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Rapid prototyping of electrically conductive components using 3D printing technology
Journal of Materials Processing Technology 209 (2009) 5281–5285
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Rapid prototyping of electrically conductive components using 3D printing technology a,∗ a ˙ ´ J. Czyzewski , P. Burzynski , K. Gaweł b , J. Meisner c a b c
ABB Corporate Research Center in Krakow, ul. Starowi´slna 13A, 31-038 Kraków, Poland Faculty of Chemistry, Jagellonian University, ul. Ingardena 3, 30-060 Kraków, Poland Institute of Physics, Jagellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
a r t i c l e
i n f o
Article history: Received 30 December 2008 Accepted 20 March 2009 PACS: 72.80.Tm 64.60.ah Keywords: Rapid prototyping 3D printing Electric conductivity Carbon nanofibers Percolation
a b s t r a c t A method of rapid prototyping of electrically conductive components is described. The method is based on 3D printing technology. The prototyped model is made of plaster-based powder bound layer-by-layer by an inkjet printing of a liquid binder. The resulting model is highly porous and can be impregnated by various liquids. In a standard prototyping process, the model is impregnated by epoxy or polyurethane resin, wax solution, etc. In the test described in this paper, to obtain the electric conductivity, the model has been impregnated by a dispersion of carbon nanofibers (CNF) in epoxy resin. Surface resistivity of the model below 800 /sq has been obtained when impregnated by a mixture containing less than 4 wt.% CNF. Volume resistivity of the molded and hardened CNF dispersion used for model impregnation have also been measured and a value less than 200 cm has been obtained at 3 wt.% CNF content. Unexpectedly, the onset of electric conductivity (percolation threshold) occurred at lower mass fraction of CNF for a dispersion containing CNF agglomerates, when compared to the mixture with well uniformly dispersed fibers. This happened both for the impregnated model and for the molded CNF dispersion itself. An explanation of this phenomenon, based on percolation theory is given. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Rapid prototyping techniques are nowadays broadly used in product development process. They allow for fast and low-cost manufacturing a small series of components directly from the component geometry parameterization stored in a 3-dimensional CAD model. The physical prototype allows for assessment of many aspects of functionality of the prototyped component in the developed product. For a review of various methods of rapid prototyping see Venuvinod and Ma (2004). One of the limitations of the common rapid prototyping techniques is the narrow choice of materials the prototype can be made of, thus limiting the scope of the material properties assigned to the prototype. This limits the extent of tests which can be made with the component in the prototype product. The example of the area in which the applicability of a prototype component cannot be tested without the adequate material properties is the medium- and highvoltage product engineering (products operating at 3–50 kV and >50 kV voltage, respectively). In such applications, the shape of a component together with the electric properties of the material determines the distribution of electric fields which is critical for
∗ Corresponding author. Tel.: +48 12 4244110; fax: +48 12 4244101. ˙ E-mail address: [email protected] (J. Czyzewski). 0924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2009.03.015
operation of the device. Electric conductivity of the component is of primary importance in such a case. A number of techniques are available to prototype electrically conductive components. For example, significant amount of work has been done towards application of the rapid prototyping methods to manufacture electric discharge machining (EDM) metal electrodes. The selective laser sintering (SLS) described by Dürr et al. (1999) and later by Tang et al. (2003) is one of the promising technologies, being currently the virtually unique commercial technology allowing for prototyping in metals. For the EDM application, SLS can also be followed by additional metal infiltration as proposed by Tay and Haider (2001) or metal plating process as described by Zhao et al. (2003) which improves the performance of the electrodes. Another example of technology which allows for direct metal prototyping is plasma deposition manufacturing reported by Zhang et al. (2003), a technology under development. These technologies offer very high conductivity of the components and resistance to wear related to the EDM process but require sophisticated, costly equipment. In this paper we report on a test of a simple method to manufacture an electrically conductive prototype. The method has been developed to prototype conductive components which in the final product have been expected to be made of an electrically conductive, carbon-black-filled thermoplastic polymer compound, of moderate conductivity. The volume resistivity of such compounds
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is typically of 101 –103 cm and the typical surface resistivity is of 102 –104 /sq. The aim was to reproduce these values in the rapid prototype model. 3D printing technology has been chosen for the task. It consists of two steps. First, a model is made of powder deposited layer-bylayer and bound by an inkjet printed liquid binding agent. As a result a relatively weakly bound, fragile, porous, and permeable structure is formed. In the second step, the structure is impregnated by a hardenable infiltrant, e.g. based on epoxy resin, which, after curing makes the prototype stiff and durable enough to be handled. The electric conductivity can be added to the model in that second step by adding an electrically conductive filler to the infiltrant. However, using common conductive fillers such as carbon-black or metal powders increases the viscosity of the infiltrant so that it is not able to impregnate the 3D model structure. One of the alternative fillers which can be used is carbon nanofibers (CNF). The very small diameter of the fibers allows them to penetrate together with the infiltrant deeply into the structure of the 3D model. In the same time, due to a low concentration of CNF needed to achieve the required conductivity, the viscosity of the resin—CNF mixture can be low enough to effectively impregnate the structure. A test of application of the CNF filled epoxy resin as the infiltrant of a model in the 3D printing process is the subject of this paper.
Fig. 1. Microscopic picture of the aggregated-CNF mixture; the measured diameter of the CNF aggregate is marked.
2. Procedure of manufacturing samples For all the tests, prototypes have been made by 3D printing technology using a printer from Z Corporation. Plaster-based powder has been used as the model building material. Prototypes have been impregnated by a dispersion of CNF in epoxy-based infiltrant being a mixture of EPOLAM 5015 resin and EPOLAM 5015 hardener by Axson Technologies. CNF used was Pyrograf-III PR-24 XT-LHT by Pyrograf Products Inc. As reported by the manufacturer, the average diameter of the fibers is 100 nm and typical length is 50–200 m. The fibers are heat-treated at 1500 ◦ C by the manufacturer to convert any chemically vapor deposited carbon present on the surface of the fiber to a short range ordered structure and to increase the electric conductivity. The fibers are also processed with an improved debulking method so that the fibers require less energy to achieve dispersion (Pyrograf Products Inc., 2007). The mixing procedure to achieve the CNF dispersion has been as follows: • preparing a required amount of CNF to obtain the desired CNF mass fraction; • adding 15 ml of resin and stirring; • long ultrasonic mixing; • adding 5.5 ml of hardener; • short ultrasonic mixing. Two versions of the procedure have been applied: • long ultrasonic mixing in sonication bath, 30 min time; • long ultrasonic mixing using a probe sonicator, 40 min time with a 50% duty cycle and external water cooling of the container with the mixture.
Fig. 2. Microscopic picture of the dispersed-CNF mixture.
dispersed-CNF mixture. The length of the fibers is in both cases shorter than that reported by the manufacturer. In particular, the dispersed-CNF mixture consists of fibers of length around 3–10 m. Shortening of the length of the fibers is most probably the result of the ultrasonic mixing. For each CNF dispersion obtained, a number of 3D printing samples impregnated by the dispersion have been manufactured, being plates of 2 mm thickness, 20 mm width and 50 mm length. The samples have been cured at 80 ◦ C during 1 h. Additionally, samples made of the dispersion itself have been molded and cured in the same conditions to be able to measure the volume resistivity of the obtained epoxy resin–CNF compound. Examples of the samples are shown in Figs. 3 and 4, respectively. For measurements of the resistivities, contacts have been applied on the samples using electrically conductive, silver-filled epoxy-resin-based adhesive, CW2400 Circuit Works by ITW Chemtronics, as is shown in Figs. 3 and 4. 3. Results of resistivity measurements
The procedure no. 1 resulted in the dispersion containing CNF mostly in form of aggregates and will be referred to further in the text as “aggregated-CNF”. The procedure no. 2 resulted in a highly dispersed mixture and will be referred to as “dispersed-CNF”. Fig. 1 shows a typical CNF aggregate present in the dispersion prepared according the procedure no. 1 and Fig. 2 shows the
The results of the measurements of the volume resistivity of the CNF-resin compound are shown in Fig. 5. The onset of conductivity occurs at lower CNF mass fraction for the aggregated-CNF mixture than for the dispersed-CNF one. This effect was originally not expected by the authors, as usually it is believed that higher
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Fig. 6. Surface resistivity of 3D printed samples impregnated by the CNF dispersion vs. the mass fraction of CNF in the dispersion. Full lines represent the fit with all free parameters; dashed lines are a result of the fit with fixed critical exponent ˇ = 1.33. For fit parameters see Tables 1 and 2. Fig. 3. Sample of 3D printing prototype material used for measuring surface resistivity.
Fig. 6 shows the surface resistivities of the 3D printout samples. Here again the onset of conductivity occurs at much lower CNF mass fraction for the samples impregnated by the aggregated-CNF mixture than for those impregnated by the dispersed-CNF compound. The lowest surface resistivity obtained for 3D printouts impregnated both by the dispersed-CNF and the aggregated-CNF mixture is below 800 /sq for mass fractions above 3.4% and 3%, respectively. This level of resistivity is fully satisfactory for using the prototypes as models of components made of carbon-black-filled thermoplastic polymers, a goal described in Section 1. As the shape of the 3D printout reproduces very well the expected shape of the component, and its electric conductivity matches that of its expected material, the 3D-printed prototype manufactured according to the described method can be used, for example, for checking the functionality of the component when operating under high voltage. In such a test, the thresholds for corona discharges, breakdown strength, and other aspects of functionality of the prototype can be checked. 4. Discussion of results according to percolation theory
Fig. 4. Sample of hardened CNF-resin compound used to measure its volume resistivity.
level of dispersion of the fibers leads to higher conductivities, as shown by Song and Youn (2005). As it will be shown in Section 4, the observed effect can be explained by the theory of percolation. For the curves fitted to the experimental data both in Fig. 5 and Fig. 6, refer also to Section 4.
To understand the results of the measurements, analysis according to percolation theory has been performed. To this end, the experimental data have been fitted to the formula describing electric resistivity in percolation systems (see Stauffer, 1985), = 0 (m − mc )−ˇ .
(1)
The resulting parameters of the fit are listed in Table 1. The parameters seem not to be fully consistent. In particular, the very large difference of 0 between the two dispersions is not expected, as it represents the resistivity of the filler itself. This should not differ so much between the two cases. Moreover, in both cases of the volume- and the surfaceresistivity of the samples, the obtained critical exponents ˇ are rather far from the theoretical values for percolation in Table 1 Percolation parameters fitted according to Eq. (1). Fitted parameter
Fig. 5. Volume resistivity of CNF-resin compound vs. the mass fraction of CNF in the dispersion. Full lines represent the fit with all free parameters; dashed lines are a result of the fit with fixed critical exponent ˇ = 2, as described in Section 4. For fit parameters see Tables 1 and 2.
Dispersed-CNF
Aggregated-CNF
Volume resistivity samples ˇ % mc cm 0
Unit
1.1 3.1 6.1
0.7 1.3 10.1
Surface resistivity samples ˇ % mc 0
2.0 2.1 0.2
0.8 0.3 41.7
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Table 2 Percolation parameters fitted according to Eq. (1) with keeping the critical exponents ˇ fixed.
Table 3 Calculated critical volume fractions for the volume resistivity of CNF-resin compounds.
Fitted parameter
Aggregated CNF
Parameter
Dispersed-CNF
Aggregated-CNF
Critical mass fraction, mc (%) Effective density of CNF, dCNF (g/cm3 ) Density of resin, dresin (g/cm3 ) Calculated critical volume fraction, V c (%)
2.9 1.6 1.2 2.2
1.1 0.11 1.2 12.1
Dispersed CNF
Volume resistivity samples ˇ (fixed) mc (%) 0 ( cm)
2.0 2.9 0.10
2.0 1.1 0.04
Surface resistivity samples ˇ (fixed) mc (%) 0 ()
1.33 2.1 3.0
1.33 0.1 4.5
3-dimensional and 2-dimensional systems of ˇ = 2 and ˇ = 1.33, respectively (Stauffer, 1985). Other experimental studies on volume resistivity of 3D systems of carbon nanotube–polymer compounds, for example by Benoit et al. (2001, 2002), have confirmed the value of ˇ = 2 and it should be expected for our system as well. To check if this can be a case in our study, we fitted the volume resistivity data to the Eq. (1), keeping the critical exponent fixed at ˇ = 2 for the CNF-resin compound (a 3-dimensional system). For the surface resistivity of the impregnated 3D printouts we fixed ˇ = 1.33, as the conductive matrix in the 3D printout can be well approximated by a 2-dimensional structure; the conductive matrix is formed by a relatively thin layer of the conductive compound coating the grains of the powder forming the 3D printout structure. The parameters of the resulting fit are listed in Table 2. The fitted curves are represented by the dashed lines in Figs. 5 and 6. One can observe that, taking into account the errors on the measured points, the quality of that fit is almost as good as the free-parameter one, plotted in full lines. Also the other parameters of the fit with fixedˇ seem to be more consistent, in particular with 0 being of the same order of magnitude for both dispersion types. Due to these facts, we will do the further analysis using the values of the fixed-ˇ fit (anyway, the values of mc , being subject of the analysis, do not differ significantly between both fits). To understand the reason of the fact of mc being lower for the aggregated-CNF compounds, one can refer to the theoretical results related to percolation of random elongated objects. An extensive analysis based on simulations has been done by Munson-McGee (1991), confirming and extending the earlier results obtained by Balberg and Binnenbaum (1984, 1985). Munson-McGee (1991) calculated the critical volume fractions for random systems of elongated objects of aspect ratio (ratio of the length to the diameter of the object) ranging from 2 to 1000 and for various probability distributions of angular orientation of the objects. The obtained critical volume fraction is much lower for the objects of large aspect ratio (corresponding to the dispersed-CNF compound of our study) than for the spherical objects of aspect ratio approaching 1 (corresponding to CNF aggregates in our case). This can, at the first sight, seem to contradict the reported results of our measurements. However, one has to take into account the fact that it is the volume fraction and not the mass fraction which decides about the onset of percolation. So, to compare with the theoretical results one has to take into account the density of the percolating objects. As provided in the data by the manufacturer, the density of the CNF fibers themselves is of 1.4–1.8 g/cm3 and the average of these, i.e. 1.6 g/cm3 can be taken as the effective density. For the aggregates present in the aggregated-CNF mixture, one can assume the effective density to be the average of the bulk density of CNF as delivered by the manufacturer ranging from 0.064 to 0.16 g/cm3 , that is on average 0.11 g/cm3 . All data have been obtained from Pyrograf Products Inc. (2007). Based on these values and knowing the density of the resin, one can calculate the critical volume fractions corresponding to our measurements. The results are given in Table 3. Indeed, as predicted
by the theory, the onset of percolation of the virtually spherical CNF aggregates occurs at much higher volume fraction than for the high-aspect-ratio dispersed-CNF. The corresponding values of 12% and 2.2%, respectively, are in agreement with the predictions by the theory. For the probability of forming the percolative network of 0.25–0.5, Munson-McGee (1991) gives the critical volume fractions between 12% and 20% for spherical objects, 9–16% for the aspect ratio equal to 5, 2–4% for the aspect ratio equal to 50, and less than 1% for objects of the aspect ratio equal to 500. In the case of aggregated-CNF compound, the observed aspect ratio (of the aggregates) ranges from 1 to 2. For the dispersed-CNF compound, the aspect ratio of the fibers as delivered, with their length on average being 100 m, is around 1000. However, due to the ultrasonic mixing process, the fibers are shortened, and, as discussed before, the length of the fibers is around 3–10 m, giving the aspect ratio somewhere between 30 and 100. These facts explain very well the observed values of critical concentrations when compared to the results obtained by Munson-McGee (1991) for the probability of forming the percolative network equal to 0.25. Such probability can very well correspond to the observed point of onset of percolation in such systems. 5. Conclusions In this paper a test of a method of rapid prototyping of electrically conductive components is described. The method is based on manufacturing a 3D model using the 3D printing technology. The model is made of plaster-based powder bound layer-by-layer by inkjet printed liquid binder. Impregnation of the model by a dispersion of carbon nanofibers in epoxy resin leads to an electrically conductive rapid prototype. Surface resistivity of the prototype material of below 800 /sq has been obtained with less than 4 wt.% carbon content in the resin. That level of conductivity allows for using such prototypes to model components made of carbon-blackfilled thermoplastic polymer materials. The onset of conductivity in a mixture containing aggregates of carbon nanofibers occurs at lower mass fraction of the fibers than for the well-dispersed mixture. It has been shown that such an unexpected result can be explained by the theory of percolation. It means that, in some cases, a material of required electric conductivity but containing the lowest amount of conductive filler can be obtained for a mixture containing aggregates of conductive fibers and not, as usually expected, for well uniformly dispersed conductive fibers. References Balberg, I., Binnenbaum, N., 1984. Percolation thresholds in the three-dimensional sticks system. Phys. Rev. Lett. 52, 1465–1468. Balberg, I., Binnenbaum, N., 1985. Cluster structure and conductivity of threedimensional continuum system. Phys. Rev. A 31, 1222–1225. Benoit, J.-M., Corraze, B., Chauvet, O., 2002. Localization, Coulomb interactions, and electrical heating in single-wall carbon nanotubes/polymer composites. Phys. Rev. B 65, 241405. Benoit, J.-M., Corraze, B., Lefrant, S., Blau, W.J., Bernier, P., Chauvet, O., 2001. Transport properties of PMMA-carbon nanotubes composites. Synth. Met. 121, 1215–1216. Dürr, H., Pilz, R., Eleser, N.S., 1999. Rapid tooling of EDM electrodes by means of selective laser sintering. Comput. Ind. 39, 35–45.
˙ J. Czyzewski et al. / Journal of Materials Processing Technology 209 (2009) 5281–5285 Munson-McGee, S., 1991. Estimation of the critical concentration in an anisotropic percolation network. Phys. Rev. B 43, 3331–3336. Pyrograf Products Inc., 2007. pyrografproducts.com. Song, Y.S., Youn, J.R., 2005. Influence of dispersion states of carbon nanotubes on physical properties of epoxy nanocomposites. Carbon 43, 1378–1385. Stauffer, D., 1985. Introduction to Percolation Theory. Taylor and Francis, London. Tang, Y., Loh, H.T., Wong, Y.S., Fuh, J.Y.H., Lu, L., Wang, X., 2003. Direct laser sintering of a copper-based alloy for creating three-dimensional metal parts. J. Mat. Proc. Tech. 140, 368–372.
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Tay, F.E.H., Haider, E.A., 2001. The potential of plating techniques in the development of rapid EDM tooling. Int. J. Adv. Manufacturing Technol. 18, 892–896. Venuvinod, P.K., Ma, W., 2004. Rapid Prototyping: Laser-based and Other Technologies. Kluwer Academic Publishers, Boston, USA. Zhang, H., Xu, J., Wang, G., 2003. Fundamental study on plasma deposition manufacturing. Surf. Coatings Technol. 171, 112–118. Zhao, J., Li, Y., Zhang, J., Yu, C., Zhang, Y., 2003. Analysis of the wear characteristics of an EDM electrode made by selective laser sintering. J. Mat. Proc. Tech. 138, 475–478.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Rapid prototyping of electrically conductive components using 3D printing technology a,∗ a ˙ ´ J. Czyzewski , P. Burzynski , K. Gaweł b , J. Meisner c a b c
ABB Corporate Research Center in Krakow, ul. Starowi´slna 13A, 31-038 Kraków, Poland Faculty of Chemistry, Jagellonian University, ul. Ingardena 3, 30-060 Kraków, Poland Institute of Physics, Jagellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
a r t i c l e
i n f o
Article history: Received 30 December 2008 Accepted 20 March 2009 PACS: 72.80.Tm 64.60.ah Keywords: Rapid prototyping 3D printing Electric conductivity Carbon nanofibers Percolation
a b s t r a c t A method of rapid prototyping of electrically conductive components is described. The method is based on 3D printing technology. The prototyped model is made of plaster-based powder bound layer-by-layer by an inkjet printing of a liquid binder. The resulting model is highly porous and can be impregnated by various liquids. In a standard prototyping process, the model is impregnated by epoxy or polyurethane resin, wax solution, etc. In the test described in this paper, to obtain the electric conductivity, the model has been impregnated by a dispersion of carbon nanofibers (CNF) in epoxy resin. Surface resistivity of the model below 800 /sq has been obtained when impregnated by a mixture containing less than 4 wt.% CNF. Volume resistivity of the molded and hardened CNF dispersion used for model impregnation have also been measured and a value less than 200 cm has been obtained at 3 wt.% CNF content. Unexpectedly, the onset of electric conductivity (percolation threshold) occurred at lower mass fraction of CNF for a dispersion containing CNF agglomerates, when compared to the mixture with well uniformly dispersed fibers. This happened both for the impregnated model and for the molded CNF dispersion itself. An explanation of this phenomenon, based on percolation theory is given. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Rapid prototyping techniques are nowadays broadly used in product development process. They allow for fast and low-cost manufacturing a small series of components directly from the component geometry parameterization stored in a 3-dimensional CAD model. The physical prototype allows for assessment of many aspects of functionality of the prototyped component in the developed product. For a review of various methods of rapid prototyping see Venuvinod and Ma (2004). One of the limitations of the common rapid prototyping techniques is the narrow choice of materials the prototype can be made of, thus limiting the scope of the material properties assigned to the prototype. This limits the extent of tests which can be made with the component in the prototype product. The example of the area in which the applicability of a prototype component cannot be tested without the adequate material properties is the medium- and highvoltage product engineering (products operating at 3–50 kV and >50 kV voltage, respectively). In such applications, the shape of a component together with the electric properties of the material determines the distribution of electric fields which is critical for
∗ Corresponding author. Tel.: +48 12 4244110; fax: +48 12 4244101. ˙ E-mail address: [email protected] (J. Czyzewski). 0924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2009.03.015
operation of the device. Electric conductivity of the component is of primary importance in such a case. A number of techniques are available to prototype electrically conductive components. For example, significant amount of work has been done towards application of the rapid prototyping methods to manufacture electric discharge machining (EDM) metal electrodes. The selective laser sintering (SLS) described by Dürr et al. (1999) and later by Tang et al. (2003) is one of the promising technologies, being currently the virtually unique commercial technology allowing for prototyping in metals. For the EDM application, SLS can also be followed by additional metal infiltration as proposed by Tay and Haider (2001) or metal plating process as described by Zhao et al. (2003) which improves the performance of the electrodes. Another example of technology which allows for direct metal prototyping is plasma deposition manufacturing reported by Zhang et al. (2003), a technology under development. These technologies offer very high conductivity of the components and resistance to wear related to the EDM process but require sophisticated, costly equipment. In this paper we report on a test of a simple method to manufacture an electrically conductive prototype. The method has been developed to prototype conductive components which in the final product have been expected to be made of an electrically conductive, carbon-black-filled thermoplastic polymer compound, of moderate conductivity. The volume resistivity of such compounds
5282
˙ J. Czyzewski et al. / Journal of Materials Processing Technology 209 (2009) 5281–5285
is typically of 101 –103 cm and the typical surface resistivity is of 102 –104 /sq. The aim was to reproduce these values in the rapid prototype model. 3D printing technology has been chosen for the task. It consists of two steps. First, a model is made of powder deposited layer-bylayer and bound by an inkjet printed liquid binding agent. As a result a relatively weakly bound, fragile, porous, and permeable structure is formed. In the second step, the structure is impregnated by a hardenable infiltrant, e.g. based on epoxy resin, which, after curing makes the prototype stiff and durable enough to be handled. The electric conductivity can be added to the model in that second step by adding an electrically conductive filler to the infiltrant. However, using common conductive fillers such as carbon-black or metal powders increases the viscosity of the infiltrant so that it is not able to impregnate the 3D model structure. One of the alternative fillers which can be used is carbon nanofibers (CNF). The very small diameter of the fibers allows them to penetrate together with the infiltrant deeply into the structure of the 3D model. In the same time, due to a low concentration of CNF needed to achieve the required conductivity, the viscosity of the resin—CNF mixture can be low enough to effectively impregnate the structure. A test of application of the CNF filled epoxy resin as the infiltrant of a model in the 3D printing process is the subject of this paper.
Fig. 1. Microscopic picture of the aggregated-CNF mixture; the measured diameter of the CNF aggregate is marked.
2. Procedure of manufacturing samples For all the tests, prototypes have been made by 3D printing technology using a printer from Z Corporation. Plaster-based powder has been used as the model building material. Prototypes have been impregnated by a dispersion of CNF in epoxy-based infiltrant being a mixture of EPOLAM 5015 resin and EPOLAM 5015 hardener by Axson Technologies. CNF used was Pyrograf-III PR-24 XT-LHT by Pyrograf Products Inc. As reported by the manufacturer, the average diameter of the fibers is 100 nm and typical length is 50–200 m. The fibers are heat-treated at 1500 ◦ C by the manufacturer to convert any chemically vapor deposited carbon present on the surface of the fiber to a short range ordered structure and to increase the electric conductivity. The fibers are also processed with an improved debulking method so that the fibers require less energy to achieve dispersion (Pyrograf Products Inc., 2007). The mixing procedure to achieve the CNF dispersion has been as follows: • preparing a required amount of CNF to obtain the desired CNF mass fraction; • adding 15 ml of resin and stirring; • long ultrasonic mixing; • adding 5.5 ml of hardener; • short ultrasonic mixing. Two versions of the procedure have been applied: • long ultrasonic mixing in sonication bath, 30 min time; • long ultrasonic mixing using a probe sonicator, 40 min time with a 50% duty cycle and external water cooling of the container with the mixture.
Fig. 2. Microscopic picture of the dispersed-CNF mixture.
dispersed-CNF mixture. The length of the fibers is in both cases shorter than that reported by the manufacturer. In particular, the dispersed-CNF mixture consists of fibers of length around 3–10 m. Shortening of the length of the fibers is most probably the result of the ultrasonic mixing. For each CNF dispersion obtained, a number of 3D printing samples impregnated by the dispersion have been manufactured, being plates of 2 mm thickness, 20 mm width and 50 mm length. The samples have been cured at 80 ◦ C during 1 h. Additionally, samples made of the dispersion itself have been molded and cured in the same conditions to be able to measure the volume resistivity of the obtained epoxy resin–CNF compound. Examples of the samples are shown in Figs. 3 and 4, respectively. For measurements of the resistivities, contacts have been applied on the samples using electrically conductive, silver-filled epoxy-resin-based adhesive, CW2400 Circuit Works by ITW Chemtronics, as is shown in Figs. 3 and 4. 3. Results of resistivity measurements
The procedure no. 1 resulted in the dispersion containing CNF mostly in form of aggregates and will be referred to further in the text as “aggregated-CNF”. The procedure no. 2 resulted in a highly dispersed mixture and will be referred to as “dispersed-CNF”. Fig. 1 shows a typical CNF aggregate present in the dispersion prepared according the procedure no. 1 and Fig. 2 shows the
The results of the measurements of the volume resistivity of the CNF-resin compound are shown in Fig. 5. The onset of conductivity occurs at lower CNF mass fraction for the aggregated-CNF mixture than for the dispersed-CNF one. This effect was originally not expected by the authors, as usually it is believed that higher
˙ J. Czyzewski et al. / Journal of Materials Processing Technology 209 (2009) 5281–5285
5283
Fig. 6. Surface resistivity of 3D printed samples impregnated by the CNF dispersion vs. the mass fraction of CNF in the dispersion. Full lines represent the fit with all free parameters; dashed lines are a result of the fit with fixed critical exponent ˇ = 1.33. For fit parameters see Tables 1 and 2. Fig. 3. Sample of 3D printing prototype material used for measuring surface resistivity.
Fig. 6 shows the surface resistivities of the 3D printout samples. Here again the onset of conductivity occurs at much lower CNF mass fraction for the samples impregnated by the aggregated-CNF mixture than for those impregnated by the dispersed-CNF compound. The lowest surface resistivity obtained for 3D printouts impregnated both by the dispersed-CNF and the aggregated-CNF mixture is below 800 /sq for mass fractions above 3.4% and 3%, respectively. This level of resistivity is fully satisfactory for using the prototypes as models of components made of carbon-black-filled thermoplastic polymers, a goal described in Section 1. As the shape of the 3D printout reproduces very well the expected shape of the component, and its electric conductivity matches that of its expected material, the 3D-printed prototype manufactured according to the described method can be used, for example, for checking the functionality of the component when operating under high voltage. In such a test, the thresholds for corona discharges, breakdown strength, and other aspects of functionality of the prototype can be checked. 4. Discussion of results according to percolation theory
Fig. 4. Sample of hardened CNF-resin compound used to measure its volume resistivity.
level of dispersion of the fibers leads to higher conductivities, as shown by Song and Youn (2005). As it will be shown in Section 4, the observed effect can be explained by the theory of percolation. For the curves fitted to the experimental data both in Fig. 5 and Fig. 6, refer also to Section 4.
To understand the results of the measurements, analysis according to percolation theory has been performed. To this end, the experimental data have been fitted to the formula describing electric resistivity in percolation systems (see Stauffer, 1985), = 0 (m − mc )−ˇ .
(1)
The resulting parameters of the fit are listed in Table 1. The parameters seem not to be fully consistent. In particular, the very large difference of 0 between the two dispersions is not expected, as it represents the resistivity of the filler itself. This should not differ so much between the two cases. Moreover, in both cases of the volume- and the surfaceresistivity of the samples, the obtained critical exponents ˇ are rather far from the theoretical values for percolation in Table 1 Percolation parameters fitted according to Eq. (1). Fitted parameter
Fig. 5. Volume resistivity of CNF-resin compound vs. the mass fraction of CNF in the dispersion. Full lines represent the fit with all free parameters; dashed lines are a result of the fit with fixed critical exponent ˇ = 2, as described in Section 4. For fit parameters see Tables 1 and 2.
Dispersed-CNF
Aggregated-CNF
Volume resistivity samples ˇ % mc cm 0
Unit
1.1 3.1 6.1
0.7 1.3 10.1
Surface resistivity samples ˇ % mc 0
2.0 2.1 0.2
0.8 0.3 41.7
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Table 2 Percolation parameters fitted according to Eq. (1) with keeping the critical exponents ˇ fixed.
Table 3 Calculated critical volume fractions for the volume resistivity of CNF-resin compounds.
Fitted parameter
Aggregated CNF
Parameter
Dispersed-CNF
Aggregated-CNF
Critical mass fraction, mc (%) Effective density of CNF, dCNF (g/cm3 ) Density of resin, dresin (g/cm3 ) Calculated critical volume fraction, V c (%)
2.9 1.6 1.2 2.2
1.1 0.11 1.2 12.1
Dispersed CNF
Volume resistivity samples ˇ (fixed) mc (%) 0 ( cm)
2.0 2.9 0.10
2.0 1.1 0.04
Surface resistivity samples ˇ (fixed) mc (%) 0 ()
1.33 2.1 3.0
1.33 0.1 4.5
3-dimensional and 2-dimensional systems of ˇ = 2 and ˇ = 1.33, respectively (Stauffer, 1985). Other experimental studies on volume resistivity of 3D systems of carbon nanotube–polymer compounds, for example by Benoit et al. (2001, 2002), have confirmed the value of ˇ = 2 and it should be expected for our system as well. To check if this can be a case in our study, we fitted the volume resistivity data to the Eq. (1), keeping the critical exponent fixed at ˇ = 2 for the CNF-resin compound (a 3-dimensional system). For the surface resistivity of the impregnated 3D printouts we fixed ˇ = 1.33, as the conductive matrix in the 3D printout can be well approximated by a 2-dimensional structure; the conductive matrix is formed by a relatively thin layer of the conductive compound coating the grains of the powder forming the 3D printout structure. The parameters of the resulting fit are listed in Table 2. The fitted curves are represented by the dashed lines in Figs. 5 and 6. One can observe that, taking into account the errors on the measured points, the quality of that fit is almost as good as the free-parameter one, plotted in full lines. Also the other parameters of the fit with fixedˇ seem to be more consistent, in particular with 0 being of the same order of magnitude for both dispersion types. Due to these facts, we will do the further analysis using the values of the fixed-ˇ fit (anyway, the values of mc , being subject of the analysis, do not differ significantly between both fits). To understand the reason of the fact of mc being lower for the aggregated-CNF compounds, one can refer to the theoretical results related to percolation of random elongated objects. An extensive analysis based on simulations has been done by Munson-McGee (1991), confirming and extending the earlier results obtained by Balberg and Binnenbaum (1984, 1985). Munson-McGee (1991) calculated the critical volume fractions for random systems of elongated objects of aspect ratio (ratio of the length to the diameter of the object) ranging from 2 to 1000 and for various probability distributions of angular orientation of the objects. The obtained critical volume fraction is much lower for the objects of large aspect ratio (corresponding to the dispersed-CNF compound of our study) than for the spherical objects of aspect ratio approaching 1 (corresponding to CNF aggregates in our case). This can, at the first sight, seem to contradict the reported results of our measurements. However, one has to take into account the fact that it is the volume fraction and not the mass fraction which decides about the onset of percolation. So, to compare with the theoretical results one has to take into account the density of the percolating objects. As provided in the data by the manufacturer, the density of the CNF fibers themselves is of 1.4–1.8 g/cm3 and the average of these, i.e. 1.6 g/cm3 can be taken as the effective density. For the aggregates present in the aggregated-CNF mixture, one can assume the effective density to be the average of the bulk density of CNF as delivered by the manufacturer ranging from 0.064 to 0.16 g/cm3 , that is on average 0.11 g/cm3 . All data have been obtained from Pyrograf Products Inc. (2007). Based on these values and knowing the density of the resin, one can calculate the critical volume fractions corresponding to our measurements. The results are given in Table 3. Indeed, as predicted
by the theory, the onset of percolation of the virtually spherical CNF aggregates occurs at much higher volume fraction than for the high-aspect-ratio dispersed-CNF. The corresponding values of 12% and 2.2%, respectively, are in agreement with the predictions by the theory. For the probability of forming the percolative network of 0.25–0.5, Munson-McGee (1991) gives the critical volume fractions between 12% and 20% for spherical objects, 9–16% for the aspect ratio equal to 5, 2–4% for the aspect ratio equal to 50, and less than 1% for objects of the aspect ratio equal to 500. In the case of aggregated-CNF compound, the observed aspect ratio (of the aggregates) ranges from 1 to 2. For the dispersed-CNF compound, the aspect ratio of the fibers as delivered, with their length on average being 100 m, is around 1000. However, due to the ultrasonic mixing process, the fibers are shortened, and, as discussed before, the length of the fibers is around 3–10 m, giving the aspect ratio somewhere between 30 and 100. These facts explain very well the observed values of critical concentrations when compared to the results obtained by Munson-McGee (1991) for the probability of forming the percolative network equal to 0.25. Such probability can very well correspond to the observed point of onset of percolation in such systems. 5. Conclusions In this paper a test of a method of rapid prototyping of electrically conductive components is described. The method is based on manufacturing a 3D model using the 3D printing technology. The model is made of plaster-based powder bound layer-by-layer by inkjet printed liquid binder. Impregnation of the model by a dispersion of carbon nanofibers in epoxy resin leads to an electrically conductive rapid prototype. Surface resistivity of the prototype material of below 800 /sq has been obtained with less than 4 wt.% carbon content in the resin. That level of conductivity allows for using such prototypes to model components made of carbon-blackfilled thermoplastic polymer materials. The onset of conductivity in a mixture containing aggregates of carbon nanofibers occurs at lower mass fraction of the fibers than for the well-dispersed mixture. It has been shown that such an unexpected result can be explained by the theory of percolation. It means that, in some cases, a material of required electric conductivity but containing the lowest amount of conductive filler can be obtained for a mixture containing aggregates of conductive fibers and not, as usually expected, for well uniformly dispersed conductive fibers. References Balberg, I., Binnenbaum, N., 1984. Percolation thresholds in the three-dimensional sticks system. Phys. Rev. Lett. 52, 1465–1468. Balberg, I., Binnenbaum, N., 1985. Cluster structure and conductivity of threedimensional continuum system. Phys. Rev. A 31, 1222–1225. Benoit, J.-M., Corraze, B., Chauvet, O., 2002. Localization, Coulomb interactions, and electrical heating in single-wall carbon nanotubes/polymer composites. Phys. Rev. B 65, 241405. Benoit, J.-M., Corraze, B., Lefrant, S., Blau, W.J., Bernier, P., Chauvet, O., 2001. Transport properties of PMMA-carbon nanotubes composites. Synth. Met. 121, 1215–1216. Dürr, H., Pilz, R., Eleser, N.S., 1999. Rapid tooling of EDM electrodes by means of selective laser sintering. Comput. Ind. 39, 35–45.
˙ J. Czyzewski et al. / Journal of Materials Processing Technology 209 (2009) 5281–5285 Munson-McGee, S., 1991. Estimation of the critical concentration in an anisotropic percolation network. Phys. Rev. B 43, 3331–3336. Pyrograf Products Inc., 2007. pyrografproducts.com. Song, Y.S., Youn, J.R., 2005. Influence of dispersion states of carbon nanotubes on physical properties of epoxy nanocomposites. Carbon 43, 1378–1385. Stauffer, D., 1985. Introduction to Percolation Theory. Taylor and Francis, London. Tang, Y., Loh, H.T., Wong, Y.S., Fuh, J.Y.H., Lu, L., Wang, X., 2003. Direct laser sintering of a copper-based alloy for creating three-dimensional metal parts. J. Mat. Proc. Tech. 140, 368–372.
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Tay, F.E.H., Haider, E.A., 2001. The potential of plating techniques in the development of rapid EDM tooling. Int. J. Adv. Manufacturing Technol. 18, 892–896. Venuvinod, P.K., Ma, W., 2004. Rapid Prototyping: Laser-based and Other Technologies. Kluwer Academic Publishers, Boston, USA. Zhang, H., Xu, J., Wang, G., 2003. Fundamental study on plasma deposition manufacturing. Surf. Coatings Technol. 171, 112–118. Zhao, J., Li, Y., Zhang, J., Yu, C., Zhang, Y., 2003. Analysis of the wear characteristics of an EDM electrode made by selective laser sintering. J. Mat. Proc. Tech. 138, 475–478.