Printer Friendly

Dielectric Properties of Epoxy-Matrix Composites with Tungsten Disulfide Nanotubes.

1. Introduction

Nanoparticles are very interesting objects for investigations due to the possibility to control properties at the nanoscale and to find new physical phenomena. The nanotubes are a very important type of nanoparticles, due to the high aspect ratio of these structures. The nanotubes are typical for all layered materials, including tungsten disulfide (W[S.sub.2]). Recently, it was demonstrated that W[S.sub.2] nanotubes and composites with these inclusions can be applied in various fields, including lithium ion batteries [1], bone tissue engineering [2], ultrafast photonics [3], and solar cells [4]. A lot of papers was already published on mechanical [5] and tribological [6] applications of W[S.sub.2] nanotubes and composites with these inclusions [7-12].

Moreover, due to the needle-like shape of W[S.sub.2] nanotubes and the appearance of chemical bonds between W[S.sub.2] nanotubes and polymer matrix, preparation of composites with these inclusions should be simpler than the carbon-based polymer composite preparation [13, 14]. Chemical bonds between W[S.sub.2] nanotubes and polymer matrix and unique mechanical and thermal properties of W[S.sub.2] nanotubes [5] are responsible for improved mechanical behavior and thermal stability of polymer composites [14]. Moreover, the functionalization of W[S.sub.2] for obtaining composites in various polymer matrices is not needed [15]. This is due to unique chemical properties of the W[S.sub.2] nanotubes surface.

Despite the fact that the electrical conductivity of W[S.sub.2] nanotubes is about 103S/m [16, 17] and these nanotubes can be used in transistors, photodetectors, and other electronic devices [2, 18, 19], the amount of publications on electromagnetic properties of polymer composites with W[S.sub.2] nanotubes is still very small [20-22]. Therefore, being of nanosize, having excellent mechanical and electrical properties, and possessing good dispersion and adhesion to polymers, inorganic nanotubes of W[S.sub.2] could be a good candidate for broadband electromagnetic composite applications.

In the earlier studies, it was established that the percolation threshold in W[S.sub.2]/epoxy composites can be close to 25 vol% [20] and in polyurethane/W[S.sub.2] composites-larger than 2 wt% [21]. No electrical percolation for polyvinylidene fluoride (PVDF) composites with W[S.sub.2] was observed in reference [20]; however, in this work was established that pellets of W[S.sub.2] nanotubes are quite conductive. Such high values of electrical percolation, established in the previous works, are quite surprising, because of the W[S.sub.2] nanotube shape comparable to one of the carbon nanotubes, where percolation threshold in epoxy resin can be 0.0025 wt% [23]. Namely, W[S.sub.2] nanotubes have a high aspect ratio (30-120 nm in diameter and 5-20 fm in length [13]); therefore, the electrical percolation in composites with W[S.sub.2] nanoinclusions should be low enough, while electromagnetic properties of these composites are quite high. The comparison with carbon nanotube composites [24], where a wide range of percolation thresholds was observed depending on composite preparation technology, suggests that the composite with W[S.sub.2] nanotube preparation technology and W[S.sub.2] nanotube dispersion inside the polymer matrix should be important for electrical percolation in W[S.sub.2] nanotube composites as well. So, the open question was as following: is it possible to make the percolation threshold value in W[S.sub.2] nanotubes as low as in carbon nanotube composites? Other challenging tasks were to study the dielectric properties of composites with W[S.sub.2] nanotubes and the properties of conductive polymers modified with W[S.sub.2] nanoparticles. For example, to investigate an impact of W[S.sub.2] nanotubes on the electromagnetic properties of epoxymatrix composites in a wide temperature and frequency ranges. These questions are crucial for further development of the W[S.sub.2] composite engineering and promising applications. Therefore, this paper is focused on the above questions, answers to which were not given hitherto. In order to address these points, an investigation of the broadband (20 Hz-1 MHz) electromagnetic properties of W[S.sub.2]/epoxy-matrix composites in the broad temperature range (250K-500K) presented.

2. Materials and Methods

W[S.sub.2] nanotubes were produced through the chemical reaction of W[O.sub.3-x] nanoparticles with [H.sub.2]S and [H.sub.2] gases at high temperatures. Actually, the process consists of two main parts: formation of suboxide whiskers, by which majority is 5-20 [micro]m in length and 30-120 nm in diameter, and their subsequent sulfidization into W[S.sub.2] nanotubes. More details about the W[S.sub.2] nanotube preparation mechanism are in [13]; according to the formation mechanism of nanotubes, the sizes of W[S.sub.2] nanotubes repeat those of suboxide whiskers, being in average of 20 [micro]m in length and 60 nm in diameter.

As synthesized, these nanotubes at different concentrations (0.15, 0.3, 0.94, and 1.6 vol%, which is corresponding to 0.5, 1, 3, and 5 wt%) were dispersed in epoxy resin diglycidyl ether of bisphenol-A (DGEBA) (D.E.R. 331 product of Dow Chemical, Midland, MI, USA), and further, polyetheramine, used as a curing agent (JEFFAMINE T-403 product of Huntsman), was added, taken in a ratio of 100:40 w/w. The mixture of W[S.sub.2] nanotubes and DGEBA was sonicated for 1 hr under controlled temperature and constant mechanical stirring. The sonicator was a high-intensity ultrasonic processor with a tip diameter of 19 mm that resonates at 20 kHz [+ or -]50 Hz (VCX 400 (ultrasonic processor) and CV26 (tip), Sonics & Materials Inc., Newtown, CT, USA). The sonication process was performed in a pulsed on/off mode of 6 and 4 sec, respectively. The curing agent was added to the epoxy/W[S.sub.2] nanotube mixture and mixed manually. The curing conditions were 100[degrees]C for 6 hours; before the curing process took place, all the mixtures were degassed for 20 minutes at 45[degrees]C. All composite preparation technology conditions were varied in order to obtain the biggest complex dielectric permittivity value of samples at room temperature; it was determined that the above listed conditions are optimal. These conditions are different from those, which applied for epoxy/W[S.sub.2] composite preparation in [21].

To make sure of the morphological and structural quality of the nanotubes, a transmission electron microscope (TeM, Philips CM 120 operated at 120 kV) and scanning electron microscope (E-SEM, model FEI XL-30) were used. The crystallographic phase of the reaction product was confirmed by an X-ray powder diffractometer (XRD, Ultima III, Rigaku, Japan) operated at 40 kV and 40 mA (not shown). TEM, SEM, and XRD analyses were carried out after each synthesis and before impregnation into the polymer matrix. The dispersion of the nanoparticles inside the polymer was characterized by E-SEM analysis of sample's cross section.

The dielectric properties of the samples were investigated using a LCR meter (HP4284 A) in the frequency range 20 Hz-1 MHz. The measurements were done by heating and cooling in the temperature interval of 300 K-500 K at the constant temperature rate of 0.5 K/min. No noticeable hysteresis in experimental results was observed in both temperature change modes. The picture of measurement equipment is presented in Figure 1. The dielectric measurement accuracy was as better as 1%.

3. Results and Discussion

SEM and TEM images of W[S.sub.2] nanotubes are presented in Figures 2(a) and 2(b)), respectively. SEM images of epoxy/W[S.sub.2] nanotube cross section are presented in Figure 3. The W[S.sub.2] nanotubes are very well dispersed in the polymer matrix and no agglomerates of the W[S.sub.2] nanotubes are observed.

Temperature dependencies of complex relative dielectric permittivity for all composites at 1 kHz are presented in Figure 4. The complex relative dielectric permittivity strongly increases with W[S.sub.2] concentration; however, its value at room temperature remains very low even for the biggest concentration (1.6 vol%, [epsilon]' < 6, [epsilon]" < 0.3). Therefore, all composites are below the percolation threshold.

However, the complex relative dielectric permittivity increases with temperature and has two anomalies: first, below room temperature, which is related to [alpha] relaxation [25], and second, in the temperature range of 350-400 K, which is related to the Maxwell-Wagner relaxation [26] and the onset of electrical conductivity [27]. Both anomalies are strongly affected by the presence of W[S.sub.2] nanotubes. Temperature dependencies of complex relative dielectric permittivity for composites with 1.6 vol% of W[S.sub.2] at different frequencies are presented in Figure 5. Below room temperature, the maximum of losses is frequency-dependent and it is related to a relaxation [25]. Above 350 K, the step-like anomaly is related to the Maxwell-Wagner relaxation [26]. At higher temperatures, the electrical conductivity strongly affects results [27]. The temperature of the maximum of the dielectric losses ([T.sub.m]) is strongly frequency-dependent (Figure 6). The behavior was characterized by the Vogel-Fulcher-Tammann law [28]:

v = [v.sub.0] exp -[E.sub.f]/k([T.sub.m] - [T.sub.0]), (1)

where k is the Boltzmann constant, [v.sub.0] is the frequency approached with [T.sub.m] [right arrow] [infinity], [E.sub.f] is the pseudoactivation energy, and [T.sub.0] is the Vogel temperature.

Obtained parameters are listed in Table 1.

The best-fit value of [v.sub.0] was determined as 1 THz for all investigated composites. The value is consistent with phonon spectra of epoxy resin [29]. The Vogel temperature [T.sub.0] has the minimum for concentration 0.15 vol%. The decrease of [T.sub.0] is related to the intensified polymer molecule dynamics due to the additional free space at the polymer-filler junction. A similar change of the glass transition temperature (which is related to the Vogel temperature [30]) in polymeric composites with nanoinclusions was observed in reference [31]. On the other hand, the increasing of the Vogel temperature can be clarified by the strong interplay between epoxy resin and W[S.sub.2] nanotubes. Furthermore, the density of the composite could be higher than the pure polymer density, and consequently, the increasing of the glass transition temperature with the concentration of inclusions could be observed [32].

Frequency dependencies at different temperatures of complex relative dielectric permittivity for composites with 1.6 vol% inclusions are presented in Figure 7.

At low temperatures, the maximum of dielectric losses is observed, which shifts to the higher frequencies with temperature. The mean relaxation time was calculated as [tau] = 1/[v.sub.max], where [v.sub.max] is the frequency at which dielectric losses have the maximum. The temperature dependence of the mean relaxation time is presented in Figure 8.

The mean relaxation time increases on cooling according to the Vogel-Fulcher law [28]:

[tau] = [[tau].sub.0] exp [E.sub.f]/k(T - [T.sub.0]), (2)

where [[tau].sub.0] is the relaxation time at very high temperatures, [E.sub.f] is the activation energy, and [T.sub.0] is the Vogel-Fulcher temperature. Obtained parameters are listed in Table 2. The behavior is more diffused in comparison with the data presented in Table 1.

Spectra of the electrical conductivity for epoxy-matrix composites with 1.6 vol% (5 wt%) inclusions of the W[S.sub.2] nanotubes are presented in Figure 9. Above 420 K, the accidental distribution of the electrons according to energies causes a frequency-independent conductivity (DC conductivity) (Figure 9). The electrical conductivity of composites is caused by the electrical conductivity of the pure epoxy resin matrix. Above some critical frequency, the electrical conductivity strongly increases with frequency. The spectra of [sigma] have been fitted according to the Almond-West type power law [33]:

[sigma] = [[sigma].sub.DC] + A[[omega].sup.s], (3)

where [[sigma].sub.DC] is the DC conductivity and A[[omega].sup.s] is the AC conductivity. The model fits the electrical conductivity spectra of the investigated composites quite well; only at lower frequencies, the divergence is observed due to the nonohmic contact impact.

In order to separate effects of contacts and volume conductivity materials, we calculated the real part ([rho]') and the imaginary part ([rho]") of the complex specific resistance [[rho].sup.*] = [rho]' - i[rho]":

[rho]' = [epsilon]"/[[epsilon]'.sup.2] + [[epsilon]".sup.2] 1/[[epsilon].sub.0][omega],

[rho]" = [epsilon]'/[[epsilon]'.sup.2] + [[epsilon]".sup.2] 1/[[epsilon].sub.0][omega], (4)

where [omega] = 2[pi]v and v is the measurement frequency. In the plot [rho]" ([rho]'), the half circles at higher frequencies are caused by volume conductivity of the composite, and the higher values of [[rho].sup.*] are already influenced by contacts (Figure 10). The contact influence is playing an important role at higher temperatures and low frequencies.

The temperature dependence of ln ([[sigma].sub.DC]) of epoxymatrix composites with various W[S.sub.2] concentrations is presented in Figure 11. The DC conductivity strongly increases with the W[S.sub.2] concentration. Therefore, electrical contacts between epoxy resin and W[S.sub.2] are rather ohmic. ln ([[sigma].sub.DC]) (1/T) is the linear temperature dependence. Therefore, from this dependence, the activation energy [E.sub.B] of the conductivity and the prefactor [[sigma].sub.0] were determined (the conductivity at very high temperatures) according to the Arrhenius law:

[[sigma].sub.DC] = [[sigma].sub.0] exp -[E.sub.B]/kT. (5)

The obtained parameters are presented in Table 3. The activation energy [E.sub.B] and the conductivity [[sigma].sub.0] are practically not impacted by the concentration of nanoinclusions. However, the activation energy in composites is higher than in that in pure epoxy.

4. Conclusions

Broadband dielectric properties of tungsten disulfide (W[S.sub.2]) nanotube epoxy-matrix composites over a wide temperature range (250 K-500 K) are presented for concentrations up to 1.6 vol% (5 wt%). The electrical percolation was not detected in the investigated composites at room temperature. The relative dielectric permittivity of composites with 1.6 vol% inclusions is almost 3 times higher than the relative dielectric permittivity of the pure polymer, and the DC electrical conductivity of composites is about [10.sup.-6] S/m at 500 K, which indicates that the composites are appropriate for antistatic applications at higher temperatures [34], similarly to W[S.sub.2]/polyurethane composites [22]. Broadband electromagnetic spectra of the composites are largely governed by the dynamics of epoxy resin molecules. The Vogel temperature [T.sub.0] has the minimum for concentration 0.15 vol%. Above 410 K, the electrical conductivity is typical for W[S.sub.2]/epoxy composites with the W[S.sub.2] inclusions as well. The DC conductivity increases with the W[S.sub.2] concentration, while its activation energy is almost uncontrolled by the concentration of nanoinclusions; however, in composites, it is higher than in pure epoxy resin. Therefore, the electrical transport occurs between W[S.sub.2] nanotubes and epoxy matrix at higher temperatures (above 410 K).

DOI: https://doi.org/10.1155/2019/5761439

Data Availability

The underlying data related to this article are available upon request.

Conflicts of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Acknowledgments

A. Zak is grateful for the financial support to the Israel PAZI Foundation and to the Israel "Ministry of Science, Technology and Space" grant (number 3-11839).

References

[1] R. J. Chen, T. Zhao, W. P. Wu et al., "Free-standing hierarchically sandwich-type tungsten disulfide nanotubes/graphene anode for lithium-ion batteries," Nano Letters, vol. 14, no. 10, pp. 5899-5904, 2014.

[2] G. Lalwani, A. M. Henslee, B. Farshid et al., "Tungsten disulfide nanotubes reinforced biodegradable polymers for bone tissue engineering," Acta Biomaterialia, vol. 9, no. 9, pp. 8365-8373, 2013.

[3] P. G. Yan, A. J. Liu, Y. S. Chen et al., "Microfiber-based W[S.sub.2]-film saturable absorber for ultra-fast photonics," Optical Materials Express, vol. 5, no. 3, pp. 479-489, 2015.

[4] M. Shangmugam, T. Bansal, C. A. Durcan, and B. Yu, "Schotky-barrier solar cell based on layered semiconductor tungsten disulfide nanofilm," Applied Physics Letters, vol. 101, no. 26, article 263902, 2012.

[5] I. Kaplan-Ashiri, S. R. Cohen, K. Gartsman, R. Rosentsveig, G. Seifert, and R. Tenne, "Mechanical behavior of individual W[S.sub.2] nanotubes," Journal of Materials Research, vol. 19, no. 2, pp. 454-459, 2004.

[6] D. Maharaj and B. Bhushan, "Characterization of nanofriction of Mo[S.sub.2] and W[S.sub.2]," Materials Letters, vol. 142, pp. 207-210, 2015.

[7] C. S. Reddy, A. Zak, and E. Zussman, "W[S.sub.2] nanotubes embedded in PMMA nanofibers as energy absorptive material," Journal of Materials Chemistry, vol. 21, no. 40, pp. 16086-16093, 2011.

[8] X. F. Zhang, B. Luster, A. Church et al., "Carbon nanotube--Mo[S.sub.2] composites as solid state lubricants,\" ACS Applied Materials & Interfaces, vol. 1, no. 3, pp. 735-739, 2009.

[9] M. Sahu, L. Narashimhan, O. Prakash, and A. M. Raichur, "Noncovalently functionalized tungsten disulfide nanosheets for enhanced mechanical and thermal properties of epoxy nanocomposites," ACS Applied Materials and Interfaces, vol. 9, no. 16, pp. 14347-14357, 2017.

[10] D. Haba, A. J. Brunner, M. Barbezat, D. Spetter, W. Tremel, and G. Pinter, "Correlation of epoxy material properties with the toughening effect of fullerene-like W[S.sub.2] nanoparticles," European Polymer Journal, vol. 84, pp. 125-136, 2016.

[11] Y. Wang, Y. Zhao, X. Han, and M. Liu, "Epoxy nanocomposites with two-dimensional tungsten disulfide additives," in 2015ICCM International Conferences on Composite Materials, Copenhagen, July 2015.

[12] M. Naffakh, C. Marco, G. Ellis et al., "Novel poly(3-hydroxybutyrate) nanocomposites containing W[S.sub.2] inorganic nanotubes with improved thermal, mechanical and tribological properties," Materials Chemistry and Physics, vol. 147, no. 1-2, pp. 273-284, 2014.

[13] A. Zak, L. Sallacan-Ecker, A. Margolin et al., "Scaling up of the W[S.sub.2] nanotubes synthesis," Fullerenes, Nanotubes and Carbon Nanostructures, vol. 19, no. 1-2, pp. 18-26, 2011.

[14] M. Shneider, H. Dodiuk, S. Kenig, and R. Tenne, "The effect of tungsten sulfide fullerene-like nanoparticles on the toughness of epoxy adhesives," Journal of Adhesion Science and Technology, vol. 24, no. 6, pp. 1083-1095, 2010.

[15] M. Naffakh, Z. Martin, N. Fanegas, C. Marco, M. A. Gomez, and I. Jimenez, "Influence of inorganic fullerene-like W[S.sub.2] nanoparticles on the thermal behavior of isotactic polypropylene," Journal of Polymer Science Part B: Polymer Physics, vol. 45, no. 16, pp. 2309-2321, 2007.

[16] M. Naffakh, C. Marcoa, M. A. Gomeza, and I. Jimenez, "Novel melt-processable nylon-6/inorganic fullerene-like W[S.sub.2] nanocomposites for critical applications," Materials Chemistry and Physics, vol. 129, no. 1-2, pp. 641-648, 2011.

[17] C. Zhang, Z. Ning, Y. Liu et al., "Electrical transport properties of individual W[S.sub.2] nanotubes and their dependence of water and oxygen absorption," Applied Physics Letters, vol. 101, no. 11, article 113112, 2012.

[18] R. Levi, O. Bitton, G. Leitus, R. Tenne, and E. Joselevich, "Field-effect transistors based on W[S.sub.2] nanotubes with high current-carrying capacity," Nano Letters, vol. 13, no. 8, pp. 3736-3741, 2013.

[19] G. Viskadouros, A. Zak, M. Stylianakis, E. Kymakis, R. Tenne, and E. Stratakis, "Enhanced field emission of W[S.sub.2] nanotubes," Small, vol. 10, no. 12, pp. 2398-2403, 2014.

[20] J. Petzelt, D. Nuzhnyy, V. Bovtun, M. Savinov, M. Kempa, and I. Rychetsky, "Broadband dielectric and conductivity spectroscopy of inhomogeneous and composite conductors," Physica Status Solidi A: Applications and Materials Science, vol. 210, no. 11, pp. 2259-2271,2013.

[21] A. Sedova, S. Khodorov, D. Ehre et al., "Dielectric and electrical properties of W[S.sub.2] nanotubes/epoxy composites and their use for stress monitoring of structures," Journal of Nanomaterials, vol. 2017, Article ID 4838095, 13 pages, 2017.

[22] J. Macutkevic, J. Belovickis, G. Otorgust et al., "Broadband dielectric and ultrasonic properties of W[S.sub.2] nanotubes/polyurethane composites," Polymer Composites, vol. 39, no. 12, pp. 4477-4485, 2018.

[23] J. K. W. Sandler, J. E. Kirk, I. A. Kinloch, M. S. P. Shaffer, and A. H. Windle, "Ultra-low electrical percolation threshold in carbon-nanotube-epoxy composites," Polymer, vol. 44, no. 19, pp. 5893-5899, 2003.

[24] H. Deng, L. Lin, M. Z. Ji, S. Zhang, M. Yang, and Q. Fu, "Progress on the morphological control of conductive network in conductive polymer composites and the use as electroactive multifunctional materials," Progress in Polymer Science, vol. 39, no. 4, pp. 627-655, 2014.

[25] G. A. Pogany, "The a relaxation in epoxy resins," European Polymer Journal, vol. 6, no. 2, pp. 343-353, 1970.

[26] H. Neumann and G. Arlt, "Maxwell-wagner relaxation and degradation of SrTi[O.sub.3] and BaTi[O.sub.3] ceramics," Ferroelectrics, vol. 69, no. 1, pp. 179-186, 1986.

[27] J. Macutkevic, P. P. Kuzhir, A. G. Paddubskaya et al., "Broadband dielectric/electric properties of epoxy thin films filled with multiwalled carbon nanotubes," Journal of Nanophotonics, vol. 7, no. 1, article 073593, 2013.

[28] A. K. Tagantsev, "Vogel-Fulcher relationship for the dielectric permittivity of relaxor ferroelectrics," Physical Review Letters, vol. 72, no. 7, pp. 1100-1103, 1994.

[29] K. E. Chike, M. L. Myrick, and R. R. Lyon, "Raman and near-infrared studies of an epoxy resin," Applied Spectroscopy, vol. 47, no. 10, pp. 1631-1635, 1993.

[30] P. Frubing, H. Kruger, H. Goering, and R. Gerhard-Multhaupt, "Relaxation behaviour of thermoplastic polyurethanes with covalently attached nitroaniline dipoles," Polymer, vol. 43, no. 9, pp. 2787-2794, 2002.

[31] L. C. Tang, Y. J. Wan, K. Peng et al., "Fracture toughness and electrical conductivity of epoxy composites filled with carbon nanotubes and spherical particles," Composites Part A: Applied Science and Manufacturing, vol. 45, pp. 95-101, 2013.

[32] C. Wei, D. Srivastava, and K. Cho, "Thermal expansion and diffusion coefficients of carbon nanotube-polymer composites," Nano Letters, vol. 2, no. 6, pp. 647-650, 2002.

[33] P. G. Bruce, A. R. West, and D. P. Almond, "A new analysis of ac conductivity data in single crystal [beta]-alumina," Solid State Ionics, vol. 7, no. 1, pp. 57-60, 1982.

[34] N. A. Aal, F. El-Tantawy, A. Al-Hajry, and M. Bououdina, "New antistatic charge and electromagnetic shielding effectiveness from conductive epoxy resin/plasticized carbon black composites," Polymer Composites, vol. 29, no. 2, pp. 125-132, 2008.

Povilas Bertasius, (1) Mark Shneider, (2) Jan Macutkevic (iD), (3) Vytautas Samulionis, (1) Juras Banys, (2) and Alla Zak (4)

(1) Physics Faculty, Vilnius University, Vilnius 00122, Lithuania

(2) Weizmann Institute of Science, 234 Herzl St., Rehovot 7610001, Israel

(3) Center for Physical Sciences and Technology, Vilnius 10257, Lithuania

(4) HIT (Holon Institute of Technology), 52 Golomb St., Holon 58102, Israel

Correspondence should be addressed to Jan Macutkevic; jan.macutkevic@gmail.com

Received 5 March 2019; Accepted 25 June 2019; Published 8 August 2019

Guest Editor: Emad M. Masoud

Caption: Figure 1: View of the LCR meter and the sample holder for measuring dielectric properties of composites in the 20 Hz-1 MHz frequency range.

Caption: Figure 2: Scanning electron microscopy (SEM) (a) and transmission electron microscopy (b) images of W[S.sub.2] nanotubes.

Caption: Figure 3: SEM images of epoxy/W[S.sub.2] nanotubes.

Caption: Figure 4: Temperature dependence of complex dielectric permittivity for epoxy/W[S.sub.2] composites at 1 kHz frequency.

Caption: Figure 5: Temperature dependence of complex dielectric permittivity for epoxy with 1.6 vol% W[S.sub.2] inclusions at different frequencies.

Caption: Figure 6: Measured frequencies v versus [T.sub.m] of W[S.sub.2]/epoxy composites.

Caption: Figure 7: Frequency dependence of complex dielectric permittivity for epoxy with 1.6 vol% W[S.sub.2] inclusions at different temperatures.

Caption: Figure 8: Temperature dependence of the mean relaxation time of W[S.sub.2]/epoxy composites. The solid lines are calculated according to equation (2).

Caption: Figure 9: Frequency dependence of the electrical conductivity of W[S.sub.2]/epoxy composites with 1.6 vol% inclusions at different temperatures.

Caption: Figure 10: Cole-Cole diagram of [[rho].sup.*] = [rho]' - i[rho]" for epoxy with 1.6 vol% W[S.sub.2] inclusions at different temperatures.

Caption: Figure 11: Temperature dependence of the DC electrical conductivity of W[S.sub.2]/epoxy composites.
Table 1: Parameters of the Vogel-Fulcher relationship
(equation (1)) for W[S.sub.2]/epoxy composites.

              [E.sub.f]/[k.sub.B] (K(eV))     [T.sub.0] (K)

Epoxy       3839 (0.33) [+ or -] 209 (0.01)   81 [+ or -] 11
0.15 vol%   4651 (0.4) [+ or -] 135 (0.01)    25 [+ or -] 7
0.3 vol%    3660 (0.31) [+ or -] 114(0.01)    72 [+ or -] 6
0.94 vol%    4044 (0.35) [+ or -] 77(0.01)    65 [+ or -] 4
1.6 vol%    4047 (0.35) [+ or -] 126 (0.01)   65 [+ or -] 7

Table 2: Parameters of the Vogel-Fulcher law (equation (2)) for
W[S.sub.2]/epoxy composites.

                  E/[k.sub.B] (K(eV))         [T.sub.0] (K)

Epoxy       2981 (0.26) [+ or -] 61 (0.01)    109 [+ or -] 3
0.15 vol%    2363 (0.2) [+ or -] 88 (0.01)    150 [+ or -] 5
0.3 vol%    3167 (0.27) [+ or -] 111 (0.01)   90 [+ or -] 6
0.94 vol%   2877 (0.25) [+ or -] 114 (0.01)   111 [+ or -] 6
1.6 vol%    2826 (0.24) [+ or -] 75 (0.01)    114 [+ or -]4

Table 3: Arrhenius law fit parameters for W[S.sub.2]/epoxy composites.

            ln {[[sigma].sub.0],     [E.sub.A]/[k.sub.B] (K(eV))
                    S/m}

Epoxy         8.7 [+ or -] 0.1     10727 (0.92) [+ or -] 85 (0.01)
0.15 vol%    16.9 [+ or -] 0.3     14367 (1.24) [+ or -] 132 (0.01)
0.3 vol%     11.4 [+ or -] 0.3     11702 (1.01) [+ or -] 143 (0.01)
0.94 vol%     13.7 [+ or -] 01      12681 (1.1) [+ or -] 74 (0.01)
1.6 vol%      15.4 [+ or -] 01      13457(1.16) [+ or -] 74 (0.01)
COPYRIGHT 2019 Hindawi Limited
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2019 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Title Annotation:Research Article
Author:Bertasius, Povilas; Shneider, Mark; Macutkevic, Jan; Samulionis, Vytautas; Banys, Juras; Zak, Alla
Publication:Journal of Nanomaterials
Date:Aug 31, 2019
Words:4290
Previous Article:Controlled Gold Nanoparticle Placement into Patterned Polydimethylsiloxane Thin Films via Directed Self-Assembly.
Next Article:Synthesis, Characterization, and In Vitro Drug Delivery of Chitosan-Silica Hybrid Microspheres for Bone Tissue Engineering.
Topics:

Terms of use | Privacy policy | Copyright © 2020 Farlex, Inc. | Feedback | For webmasters