Electrical conductivity and mechanical properties of melt-spun ternary composites comprising PMMA, carbon fibers and carbon black

Composites Science and Technology 150 (2017) 24e31

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Electrical conductivity and mechanical properties of melt-spun ternary composites comprising PMMA, carbon fibers and carbon black Muchao Qu a, *, Fritjof Nilsson b, *, 1, Yijing Qin a, Guanda Yang a, Yamin Pan a, Xianhu Liu c, Gabriel Hernandez Rodriguez a, Jianfan Chen a, Chunhua Zhang d, Dirk W. Schubert a, * a

Institute of Polymer Materials, Friedrich-Alexander-University Erlangen-Nuremberg, Martensstr. 7, 91058 Erlangen, Germany KTH Royal Institute of Technology, School of Chemical Science and Engineering, Fibre and Polymer Technology, SE-100 44 Stockholm, Sweden National Engineering Research Center for Advanced Polymer Processing Technology, Zhengzhou University, Zhengzhou 450002, China d School of Chemical Engineering and Technology, Harbin Institute of Technology, 150001 Harbin, China b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 March 2017 Received in revised form 23 May 2017 Accepted 2 July 2017 Available online 6 July 2017

In this study, the electrical conductivity of melt spun composites consisting of PMMA containing both aligned carbon fibers (CF) and carbon black (CB) has been investigated. A broad range of composite compositions (up to 50 vol % CF and 20 vol % CB) was studied. The percolation thresholds of binary PMMA/CF and PMMA/CB composites were determined to 31.8 and 3.9 vol %, respectively. Experimental conductivity contour plots for PMMA/CF/CB ternary composites were presented for the first time. Additionally, based on a model for predicting the percolation threshold of ternary composites, a novel equation was proposed to predict the conductivity of ternary composites, showing results in agreement with corresponding experimental data. Finally, two mechanical contour plots for elastic modulus and tensile strength were presented, showing how the decreasing tensile strength and increasing E-modulus of the PMMA/CF/CB ternary composites was depending on the CB and CF filling fractions. The systematic measurements and novel equations presented in this work are especially valuable when designing ternary conductive polymer composites with two different fillers. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Carbon fibers Carbon black Electrical properties Melt-spinning

1. Introduction Conductive polymer composites (CPCs) have been widely used in many fields, such as anti-static materials, electromagnetic interference (EMI) shielding, sensor and conductors. CPCs have been extensively investigated in both academia and industry, because the combination of promising material properties and comparatively simple manufacturing processes often imply commercially interesting materials [1,2]. Nowadays, the conductivity of CPCs is generally explained by “conductive pathways” in the composites, which are formed by conductive fillers [3e6]. As the fillers fraction increases, the number of “conductive pathways” growth, and consequently, the conductivity of the composite also increases. An electrical percolation threshold is defined as a certain

* Corresponding authors. E-mail addresses: [email protected] (M. Qu), [email protected] (F. Nilsson), [email protected] (D.W. Schubert). 1 The author Fritjof Nilsson contributed equally to this work and should be considered as co-first authors. http://dx.doi.org/10.1016/j.compscitech.2017.07.004 0266-3538/© 2017 Elsevier Ltd. All rights reserved.

critical value filler fraction when the conductivity of the composite increases by several orders of magnitude [7e9]. Carbon black (CB) and carbon fibers (CFs) are the most commonly used conductive fillers, which can be incorporated into a polymer matrix for facilitating the formation of a CPCs. The CF are elongated while the primary CB particles are spherical. This kind of CB (XE2) is however highly structured and the primary particles are fused to small aggregates which in turn form agglomerates [10], resulting in a significantly reduced percolation threshold. Synergistic effects of CPCs containing both CFs and CB have been reported [11e16]. In a system with randomly dispersed CFs and CB particles, clusters of CB may form short “conductive pathways” between the CFs. Therefore, the conductivity of composites containing both fillers can be enhanced, as compared to those with only CFs or CB at the same concentration of fillers. However, in a CPC system with randomly dispersed fillers (Fig. 1a), the conductive pathways formed between CFs also contribute to the conductive networks [11e16]. To evaluate the real synergic effect between CFs and CB, the effect of the CF-pathways in a PMMA/CB/CF system should be minimized. Therefore, the melt

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Fig. 1. Schematic of the conductive pathway formed by CB and CFs in the CPCs. (a) CPCs with randomly dispersed CFs, conductive pathway are contributed also by CFs themselves; (b) CPCs with highly orientated CFs, the contacts between CFs are reduced. With the addition of CB particles, a fence-like structure can be formed; (c) cross section view of fiber composites with fence-like structure.

spinning process [25] is applied in this study, in order to induce a maximum alignment of the CFs in the CPCs and consequently, to reduce the contacts between the CFs. With the addition of CB particles, “conductive pathways” can also be formed between the parallel CFs, such that fence-like structure is formed. (A side view and a cross section view of an idealized fence-like geometry is shown in Fig. 1b and c, respectively). Then the real synergistic effect between CB and CFs can be revealed. Synergistic effects were also reported between CB and carbon nanotubes (CNT) in ternary composites [17e19]. CNT and CF are both suitable conductive 1-D fillers. In this study CFs were chosen due to their (1) improved melt mixing dispersion (2) more distinct cylindrical shape, (3) larger size, which simplifies microscopy analysis and (4) higher percolation threshold, which enabled a more genuine validation of our analytical conductivity model. Several theories [20,21] have been suggested to describe the conductivity of binary composites, but few models consider the conductivity of ternary composites with two conductive fillers. Sun et al. [24] have proposed a percolation threshold model based on the assumption that the excluded volume of the two fillers can be added together linearly. The percolation threshold of a conductive composite with two fillers can then be predicted as:

fA f þ B ¼K fc;A fc;B

(1)

where fA and fB are the volume fractions of filler A and filler B in ternary composites, respectively, while fc,A and fc,B are the corresponding percolation concentrations when filler A or B is used alone in binary composites. When K ¼ 1, the percolation threshold is just reached. When K > 1 the fillers in the composites connect each other (i.e. the composites are conductive) and when K < 1 the composites are insulating. Based on this model, the potential synergic effects between CFs and CB have been discussed [13], defining “synergy” as a lower percolation threshold of the mixture than predicted by Eq. (1) with K ¼ 1. It should be noted that, according to Eq. (1), a linear relationship between volume fractions fA and fB can be established once the percolation thresholds fc,A and fc,B are determined. Therefore, a conductivity contour plot versus fCFs and fCB was presented in this work, such that the linear equation (Eq. (1)) could be evaluated. Since the experimental conductivity measurements did not fully support Eq. (1), an improved original equation was proposed in this work for predicting the electrical percolation threshold of ternary composites containing two different conductive fillers. In addition, based on the improved percolation threshold equation, a novel equation for predicting the electrical conductivity of ternary composite was also developed.

2. Experimental methods 2.1. Materials €hm The polymer matrix was PMMA Plexiglas 7N from Evonik Ro GmbH (Germany), with a weight-average molar mass of 99 kg/mol, a polydispersity index of 1.52, and a density 1.19 g/cm3. CF segments were obtained from Tenax® - JHT C493 6 mm (Toho Tenax Europe GmbH) with a diameter of 7 mm, a specific resistance of 1.7  103 U/cm, and a density 1.79 g/cm3. CB was Printex XE2 from Evonik Degussa, with a specific surface area of 900 m2/g measured by the BET-method. The mean diameter of the primary CB particles was around 35 nm and the density at room temperature was 2.13 g/ cm3. 2.2. Sample preparation All the materials were dried in vacuum at 80  C prior to processing. Both the PMMA/CF composites (with parallel fiber orientations) and the PMMA/CB composites were prepared by melt mixing in an internal kneader PolyDrive (Haake, 557e8310) at a temperature of 200  C and a rotation speed of 60 rpm, 20 min. Composites with 50 vol % CFs were treated as master batches, and further diluted with pure PMMA or PMMA/CB. Using this two-step melt mixing procedure, PMMA/CF binary composites with CFs concentration varies from 10 vol % to 50 vol % were produced, and the aspect ratio (AR ¼ 9.2 ± 1.3) of CFs from different samples was well controlled (Fig. 2) [25]. After melt mixing, all the composites were ground into granules and dried under vacuum at 80  C for 24 h. After drying, the composite granules were melt spun at 200  C €ttfert, Rheograph 2003), with a die in a capillary rheometer (Go 10 mm long and 1 mm in diameter, at an extrusion speed of 0.08 mm/s. The following nomenclature is used for the samples: aCB and bCF denote the composites with a % volume fraction of CB, and b % volume fraction of CFs, respectively. Thus, the sample with the name aCBbCF presents the ternary composite filled with a vol. % CB and b vol. % CFs and (100-a-b) vol. % PMMA. In this study, a 2 [0, 20], and b 2 [0, 50]. 2.3. Sample characterization The melt-spun composite samples were fractured in liquid nitrogen, the broken sections were sputtered with a thin layer of palladium, and were then analyzed using a SEM (Leica, LEO 435VP) equipped with a secondary electron detector at an acceleration voltage of 3 kV. The fiber composites were cut into samples of 20 mm length and their end-sections were polished in order to remove isolate

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M. Qu et al. / Composites Science and Technology 150 (2017) 24e31

Fig. 2. Process flow chart of the two-step melt mixing method.

polymer. Silver conductive paste was then coated (exclusively) at the polished ends, to ensure enough contact between the samples and the copper electrode, as shown in Fig. 3. The electrical resistance R of the samples at room temperature was measured using a Keithley 6487 Pico ammeter at a constant voltage 1 V. The volume conductivity s was calculated as follows:

s¼

4L

p,D2 ,R

(2)

where R is the electrical resistance of the composite, L is the distance between two silver-coated ends of the sample, and D is the diameter of the fiber composite. An average of 10 specimens from each composition of fiber composites was measured to obtain the volume conductivity s. The tensile test was performed at a strain rate of 20 mm/min on a Zwick Z050 Test Machine with a 50 kN load cell, until the samples were broken. The length of the cylindrical specimens between two clamps was 20 mm, and the elastic modulus (E-modulus) of the samples was calculated by computer. An average of 10 specimens of fiber composites with each composition was used to calculate the E-modulus of each fiber composite. 3. Results and discussion 3.1. Morphology Fig. 4 shows a cross section of a PMMA/CF/CB composite (with parallel CF fibers), which reveals the assumed fence-like structure of Fig. 1b. In Fig. 4 a and b, the cross section of the complete sample is presented. CFs as well as “black holes” (positions of pulled out CFs) can be observed inside the composite. Almost all the CFs and the “black holes” are parallel to the axis of the fiber composite, which indicates that the CFs are highly oriented in the fiber composites (more discussion about CF orientation can be found in Ref. [25]). Due to the uniaxial alignment of the CFs, almost no conductive pathways are formed directly between the CFs. Fig. 4c,

Fig. 3. Schematic of polished and coated sample for the conductivity measurement.

shows a single CF surrounded by CB particles. The small CB particles connect the parallel CFs together such that conductive pathways are formed through the PMMA matrix. Typical conductive pathways in PMMA/CF/CB systems can thus be visualized with images like Fig. 4c. Moreover, the CB particles are well dispersed and no significant cluster or agglomerates are found (Fig. 4d). 3.2. Conductivity of the fiber composites 3.2.1. Percolation threshold of melt spun PMMA/CF and PMMA/CB fiber composites For PMMA/CB and PMMA/CF binary composites, the electrical conductivity, as function of filler fraction, is presented in Fig. 5. The X- and Y-axis present the CB and CF volume fractions in the composites, respectively. Several models have been proposed to describe percolation phenomena at critical levels of conductive fillers and to predict the electrical conductivity behavior of CPCs. The most classical percolation theory equation is [22,23]:

s ¼ s0 ðf  fc Þt

(3)

where s and s0 are the conductivities of the composite and the polymer matrix, respectively. f is the volume fraction of fillers and fc is the percolation threshold. For composites with filler concentrations f>fc, the experimental results are fitted by plotting log s against log (f-fc) and regulating fc until the best linear fit is obtained. Thus, the estimated percolation thresholds for the melt spun PMMA matrix fiber composite become: fc, CB ¼ 3.9 vol %, and fc, CF ¼ 31.8 vol % (Fig. 5). A strong alignment of the anisotropic CFs is induced by the melt spinning process, and consequently, the percolation threshold of the PMMA/CFs fiber composites becomes much higher than of the reported PMMA/CFs binary composites with randomly dispersed CFs [11e15,25]. 3.2.2. Contour plot of conductivity on fiber composites A conductivity contour plot diagram based on all experimental data is presented in Fig. 6, where the X-axis and Y-axis correspond to CB volume fraction and CF volume fraction, respectively. The black squares on the contour plot are the actual tested samples. The 10-logarithm of the conductivity is presented in colors while isocontour lines equating 1 magnitude are drawn in black. The composite conductivity obviously increases steeply with growing filler concentration. The percolation concentrations of CB and CF are marked on the X-axis (3.9, 0) and Y-axis (0, 31.8), respectively. The white dashed diagonal line a (Y¼-8.17Xþ31.8), which connect the two percolation points, correspond to Eq. (1) with K ¼ 1. The percolation

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Fig. 4. SEM micrographs of cross sections of fiber composites with different magnification, sample: 2CB3CF.

Fig. 6. Logarithm value of conductivity of fiber composites as a function of filler volume fraction of CFs and CB in a contour plot diagram presented in this work. Fig. 5. Conductivity of PMMA/CF and PMMA/CB composites vs. filler volume fraction in three-dimensional coordinates. Standard deviations, based on 10 measurements/ datapoint, are shown with error bars. The two insets illustrate the linear fit of the tvalue for PMMA/CF (red square) and PMMA/CB (blue spheroids), respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

threshold should follow this line if the excluded particle volumes are linearly additive, i.e if Eq. (1) is valid. Since the dramatic changes in conductivity close to the percolation concentration can result in a large standard deviation for the experimental measurements (See Figs. 5 and 9 and supporting

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information), two additional parallel lines (line b and c) were also added above the percolation threshold. Line c was created by passing the maximum investigated CF volume fraction (0, 50), with the same slope as line a. The intermediate value of y-intercepts from line a and line c, was applied as the y-intercept of line b. These lines correspond to K ¼ 1.28 and K ¼ 1.56, i.e. filler fractions 1.28 respective 1.56 times larger than the percolation threshold filler fractions. Conductivities of fiber composites with CF/CB compositions following the three diagonal lines were investigated and presented in Fig. 7. For all three diagonal lines (on X-Y plane), the conductivities (Z value) at the ends of the line were higher than in the middle, indicating a negative collective effect between CB and CF in melt spun PMMA/CF/CB composites. This result is in agreement with the right-pointed protrusion of contour lines in Fig. 6, which is in contrast to the slight “synergetic effect” [11e15] previously observed. However, small protrusions to the left of the contour lines can be observed for CF filler fractions below 10 vol %, indicating local synergetic effects similar to those previously reported [11e16]. The conductivity contour-lines of our composites are clearly concave and materials showing synergetic effects must by definition also show non-linear behavior. In order to describe such materials, the linear assumption of Eq. (1) is thus clearly not valid, although the equation still can be used for determining synergy. Therefore, an extended and more general equation is required for predicting the conductivities of CPCs containing two (or more) fillers. As a complement to our own measurements, the literature on conducting polymer composites with randomly dispersed CF and CB in polymer matrix (thermosetting based shape-memory polymer [11], acrylonitrile butadiene styrene [12] and polypropylene [13e15]) have been reanalyzed and a conductivity contour plot of the results is presented in Fig. 8. The literature data show higher composite conductivities than measured in this work (Fig. 6), probably mainly because the axial CF-orientations in this work obstruct the construction of conductive networks and thus reduce the composite conductivities [25]. It should thus also be noted that the polymer matrix in the literature review is other polymer matrix rather than PMMA.

Fig. 8. Logarithm value of conductivity of fiber composites vs. filler volume fraction of CFs and CB in a contour plot diagram on the basis of literature reanalysis.

Fig. 9. Conductivity of fiber composites vs. filler volume fraction of aligned CFs and CB, fitting with McLachlan equation to determine the electrical conductivity of fillers in the melt spun fiber consisting of ternary composites.

3.3. Novel equations for predicting the percolation threshold and the electrical conductivity If Eq. (1) would hold, the iso-curve between fc,CB and fc,CF in Fig. 6 would be a straight line. Since the measured electrical conductivities showed distinctly curved iso-curves, a new equation was required for describing the percolation behavior of CPC's containing two kinds of fillers more accurately. This conclusion was further strengthened by literature data [10e14], showing synergetic (i.e. non-linear) effects by combining certain kinds of conductive fillers. In order to simplify the mathematical expressions, the relative filler fractions a and b were introduced, defined as the ratios between present volume fraction f and percolation threshold fC, for CFs and CB, respectively:

Fig. 7. Logarithm value of conductivity of composites with composition of CFs/CB on the three diagonal lines (from Fig. 6) vs. filler volume fraction of aligned CFs and CB in this work.




a ¼ fCF fc;CF

(4)

M. Qu et al. / Composites Science and Technology 150 (2017) 24e31




b ¼ fCB fc;CB

(5)

Eq. (1) could thus be reformulated as:

aþb¼K

(6)

A corresponding improved non-linear equation should be able to describe both linear, concave and convex curves and give correct values at a ¼ 0 or b ¼ 0. The least complicated function fulfilling those criteria is probably:

 k 1=k Z ¼ ak þ b

(7)

where the physical meaning of Z is the same as K in Eq. (1) and Eq. (6), i.e. when Z ¼ 1, the percolation threshold just reached. k is an adjustable interaction parameter. If k ¼ 1 the equation becomes linear, if k < 1 the two fillers are synergetic and if k > 1 the fillers are anti-synergetic. Eq. (7) can thus be used as an improved alternative to Eq. (1) for describing the percolation threshold of mixtures. However, the property of main interest is often the composite conductivity rather than the percolation threshold. Therefore, an equation for predicting the conductivity of three-component composites was also developed. The conductivity of a composite containing only one filler can often be accurately described, as function of filler fraction f, with the McLachlan equation [26,27]:

!

0

1

1=s s1=t  s1=t s1=s f m s A @ ð1  fÞ 1=s þ f 1=t sm þ s1=s ð1  fc Þ=fc sf þ s1=t ð1  fc Þ=fc

¼0 (8) with sm, s, sf as the conductivities of the (PMMA) matrix, the composite and the fillers, respectively. The concentration of fillers was denoted f while fc is the percolation threshold of the

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composites. The values in the exponent (s and t) are generally chosen as 2 and 0.87, respectively, for 3-D systems [26,27]. Our hypothesis was that a linear combination of the conductivities of two binary composites, each with one single type of filler, could be used to describe the conductivity of a ternary composite, containing both types of fillers. This hypothesis correspond to coupling the binary composites in parallel. According to this hypothesis, the new equation (assuming CB and CF fillers) could be written:

stot ðfCF ; fCB Þ ¼

   a ,s min 1; Z4c;CF CF aþb    b þ ,s min 1; Zfc;CB CB aþb

(9)

The single-filler percolation thresholds fc,CF and fc,CB as well as the f-dependent single-filler conductivities s(fCF)CF and s(fCB)CB are determined with Eq. (8). As a safety routine, a restriction was added such that the functions could not exceed the values of their corresponding filler conductivities. The prediction capability of Eqs (4)e(9) was evaluated using the experimental data presented in Figs. 5e7. As a first step, the single filler conductivities of PMMA/CB and (un-axial) PMMA/CF composites were fitted with the McLachan equation (Eq. (8)), resulting in two log(s) versus f curves. The estimated filler conductivities were sCB ¼ 1.34  102 S/cm for CB and sCF ¼ 4.06 S/cm for CF. The fitted percolation thresholds with McLachan equation were fc,CF ¼ 33.5 vol %. and fc,CB ¼ 3.9 vol %, which are consistent with the value obtained from Eq. (3): fc, CF ¼ 31.8 vol % and fc, CB ¼ 3.9 vol %. The result, as presented in Fig. 9, shows a good agreement between the experimental conductivities and the best fit of Eq. (8). Eq. (9), as implemented in the Matlab(R) software, was then used for creating a two-dimensional conductivity contour plot. Eq. (8) (with parameters as in Fig. 9: sCF, sCB, fc,CF, fc,CB), and Eq. (7) (with k ¼ 1.47) were used as input. The resulting model contour plot (Fig. 10) show a trend which fits the corresponding the experimental contour plot (Fig. 6) well.

Fig. 10. Logarithm value of conductivity of fiber composites vs. filler volume fraction of CFs and CB in a contour plot diagram, as generated with Eq. (9).

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M. Qu et al. / Composites Science and Technology 150 (2017) 24e31

Finally, Eq. (9), with settings as above, was compared to the experimental conductivity data along the lines of Fig. 7. The result was presented in Fig. 11. Since the experimental non-linear trend was approximately in agreement with Eq. (9), our new equations are clearly more accurate than previously existing models for describing the electrical conductivity and the percolation threshold for composites containing two different conductive fillers. 3.4. Mechanical properties of fiber composites Tensile tests were conducted to examine the how the addition of various fractions of CB and CF influenced the mechanical properties (yield strength, ultimate tensile strength, E-modulus etc.) of PMMA/CB/CF composites. Due to the brittle PMMA matrix, hardly any deformation of the fiber composites were found before the samples were broken during the tensile test, i.e. the yield strength and ultimate tensile strength were identical. A contour plot for tensile strength versus filler fraction is presented in Fig. 12. As the filler volume fraction increased, the tensile strength of

Fig. 13. E-modulus of fiber composites vs. filler volume fraction of CFs and CB in a contour plot diagram.

the melt spun composites decreased, compared with that of the pure melt spun PMMA fibers (149.8 MPa). Due to the addition of fillers, more interfaces between matrix and fillers were induced, which led to weaker composites. On the other hand, the E-modulus of the composites increased distinctly with the addition of fillers particles (Fig. 13). The reinforcing effect was slightly more pronounced for the aligned anisotropic CF than for the isotropic CB, but surprisingly the difference was almost negligible below 10 vol % filling. 4. Conclusion

Fig. 11. Logarithm value of conductivity of fiber composites vs. filler volume fraction of CB in a 2-D coordinates system. Filled symbols represent experimental data while solid lines represent the simulation curves with predicted data from Eq. (9), where line a-c are from Fig. 6.

In this paper, melt spun PMMA/CB/CF ternary composites, with a broad range of composites compositions (up to 50 vol % CF and 20 vol % CB) were studied. SEM micrographs exposed a “fence-like” morphological structure between the CB and the CF. Electrical conductivity measurements were used to determine the electrical percolation thresholds of binary PMMA/CF and PMMA/CB composites and to reveal the relation between filler fraction and composite conductivity for PMMA/CB/CF. Conductivity contour plots, showing conductivity as function of filler fraction, were presented for PMMA/CF/CB composites for the first time; one extensive plot based on data from this study and one based on already existing literature data. Distinctly curved iso-lines were observed. Synergetic effects between CFs and CB were found in the regions below 10 vol % CF, observed as left-pointed protrusions of the contourlines. Moreover, based on a model for predicting the percolation threshold of ternary composites, a novel equation for predicting the electrical volume conductivity of ternary composites was proposed, showing results close to corresponding experimental data. Finally, two mechanical contour plots were presented, showing a decreased tensile strength and an increased E-modulus with the addition of fillers. Since our work comprises highly systematic measurements of tensile strength and electric conductivity for PMMA/CB/CF composites as well as novel and significantly improved effective-media equations for conductive ternary composites, it provides a general guidance for the design and analysis of CPCs. Acknowledgement

Fig. 12. Tensile strength of fiber composites vs. filler volume fraction of CFs and CB in a contour plot diagram.

The support from Svenska Vetenskapsrådet VR (VR grant 621-

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