Temperature-dependent charge transport in TiO2–multiwalled carbon nanotube composites

Temperature-dependent charge transport in TiO2–multiwalled carbon nanotube composites

CARBON 6 7 ( 2 0 1 4 ) 6 8 8 –6 9 3 Available at www.sciencedirect.com ScienceDirect journal homepage: www.elsevier.com/locate/carbon Temperature-...

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6 7 ( 2 0 1 4 ) 6 8 8 –6 9 3

Available at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/carbon

Temperature-dependent charge transport in TiO2–multiwalled carbon nanotube composites Seul Gi Seo a,b, Woo Hyun Nam c, Young Soo Lim Jeong Yong Lee c,d

a,* ,

Won-Seon Seo a, Yong Soo Cho b,


Energy and Environmental Division, Korea Institute of Ceramic Engineering and Technology, 233-5 Gasan-dong, Geumcheon-gu, Seoul 153-801, Republic of Korea b Department of Materials Science and Engineering, Yonsei University, 134 Sinchon-dong, Seodaemun-gu, Seoul 120-749, Republic of Korea c Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea d Center for Nanomaterials and Chemical Reactions, Institute for Basic Science, Daejeon 305-701, Republic of Korea



Article history:

Charge transport properties of TiO2–multiwalled carbon nanotube (MWCNT) composites

Received 29 May 2013

were investigated. The TiO2–MWCNT composites were fabricated by spark plasma sintering

Accepted 18 October 2013

of a mixture of TiO2 nanoparticles and MWCNTs. Temperature-dependent electrical con-

Available online 30 October 2013

ductivities of the composites reveal that the percolation threshold for the MWCNT network is affected by temperature, and that the activation process for electron hopping is also influenced by the percolation. Based on this interdependence, an integrated charge transport model, including both the effects of the percolation and the electron hopping, is proposed for this system.  2013 Elsevier Ltd. All rights reserved.



Inorganic- and organic-carbon nanotube (CNT) composites have attracted broad interest due to their great potentials in electronic, energy and environmental applications, such as electrode materials for various electronics [1], photovoltaic and thermoelectric energy conversion materials [2–5], energy storage materials for secondary ion battery and supercapacitor [6–8], and photocatalysts [9–11]. Basically, these applications are based upon the excellent intrinsic electric properties of CNTs and also upon proper band alignments between the CNT and matrix materials in the composites. However, the electrical properties of such nanocomposites can be difficult to understand given the nature of the CNT itself, and should be interpreted in terms of a CNT network, formed in inorganic or organic base materials. Charge transport of the CNT network is governed both by electrical percolation between individual CNTs and by the

charge transfer mechanism from one CNT to another at a junction [12–14]. The percolation model concerns the electrical conductivity of the CNT network as a function of the amount of CNT in the matrix [12]. On the other hand, the known charge transfer mechanisms at the junction, such as hopping and tunneling, are critically dependent on temperature [13,14]. Therefore, charge transport in the CNT network has been fragmentarily treated as a function of the amount of CNT, or, as a function of temperature [15–19]. A combined integrated charge transport model incorporating both the percolation and temperature-dependent mechanisms has not yet been proposed for CNT network-based materials. Herein, we propose a charge transport model based on a multiwalled CNT (MWCNT) network in TiO2–MWCNT composites. By characterizing temperature-dependent electrical conductivities within a temperature range of 300–1050 K, we realized that the percolation limit of the network was strongly dependent on temperature. Also, the activation

* Corresponding author. E-mail address: [email protected] (Y.S. Lim). 0008-6223/$ - see front matter  2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carbon.2013.10.060


6 7 (2 0 1 4) 6 8 8–69 3


energy for hopping conduction was also significantly influenced by the degree of percolation in the composites. Based on these results, we define a new temperature-dependent parameter which is related to the percolation-dependency of the electrical conductivity of the MWCNT network, and propose an integrated charge transport model including both the effects of the percolation and the hopping process, to understand the electrical conduction behavior in TiO2–MWCNT composites.


Experimental details

In this experiment, MWCNTs (Sigma–Aldrich) and TiO2 nanopowder (P25, Degussa) were used as raw materials. The MWCNTs were dispersed in dimethylformamide (DMF, Sigma Aldrich) by using ultrasonication for 1 h. Different amounts of MWCNTs (0, 0.5, 1.0, 2.0, 4.0 and 8.0 wt%) in the DMF solution were mixed with the TiO2 nanopowder (average diameter 20 nm) by ball-milling for 20 h. After the ball-milling, the mixture of TiO2 and MWCNTs was dried at 100 C for 24 h, and consolidated by spark plasma sintering at 1173 K for 5 min under a uniaxial pressure of 50–70 MPa. Densities of the TiO2–MWCNT composites were measured by the Archimedes method. The relative densities in all composites were higher than 90%. Microstructural characterizations of the TiO2–MWCNT composites were carried out by using a scanning electron microscope (SEM, JSM-6700, JEOL), and detailed structural investigations were performed by using a transmission electron microscope (TEM, JEM-4010, JEOL). Temperature-dependent charge transport was investigated by using a four-point probe method (RZ-2001i, Ozawa Science).


Results and discussion


Microstructures of TiO2–MWCNT composites

Fig. 1a is the SEM micrograph of MWCNTs used as starting material. Their average diameter was around 5–10 nm with closed-ended shape, and their length was in the range of a few lm. Effects of the amount of MWCNTs on microstructures of the TiO2–MWCNT composites sintered by spark plasma are shown in Fig. 1b–g. The grain size of TiO2 composite without MWCNT (0 wt%) was around 400–500 nm due to the inevitable grain growth of TiO2 nanoparticles during the consolidation process. On the other hand, TiO2 grain growth in the TiO2–MWCNT composite was significantly suppressed by the presence of MWCNTs, resulting in smaller grain sizes of 200–300 nm. Regardless of the amount of MWCNTs, the MWCNTs were quite homogeneously dispersed in the TiO2 matrix. Fig. 1h corresponds to the bright-field TEM micrograph of the 8 wt% MWCNT composite, which shows that TiO2 grains are surrounded by MWCNTs. The existence of MWCNT dispersed at the grain boundary can be further elucidated by highresolution TEM micrograph (HRTEM) as shown in the inset. Therefore, it is confirmed that TiO2–MWCNT composites were successfully prepared by spark plasma sintering, with the ideal network structure of MWCNTs dispersed along the grain boundaries of TiO2 nanograins.

Fig. 1 – SEM micrographs of (a) as-received MWCNTs, (b) fractured surface of TiO2 composite without MWCNT (0 wt%), (c)–(g) fractured surfaces of TiO2–MWCNT composites with 0.5, 1, 2, 4 and 8 wt% of MWCNT, respectively. (h) A bright-field TEM micrograph of TiO2– MWCNT (8 wt%) composite and a HRTEM micrograph of a MWCNT embedded in the TiO2 matrix (inset).

3.2. Conventional models for charge transport in the composites To understand charge transport in the TiO2–MWCNT composites, temperature-dependent electrical conductivities were characterized as a function of MWCNT content within a temperature range of 300–1050 K as shown in Fig. 2a. In all composites, electrical conductivities increase with temperature. As expected, the TiO2 composite without MWCNT (0 wt%) did not show electrical conduction behavior at room temperature. Its electrical conductivity was 7 · 105 S/cm at 300 K and became higher with increased temperature, as exemplified by 1.36 · 102 S/cm at 1050 K. In the TiO2–MWCNT composites, electrical conductivities increased with the increasing amount of MWCNT, presumably due to the formation of more effective conduction paths through the MWCNT network. Higher values, up to 16.7 S/cm, were found at 300 K as the content of MWCNT was increased to 8 wt%. This phenomenon can be well described by a percolation model, as expressed by the following equation, which has been generally accepted for the interpretation of charge transport



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Fig. 2 – Electrical conductivities of the composites interpreted by (a) percolation model and (b) 3D VRH model. Inset in (a) represents the best-fitted results to Eq. (1). (A colour version of this figure can be viewed online.)

phenomena in various kinds of composites containing CNTs with insulating materials [12,15–18]. t

rðqÞ ¼ r1 ðq  qc Þ


where r1 is the proportional constant, q is the volume fraction of MWCNT, qc is the percolation threshold and t is the critical exponent. Best fitted results are shown as an inset in Fig. 2a and the fitting parameters are listed in Table 1. The critical exponent was estimated to be 0.8 in all composites which is quite lower than the values reported in the literature (1.2–3.1) [15–18]. Although the theoretical value is known to be directly correlated to the dimensionality of the network

connection (t = 1–1.35 for 2-dimension and 1.6–2.0 for 3dimension) [20], Rul et al. reported that a smaller aspect ratio of MWCNT can lead to a critical exponent lower than the value expected from the dimensionality [15]. Furthermore, they proposed that the lowered t is partially a consequence of a weakly-connected local part in the CNT network, which is associated with a thermally-activated hopping process [15]. In Eq. (1), there is no explicit temperature-dependent parameter and the electrical conductivity depends solely on the amount of MWCNT in the composites. Using this model, we could obtain the percolation threshold of 0.462 wt% at 300 K as shown in Table 1. The threshold was drastically reduced with increasing temperature, and as an example it became 0.025 wt% at 1050 K. This drastic reduction in the percolation threshold with temperature indicates that the conduction path becomes more effective at a higher temperature due to the activation process of the charge transfer between MWCNTs [21]. Therefore, it is obvious that the percolation-dependent charge transport in the TiO2–MWCNT composite is influenced by a certain activation process. Note that the sintering temperature by spark plasma was 1173 K, which is higher than the measurement temperatures. Therefore, we assume that there is no change in physical properties during the high temperature measurements. By replotting Fig. 2a as a function of temperature, we characterized the temperature-dependent charge transport in the TiO2–MWCNT composites. As shown in Fig. 2b, the electrical conductivity has a linear relation with T1/4 in a logarithmic scale. This observation indicates clearly that charge transfer between the percolated MWCNTs follows the 3-dimensional variable-range hopping (VRH) model expressed by the following, Mott’s equation [13].  1=4 T0 rðTÞ ¼ r2 exp ð2Þ T where r2 is the high temperature limit of electrical conductivity and T0 is the characteristic Mott temperature. The activation energy for the hopping transport can be given by    1=4 1 T0 Wa ¼ ð3Þ kB T 4 T where Wa is the activation energy for hopping transport and kB is the Boltzmann constant [19]. From Eqs. (2) and (3), the values of r2, T0, and Wa were determined as listed in Table 2. T0 decreases continuously with increasing wt% of MWCNT, suggesting that the effective activation energy for charge

Table 1 – Temperature-dependent percolation thresholds (qc) and critical exponents (t) in the TiO2–MWCNT composite system. Temperature (K)

qc (wt%)


300 350 450 550 650 750 850 950 1050

0.462 0.432 0.321 0.217 0.173 0.135 0.131 0.052 0.025

0.78 0.81 0.81 0.79 0.79 0.78 0.83 0.79 0.78



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Table 2 – Percolation-dependent parameters for the 3D VRH model and the activation energies for electron hopping in the TiO2–MWCNT composite system. Composites TiO2–0.5 wt% TiO2–1.0 wt% TiO2–2.0 wt% TiO2–4.0 wt% TiO2–8.0 wt%


3149.6 42.6 47.8 74.4 104.3

transfer decreases due to more extensive formation of MWCNT network with more percolated MWCNTs available. Therefore, it confirms that the VRH model as a function of temperature is also influenced by the amount of MWCNT.


n-Type charge transport in the composites

Because the intrinsic thermopower of CNT is positive [22], the conduction of the CNT-insulator composite should be determined by the hole transport in the composite if there is no electron injection from the matrix by the proper band alignment. Therefore, p-type Seebeck coefficients have been reported in most composites containing CNT [3–5,22–25]. However, negative Seebeck coefficients were observed in all composites studied here, as shown in Fig. 3a. This indicates that the majority charge carrier in the composites are electrons. The origin of the charge carriers can be explained by band alignments between TiO2 and MWCNT as shown in the inset of Fig. 3a. The conduction band position of TiO2 (anatase) is 4.2 eV and its band gap is around 3.2 eV [26]. The electron affinity of the MWCNT, which was derived from the parameters of graphite, is about 4.4 eV [27] and the MWCNT has a narrow band gap (<1.1 eV) [28]. Therefore, excited electrons in TiO2 grains can be transferred to the conduction band of the MWCNT network [9], while holes remain in TiO2, as proposed by Kamat and his co-workers [2,6]. Furthermore, Wang et al. proposed that the excitation of electron–hole pairs in a CNT network also leads to the removal of electrons from the valence band of TiO2 by leaving holes for charge compensation [29]. The recombination of

T0 (K)

Wa (meV) 6

2.24 · 10 2.59 · 104 1.32 · 104 8.19 · 103 3.55 · 103

60.1 19.7 16.6 14.8 12.0

the electron–hole pairs can be hindered by a Schottky barrier between CNT and TiO2 [9]. Considering both the percolation and VRH models, the schematic for the charge transport mechanism in the composites is depicted in Fig. 3b. First, electrons are excited in a TiO2 grain, and then transfer into a nearby MWCNT (step 1). Next, the electrons flow through the MWCNT which act as a conducting path, but they often meet a physical gap with other MWCNTs in the network of percolated MWCNTs (step 2). In this case, electron conduction to the other MWCNTs likely happens by the VRH mechanism (step 3), and series of these steps occurs continuously in this system. Therefore, the charge transport of the MWCNT network surrounded by TiO2 grains is understood by including contributions from both percolation and VRH, and an integrated model is needed to explain the overall charge transport in the composites.

3.4. Charge transport model driven by the MWCNT network The electrical conductivities in Fig. 1a are replotted in a linear scale as shown in Fig. 4a. It is noteworthy that the electrical conductivities are linearly proportional to the amount of MWCNT, especially beyond the percolation threshold. Because the percolation limit was decreased by increasing temperature as shown in Table 1, the linearity became much more obvious at relatively high temperatures. Basically, the slope in Fig. 4a indicates the percolation-dependence of the electrical conductivity of the MWCNT network. In other words, it implies that the dependence of the electrical

Fig. 3 – (a) Seebeck coefficients of the TiO2–MWCNT composites and (b) a schematic for charge transport in the composites. Inset in (a) is an illustration to depict the electron transfer from TiO2 to MWCNT. (A colour version of this figure can be viewed online.)



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Fig. 4 – (a) Temperature-dependent electrical conductivities of TiO2–MWCNT composites as a function of wt% of MWCNT in a linear scale and (b) temperature-dependence of the slope, a(T), in (a). (A colour version of this figure can be viewed online.)

conductivity on the degree of completeness of the network formed by the percolated MWCNTs. Interestingly, the slope of electrical conductivity, a(T), increases with increasing temperature, indicating that the effectiveness of the network becomes more significant at relatively high temperatures, as discussed in Fig. 2a. From these results, the charge transport of the MWCNT network in the composites may be described as follows, rðq; TÞ ¼ r3 þ aðTÞq


where r3 is the extrapolated conductivity to q = 0. To prove the integrated charge transport model, the temperature dependence of aðTÞ was estimated in the composites. As shown in Fig. 4b, aðTÞ represented an apparent linear relationship with T1/4 in a logarithmic scale. The temperature dependence of the charge transport in each composite (marked by an arrow) has been interpreted by the conventional VRH model discussed in Fig. 2b. However, this result demonstrates that the percolation-dependence of the electrical conductivity in this composite system, aðTÞ, is also governed by the VRH model as shown in Fig. 4b. Therefore, an integrated charge transport model for the MWCNT network in this system can be expressed as  1=4 T0 rðq; TÞ ¼ r3 þ A exp q ð5Þ T where A is the proportional constant. Our proposed charge transport model accommodates the attributes of the linearity of aðTÞ in the TiO2–MWCNT composites. It explains both the effects of the percolation of MWCNT and the charge transfer by hopping in a composite system based on an MWCNT network.



A charge transport model in TiO2–MWCNT composites is proposed. The composites, prepared by spark plasma sintering of a mixture of TiO2 nanoparticles with MWCNTs, showed a relatively uniform distribution of MWCNTs along with TiO2 nanograins, which became clearer with higher contents of MWCNTs. It showed n-type charge transport behavior as understood by the band alignment between TiO2 and MWCNT. Charge transport phenomena in the composites

were interpreted not only by a conventional percolation model, in terms of the amount of MWCNT, but also by a known VRH model in terms of temperature dependence. Conclusively, we confirm that there is strong interdependency between the percolation model and the VRH model. The percolation threshold is correlatively affected by temperature while the activation energy for the hopping process is significantly influenced by the percolation. From the results, we propose an integrated charge transport model including both the effects of the percolation and the temperature on the electrical conduction behavior of the TiO2–MWCNT composite.

Acknowledgements This research was supported by Korea Institute of Ceramic Engineering and Technology and also supported by NanoÆMaterial Technology Development Program (20110030147) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology, Republic of Korea.


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