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Study on dosimetry characteristics of polymer–CNT nanocomposites: Effect of polymer matrix
Nuclear Instruments and Methods in Physics Research A ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Study on dosimetry characteristics of polymer–CNT nanocomposites: Effect of polymer matrix Shahryar Malekie, Farhood Ziaie n Radiation Application Research School, Nuclear Science & Technology Research Institute, PO Box 11365-3486, Tehran, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 11 November 2015 Received in revised form 23 January 2016 Accepted 26 January 2016
In this research work, the current density of polymer–carbon nanotube nanocomposite in different weight percentages of nanotubes, over the radiation absorbed dose under a fixed DC voltage for different polymer matrices such as high density polyethylene, polycarbonate, polyethylene terephthalate, polymethyl methacrylate, and polystyrene was investigated via finite element method. The predicted electrical percolation threshold values in different composites were validated by experimental results published by other scientists. The absorbed dose value was considered as multiplying of heat capacity and temperature rise of the composite, regarding the calorimetric approach. Results show that the polymer type having different characteristics of relative permittivity and heat capacity could affect the sensitivity and working dose range of the composite as a dosimeter. & 2016 Published by Elsevier B.V.
Keywords: Carbon nanotube Percolation Electrical conductivity Composite Dosimetry
1. Introduction The electrically conductive polymer–carbon nanotube composites have great potential in many applications, such as electromagnetic interference shielding, sensors, batteries, antistatic devices, lightweight energy storages, and dosimeters [1–6]. Dosimetry and detection of ionizing radiation are important investigation fields in the nuclear industry. The discovery of carbon nanotube (CNT) [7] opened the door to enhance the properties of polymer composites for structural and multifunctional applications [8]. The nano-sized, high surface area and the high aspect ratio (AR) of CNTs, offer the great opportunities to enhance the electrical conductivity of the polymer nano-composites even at a very low loading of CNTs in the polymer matrix [9,10]. In fact, carbon nanotubes via adding to a polymer matrix in a particular weight percentage (wt%), entitled electrical percolation threshold (EPT), leads to a suddenly several orders of magnitude increasing of electrical conductivity of polymer–CNT composite [1]. The considerable difference between the electrical conductivity of these materials makes electrical percolation theory as an ideal modeling tool to predict electrical characteristics of polymer–CNT composite in different wt% of inclusions [11]. Since polymer–CNT composite is light, tissue equivalent, low cost and also due to easy processing, this kind of material has potential applications as ionizing radiation dosimeter. The effects n
Corresponding author. E-mail address: [email protected] (F. Ziaie).
of length and critical density of CNTs on the electrical conductivity of a radiation sensor based on percolation theory were studied [12]. Other researchers were investigated the interaction of radiation with functionalized carbon nanotubes that have been incorporated into various host materials, particularly polymeric ones [13]. In our previous work, it was shown that the EPT of polymer–CNT composite is the best point for dosimetry purposes [1]. In this research work the dosimetry characteristics of the composites in different wt% were evaluated and compared for different polymer matrices such as high density polyethylene (HDPE), polycarbonate (PC), polyethylene terephthalate (PET), polymethyl methacrylate (PMMA), and polystyrene (PS).
2. Simulation methodology According to effective medium theory (EMT), studying on a piece of material can be generalized to whole of the system. EMT is a physical model based on properties of individual components and their fractions in the composite [14]. Scaling law and percolation theory are used to predict the critical phenomena related to disorder systems [11]. Thus, determination of EPT in polymer–CNT composites has an important role in evaluation of dosimetric characteristics of the materials. In this simulation, assessment of the EPT region for polymer–CNT composites is based on producing random numbers for achieving dispersed homogeneous CNTs network. This issue is accompanied by statistical fluctuations and
http://dx.doi.org/10.1016/j.nima.2016.01.077 0168-9002/& 2016 Published by Elsevier B.V.
Please cite this article as: S. Malekie, F. Ziaie, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.01.077i
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unavoidable uncertainty subsequently.
in
determination
of
EPT
region
two-phase system—with the defined mass fractions of φPolymer and φCNT , the Cp value of the composite was calculated according to the rule of mixture [20]:
2.1. Prediction of electrical conductivity
C p ¼ φCNT C p; CNT þ φPolymer C p; Polymer
To predict the electrical conductivity of the composites (σcom), general effective medium equation was used [15]:
where C p; Polymer and C p; CNT are the heat capacity of polymer and CNT respectively. The heat capacities of CNT and applied polymers are extracted from references [1,20–23].
ð1 φÞðσ m s σ com s Þ 1
1
ðσ m þ Aσ com Þ 1 s
1 s
φðσ CNT t σ com t Þ ¼0 1 1 ðσ CNT t þ Aσ com t Þ 1
þ
1
ð1Þ
where φ is the volume fraction of the inclusions, A ¼ ð1 φc Þ=φc , φC is the critical volume fraction, s and t are critical exponents, σm and σCNT represent the electrical conductivity of the matrix and CNTs, respectively. This theory applies throughout the nano, micro and macromedia [15]. In previously published work a new method to predict the electrical conductivity of polymer–CNT composites was proposed by the authors, which considered dispersed randomly oriented CNTs in a polymer matrix as elliptical cross-sections [1]. In this method, firstly, 2D media with size of 10 mm 10 mm in which there are 200 ellipses are introduced randomly as designated. Depending on the angular orientation of CNTs and considering an AR ¼1000, the length of ellipses can vary from 2 nm to 2 mm randomly (Fig.1). Also, the overlap of two ellipses is not allowed according to the excluded area approach. In this simulation b remains fixed at 1 nm for all situations. The electrical potential was calculated through solving Laplace's equation numerically by the finite element method in defined boundary conditions. For assessment of the composite photocurrent for dosimetry and monitoring utilizations, two models of variable range hopping (VRH) and thermally activated hopping (TAH) to describe the electrical properties of CNT and polymer, respectively, were utilized [16–18]. 2.2. Dose–temperature relation The absorption of ionizing energy causes temperature rise (ΔT) in the material, the relation of temperature with the absorbed dose is given by [19]: D ¼ C p U ΔT
ð2Þ
where D is the average absorbed dose and Cp is the heat capacity of the material at constant pressure. In this research work, we assume that all the ionizing energy is converted to heat and leads to an increase in temperature. For polymer–CNT composite—as a
Fig. 1. Spatial representation of CNT with related elliptical cross-section [1].
ð3Þ
2.3. Studying materials The physical characteristics of the applied materials in this simulation are represented in Table 1.
3. Results and discussion 3.1. EPT determination Fig. 2 demonstrates the variation of electrical conductivity of the composites with different polymer matrices of HDPE, PC, PET, PMMA, and PS, against the CNT wt% which simulated at a fixed voltage of 3 V. At low CNT wt%, the value of electrical conductivity is close to pure polymer, where in percolation region 105–108 order of magnitudes increments were observed in electrical conductivity. As can be easily seen from Fig. 2, electrical conductivity of polymer–CNT composites strongly depends on CNT wt%. Herein, for explanation of abrupt change in the electrical conductivity of these composites, it seems that adding CNTs to polymeric matrix creates traps between valence band and conduction band of polymer. This leads to decrease energy separation and also decrease tunneling distance for electrons, so the probability of hopping conduction increases. Grossiord et al. proposed that the conductive properties of polymer composites might depend on the effect of tunneling mechanism [25]. Addition of more CNTs over EPT region, does not change the electrical conductivity, due to the fact that the electrons are taking the easiest conductive path [26]. According to Fig. 2 and considering Table 1, it is obvious that increasing the electrical conductivity of the polymer matrix causes to decrease the EPT of the composite. In fact, polymers having higher electrical conductivity, exhibited narrower band gap, therefore adding CNTs resulted in decrease of energy band gap of the composite and the value of EPT consequently. The obtained results via our simulated model for each composite are depicted in Table 2. This data are validated and compared with the results of EPT values in polymer–CNT composites obtained via experiments down by other researchers. According to Table 2, the level of uncertainty for EPT values in most of the composites is sufficiently reliable to compare simulated results with experiment data. There are several factors that make differences between the experimental and simulation results in determination of EPT value in composites. These factors are including dispersion [41], alignment, aspect ratio, and degree of functionalization of CNTs, adding surfactants, dispersants, type of polymer (viscosity) and processing method of composite (melt mixing, solution processing, or insitu polymerization) [42]. In the simulation method, we considered constant aspect ratio L/D ¼1000, while in the experimental methods for example solution processing, nanotubes undergo scission during sonication, thus CNTs length is reduced [1]. It should be emphasized that the higher CNTs aspect ratios result a lower EPT value in a polymer–CNT composite, and vice versa. On the other hand, interfacial bonding in the interphase region between the embedded CNT and its surrounding polymer is a crucial issue for the load transferring and reinforcement phenomena [43]. CNTs naturally interact with the polymer chains of
Please cite this article as: S. Malekie, F. Ziaie, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.01.077i
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3
Table 1 Physical characteristics of applied materials at room temperature [24]. Material
Electrical conductivity (S/m)
Thermal conductivity (W/m K)
Relative permittivity
Heat capacity (J/kg K)
Density (g/cm3)
SWCNT HDPE PET PS PC PMMA
104–107 1.0 10 15 1.0 10 12 1.0 10 16 5.0 10 15 1.82 10 13
3000 0.48 0.20 0.13 0.21 0.19
200–2000 2.3 3.65 2.6 2.9 3
693 763 1000 1192 1250 1347
1.5 0.91 1.35 1.05 1.2 1.19
Fig. 2. Variation of electrical conductivity of the polymer–CNT composite via CNT wt% at a fixed voltage of 3 V.
Fig. 3. Changes of normalized current densities (J J0)/J0 via absorbed dose before the EPT region of the polymer–CNT composites with different matrices, at the voltage of 3 V.
Table 2 The calculated EPT values and working dose range, in comparison with the experimental data for different polymer–CNT composites. Polymer matrix
Method
HDPE
Experiment 0.45 [27] 0.13 [28] Calculated 0.249 7 0.056 This work
– – 0–200
PMMA
Experiment 0.17 0.33 0.37 0.39 0.5 0.7 Calculated 0.1897 0.043
[29] [30] [31] [32] [33] [34] This work
– – – – – – 0–600
PS
Experiment 0.05 0.27 0.28 Calculated 0.2337 0.050
[35] [36] [34] This work
– – – 0–400
PC
Experiment 0.1 0.3 0.5 Calculated 0.1767 0.042
[35] [37] [38] This work
– – – 0–500
Experiment 0.7 0.5 Calculated 0.156 70.038
[39] [40] This work
– – 0–300
PET
EPT (wt%)
Reference Working dose range (mGy)
the matrix just through weakly non-bonded Van der Waals and electrostatic forces [43]. In this simulation we considered polymeric matrices as uniform media without polymeric chains, thus this assumption may result in discrepancies in EPT value of composites consequently. Also, in this simulation, we considered CNTs as a simple cylinder with elliptical cross-section, where the actual shape of CNTs is not straight but entwined. There is seemingly our method, in spite of structural alterations in different processing procedures of fabricating these nano-composites, has enough precision and accuracy to predict EPT value in polymer–CNT composites.
Fig. 4. Changes of normalized current densities (J J0)/J0 via absorbed dose at the EPT value of the polymer–CNT composites with different matrices, at the voltage of 3 V.
3.2. Dosimetric characteristics Fig. 3 shows the dependence of normalized current densities (J J0)/J0 to absorbed dose for different polymer–CNT composites assumed as before EPT region at the same fixed voltage of 3 V, where J and J0 are the photocurrent and dark current passing through composites, respectively. As can be seen in this figure, the value of current density for most composites firstly increases in a dose interval and saturates afterward. According to Eq. (2), at a constant dose, lower heat capacity (Cp) of the composite resulted in higher temperature rise. Thus, according to Table 1, polymers having lower Cp possessed higher sensitivity and saturated rapidly. On the other hand, the linearity of dose response or working dose range of polymer–CNT composite increased as heat capacity of the polymer increases. Fig. 4 shows the dependence of (J J0)/J0 to absorbed dose for different polymer–CNT composites assumed at EPT value. According to this figure, the sensitivity of composites in this situation increased remarkably in comparison to those composites with CNT wt% before the EPT region (Fig. 4). In fact, adding CNTs to
Please cite this article as: S. Malekie, F. Ziaie, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.01.077i
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3.3. Uncertainty discussions
Fig. 5. Changes of normalized current densities (J J0)/J0 via absorbed dose after the EPT region of the polymer–CNT composites with different matrices, at the voltage of 3 V.
a polymer matrix at the EPT value, converts the polymer to a semiconductor material. Exposure of a semiconductor to ionizing radiation may produce a temporary increase in population of free charge carriers, and the extra flow of current under the influence of an applied electric field [44]. The photons interact with semiconductor in a variety of ways such as photoelectric effect, Compton scattering, and pair production to generate charge carriers. In fact generation of free carrier requires the electron–hole excitation having sufficient energy to overcome their Coulomb attraction; otherwise recombination is inevitable. Fig. 5 shows the dependence of (J J0)/J0 to absorbed dose for different polymer–CNT composites assumed as after the EPT region. The amount of ΔJ/J0 versus dose after EPT region reduced in comparison to those composite with CNT wt% at EPT value due to increasing of dark current [1]. On the other hand because of dominance of dark current in all the composites, the responses do not show a considerable difference between the different composites. According to Table 1 and Figs. 3 and 4, sensitivity is inversely proportional to permittivity of the polymer matrix in different polymer–CNT composites. The only PET–CNT composite does not behave via this role, which could be due to the lower CNT wt% which was resulted through simulation and higher density of PET in comparison to the other composites. These results are in correlation with what have been predicted for polymer–CNT composite when irradiated by ionization radiation [44]. The sensitivity of a semiconductor is affected by both the relative permittivity and polarization of the material. For the polymers with high relative permittivity and polarization, Coulomb capture radius (CCR) will be small, and the direct generation of charge carriers will be easy [44]. Conversely, where CCR quantity is large the recombination occurs, therefore sensitivity of semiconductor decreases. Also, the working dose range increases with increasing of polymer heat capacity. This is due to the fact that the higher heat capacity of polymer results in higher capability in absorbing radiation energy or wider dose range. For detection and dosimetry of ionization radiations such as gamma rays, it should be pointed out that dark current must be smaller than photocurrent. Regarding this fact, for a polymer–CNT composite as an understudy dosimeter, dark current depends on the amount of CNTs concentration in the composite. Electrical percolation theory is an appropriate approach to precise control of CNTs amount in the polymer–CNT composite [1]. In polymer–CNT composite, the EPT is a critical phenomenon that plays an important role in determination of dark current in such systems.
In this research work, arrangement and distribution of carbon nanotubes in polymer matrices for prediction of EPT region in polymer–CNT composites is based on a random process including statistical fluctuation and unavoidable uncertainty. These statistical fluctuations and uncertainties propagate through the calculations for prediction of EPT region in the nanocomposites. Thus, for obtaining the mean and standard deviation of EPT value, assumed as upper-right edge of the curve demonstrated in Fig. 2, the calculations were repeated with producing random numbers 10 times independently. The level of uncertainties in Table 2 propagates to the next calculations for obtaining dark current J0 subsequently. In the absence of ionization radiation, J0 is proportional to electrical conductivity of the composite at room temperature. In this simulation, since the precision of ΔT is 10 5 K, regarding heat capacity of the polymer matrices that are in the range of 763–1347 J/(kg K), it appears that calculation of absorbed dose resulted in mGy scale. It seems that level of uncertainty in determination of EPT region for various composites is sufficiently reliable to calculate dosimetric characteristics of these composites. Another parameter that affects the dosimetric characteristics of polymer–CNT composites is crystallinity of the polymeric matrices. It is worth pointing out that the CNTs have been shown to act as a nucleating agent for polymer crystallization [45]. Since G-value (the mean number of entities produced, destroyed or changed by an energy imparted of 100 eV [46]) is proportional to crystallinity degree of the polymer [47], it is expected that irradiation of composite leads to produce more electron–hole in sensitive volume. In general, amorphous materials do not have the tendency to produce trapped electrons. More crystallinity in polymer resulted in more yield of trapped electrons G-value [47]. In fact in this research work, crystallinity of the polymeric matrices is not considered in the simulation. This ignorance may also affect the dosimetric characteristics such as dose response of the various composites.
4. Conclusion This paper focuses on the behavior of dose response, sensitivity and working dose range of polymer–CNT composite for HDPE, PC, PET, PMMA, and PS matrices. The predictions of EPT value in polymer–CNT nanocomposite were validated by experimental ones. It was deduced that the relative permittivity and heat capacity of polymers can affect the sensitivity and working dose range of polymer–CNT composite as dosimeter. It was concluded that the composite containing polymer of higher heat capacity, exhibits a higher working dose range and lower sensitivity for dosimetry purposes. Also we deduced that sensitivity is inversely proportional to permittivity of the polymer matrix in different polymer–CNT composites. Also, the difference between the simulation and experimental results was discussed and seems to be due to the factors that depends on the characteristics of the polymer matrices and CNTs which were not involved in simulation procedure, but affect the experimental results.
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Please cite this article as: S. Malekie, F. Ziaie, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.01.077i
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Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Study on dosimetry characteristics of polymer–CNT nanocomposites: Effect of polymer matrix Shahryar Malekie, Farhood Ziaie n Radiation Application Research School, Nuclear Science & Technology Research Institute, PO Box 11365-3486, Tehran, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 11 November 2015 Received in revised form 23 January 2016 Accepted 26 January 2016
In this research work, the current density of polymer–carbon nanotube nanocomposite in different weight percentages of nanotubes, over the radiation absorbed dose under a fixed DC voltage for different polymer matrices such as high density polyethylene, polycarbonate, polyethylene terephthalate, polymethyl methacrylate, and polystyrene was investigated via finite element method. The predicted electrical percolation threshold values in different composites were validated by experimental results published by other scientists. The absorbed dose value was considered as multiplying of heat capacity and temperature rise of the composite, regarding the calorimetric approach. Results show that the polymer type having different characteristics of relative permittivity and heat capacity could affect the sensitivity and working dose range of the composite as a dosimeter. & 2016 Published by Elsevier B.V.
Keywords: Carbon nanotube Percolation Electrical conductivity Composite Dosimetry
1. Introduction The electrically conductive polymer–carbon nanotube composites have great potential in many applications, such as electromagnetic interference shielding, sensors, batteries, antistatic devices, lightweight energy storages, and dosimeters [1–6]. Dosimetry and detection of ionizing radiation are important investigation fields in the nuclear industry. The discovery of carbon nanotube (CNT) [7] opened the door to enhance the properties of polymer composites for structural and multifunctional applications [8]. The nano-sized, high surface area and the high aspect ratio (AR) of CNTs, offer the great opportunities to enhance the electrical conductivity of the polymer nano-composites even at a very low loading of CNTs in the polymer matrix [9,10]. In fact, carbon nanotubes via adding to a polymer matrix in a particular weight percentage (wt%), entitled electrical percolation threshold (EPT), leads to a suddenly several orders of magnitude increasing of electrical conductivity of polymer–CNT composite [1]. The considerable difference between the electrical conductivity of these materials makes electrical percolation theory as an ideal modeling tool to predict electrical characteristics of polymer–CNT composite in different wt% of inclusions [11]. Since polymer–CNT composite is light, tissue equivalent, low cost and also due to easy processing, this kind of material has potential applications as ionizing radiation dosimeter. The effects n
Corresponding author. E-mail address: [email protected] (F. Ziaie).
of length and critical density of CNTs on the electrical conductivity of a radiation sensor based on percolation theory were studied [12]. Other researchers were investigated the interaction of radiation with functionalized carbon nanotubes that have been incorporated into various host materials, particularly polymeric ones [13]. In our previous work, it was shown that the EPT of polymer–CNT composite is the best point for dosimetry purposes [1]. In this research work the dosimetry characteristics of the composites in different wt% were evaluated and compared for different polymer matrices such as high density polyethylene (HDPE), polycarbonate (PC), polyethylene terephthalate (PET), polymethyl methacrylate (PMMA), and polystyrene (PS).
2. Simulation methodology According to effective medium theory (EMT), studying on a piece of material can be generalized to whole of the system. EMT is a physical model based on properties of individual components and their fractions in the composite [14]. Scaling law and percolation theory are used to predict the critical phenomena related to disorder systems [11]. Thus, determination of EPT in polymer–CNT composites has an important role in evaluation of dosimetric characteristics of the materials. In this simulation, assessment of the EPT region for polymer–CNT composites is based on producing random numbers for achieving dispersed homogeneous CNTs network. This issue is accompanied by statistical fluctuations and
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unavoidable uncertainty subsequently.
in
determination
of
EPT
region
two-phase system—with the defined mass fractions of φPolymer and φCNT , the Cp value of the composite was calculated according to the rule of mixture [20]:
2.1. Prediction of electrical conductivity
C p ¼ φCNT C p; CNT þ φPolymer C p; Polymer
To predict the electrical conductivity of the composites (σcom), general effective medium equation was used [15]:
where C p; Polymer and C p; CNT are the heat capacity of polymer and CNT respectively. The heat capacities of CNT and applied polymers are extracted from references [1,20–23].
ð1 φÞðσ m s σ com s Þ 1
1
ðσ m þ Aσ com Þ 1 s
1 s
φðσ CNT t σ com t Þ ¼0 1 1 ðσ CNT t þ Aσ com t Þ 1
þ
1
ð1Þ
where φ is the volume fraction of the inclusions, A ¼ ð1 φc Þ=φc , φC is the critical volume fraction, s and t are critical exponents, σm and σCNT represent the electrical conductivity of the matrix and CNTs, respectively. This theory applies throughout the nano, micro and macromedia [15]. In previously published work a new method to predict the electrical conductivity of polymer–CNT composites was proposed by the authors, which considered dispersed randomly oriented CNTs in a polymer matrix as elliptical cross-sections [1]. In this method, firstly, 2D media with size of 10 mm 10 mm in which there are 200 ellipses are introduced randomly as designated. Depending on the angular orientation of CNTs and considering an AR ¼1000, the length of ellipses can vary from 2 nm to 2 mm randomly (Fig.1). Also, the overlap of two ellipses is not allowed according to the excluded area approach. In this simulation b remains fixed at 1 nm for all situations. The electrical potential was calculated through solving Laplace's equation numerically by the finite element method in defined boundary conditions. For assessment of the composite photocurrent for dosimetry and monitoring utilizations, two models of variable range hopping (VRH) and thermally activated hopping (TAH) to describe the electrical properties of CNT and polymer, respectively, were utilized [16–18]. 2.2. Dose–temperature relation The absorption of ionizing energy causes temperature rise (ΔT) in the material, the relation of temperature with the absorbed dose is given by [19]: D ¼ C p U ΔT
ð2Þ
where D is the average absorbed dose and Cp is the heat capacity of the material at constant pressure. In this research work, we assume that all the ionizing energy is converted to heat and leads to an increase in temperature. For polymer–CNT composite—as a
Fig. 1. Spatial representation of CNT with related elliptical cross-section [1].
ð3Þ
2.3. Studying materials The physical characteristics of the applied materials in this simulation are represented in Table 1.
3. Results and discussion 3.1. EPT determination Fig. 2 demonstrates the variation of electrical conductivity of the composites with different polymer matrices of HDPE, PC, PET, PMMA, and PS, against the CNT wt% which simulated at a fixed voltage of 3 V. At low CNT wt%, the value of electrical conductivity is close to pure polymer, where in percolation region 105–108 order of magnitudes increments were observed in electrical conductivity. As can be easily seen from Fig. 2, electrical conductivity of polymer–CNT composites strongly depends on CNT wt%. Herein, for explanation of abrupt change in the electrical conductivity of these composites, it seems that adding CNTs to polymeric matrix creates traps between valence band and conduction band of polymer. This leads to decrease energy separation and also decrease tunneling distance for electrons, so the probability of hopping conduction increases. Grossiord et al. proposed that the conductive properties of polymer composites might depend on the effect of tunneling mechanism [25]. Addition of more CNTs over EPT region, does not change the electrical conductivity, due to the fact that the electrons are taking the easiest conductive path [26]. According to Fig. 2 and considering Table 1, it is obvious that increasing the electrical conductivity of the polymer matrix causes to decrease the EPT of the composite. In fact, polymers having higher electrical conductivity, exhibited narrower band gap, therefore adding CNTs resulted in decrease of energy band gap of the composite and the value of EPT consequently. The obtained results via our simulated model for each composite are depicted in Table 2. This data are validated and compared with the results of EPT values in polymer–CNT composites obtained via experiments down by other researchers. According to Table 2, the level of uncertainty for EPT values in most of the composites is sufficiently reliable to compare simulated results with experiment data. There are several factors that make differences between the experimental and simulation results in determination of EPT value in composites. These factors are including dispersion [41], alignment, aspect ratio, and degree of functionalization of CNTs, adding surfactants, dispersants, type of polymer (viscosity) and processing method of composite (melt mixing, solution processing, or insitu polymerization) [42]. In the simulation method, we considered constant aspect ratio L/D ¼1000, while in the experimental methods for example solution processing, nanotubes undergo scission during sonication, thus CNTs length is reduced [1]. It should be emphasized that the higher CNTs aspect ratios result a lower EPT value in a polymer–CNT composite, and vice versa. On the other hand, interfacial bonding in the interphase region between the embedded CNT and its surrounding polymer is a crucial issue for the load transferring and reinforcement phenomena [43]. CNTs naturally interact with the polymer chains of
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3
Table 1 Physical characteristics of applied materials at room temperature [24]. Material
Electrical conductivity (S/m)
Thermal conductivity (W/m K)
Relative permittivity
Heat capacity (J/kg K)
Density (g/cm3)
SWCNT HDPE PET PS PC PMMA
104–107 1.0 10 15 1.0 10 12 1.0 10 16 5.0 10 15 1.82 10 13
3000 0.48 0.20 0.13 0.21 0.19
200–2000 2.3 3.65 2.6 2.9 3
693 763 1000 1192 1250 1347
1.5 0.91 1.35 1.05 1.2 1.19
Fig. 2. Variation of electrical conductivity of the polymer–CNT composite via CNT wt% at a fixed voltage of 3 V.
Fig. 3. Changes of normalized current densities (J J0)/J0 via absorbed dose before the EPT region of the polymer–CNT composites with different matrices, at the voltage of 3 V.
Table 2 The calculated EPT values and working dose range, in comparison with the experimental data for different polymer–CNT composites. Polymer matrix
Method
HDPE
Experiment 0.45 [27] 0.13 [28] Calculated 0.249 7 0.056 This work
– – 0–200
PMMA
Experiment 0.17 0.33 0.37 0.39 0.5 0.7 Calculated 0.1897 0.043
[29] [30] [31] [32] [33] [34] This work
– – – – – – 0–600
PS
Experiment 0.05 0.27 0.28 Calculated 0.2337 0.050
[35] [36] [34] This work
– – – 0–400
PC
Experiment 0.1 0.3 0.5 Calculated 0.1767 0.042
[35] [37] [38] This work
– – – 0–500
Experiment 0.7 0.5 Calculated 0.156 70.038
[39] [40] This work
– – 0–300
PET
EPT (wt%)
Reference Working dose range (mGy)
the matrix just through weakly non-bonded Van der Waals and electrostatic forces [43]. In this simulation we considered polymeric matrices as uniform media without polymeric chains, thus this assumption may result in discrepancies in EPT value of composites consequently. Also, in this simulation, we considered CNTs as a simple cylinder with elliptical cross-section, where the actual shape of CNTs is not straight but entwined. There is seemingly our method, in spite of structural alterations in different processing procedures of fabricating these nano-composites, has enough precision and accuracy to predict EPT value in polymer–CNT composites.
Fig. 4. Changes of normalized current densities (J J0)/J0 via absorbed dose at the EPT value of the polymer–CNT composites with different matrices, at the voltage of 3 V.
3.2. Dosimetric characteristics Fig. 3 shows the dependence of normalized current densities (J J0)/J0 to absorbed dose for different polymer–CNT composites assumed as before EPT region at the same fixed voltage of 3 V, where J and J0 are the photocurrent and dark current passing through composites, respectively. As can be seen in this figure, the value of current density for most composites firstly increases in a dose interval and saturates afterward. According to Eq. (2), at a constant dose, lower heat capacity (Cp) of the composite resulted in higher temperature rise. Thus, according to Table 1, polymers having lower Cp possessed higher sensitivity and saturated rapidly. On the other hand, the linearity of dose response or working dose range of polymer–CNT composite increased as heat capacity of the polymer increases. Fig. 4 shows the dependence of (J J0)/J0 to absorbed dose for different polymer–CNT composites assumed at EPT value. According to this figure, the sensitivity of composites in this situation increased remarkably in comparison to those composites with CNT wt% before the EPT region (Fig. 4). In fact, adding CNTs to
Please cite this article as: S. Malekie, F. Ziaie, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.01.077i
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3.3. Uncertainty discussions
Fig. 5. Changes of normalized current densities (J J0)/J0 via absorbed dose after the EPT region of the polymer–CNT composites with different matrices, at the voltage of 3 V.
a polymer matrix at the EPT value, converts the polymer to a semiconductor material. Exposure of a semiconductor to ionizing radiation may produce a temporary increase in population of free charge carriers, and the extra flow of current under the influence of an applied electric field [44]. The photons interact with semiconductor in a variety of ways such as photoelectric effect, Compton scattering, and pair production to generate charge carriers. In fact generation of free carrier requires the electron–hole excitation having sufficient energy to overcome their Coulomb attraction; otherwise recombination is inevitable. Fig. 5 shows the dependence of (J J0)/J0 to absorbed dose for different polymer–CNT composites assumed as after the EPT region. The amount of ΔJ/J0 versus dose after EPT region reduced in comparison to those composite with CNT wt% at EPT value due to increasing of dark current [1]. On the other hand because of dominance of dark current in all the composites, the responses do not show a considerable difference between the different composites. According to Table 1 and Figs. 3 and 4, sensitivity is inversely proportional to permittivity of the polymer matrix in different polymer–CNT composites. The only PET–CNT composite does not behave via this role, which could be due to the lower CNT wt% which was resulted through simulation and higher density of PET in comparison to the other composites. These results are in correlation with what have been predicted for polymer–CNT composite when irradiated by ionization radiation [44]. The sensitivity of a semiconductor is affected by both the relative permittivity and polarization of the material. For the polymers with high relative permittivity and polarization, Coulomb capture radius (CCR) will be small, and the direct generation of charge carriers will be easy [44]. Conversely, where CCR quantity is large the recombination occurs, therefore sensitivity of semiconductor decreases. Also, the working dose range increases with increasing of polymer heat capacity. This is due to the fact that the higher heat capacity of polymer results in higher capability in absorbing radiation energy or wider dose range. For detection and dosimetry of ionization radiations such as gamma rays, it should be pointed out that dark current must be smaller than photocurrent. Regarding this fact, for a polymer–CNT composite as an understudy dosimeter, dark current depends on the amount of CNTs concentration in the composite. Electrical percolation theory is an appropriate approach to precise control of CNTs amount in the polymer–CNT composite [1]. In polymer–CNT composite, the EPT is a critical phenomenon that plays an important role in determination of dark current in such systems.
In this research work, arrangement and distribution of carbon nanotubes in polymer matrices for prediction of EPT region in polymer–CNT composites is based on a random process including statistical fluctuation and unavoidable uncertainty. These statistical fluctuations and uncertainties propagate through the calculations for prediction of EPT region in the nanocomposites. Thus, for obtaining the mean and standard deviation of EPT value, assumed as upper-right edge of the curve demonstrated in Fig. 2, the calculations were repeated with producing random numbers 10 times independently. The level of uncertainties in Table 2 propagates to the next calculations for obtaining dark current J0 subsequently. In the absence of ionization radiation, J0 is proportional to electrical conductivity of the composite at room temperature. In this simulation, since the precision of ΔT is 10 5 K, regarding heat capacity of the polymer matrices that are in the range of 763–1347 J/(kg K), it appears that calculation of absorbed dose resulted in mGy scale. It seems that level of uncertainty in determination of EPT region for various composites is sufficiently reliable to calculate dosimetric characteristics of these composites. Another parameter that affects the dosimetric characteristics of polymer–CNT composites is crystallinity of the polymeric matrices. It is worth pointing out that the CNTs have been shown to act as a nucleating agent for polymer crystallization [45]. Since G-value (the mean number of entities produced, destroyed or changed by an energy imparted of 100 eV [46]) is proportional to crystallinity degree of the polymer [47], it is expected that irradiation of composite leads to produce more electron–hole in sensitive volume. In general, amorphous materials do not have the tendency to produce trapped electrons. More crystallinity in polymer resulted in more yield of trapped electrons G-value [47]. In fact in this research work, crystallinity of the polymeric matrices is not considered in the simulation. This ignorance may also affect the dosimetric characteristics such as dose response of the various composites.
4. Conclusion This paper focuses on the behavior of dose response, sensitivity and working dose range of polymer–CNT composite for HDPE, PC, PET, PMMA, and PS matrices. The predictions of EPT value in polymer–CNT nanocomposite were validated by experimental ones. It was deduced that the relative permittivity and heat capacity of polymers can affect the sensitivity and working dose range of polymer–CNT composite as dosimeter. It was concluded that the composite containing polymer of higher heat capacity, exhibits a higher working dose range and lower sensitivity for dosimetry purposes. Also we deduced that sensitivity is inversely proportional to permittivity of the polymer matrix in different polymer–CNT composites. Also, the difference between the simulation and experimental results was discussed and seems to be due to the factors that depends on the characteristics of the polymer matrices and CNTs which were not involved in simulation procedure, but affect the experimental results.
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