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1.
Sci Rep ; 14(1): 13629, 2024 Jun 13.
Artigo em Inglês | MEDLINE | ID: mdl-38871761

RESUMO

This study examines how various nanofillers impact thermal conductivity, dielectric characteristics, and electromagnetic interference (EMI) shielding potential of bio-based and biodegradable poly(butylene succinate-co-adipate) (PBSA). TiO2, NiFe2O4, Fe2O3, and Fe3O4 were selected as fillers for nanocomposites at 4-50 vol.% (12-81 wt.%). The nanocomposites were analyzed in three domains: structural (scanning electron microscopy, energy dispersive X-ray spectroscopy mapping, density, tensile testing), thermal (light flash analysis, literature models), and dielectric (AC conductivity, permittivity, EM shielding effectiveness (SE)). The investigated fillers showed good dispersion and compatibility with the PBSA matrix. LFA was analyzed according to literature models, where Bruggeman and Agari models showed the best fit at high concentrations. The dielectric analysis revealed that most of the nanocomposites did not reach percolation; thus, producing thermally conductive plastics that are electrically insulating. EMI shielding was limited to frequencies below 10 Hz, with the notable exception of Fe3O4 (100 nm and loading of > 25 vol.%), which showed shielding at frequencies up to 105 Hz. The investigated composites based on a biodegradable polyester and abundant metal oxide nanofillers are suitable for the production of cheap, ecological, and electrically insulating heat dissipation solutions required for modern and lightweight applications.

2.
Polymers (Basel) ; 16(5)2024 Feb 22.
Artigo em Inglês | MEDLINE | ID: mdl-38475287

RESUMO

This work presents the dielectric and ultrasonic properties of polydimethylsiloxane (PDMS) nanocomposites filled with titanium dioxide nanoparticles. The dielectric study was performed over a very broad range of frequencies (20 Hz-3 THz). The dielectric permittivity was almost frequency-independent in all the composites at room temperature over the whole range of measurement frequencies, and the dielectric losses were very low under these conditions (less than 2). The dielectric permittivity strongly increases with the nanoparticle concentration according to the Maxwell-Garnet model. Therefore, the investigated composites are suitable for various flexible electronic applications, particularly in the microwave and terahertz frequency ranges. Dielectric dispersion and increased attenuation of ultrasonic waves were observed at lower temperatures (below 280 K) due to the relaxation of polymer molecules at the PDMS/TiO2 interface and in the polymer matrix. The relaxation time followed the Vogel-Vulcher law, while the freezing temperature increased with the titanium dioxide concentration due to interactions between the polymer molecules and nanoparticles. The significant hysteresis in the ultrasonic properties indicated that titanium dioxide acts as a crystallization center. This is confirmed by the correlation between the hysteresis in the ultrasonic properties and the structure of the composites. The small difference in the activation energy values obtained from the ultrasonic and dielectric investigations is related to the fact that the dielectric dispersion is slightly broader than the Debye-type dielectric dispersion.

3.
ACS Omega ; 8(15): 13911-13919, 2023 Apr 18.
Artigo em Inglês | MEDLINE | ID: mdl-37091415

RESUMO

A series of highly flexible and environmentally friendly composites based on polydimethylsiloxane (PDMS) filled with 200 nm size ferroelectric BaTiO3 (BTO) particles at different concentrations (from 7 to 23 vol %) have been fabricated by a simple dispersion method. The dielectric, piezoelectric, and ultrasonic properties have been studied. The ferroelectric state of BTO was confirmed by differential scanning calorimetry and ultrasonic spectroscopy. The addition of BTO into PDMS strongly affects the dielectric properties of the composites. At low temperatures close to 160 K, the PDMS matrix exhibits a dielectric anomaly related to a dynamic glass transition, which shifts to higher temperatures as the BTO content increases due to the strong interaction between polymer chains and nanoparticles. Ultrasonic measurements demonstrate the appearance of a piezoelectric voltage signal on a thin plate of the composite with the highest available filler concentration (23 vol %) under longitudinal stress applied by a 10 MHz ultrasonic wave. As a result, at room temperature, the detected signal is characterized by output voltage and specific stored energy values of 10 mV and 367.3 MeV/m2, respectively, followed by a further increase with cooling to 35 mV at 150 K. The proposed BTO/PDMS composite system is thus a potential candidate for nanogenerators, namely, a simple, flexible, and lead-free device converting high-frequency (10 MHz) mechanical vibrations into electrical voltage.

4.
Polymers (Basel) ; 15(4)2023 Feb 20.
Artigo em Inglês | MEDLINE | ID: mdl-36850335

RESUMO

Bulk polylactic acid (PLA)/multiwall carbon nanotube (MWCNT) composites were prepared and investigated in wide frequency ranges (20 Hz-1 MHz and 24-40 GHz). It was determined that the percolation threshold in bulk PLA/MWCNT composites is close to 0.2 vol.% MWCNT. However, the best microwave dielectric properties and absorption were observed in composites with 3.0-5.0 vol.% MWCNT. Therefore, for future investigations, we selected layered (laminate) polymeric structures with gradual changes in MWCNT concentration from 0.2 to 8.0 vol.% MWCNT. Two approaches to laminate structure designs were examined and compared: a five-layer composite and a nine-layer composite that included four pure PLA middle layers. The addition of MWCNT enhanced the elastic modulus by up to 1.4-fold and tensile strength by up to 1.2-fold, with the best performance achieved at 5.0 vol.% loading. High microwave shielding was observed for these layered PLA/MWCNT structures with a gradient change in MWCNT concentration (up to 26 dB in both transmission and absorption coefficients) in the broad frequency range (from 24 to 40 GHz). Obtained structures are highly anisotropic, and the absorption coefficient is 2-5 dB higher in the direction of MWCNT concentration increase; however, the transmission coefficient is the same in both directions. The properties of microwave absorption are mainly unaffected by the additional polymeric layers. The absorption of the layered structure is greater than the absorption of single-layer composites with an optimal MWCNT concentration of the same thickness. The proposed laminate structure design is promising in the field of efficient electromagnetic shielding.

5.
Polymers (Basel) ; 15(3)2023 Jan 18.
Artigo em Inglês | MEDLINE | ID: mdl-36771816

RESUMO

To address the ever-increasing electromagnetic interference (EMI) pollution, a hybrid filler approach for novel composites was chosen, with a focus on EMI absorbance. Carbon nanofiller loading was limited to 0.6 vol.% in order to create a sustainable and affordable solution. Multiwall carbon nanotubes (MWCNT) and iron oxide (Fe3O4) nanoparticles were mixed in nine ratios from 0.1 to 0.6 vol.% and 8.0 to 12.0 vol.%, respectively. With the addition of surfactant, excellent particle dispersion was achieved (examined with SEM micrographs) in a bio-based and biodegradable poly(butylene succinate) (PBS) matrix. Hybrid design synergy was assessed for EMI shielding using dielectric spectroscopy in the microwave region and transmittance in the terahertz range. The shielding effectiveness (20-52 dB) was dominated by very high absorption at 30 GHz, while in the 0.1 to 1.0 THz range, transmittance was reduced by up to 6 orders of magnitude. Frequency-independent AC electrical conductivity (from 10-2 to 107 Hz) was reached upon adding 0.6 vol.% MWCNT and 10 vol.% Fe3O4, with a value of around 3.1 × 10-2 S/m. Electrical and thermal conductivity were mainly affected by the content of MWCNT filler. The thermal conductivity scaled with the filler content and reached the highest value of 0.309 W/(mK) at 25 °C with the loading of 0.6 vol.% MWCNT and 12 vol.% Fe3O4. The surface resistivity showed an incremental decrease with an increase in MWCNT loading and was almost unaffected by an increase in iron oxide loading. Thermal conductivity was almost independent of temperature in the measured range of 25 to 45 °C. The nanocomposites serve as biodegradable alternatives to commodity plastic-based materials and are promising in the field of electromagnetic applications, especially for EMI shielding.

6.
Materials (Basel) ; 15(23)2022 Dec 05.
Artigo em Inglês | MEDLINE | ID: mdl-36500156

RESUMO

We present studies on the microwave properties, electrical resistivity, and low-frequency (10 Hz-20 kHz) noise characteristics in the temperature range of 78 K to 380 K of composite materials made from bisphenol A-based epoxy resin and carbon fiber felts. Two types of carbon fibers were used, derived from polyacrylonitrile or regenerated cellulose. We show that these structures are suitable for electromagnetic shielding applications, especially in the direction parallel to the carbon fibers. The low-frequency voltage fluctuations observed in these materials are of the 1/fα, and the noise intensity is proportional to the square of the voltage. The characteristics of the investigated materials show an instability in the temperature range from 307 K to 332 K. This effect is followed by an increase in resistivity and noise intensity, but it does not change the character of the noise, and this instability vanishes after a few repeated heating and cooling cycles.

7.
Materials (Basel) ; 15(20)2022 Oct 13.
Artigo em Inglês | MEDLINE | ID: mdl-36295168

RESUMO

Ceramic composites with nanoparticles are intensively investigated due to their unique thermal, mechanic and electromagnetic properties. In this work, dielectric properties of phosphate ceramics with round silver nanoparticles of various sizes were studied in the wide frequency range of 20 Hz-40 GHz for microwave shielding applications. The percolation threshold in ceramics is close to 30 wt.% of Ag nanoparticles content and it is higher for bigger-sized nanoparticles. The microwave complex dielectric permittivity of ceramics above the percolation threshold is rather high (ε' = 10 and ε″ = 10 at 30 GHz for ceramics with 50 wt.% inclusions of 30-50 nm size, it corresponds to almost 61% absorption of 2 mm-thickness plate) therefore these ceramics are suitable for microwave shielding applications. Moreover, the microwave absorption is bigger for ceramics with a larger concentration of fillers. In addition, it was demonstrated that the electrical transport in ceramics is thermally activated above room temperature and the potential barrier is almost independent of the concentration of nanoparticles. At very low temperature, the electrical transport in ceramics can be related to electron tunneling.

8.
Nanomaterials (Basel) ; 12(20)2022 Oct 19.
Artigo em Inglês | MEDLINE | ID: mdl-36296860

RESUMO

Electrostatic dissipative (ESD), anti-static (AS), and electromagnetic interference (EMI) shielding materials are commonly based on commodity fossil-fuel-based plastics. This, in turn, contributes to ever-growing non-biodegradable plastic pollution. Graphene nanoplatelets (GN), multi-walled carbon nanotubes (MWCNT), nanostructured carbon black (NCB), and amorphous carbon black (CB) were utilized as nanofillers to prepare bio-based and biodegradable poly(butylene succinate-co-adipate) (PBSA) nanocomposites. Solvent-cast composites were prepared with 1.1 to 30.0 vol.% nanoparticle loading. The literature mainly focuses on relatively low loadings; therefore, for this research, filler loadings were increased up to 30 vol.% but the maximum loading for NCB and CB loadings only reached 17.4 vol.% due to a lack of dimensional stability at higher loadings. The composites were characterized using tensile testing, volumetric and surface conductivity measurements, thermal conductivity measurements, dielectric spectroscopy in the microwave region, and transmittance in the terahertz range. Tensile tests showed excellent carbon filler compatibility and enhanced tensile strength for loadings up to 5 vol.% (up to 20 vol.% for MWCNT). The highest thermal conductivity values were reached for the MWCNT filler, with the 30.0 vol.% filled composite reaching 0.756 W/mK (262% increase over PBSA). All fillers were able to produce composites that yielded volume conductivities above 10-10 S/m. Composites with MWCNT, GN, and NCB inclusions above the percolation threshold are suitable for EMI applications in the microwave and THz frequency range.

9.
Materials (Basel) ; 15(5)2022 Mar 02.
Artigo em Inglês | MEDLINE | ID: mdl-35269106

RESUMO

Polymer composites with electrically conductive inclusions are intensively developed for microwave shielding applications, where lightweight and elastic coatings are necessary. In this paper, dielectric properties of hybrid polyethylene composites containing cobalt nanoparticles and multi-wall carbon nanotubes (MWCNT) were investigated in the wide frequency range of 20-40 GHz for electromagnetic shielding applications. The percolation threshold in the hybrid system is close to 6.95 wt% MWCNT and 0.56 Co wt%. Cobalt nanoparticles (up to highest investigated concentration 4.8 wt%) had no impact on the percolation threshold, and for the fixed total concentration of fillers, the complex dielectric permittivity is higher for composites with bigger MWCNT concentrations. Moreover, the microwave complex dielectric permittivity of composites with high concentration of fillers is quite high (for composites with 13.4 wt% MWCNT and 1.1 wt% Co ε' ≈ ε″ ≈ 20 at 30 GHz, it corresponds to microwave absorption 50% of 1 mm thickness plate); therefore, these composites are suitable for electromagnetic shielding applications.

10.
Materials (Basel) ; 14(19)2021 Sep 30.
Artigo em Inglês | MEDLINE | ID: mdl-34640094

RESUMO

Polymer composites containing carbon nanofillers are extensively developed for electromagnetic shielding applications, where lightweight and flexible materials are required. One example of the microwave absorbers can be thermoplastic fibers fabricated from copolyamide hot melt adhesives and 7 wt% of multi-walled carbon nanotubes, as presented in this paper. A broadband dielectric spectroscopy confirmed that the addition of carbon nanotubes significantly increased microwave electrical properties of the thin (diameter about 100 µm) thermoplastic fibers. Moreover, the dielectric properties are improved for the thicker fibers, and they are almost stable at the frequency range 26-40 GHz and not dependent on the temperature. The variances in the dielectric properties of the fibers are associated with the degree of orientation of carbon nanotubes and the presence of bundles, which were examined using a high-resolution scanning microscope. Analyzing the mechanical properties of the nanocomposite fibers, as an effect of the carbon nanotubes addition, an improvement in the stiffness of the fibers was observed, together with a decrease in the fibers' elongation and tensile strength.

11.
Materials (Basel) ; 14(17)2021 Sep 04.
Artigo em Inglês | MEDLINE | ID: mdl-34501154

RESUMO

Composite materials with 83 wt.% of the 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 distributed in phosphate-bonded ceramics were prepared at three different pressures. A phosphate matrix comprises a mixture of an aluminum phosphate binder and melted periclase, MgO. All samples demonstrate a homogeneous distribution of the ferroelectric perovskite phase and are thermally stable up to 900 K. At higher temperatures, the pyrochlore cubic phase forms. It has been found that the density of the composites non-monotonously depends on the pressure. The dielectric permittivity and losses substantially increase with the density of the samples. The fabricated composites demonstrate diffused ferroelectric-paraelectric transition and prominent piezoelectric properties.

12.
Polymers (Basel) ; 13(7)2021 Mar 24.
Artigo em Inglês | MEDLINE | ID: mdl-33805067

RESUMO

Polymer matrix composites filled with carbon nanoparticles are promising materials for many applications, but their properties strongly depend on the particle features, concentration and distribution within the matrix. Here we present a study of the electrical resistivity and the low-frequency voltage fluctuation of composites based on epoxy resin filled with onion-like carbon (OLC) of different sizes (40-250 nm) above the percolation threshold, which should clarify the electrical transport characteristics in these materials. Electrical measurements were performed in the temperature range of 78 to 380 K, and voltage noise analysis was carried out from 10 Hz to 20 kHz. At low temperatures (below 250 K), thermally activated tunneling, variable-range hopping and generation-recombination of charge carriers take place. Above 250 K, the rapid expansion of the matrix with the temperature increases the resistivity, but above ~330 K, the conductivity of the matrix becomes significant. Quasi one-dimensional electrical transport is observed in composites with the smallest particles (40 nm), while in composites with the largest particles (220-250 nm), the dimensionality of the electrical transport is higher. The temperature dependence of the electrical conductivity of composites with smaller particles is more sensitive to matrix expansion.

13.
Nanomaterials (Basel) ; 11(2)2021 Feb 23.
Artigo em Inglês | MEDLINE | ID: mdl-33672334

RESUMO

The dielectric/electric properties of the Ni@C (carbon-coated Ni)/epoxy composites and Ni@C/MWCNTs (multi-walled carbon nanotubes)/epoxy composites loaded with fixed MWCNTs amount just below the percolation threshold (0.09 vol.%) and Ni@C at different concentrations up to 1 vol.% were investigated in broad frequency (20 Hz-40 GHz) and temperature (30 K-500 K) regions. In composites with the only Ni@C nanoparticles, the electrical percolation threshold was determined between 10 and 15 vol.%. Above the percolation threshold the dielectric permittivity (ε') and the electrical conductivity (σ) of the composites loaded with Ni@C only are high enough, i.e., ε' = 105 and σ = 0.6 S/m at 100 Hz for composites with 30 vol.% Ni@C, to be used for electromagnetic shielding applications. The annealing to 500 K was proved to be an effective and simple tool to decrease the percolation threshold in epoxy/Ni@C composites. For hybrid composites series an optimal concentration of Ni@C (0.2 vol.%) was determined, leading to the conductivity absolute values several orders of magnitude higher than that of a composite filled with MWCNTs only. The synergy effects of using both fillers have been discussed. Below room temperature the electrical transport is mainly governed by epoxy resin compression in all composites, while the electron tunnelling was observed only in hybrid composites below 200 K. At higher temperatures (above 400 K), in addition to the nanoparticles redistribution effects, the electrical conductivity of epoxy resin makes a significant contribution to the total composite conductivity. The dielectric relaxation spectroscopy allows estimating the nanoparticles distributions in polymer matrix and could be used as the non-destructive and fast alternate to microscopy techniques for general polymer composite fabrication control.

14.
Polymers (Basel) ; 12(12)2020 Dec 18.
Artigo em Inglês | MEDLINE | ID: mdl-33353036

RESUMO

Polymer composites containing nanocarbon fillers are under intensive investigation worldwide due to their remarkable electromagnetic properties distinguished not only by components as such, but the distribution and interaction of the fillers inside the polymer matrix. The theory herein reveals that a particular effect connected with the homogeneity of a composite manifests itself in the terahertz range. Transmission time-domain terahertz spectroscopy was applied to the investigation of nanocomposites obtained by co-extrusion of PLA polymer with additions of graphene nanoplatelets and multi-walled carbon nanotubes. The THz peak of permittivity's imaginary part predicted by the applied model was experimentally shown for GNP-containing composites both below and above the percolation threshold. The physical nature of the peak was explained by the impact on filler particles excluded from the percolation network due to the peculiarities of filler distribution. Terahertz spectroscopy as a versatile instrument of filler distribution diagnostics is discussed.

15.
Materials (Basel) ; 13(23)2020 Nov 28.
Artigo em Inglês | MEDLINE | ID: mdl-33260733

RESUMO

The electrical and magnetotransport properties of nanocrystalline tin dioxide films were studied in the temperature range of 4-300 K and in magnetic fields up to 8 T. SnO2-δ films were fabricated by reactive direct current (DC) magnetron sputtering of a tin target with following 2 stage temperature annealing of synthesized samples. The nanocrystalline rutile structure of films was confirmed by X-ray diffraction analysis. The temperature dependences of the resistance R(T) and the negative magnetoresistance (MR) were explained within the frame of a model, taking into account quantum corrections to the classical Drude conductivity. Extracted from the R(T) and R(B) dependences electron dephasing length values indicate the 3D character of the weak localization (WL) in our samples.

16.
Materials (Basel) ; 13(20)2020 Oct 09.
Artigo em Inglês | MEDLINE | ID: mdl-33050247

RESUMO

The polymeric adhesive used for the bonding of thermoplastic and thermoset composites forms an insulating layer which causes a real problem for lightning strike protection. In order to make that interlayer electrically conductive, we studied a new group of electrically conductive adhesives based on hot melt copolyamides and multi-walled carbon nanotubes fabricated by the extrusion method. The purpose of this work was to test four types of hot melts to determine the effect of their viscosity on the dispersion of 7 wt % multi-walled carbon nanotubes and electrical conductivity. It was found that the dispersion of multi-walled carbon nanotubes, understood as the amount of the agglomerates in the copolyamide matrix, is not dependent on the level of the viscosity of the polymer. However, the electrical conductivity, analyzed by four-probe method and dielectric spectroscopy, increases when the number of carbon nanotube agglomerates decreases, with the highest value achieved being 0.67 S/m. The inclusion of 7 wt % multi-walled carbon nanotubes into each copolyamide improved their thermal stability and changed their melting points by only a few degrees. The addition of carbon nanotubes makes the adhesive's surface more hydrophilic or hydrophobic depending on the type of copolyamide used.

17.
Materials (Basel) ; 13(12)2020 Jun 25.
Artigo em Inglês | MEDLINE | ID: mdl-32630508

RESUMO

The dielectric properties of Ba1-xCaxTiO3 (x = 0.17) ceramics were studied in a wide frequency range of 20 Hz-53 GHz. Diffused ferroelectric phase transition was revealed close to 339 K in the dielectric properties of ceramics. The behaviour of distributions of relaxation times in vicinity of the ferroelectric phase transition temperature is also typical for order-disorder ferroelectric phase transition. However, at lower temperatures (below 200 K), the most probable relaxation increased according to the Arrhenius law. At lower temperatures the maximum of the imaginary part of dielectric permittivity versus temperature strongly shifted to higher temperatures when the frequency increased (from 125 K at 1.21 kHz to 300 K at 33 GHz). This behaviour was attributed to the dynamics of Ti ions. The origin of the crossover from ferroelectric to relaxor behaviour of Ba1-xCaxTiO3 (x = 0.17) ceramics is discussed in the paper.

18.
Polymers (Basel) ; 12(3)2020 Mar 21.
Artigo em Inglês | MEDLINE | ID: mdl-32245162

RESUMO

The electrical properties of epoxy/MWCNT (multi-walled carbon nanotubes)/MnFe2O4 hybrid composites loaded with MWCNTs (below, 0.09 vol.%, and above, 0.58 vol.%, percolation threshold) and varying concentrations of MnFe2O4 up to 10 vol.% were studied in a wide frequency range (20 Hz-40 GHz) at different temperatures (20 K-500 K). At low frequencies, the dielectric permittivity and the electrical conductivity of composites with fixed amounts of MWCNT are strongly dependent on MnFe2O4 content. For MWCNT concentrations above the percolation threshold (i.e., 0.58 vol.%), the electrical conductivity highly decreases with the increase of the MnFe2O4 fraction. In contrast, for the epoxy/MWCNT just below the onset of electrical conductivity (0.09 vol.% of MWCNTs), there exists an optimal concentration of MnFe2O4 inclusions (i.e., 0.025 vol.%), leading to a dramatic increase of the electrical conductivity by three orders of magnitude. The electrical transport in composites is mainly governed by electron tunneling at lower temperatures (below 200 K), and it is highly impacted by the matrix conductivity at higher temperatures (above 400 K). The electrical properties were discussed in terms of the Maxwell-Wagner relaxation and distributions of relaxation times. A non-invasive platform based on dielectric relaxation spectroscopy was proposed for enhancing the synergetic effect coursed by using multiple nanoinclusions in polymer composites just below the percolation threshold.

19.
Materials (Basel) ; 14(1)2020 Dec 30.
Artigo em Inglês | MEDLINE | ID: mdl-33396932

RESUMO

The composite material filled with nano-sized BaTiO3 and Fe3O4 was designed and studied. The aluminium phosphate ceramics was used as a matrix. The XRD analysis demonstrates only the crystalline structure of the fillers used. The thermogravimetric analysis proves the thermal stability of the composites up to 950 K. The Maxwell-Wagner relaxation was observed in the dielectric spectra of the investigated composites. The dielectric spectroscopy proves the close contact between the nanoparticles with the different ferroic ordering. The phosphate-based composites have been proved to be a prospective candidate for the multiphase multiferroic materials design and development.

20.
Polymers (Basel) ; 11(12)2019 Dec 09.
Artigo em Inglês | MEDLINE | ID: mdl-31835436

RESUMO

The dielectric properties of epoxy/MWCNT (multi-walled carbon nanotubes)/MgO hybrid composites with a fixed MWCNT amount of 0.12 vol.% (0.2 wt.%) and varying MgO concentrations up to 3 vol.% were investigated in broad frequency (20-40 GHz) and temperature (20-500 K) ranges. The composites with up to 2 vol.% MgO nanoparticles concentration showed a significant increase of DC conductivity in relation to their non MgO-containing counterparts. The optimal content of MgO was found, i.e., 0.46 vol.%, which gave up to 2.5 orders of magnitude larger DC conductivity than those of the samples prepared without MgO additives. Using various amounts of MgO, it is possible to predictably vary the broadband electromagnetic properties of the composites, even entirely eliminating the electrical percolation. Electrical transport at different temperatures can be substantially controlled by the addition of given amounts of MgO. The broadband properties are discussed in terms of the distribution of relaxation times, which are proven to be an effective, noninvasive, and simple tool for checking composite fabrication issues, such as the distribution of MWCNT aggregates within the epoxy matrix.

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