can grow easily into the crack of catastrophic size, when the filler concentration is above certain level as discussed in [14]. As seen in Tables 3–6, models given by Eqs. (4 and 7) describe better the experimental data than NielsenÕs model does. The main advantage of Eq. (7) is that it enables to predict elongation at break of electroconductive composites from the knowledge of independent measured percolation concentration. The data confirm justification of the new introduced model, given by Eq. (7) and its applicability on the experimental data, despite of the fact that condition k1 , k2 is valid only to certain extent.
ð7Þ
where eb;c , eb , is elongation at break of the composite and the matrix, /f is volume fraction of the filler and /c is percolation concentration of the filler, determined from measurements of electrical conductivity. Eq. (7) is compared with experimental data in Figs. 1– 4. As seen, the correlation between experimental data and Eq. (7) is only approximative. On the other hand, Eq. (7) enables to predict elongation at break of electroconductive composites from the knowledge of percolation concentration determined from an independent measurement of electrical conductivity and therefore its utilization is more advantageous.
Table 2 Elongation at break of epoxy/electrically conductive filler composites Composite
f ð/max Þ ¼ emax b;c =eb;m
k1
k2
k1 =k2
Epoxy/carbon black Epoxy/graphite Epoxy/silver-coated particles Epoxy/silver-coated fibres
0.07 0.06 0.03 0.02
8.33 3.83 3.57 3.45
1.83 0.61 0.69 0.60
4.56 5.49 6.05 5.75
Elongation at break at maximum concentration of the filler (emax b;c ), elongation at break of matrix (eb;m ), derivation in the beginning (k1 ) and in the end (k2 ) of the curve, given by Eq. (4).
I. Novak et al. / European Polymer Journal 39 (2003) 585–592
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Table 3 Epoxy/carbon black composites /f
eb;c (%)
eNielsen (%) b;c
DNielsen i
eab;c (%)
Dai
emodel (%) b;c
Dmodel i
0 0.02 0.07 0.09 0.136 0.14 0.175 0.182
112 108 74 68 28 19 14 8
112 82 66 62 54 54 49 48
0 0.24 0.11 0.09 0.93 1.84 2.50 5.00
112 95 62 53 36 35 26 25
0 0.12 0.16 0.78 0.43 0.84 0.86 2.12
112 97 68 59 42 41 32 31
0 0.1 0.08 0.13 0.50 1.17 1.29 2.88
1.34
D
0.69
0.77
Volume portion of the filler (/f ), elongation at break of investigated composites (eb;c ), elongation at break determined according to ), elongation at break determined according to Eq. (4) (eab;c ), elongation at break determined according to Eq. (7) NielsenÕs model (eNielsen b;c (emodel ), relative deviation (Dai ), given by Eq. (8a) (superscripts: Nielsen, a and model mark, which values of elongation at break was b;c used), relative deviation (D) given by Eq. (8b).
Table 4 Epoxy/graphite composites /f
eb;c (%)
eNielsen (%) b;c
DNielsen i
eab;c (%)
Dai
emodel (%) b;c
Dmodel i
0 0.025 0.055 0.177 0.18 0.26 0.34 0.44 0.475 0.51
112 102 82 70 51 40 33 15 10 6
112 79 69 57 49 40 34 27 25 22
0 0.23 0.16 0.19 0.04 0 0.03 0.80 1.50 2.67
112 100 88 67 51 36 26 17 14 12
0 0.02 0.07 0.04 0 0.10 0.39 0.13 0.40 1.00
112 100 87 66 49 34 24 15 13 11
0 0.02 0.06 0.06 0.04 0.15 0.27 0 0.03 0.83
0.56
D
0.22
0.14
Volume portion of the filler (/f ), elongation at break of investigated composites (eb;c ), elongation at break determined according to NielsenÕs model (eNielsen ), elongation at break determined according to Eq. (4) (eab;c ), elongation at break determined according to Eq. (7) b;c (emodel ), relative deviation (Dai ), given by Eq. (8a) (superscripts: Nielsen, a and model mark, which values of elongation at break was b;c used), relative deviation (D) given by Eq. (8b).
Table 5 Epoxy/silver-coated particles composites /f
eb;c (%)
eNielsen (%) b;c
DNielsen i
eab;c (%)
Dai
emodel (%) b;c
Dmodel i
0 0.054 0.118 0.178 0.256 0.336 0.436 0.471 0.506
112 106 76 59 46 28 16 6 4
112 70 57 49 40 34 274 25 22
0 0.34 0.25 0.17 0.13 0.21 0.56 3.17 4.50
112 92 73 59 45 34 24 21 18
0 0.13 0.04 0 0.02 0.21 0.50 2.50 3.50
112 91 71 56 42 31 21 18 16
0 0.14 0.07 0.05 0.09 0.11 0.31 2.00 3.00
D
1.05
0.77
0.63
Volume portion of the filler (/f ), elongation at break of investigated composites (eb;c ), elongation at break determined according to NielsenÕs model (eNielsen ), elongation at break determined according to Eq. (4) (eab;c ), elongation at break determined according to Eq. (7) b;c model (eb;c ), relative deviation (Dai ), given by Eq. (8a) (superscripts: Nielsen, a and model mark, which values of elongation at break was used), relative deviation (D) given by Eq. (8b).
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Table 6 Epoxy/silver-coated fibres composites /f
eb;c (%)
eNielsen (%) b;c
DNielsen i
eab;c (%)
Dai
emodel (%) b;c
Dmodel i
0 0.054 0.118 0.178 0.256 0.336 0.436 0.471 0.506
112 110 82 64 50 33 21 18 12
112 70 57 49 40 34 274 25 22
0 0.34 0.25 0.17 0.13 0.21 0.56 3.17 4.50
112 93 75 61 46 35 25 22 20
0 0.15 0.09 0.05 0.08 0.06 0.19 0.22 0.67
112 93 75 61 46 35 25 22 20
0 0.15 0.09 0.05 0.08 0.06 0.19 0.22 0.67
D
1.05
0.17
0.17
Volume portion of the filler (/f ), elongation at break of investigated composites (eb;c ), elongation at break determined according to NielsenÕs model (eNielsen ), elongation at break determined according to Eq. (4) (eab;c ), elongation at break determined according to Eq. (7) b;c a (emodel b;c ), relative deviation (Di ), given by Eq. (8a) (superscripts: Nielsen, a and model mark, which values of elongation at break was used), relative deviation (D) given by Eq. (8b).
4. Conclusions Percolation concentrations were estimated to be 14 vol% for epoxy/carbon black composites, 22 vol% for epoxy/graphite composites, 28–29 vol% for both epoxy/ silver-coated particles and epoxy/silver-coated fibres. Electrical conductivity increases in the order of fillers: silver-coated fibres > silver-coated particles > graphite at the comparable concentrations of the filler. In the case of carbon black, the maximum concentration of the filler only 18 vol% was found due to insufficient dispergation and high agglomeration of aggregates. The decrease of elongation at break with an increase in filler content was observed in all cases. A good correlation between phenomenological model and experimental data for all investigated systems was also observed.
Acknowledgements The authors are grateful to the Slovak grant agency VEGA (grant no. 2/1060/21) for financial support of this research.
References [1] Lyons AM, Dahringer DW. In: Pizzi A, Mittal KL, editors. Handbook of adhesive technology. New York: Marcel Dekker Inc; 1994. p. 565.
[2] Lu D, Wong CP. Int J Adhes Adhes 2000;20:189. [3] Omastova M, Pionteck J, Pavlinec J, Simon F. Polym Int 1997;43:109. [4] Jiang G, Gilbert M, Hitt DJ, Wilcox GD, Balasubramanian K. Composites 2002;A33:745. [5] Lu D, Wong D, Wong CP. J Electron Manufact 2000; 23:241. [6] Lu D, Wong CP. IEEE Trans Comp Pack Technol 2000;23:620. [7] Kozlowski M, Kozlowska A. Macromol Symp 1996; 108:261. [8] Schueler R, Petermann J, Schulte K, Wetzel HP. J Appl Polym Sci 1997;63:1741. [9] Mamunya YeP, Davydenko VV, Pissis P, Lebedev EV. Eur Polym J 2002;38:1887. [10] Novak I, Krupa I, Chodak I. J Mater Sci Lett 2002; 21:1039. [11] Small DJ, Eisenach B. Surf Mount Technol Magaz 1998; 12:52. [12] Savolainen P, Kivilahti J. J Adhes 1995;49:187. [13] Sancaktar E, Dilsiz N. J Adhes Sci Technol 1999;13:763. [14] Chodak I, Krupa I. J Mater Sci Lett 1999;18:1457. [15] Krupa I, Chodak I. Eur Polym J 2001;37:2159. [16] Thongruang W, Spontak R, Balik CM. Polymer 2002; 43:2279. [17] Flandin L, Hiltner A, Baer E. Polymer 2001;42:827. [18] Nielsen R. Mechanical properties of polymers and composites 2. New York: Marcel Dekker; 1974. [19] Lux F. J Mater Sci 1993;28:285. [20] Narkis M, Srivastava S, Tchoudakov R, Breuer O. Synth Metals 2000;113:29. [21] Gul VE. Structure and properties of conducting polymer composites. Utrecht, Tokyo: VSB; 1996. [22] Lide DR, Fredrikse HPR, editors. Handbook of chemistry and physics. 75th ed. New York: CRC Press; 1995–1996.
Analysis of correlation between percolation concentration and elongation at break in filled electroconductive epoxy-based adhesives Igor Nov ak *, Igor Krupa, Ivan Chod ak Polymer Institute of the Slovak Academy of Sciences, D ubravsk a cesta 9, Bratislava 84236, Slovakia Received 21 March 2002; received in revised form 30 August 2002; accepted 25 September 2002
Abstract Electrical conductivity and elongation at break of epoxy filled with electroconductive carbon black, graphite or with silver-coated basalt particles or fibres were investigated in this paper. Percolation concentrations were determined to be 14 vol% for epoxy/carbon black composites, 22 vol% for epoxy/graphite composites, 28–29 vol% for both epoxy/silvercoated basalt particles and fibres. The steepest increase in electrical conductivity and the most pronounced decrease in elongation at break occurs at similar filler concentration range for all investigated systems. A good correlation between phenomenological model, introduced in [J. Mater. Sci. Lett. 18 (1998) 1457] and experimental data for all investigated systems was observed. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Adhesives; Electrical conductivity; Elongation; Epoxy resin; Silver; Carbon black
1. Introduction Electrically conductive adhesives have attracted great attention because of their adhesive and electrical properties and numerous potential applications [1,2]. It is well known that polymers filled with electrically conductive particles, exhibit a distinctive dependence of conductivity on the concentration of filler [3,4]. A growing interest is observed in the potential of electrically conductive metal-loaded polymer adhesives for solder replacement in surface mount technology and other microelectronic application. A growing interest is observed in the potential of electrically conductive metal-loaded polymer adhesives for solder replacement in surface mount technology and other microelectronic application [5,6] in cases when soldering is difficult or impossible because of low ther-
*
Corresponding author. E-mail address: [email protected] (I. Novak).
mal stability. An adhesive joining has to have either better properties or more simple technology compared to a traditional soldering. When an adhesive is loaded with a critical or higher concentration of electrically conductive filler, e.g. carbon black, graphite or metallic powder, known as the percolation threshold, transition of the composite adhesive from insulator to electrical conductor is observed [7–9]. The filler, e.g. silver-based particles and/or carbonbased filler, e.g. graphite or electrically conductive carbon black, form the electroconductive paths between the surfaces of the joint parts. Electrically conductive adhesives are also applicable for a formation of surface electroconductive shielding layer and for partially flexible electroconductive connections [10]. Two-component epoxy-based electrically conductive adhesives were developed for a broad application in many areas for both industry and household. Continuing technological development have enabled electrically conductive adhesives to be used not only as solder replacement, but also in many assembly applications such
0014-3057/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 4 - 3 0 5 7 ( 0 2 ) 0 0 2 7 1 - 9
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I. Novak et al. / European Polymer Journal 39 (2003) 585–592
as electromagnetic shielding, printed circuit manufacture, electronics packaging and surface mount technology [11–13]. Electrical and mechanical properties of epoxy-based electrically conductive adhesives containing graphite or metallized filler are investigated in this paper. The correlation between electrical conductivity and elongation at break has been investigated in all electrically conductive adhesive systems, related to the previously described correlation of the two parameters observed for thermoplastic matrices [14–17].
spective filler using a lab-scale mixer (Koba, SR) for 20 min at the mixing speed 20 rpm. The components of the composite adhesive were mixed together in the weight ratio 2:1. The dog-bone specimens with a working area 35 3:6 1 mm (mechanical experiments) and/or a circles with a diameter 30 mm and a thickness about 0.5 mm (measurements of electrical properties) were prepared by casting in the silicone rubber forms. The samples were tested after seven days of adhesive hardening. All procedures have been carried out at ambient temperature.
2. Experimental
2.2.3. Measurement of mechanical and electrical properties The elongation at break was measured at ambient temperature using an universal testing machine Instron 4301 (Instron, England) equipped with the 5 kN measuring cell and the software Serie IX at deformation rate 10 mm/min. The volume electrical conductivity of adhesives was measured according to ASTM D-257. Three-electrode electrometer arrangement was used for the DC measurement of the resistivity. The voltage level varied in the range 0.1–500 V.
2.1. Materials Two-component epoxy adhesive consisting of epoxy oligomer (bisphenol-A-diglycidylether) ChS Epoxy 531 (produced by Spolchemie, Czech Republic) modified by reactive solvent (1,6-hexanediol-diglycidylether) (Sachem, USA), viscosity at 25 °C ¼ 2:2 Pa s and a curing agent (diethylene triamine-based) Aminoamid DE 400 (Bohemiachem, Czech Republic) was used as a polymer matrix. Four kinds of filler were investigated, namely homemade silver-coated basalt particles prepared by a chemical method having diameter <15 lm and density 2.28 g cm3 , a thickness of metallic layer 1 lm, silver-coated basalt fibres with average aspect ratio approximately 5 and density 2.28 g cm3 , and a special grade of graphite with a carbon content >99.9%, size of particles being <15 m (KS 15), density 2.25 g cm3 (produced by Lonza, Switzerland). The special kind of carbon black Vulcan XC-72 R (Cabot, USA) having particle size approximately 30 nm, a specific area 254 m2 g1 and density 1.8 g cm3 was used. 2.2. Methods 2.2.1. Preparation of metallized particles The metal-coated particles were prepared using a method of electroless metallization. Two solutions have been prepared, namely solution A consisting of silver nitride (30 g) dissolved in 1000 ml of distilled water and solution B obtained by dissolving natrium–potassium tartrate (50 g) in distilled water (900 ml). Mixing 100 ml solution A and 20 ml solution B together at ambient temperature the bath for metallization was prepared. The particles were metallized in the bath at ambient temperature during 20 min, then washed thoroughly by distilled water and dried at 60 °C. 2.2.2. Preparation of adhesives and samples The electrically conductive adhesives were prepared by mixing both components of epoxy having the re-
3. Results and discussion 3.1. Electrical conductivity The dependencies of electrical conductivity of epoxy filled with electroconductive carbon black, graphite, silver-coated particles and fibres on the volume portion of the filler are shown in Figs. 1–4. In all cases, a dramatical increase in electrical conductivity was observed around a particular concentration of the filler. This concentration is generally called percolation concentration, i.e. the filler concentration at which the steep change in conductivity occurs and it is a basic characteristics of a conductive composite. The value of the percolation concentration was determined by fitting the experimental data using Eq. (1) and fitting parameters n and a were used to estimate the percolation concentration in terms of Eq. (2): logðrc =rm Þ ¼ Bð1 ea/f Þn
ð1Þ
/i /c ¼ lnðnÞ=a
ð2Þ
where B, a, n are adjustable parameters, rc is the electrical conductivity of composites, rm is the electrical conductivity of polymeric matrix and /f is the volume portion of the filler [14,15]. The percolation concentration /c was determined as the inflexion point /i of the dependency, given by Eq. (1). The percolation concentration was
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Fig. 1. Squares: relative electrical conductivity (rc =rm ) and circles: relative elongation at break (eb;c =eb;m ) of the carbon black filled epoxy on the volume filler content. Short-dashed line: curve fitting (Eq. (1)) (plot a), dashed line: model given by Eq. (7) (plot b), dotted line: NielsenÕs model (plot c), solid line: curve fitting by Eq. (4) (plot d).
Fig. 2. Squares: relative electrical conductivity (rc =rm ) and circles: relative elongation at break (eback =ebum ) of the graphite filled epoxy on the volume filler content. Short-dashed line: curve fitting (Eq. (1)) (plot a), dashed line: model given by Eq. (7) (plot b), dotted line: NielsenÕs model (plot c), solid line: curve fitting line by Eq. (4) (plot d).
found to be 14 vol% for epoxy/carbon black composites, 22 vol% for epoxy/graphite composites, 28 vol% for
epoxy/silver-coated fibres composites and 29 vol% for epoxy/silver-coated particles composites.
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Fig. 3. Squares: relative electrical conductivity (rc =rm ) and circles: relative elongation at break (eb;c =eb;m ) of the silver-coated particles filled epoxy on the volume filler content. Short dashed line: curve fitting (Eq. (1)) (plot a), dashed line: model given by Eq. (7) (plot b), dotted line: NielsenÕs model (plot c), solid line: curve fitting by Eq. (4) (plot d).
Fig. 4. Squares: relative electrical conductivity (rc =rm ) and circles: relative elongation at break (eb;c =eb;m ) of the silver-coated fibres filled epoxy on the volume filler content. Short dashed line: curve fitting (Eq. (1)) (plot a), dashed line: model given by Eq. (7) (plot b), dotted line: NielsenÕs model (plot c), solid line: curve fitting by Eq. (4) (plot d).
It is generally known that percolation concentration strongly depends on a shape of particles and its ability to
form network within a matrix [19]. Electrically conductive carbon black consists of very fine particles
I. Novak et al. / European Polymer Journal 39 (2003) 585–592
(10–50 nm) linked together to form aggregates [10,20]. Aggregates have a tendency to form network structures at low concentration of the filler, in dependence on the rheology of the polymers during the mixing process and in post-processing step, the wettability of particles by the polymer, solidification rates after mixing, degree of crystalline of polymeric matrix, polymer–carbon black interactions, etc. [20,21]. Graphite particles are irregularly shaped and display a significant anisotropy [22]. However, if particles are randomly oriented in the matrix, an average value of the electrical conductivity can be considered. We determined the average value of 1:4 104 S/m for dry, compressed graphite. The silver-coated particles are also irregularly shaped, but to in lower extent compared to the graphite particles. Since continuous silver layer is deposited on the surface of all particles, their electrical conductivity is similar to the electrical conductivity of pure silver (6:3 107 S/m), since electrical conductivity of core-mineral is negligible. Their main advantage, comparing to silver is significantly lower density and price. The same is true for silver-coated fibres. The lowest percolation concentration was found for epoxy/carbon black composites, higher for epoxy/graphite composites and the highest for epoxy/silver-coated particles or fibres. No significant difference in percolation concentration was observed comparing epoxy/silver-coated particles with fibres composites. On the other hand, much higher electrical conductivity was observed for epoxy filled with silver-coated particles and fibres than in the case of epoxy filled with graphite, especially at higher concentrations. For instance, electrical conductivity of epoxy filled with 51 vol% of the silver-coated fibres is 3:2 104 S/m, whereas electrical conductivity of epoxy filled with the same volume portion of graphite is only 4 102 S/m. The reason for this behaviour consists in a significantly higher electrical conductivity of silver compared to that of graphite.
589
crease in electrical conductivity as a consequence of formation of an internal network within a matrix. The investigation on low-density polyethylene/carbon black and high density polyethylene/carbon black composites revealed that the steepest decrease in elongation at breaks corresponds to the steepest increase of electrical conductivity on the dependence of the given parameter on the filler content. For more exact description of experimental dependencies new concept was suggested, which links percolation concentration with the decrease in elongation at break of the composite. In this paper more mathematical details as well as boundaries of validity are discussed. On the base of formal similarity, the exponential function ðf Þ, given by Eq. (4) was suggested for description of dependence of elongation at break on volume portion of the filler: eb;c f ¼ ¼ expðb/f Þ ð4Þ eb;m where eb;c , eb;m is elongation at break of composite or matrix, /f is volume fraction of the filler and b is adjustable parameter. We defined the ‘‘pseudopercolation’’ threshold determined as the intersection /x of the tangents of the dependence in the beginning and in the end of the curve, given by Eq. (4). Exact expression, for calculating the intersection x can be found in the following form: /x ¼
f ð0Þ f ð/f;max Þ þ k2 /f;max k2 k1
ð5Þ
where f ð0Þ is relative elongation at break for zero concentration of the filler (it equals 1), f ð/max Þ is relative elongation at break for maximally used concentration of the filler and k1 and k2 are derivations of the function in the beginning (k1 ) and in the end (k2 ) of the function, given as follows: k1 ¼ b and k2 ¼ b expðb/f;max Þ. As seen from Eq. (5), /x depends also on /f;max . This fact is not desirable for general application of the model. On the other hand, if:
3.2. Elongation at break The elongation at break of the investigated composites is shown in Figs. 1–4. Elongation at break of composites decreases with an increase in the filler content in all cases. Experimental data are compared with the most commonly used NielsenÕs model [18], given by Eq. (3): eb;c 1=3 ¼ 1 /f ð3Þ eb;m where eb;c , eb;m is elongation at break of composite or matrix and /f is volume portion of filler. It is seen that the agreement between experimental data and the model is not very good. In previous paper [14] we discussed a correlation between the decrease in elongation at break and the in-
i(i) jk1 j jk2 j and (ii) f ð0Þ f ð/f;max Þ, Eq. (5) can be rewritten to the form: 1 /x ffi b
ð6Þ
The parameters k1 , k2 and f ð/max Þ are shown in Table 1. As seen, the condition f ð0Þ ¼ 1 f ð/f;max Þ is reasonable in all cases. On the other hand, the condition jk1 j jk2 j is valid only roughly. As can be proved after some algebraical manipulation, the condition jk1 j jk2 j is valid, if /x /f;max . This fact was observed for both composites polyethylene/carbon black and high-density polyethylene/carbon black [14].
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Table 1 Percolation concentration of epoxy/electrically conductive filler composites Composite
/c
b
/x
Epoxy/carbon black Epoxy/graphite Epoxy/silver-coated particles Epoxy/silver-coated fibres
0.14 0.22 0.28 0.29
8.58 1.16 4.27 0.19 3.92 0.39 3.41 0.26
0.12 0.02 0.23 0.01 0.26 0.03 0.29 0.02
Percolation concentration (/c ) determined according to Eq. (2), parameter (b) determined from curve fitting of experimental data by Eq. (4), ‘‘pseudopercolation’’ concentration (/x ) determined according to Eq. (6).
The comparison of the accuracy of NielsenÕs model [18] and models given by Eqs. (4 and 7) is done in Table 2. Relative deviation (Di ) between experimental data and values predicted from the above-mentioned models was defined as follows:
The experimental data are compared with the model, given by Eq. (4) in Figs. 1–4. Good agreement between experimental results and the model for epoxy/graphite composites is observed. In the case of epoxy/silvercoated particles and fibres the agreement worst agreement between the model and experimental data is observed for epoxy/carbon black composites. This fact can be caused by higher agglomeration of the carbon black as well as with insufficient wetting of particles. On the other hand, if fitting parameter b was used for calculation of the ‘‘pseudopercolation’’ parameter x, these values were found to be close to the percolation concentration determined from electrical conductivity measurement in all investigated cases. This fact, as well as our previous experiments allows introducing the new function, which connects percolation concentration with elongation at break of electroconductive composites. This function is given by Eq. (4): eb;c ¼ exp eb;m
/f /c
Di ¼
: model jeexp b;c ð/f;i Þ eb;c ð/f;i Þj exp : eb;c ð/f;i Þ
Pn D¼
i¼1
ð8aÞ
Di
ð8bÞ
n
: where eexp b;c is experimentally determined elongation at break of composites, emodel are elongations at break deb;c termined according to Eqs. (3, 4 and 7), /f;i is the ith concentration of the filler and n is the number of experimental points. These results confirmed the suggestion that the clusters formed by the electroconductive particles form a path not only for the fast electron transfer but also for mechanical fracture along the formed micro-crack which can grow easily into the crack of catastrophic size, when the filler concentration is above certain level as discussed in [14]. As seen in Tables 3–6, models given by Eqs. (4 and 7) describe better the experimental data than NielsenÕs model does. The main advantage of Eq. (7) is that it enables to predict elongation at break of electroconductive composites from the knowledge of independent measured percolation concentration. The data confirm justification of the new introduced model, given by Eq. (7) and its applicability on the experimental data, despite of the fact that condition k1 , k2 is valid only to certain extent.
ð7Þ
where eb;c , eb , is elongation at break of the composite and the matrix, /f is volume fraction of the filler and /c is percolation concentration of the filler, determined from measurements of electrical conductivity. Eq. (7) is compared with experimental data in Figs. 1– 4. As seen, the correlation between experimental data and Eq. (7) is only approximative. On the other hand, Eq. (7) enables to predict elongation at break of electroconductive composites from the knowledge of percolation concentration determined from an independent measurement of electrical conductivity and therefore its utilization is more advantageous.
Table 2 Elongation at break of epoxy/electrically conductive filler composites Composite
f ð/max Þ ¼ emax b;c =eb;m
k1
k2
k1 =k2
Epoxy/carbon black Epoxy/graphite Epoxy/silver-coated particles Epoxy/silver-coated fibres
0.07 0.06 0.03 0.02
8.33 3.83 3.57 3.45
1.83 0.61 0.69 0.60
4.56 5.49 6.05 5.75
Elongation at break at maximum concentration of the filler (emax b;c ), elongation at break of matrix (eb;m ), derivation in the beginning (k1 ) and in the end (k2 ) of the curve, given by Eq. (4).
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Table 3 Epoxy/carbon black composites /f
eb;c (%)
eNielsen (%) b;c
DNielsen i
eab;c (%)
Dai
emodel (%) b;c
Dmodel i
0 0.02 0.07 0.09 0.136 0.14 0.175 0.182
112 108 74 68 28 19 14 8
112 82 66 62 54 54 49 48
0 0.24 0.11 0.09 0.93 1.84 2.50 5.00
112 95 62 53 36 35 26 25
0 0.12 0.16 0.78 0.43 0.84 0.86 2.12
112 97 68 59 42 41 32 31
0 0.1 0.08 0.13 0.50 1.17 1.29 2.88
1.34
D
0.69
0.77
Volume portion of the filler (/f ), elongation at break of investigated composites (eb;c ), elongation at break determined according to ), elongation at break determined according to Eq. (4) (eab;c ), elongation at break determined according to Eq. (7) NielsenÕs model (eNielsen b;c (emodel ), relative deviation (Dai ), given by Eq. (8a) (superscripts: Nielsen, a and model mark, which values of elongation at break was b;c used), relative deviation (D) given by Eq. (8b).
Table 4 Epoxy/graphite composites /f
eb;c (%)
eNielsen (%) b;c
DNielsen i
eab;c (%)
Dai
emodel (%) b;c
Dmodel i
0 0.025 0.055 0.177 0.18 0.26 0.34 0.44 0.475 0.51
112 102 82 70 51 40 33 15 10 6
112 79 69 57 49 40 34 27 25 22
0 0.23 0.16 0.19 0.04 0 0.03 0.80 1.50 2.67
112 100 88 67 51 36 26 17 14 12
0 0.02 0.07 0.04 0 0.10 0.39 0.13 0.40 1.00
112 100 87 66 49 34 24 15 13 11
0 0.02 0.06 0.06 0.04 0.15 0.27 0 0.03 0.83
0.56
D
0.22
0.14
Volume portion of the filler (/f ), elongation at break of investigated composites (eb;c ), elongation at break determined according to NielsenÕs model (eNielsen ), elongation at break determined according to Eq. (4) (eab;c ), elongation at break determined according to Eq. (7) b;c (emodel ), relative deviation (Dai ), given by Eq. (8a) (superscripts: Nielsen, a and model mark, which values of elongation at break was b;c used), relative deviation (D) given by Eq. (8b).
Table 5 Epoxy/silver-coated particles composites /f
eb;c (%)
eNielsen (%) b;c
DNielsen i
eab;c (%)
Dai
emodel (%) b;c
Dmodel i
0 0.054 0.118 0.178 0.256 0.336 0.436 0.471 0.506
112 106 76 59 46 28 16 6 4
112 70 57 49 40 34 274 25 22
0 0.34 0.25 0.17 0.13 0.21 0.56 3.17 4.50
112 92 73 59 45 34 24 21 18
0 0.13 0.04 0 0.02 0.21 0.50 2.50 3.50
112 91 71 56 42 31 21 18 16
0 0.14 0.07 0.05 0.09 0.11 0.31 2.00 3.00
D
1.05
0.77
0.63
Volume portion of the filler (/f ), elongation at break of investigated composites (eb;c ), elongation at break determined according to NielsenÕs model (eNielsen ), elongation at break determined according to Eq. (4) (eab;c ), elongation at break determined according to Eq. (7) b;c model (eb;c ), relative deviation (Dai ), given by Eq. (8a) (superscripts: Nielsen, a and model mark, which values of elongation at break was used), relative deviation (D) given by Eq. (8b).
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Table 6 Epoxy/silver-coated fibres composites /f
eb;c (%)
eNielsen (%) b;c
DNielsen i
eab;c (%)
Dai
emodel (%) b;c
Dmodel i
0 0.054 0.118 0.178 0.256 0.336 0.436 0.471 0.506
112 110 82 64 50 33 21 18 12
112 70 57 49 40 34 274 25 22
0 0.34 0.25 0.17 0.13 0.21 0.56 3.17 4.50
112 93 75 61 46 35 25 22 20
0 0.15 0.09 0.05 0.08 0.06 0.19 0.22 0.67
112 93 75 61 46 35 25 22 20
0 0.15 0.09 0.05 0.08 0.06 0.19 0.22 0.67
D
1.05
0.17
0.17
Volume portion of the filler (/f ), elongation at break of investigated composites (eb;c ), elongation at break determined according to NielsenÕs model (eNielsen ), elongation at break determined according to Eq. (4) (eab;c ), elongation at break determined according to Eq. (7) b;c a (emodel b;c ), relative deviation (Di ), given by Eq. (8a) (superscripts: Nielsen, a and model mark, which values of elongation at break was used), relative deviation (D) given by Eq. (8b).
4. Conclusions Percolation concentrations were estimated to be 14 vol% for epoxy/carbon black composites, 22 vol% for epoxy/graphite composites, 28–29 vol% for both epoxy/ silver-coated particles and epoxy/silver-coated fibres. Electrical conductivity increases in the order of fillers: silver-coated fibres > silver-coated particles > graphite at the comparable concentrations of the filler. In the case of carbon black, the maximum concentration of the filler only 18 vol% was found due to insufficient dispergation and high agglomeration of aggregates. The decrease of elongation at break with an increase in filler content was observed in all cases. A good correlation between phenomenological model and experimental data for all investigated systems was also observed.
Acknowledgements The authors are grateful to the Slovak grant agency VEGA (grant no. 2/1060/21) for financial support of this research.
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