A Study on Thermal and Electrical Conductivities of Ethylene-Butene Copolymer Composites with Carbon Fibers

The electrical, mechanical and thermal conductivity of ethylene butene copolymer (EBC) composites with carbon fibers were studied. EBC/carbon-fiber composites can be utilized as an electro-mechanical material which is capable of changing it electric resistance with mechanical strain. Carbon fibers were introduced to EBC with different concentrations (5-25 wt%). The results showed that the addition of carbon fibers to EBC could increase the electric resistance up to 10 times. Increasing the load to 2.9 MPa could increase the electric resistance change by 4500% compared 25% fiber sample with pure EBC. It is also noted that the electric resistance of the EBC/CF composites underwent a dramatic increase with raising the strain, for example, the resistance change was around 13 times more at 15% strain in comparison to 5% of strain; The thermal conductivity tests showed that the addition of carbon fibers could increase the thermal conductivity by 40%, from 0.19 to 0.27 (Wm-1K-1). It was also observed that the addition of carbon fibers to EBC could increase the thermal conductivity. Introduction Polymer composite containing carbon fiber is wildly used in industry due to excellent thermal, electrical and mechanical properties they can be used as a flexible electric sensor according to high sensitivity to strain and low industrial costs [1-3]. Many researchers indicated that the electrical conductivity of the polymer/carbon-fibre composite could be influenced by its deformation [4-7]. This change highly responds to the size and direction of the carbon fiber. Slobodian et al., studied on the influence of deformation on electric resistance for Carbon Nanotube (CNT)/Polyurethane (PU) and found the increase in resistance and Gauge factor which is defines the sensitivity of strain as a relative resistance change divided by applied strain to explain the effect of applied preload on the increases of Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 15 September 2020 doi:10.20944/preprints202009.0336.v1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license. relative resistance change of CNT/PU composites with introducing the strain [7]. Previous works show that the electrically conductive composite can be used in real-time like electric skins, entertainment system, human health monitoring for Parkinson disease patients due to the high response of electrical resistance to strain[8]. Li et al., reported that a change of resistance of multiwalled carbon nanotube film can be used as an electric sensor as it is highly responding to the strain [9]. Nowadays studies have indicated that the addition of fiber to a polymer matrix could influence the thermal conductivity of the composites [10-13]. Svoboda et al., [10] reported that the thermal conductivity of ethylene-octane copolymer/graphite composite increased by 245% where the fillers was increased from 0 to 50 wt% due to the uniform distribution of the graphit fibers In this research, the author tried to investigate the effect of loading on electro-mechanical properties of the ethylene-butene copolymer (EBC) and Carbon fiber (CF) under elongation/relaxation cycle with a variety of loads. Moreover, the influence of carbon-fibre material with thermal conductivity of EBC was investigated. Experiment Ethylene-butene copolymer with0 has density 0.862 g/cm, ultimate tensile strength 2.0 MPa, melt index 1.2 dg/min and tensile elongation 600% were purchased from DOW chemical company in USA. Carbon fiber was T700SC 12000-50C provided by Toray Carbon Fibers America Inc, USA. The tensile strength and modulus are 4900 MPa and 230 GPa respectively. The carbon fiber has 7 μm thickness with a 1.8 g/cm3 density and 2.1% strain. The thermal conductivity of CF is 0.0224 Cal/cm⋅s. ̊C, while the electric resistivity is 1.6 x 10 Ω⋅cm indicated by TORAYCA®. EBC/CF was prepared using a two-roll mill for 5 min at 150 ° C. Then, compression molding was used to prepare the sheets with a thickness of 1 mm at 10 MPa with 5 min preheating and 6 min pressing, at 150 °C. Finally, the dumbbell shaped films were prepared with a compression cutter for the test. The electrical resistance change during strain-relaxation cycles were analyzed with a 7338 Sefram multimeter by using a two-point technique. The tests were done using a variety of stresses (0.442, 0.884, 1.325, 1.768, and 2.219 MPa) with the strain and electric resistance change with time. The Fitch (1935) method was used to determine the thermal conductivity of the EBC/CF composites [14], where the specimen is sandwiched between a warm source and a steady temperature metal disc Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 15 September 2020 doi:10.20944/preprints202009.0336.v1


Introduction
Polymer composite containing carbon fiber is wildly used in industry due to excellent thermal, electrical and mechanical properties they can be used as a flexible electric sensor according to high sensitivity to strain and low industrial costs [1][2][3]. Many researchers indicated that the electrical conductivity of the polymer/carbon-fibre composite could be influenced by its deformation [4][5][6][7]. This change highly responds to the size and direction of the carbon fiber. Slobodian et al., studied on the influence of deformation on electric resistance for Carbon Nanotube (CNT)/Polyurethane (PU) and found the increase in resistance and Gauge factor which is defines the sensitivity of strain as a relative resistance change divided by applied strain to explain the effect of applied preload on the increases of relative resistance change of CNT/PU composites with introducing the strain [7]. Previous works show that the electrically conductive composite can be used in real-time like electric skins, entertainment system, human health monitoring for Parkinson disease patients due to the high response of electrical resistance to strain [8]. Li et al., reported that a change of resistance of multiwalled carbon nanotube film can be used as an electric sensor as it is highly responding to the strain [9].
Nowadays studies have indicated that the addition of fiber to a polymer matrix could influence the thermal conductivity of the composites [10][11][12][13]. Svoboda et al., [10] reported that the thermal conductivity of ethylene-octane copolymer/graphite composite increased by 245% where the fillers was increased from 0 to 50 wt% due to the uniform distribution of the graphit fibers In this research, the author tried to investigate the effect of loading on electro-mechanical properties of the ethylene-butene copolymer (EBC) and Carbon fiber (CF) under elongation/relaxation cycle with a variety of loads. Moreover, the influence of carbon-fibre material with thermal conductivity of EBC was investigated.

Experiment
Ethylene-butene copolymer with0 has density 0.862 g/cm 2 , ultimate tensile strength 2.0 MPa, melt index 1.2 dg/min and tensile elongation 600% were purchased from DOW chemical company in USA. Carbon fiber was T700SC 12000-50C provided by Toray Carbon Fibers America Inc, USA.
The tensile strength and modulus are 4900 MPa and 230 GPa respectively. The carbon fiber has 7 µm thickness with a 1.8 g/cm3 density and 2.1% strain. The thermal conductivity of CF is 0.0224 Cal/cm⋅s.˚C, while the electric resistivity is 1.6 x 10 -3 Ω⋅cm indicated by TORAYCA®.
EBC/CF was prepared using a two-roll mill for 5 min at 150 ° C. Then, compression molding was used to prepare the sheets with a thickness of 1 mm at 10 MPa with 5 min preheating and 6 min pressing, at 150 °C. Finally, the dumbbell shaped films were prepared with a compression cutter for the test.
The electrical resistance change during strain-relaxation cycles were analyzed with a 7338 Sefram multimeter by using a two-point technique. The tests were done using a variety of stresses (0.442, 0.884, 1.325, 1.768, and 2.219 MPa) with the strain and electric resistance change with time.
The Fitch (1935) method was used to determine the thermal conductivity of the EBC/CF composites [14], where the specimen is sandwiched between a warm source and a steady temperature metal disc as a heat sink. A schematic representation of the instrument used for thermal conductivity measurements is shown in Fig 1. The process of measurement and the instrument are explained below. At first, the 5 cm diameter central brass cylinder (CBC) was heated to T2 =45°C with the assistance of another chamber which was connected with a water indoor regulator by elastic hoses with a water thermostat with 0.1°C accuracy; it took about 3 minutes to reach a suitable temperature. Then the hot chamber was quickly removed and the sample with a 5 cm diameter was placed on top of the CBC with the second brass cylinder on top of it with a weight of 100g, which was connected to a second water thermostat with the temperature set to 25° C.
Heat was transferred from the hot CBC to the cold cylinder by passing trow the sample. The CBC temperature is reduced quickly. The CBC data were collected every 5 s for 30 min by a thermocouple which was associated with a National Instruments information obtaining hardware (NI USB-9211A, Portable USB-Based DAQ (Data Acquisition)) for Thermocouple software and using the computer through the USB port [15]. The data was analyzed using LabVIEW Signal Express 2.5.

Electrical conductivity
Tensile deformation and gauge factors which is the ratio of relative change in electrical resistance R, to the mechanical strain ε of EBC/carbon-fiber composites were determined by a twopoint technique to measure the electric resistance as a function of the strain. In this research, the change in electrical resistance was defined as: [10] = − (1) Where 0= the initial electrical resistance of the sample before the first elongation = the resistance during elongation The elongation is defined as: Where L0 represents the initial length of the EBC/CF specimen while L is the length during the stretching experiment. Micrograph of optical microscopy from EBC carbon fiber for 15 wt% and 25 wt% can be seen in   The strain caused by tensile stress and change of electrical resistance was measured. The change of electric resistance of EBC with 5% and 10% of carbon fibers could not be measured. There being zero conductivity because of the low concentration of CF. It was also observed that, the EBC composite with 15% of carbon fiber had a low change of electrical resistance with a change of strain due to the low content of carbon fibers, that might be because of the lower amount of fiber and resistivity of carbon fiber during the deformation. Furthermore, it is observed in Figure 3 that EBC/CF with 25 wt% resistance change is increasing with deformation, as increasing the connection between carbon fibers. [5,7,15]. The amount of fibers in EBC/CF 15 wt% is much lower than 25 wt% that could be measured only up to 0.884 MP. By opening the circles in the graph, the relevant resistance changes while the values of strain are signified by solid circles. Figure 3 shows that EBC/CF 25 wt% is conductive also at the peak strain of about 16% once the resistance change is about 4500%.
The relative resistance increases with strain continually with no gap. It is no longer common in the case of the conductive particulate mixture when a point of very high resistance is touched the higher strain. Furthermore, the resistance of the mixtures returns almost to unload state to the value of 0 and 3 percent for 15 wt% and 25 wt% respectively as can see in Figure 4. Where: However, equation 5 can be simplified with exponential growth with three parameters as: The coefficient b is obtained from the nonlinear regression.
The results of calculation of the thermal conductivities of EBC/CF is shown in Table 1 and Figure 6.  Fig. 7. Thermal conductivity as a function of carbon fiber content Uniform distribution of CF had a large effect on the growth in thermal and electric conductivity. Since CF has a high conductivity for both heat and electricity, the loading of CF in EBC resulted in an increase in thermal and electric conductivities of the mixture [10,12].

Conclusions
EBC/CF composites were prepared by the mixing the EBC with various levels of carbon fiber using a two roll-mill. The observations from optical microscopy indicated a fairly good dispersion of carbon fiber in the matrix. The electro-mechanical testing showed that straining of the composite led to a change of its macroscopic electrical resistance. The EBC/CF strain sensitive composites were relatively sensitive to strain, and the changes were reversible. Therefore, the results indicate a good potential of the composites to be used as an electrical sensor for strain. The thermal conductivity of the mixtures indicated an increase of thermal conductivity with loading carbon fiber.