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Materials and Interfaces
Enhanced mechanical performance of segregated carbon nanotube/poly(lactic acid) composite for efficient electromagnetic interference shielding Ling Xu, Xiao-Peng Zhang, Cheng-Hua Cui, Peng-gang Ren, Ding-Xiang Yan, and Zhong-Ming Li Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b05764 • Publication Date (Web): 27 Feb 2019 Downloaded from http://pubs.acs.org on March 1, 2019
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Enhanced mechanical performance of segregated carbon nanotube/poly(lactic acid) composite for efficient electromagnetic interference shielding
Ling Xu,† Xiao-Peng Zhang,† Cheng-Hua Cui,† Peng-Gang Ren,‡ Ding-Xiang Yan,*,† Zhong-Ming Li*,†
†College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering, Sichuan University, Chengdu 610065, China ‡Institute of Printing, Packaging Engineering and Digital Media Technology, Xi’an University of Technology, Xi’an 710048, China
ABSTRACT: Electrically conductive segregated networks were formed in carbon nanotube (CNT)/poly(lactic acid) (PLA) composite, in which CNTs are selectively located in poly(L-lactide) (PLLA) continuous phase and the continuous phase forms completed conductive networks at PLA stereocomplex crystallites (PLAsc) domains interfaces. The segregated CNT/PLLA/PLAsc composite with only 2.0 wt% CNT already
exhibits
an
average
electromagnetic
interference
(EMI)
shielding
effectiveness (SE) of 36 dB, showing 90% higher than that+++dB for the conventional CNT/PLLA composite with the same CNT loading. Owing to the high interfacial adhesion between PLLA and PLAsc, tensile strength of the CNT/PLA composite reaches 65.2 MPa, which is 52% higher than 41.8 MPa for pure PLAsc. Our work provides a novel way to development CNT/PLA composite with
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simultaneously high-performance EMI shielding and superior mechanical properties.
1. INTRODUCTION Electromagnetic wave devices, including the internet, communication equipment, and electronic organizers, not only leads to the malfunctioning of adjacent electronics, but also harms human health.1-8 Developing novel electromagnetic interference (EMI) shielding materials has attracted considerable attention. In comparison with the traditional metal materials, conductive polymer composites (CPCs) are becoming more attractive for EMI sheilding, due to the light weight, resistance to corrosion, good processability, and tunable electrical properties.9-17 Electrical conductivity of at least 1 S/m is typically required for an EMI shielding material to reach the minimum EMI shielding effectiveness (SE) of 20 dB for commercial application.18,19 The electrical conductivity of CPCs is highly related to conductive networks. Various approaches were employed to enhance the conductive filler dispersion or construct special conductive networks in CPCs, aiming to realize high-efficiency of conductive fillers to achieve high electrical conductivities at low filler loadings. The development of segregated structure has been considered as an efficient approach to improve the electrical conductivity and EMI SE of CPCs, because of the location of conductive fillers at polymer region interfaces which benefits the construction of perfect conductive networks.20-25 For instance, the average EMI SE of segregated CNT/polycarbonate composite increased to 23.1 dB with the addition of only 2.0 wt% carbon nanotube (CNT).19 Based on our group’s previous research, segregated structure was facilely fabricated in various polymer matrices
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(ultrahigh molecular weight polyethylene, polypropylene, natural rubber, etc.) and superior EMI shielding performance was also attained in comparison to conventional CPCs.21, 26-32 Although excellent EMI shielding performance was achieved, the mechanical performance of segregated CPCs was always unsatisfactory because the selectively distributed conductive fillers would prevent the interfacial diffusion between adjacent polymer domains and cause weak adhesive interaction.33,34 For instance, the segregated carbon black (CB) networks were reported to cause a significantly decreased ductility in poly(vinyl acetate) composite, leading elongation at break of the composite lower than 2.0% with 5.0 vol% CB.35 To improve mechanical performance of the segregated CPCs, the elimination of interfacial defects is urgently needed. Therein, employing a secondary polymer as location for conductive fillers, which also owns good compatibility with segregated polymer phase, was considered to be a promising strategy.28,36,37 The conductive filler-rich polymer phase could serve as a binder between the segregated phase, reducing interfacial defects and facilitating the improved mechanical performance. In our previous work, a small amount of high density polyethylene was utilized to remarkably increase the toughness and ductility of the segregated CNT/ultrahigh molecular polyethylene composite by 167% and 265%, respectively.28 Li et al. also achieved 30% improvement of tensile stress in the segregated CNT/poly(ethylene-co-octene) (CNT/POE) composite, with CNTs selectively distributed in continuous POE phase among the interfaces of cross-linked POE regions (segregated phase).36
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As documented above, the development of segregated CPCs possessing excellent electrical and mechanical performance is desirable for practical EMI shielding applications.
However,
most
of
the
current
segregated
CPCs
employed
petrochemical-derived polymers as matrices. Considering depletion of petroleum resources and ecological hazards, it is necessary to exploit biopolymers as CPC matrices. In this regard, our group established segregated CNT networks in poly(lactic acid) (PLA) by taking the advantage of different melting points between PLA stereocomplex crystallite (PLAsc) granules and poly(L-lactide) (PLLA). The resultant segregated CNT/PLA composite exhibits much higher EMI SE than conventional CNT/PLA composite.38 Herein, PLLA was used as a carrier phase for CNTs among the interfaces of PLAsc granules to develop the segregated CNT/PLLA/PLAsc composite. Thanks to the good compatibility between PLAsc granules and PLLA, the tensile strength of the segregated CNT/PLLA/PLAsc composite significantly enhances to 65.2 MPa, in comparison to 42.8 MPa for pure PLAsc. Moreover, with only 2.0 wt% CNT, electrical conductivity and EMI SE of the segregated composite can reach 19.7 S/m and 36.0 dB, respectively. Our work demonstrates a simple and efficient way to develop biopolymer based segregated CPC with outstanding EMI shielding performance and enhanced mechanical performance, revealing potential application of non-petrochemical-derived polymers in highly advanced and multifunctional materials.
2. EXPERIMENTAL SECTION
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2.1 Materials PLLA (trade 4032D) pellets were supplied by Nature Works. The weight-average molecular weight (Mw) of PLLA is 2.23 ×105 g/mol and the polydispersity index (PDI) is 2.10. PDLA pellets with Mw of 8.5 ×104 and PDI of 1.82 were used. CNTs (NC7000) were supplied by Nanocyl S.A., Belgium. The average diameter is 9.5 nm and the average length is1.5 μm. Alcohol and dichloromethane (DCM) were provided by Chengdu Kelong Chemical Reagent Factory, China. All the chemicals were used as received without any treatment. 2.2 Composite preparation The procedure for preparing the segregated CNT/PLA composite is schematically described in Figure 1. First, solution blending was used to prepare the CNT/PLLA composite. Stable suspension of CNT in ethanol was first prepared by using an ultrasonic cell disruptor for 10 min. PLLA pellets were added to DCM under mechanical stirring. The CNT/ethanol dispersion was then mixed with the PLLA/DCM solution under vigorous stirring and ultrasonic for 60 min. After that, the mixture was poured into a culture dish and the solvent was evaporated to obtain CNT/PLLA composite disk. The disk was mechanically pulverized into fine powders on a functional grinder. Subsequently, the CNT/PLLA compound containing 10 wt% CNT was localized on surfaces of PLAsc granules using a functional grinder for 4 min. The PLAsc granules were obtained through melt blending of PLLA and PDLA pellets on a HAAKE mixer at 180 oC, according to our previous work.38 Finally, the CNT/PLLA coated PLAsc granules were compression molded into disks for 5 min,
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under 10 MPa and 210 oC. CNT content in the resultant CNT/PLLA/PLAsc composite is 0.2, 0.3, 0.4, 0.5, 1.0, and 2 wt%, respectively. Pure PLAsc was also compression molding into disks with the same conditions as the preparation of the CNT/PLLA/PLAsc composite. 2.3 Characterization For the optical microscope (OM) observations, 20 μm-thick CNT/PLLA/PLAsc films were prepared by a microtome, observed via an Olympus BX51 polarizing OM (Olympus Co., Tokyo, Japan) with a Micro-Publisher 3.3 RTV CCD camera. The microstructures of the composites were also observed via a field emission scanning electron microscope (SEM, Inspect-F, FEI, Finland). Before the SEM observation, the composite specimens were cryo-fractured in liquid nitrogen and then coated with a thin layer of gold. To better identify the segregated structure, PLLA phase was further etched by solvent for SEM.39,40 The specimens were etched in a water/methanol (50/50 volume ratio) solution containing 0.002 g/mL of sodium hydroxide for 24 h and then cleaned by distilled water. The morphologies were also observed via an Olympus BX51 optical microscope (OM). Films with a thickness of 20 μm were cut from the segregated composites by a microtome. Transmission electron microscope (TEM, FEI Tecnai F20) was performed at an accelerating voltage of 200 kV. The electrical resistance of the composite was measured via a Keithley electrometer model 4200-SCS (USA). The composites were cut into rectangular specimens, with silver paste coated on both ends to eliminate the contact resistance during testing. Electrical conductivity (σ) was calculated by the equation σ = 𝐿 (𝑆 ∙ 𝑅), where 𝐿 is the length,
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𝑆 is the sectional area, and 𝑅 is the electrical resistance, respectively. The EMI shielding performance was measured via Agilent N5230 vector network analyzer in the frequency range of 8.2-12.4 GHz. Specimens with 13 mm in diameter and 2.0 mm in thickness were prepared for the measurement. The EMI SE (𝑆𝐸total) was defined as the logarithmic ratio of incoming power (Pin) to outgoing power (Pout).41-44 𝐸𝑀𝐼 𝑆𝐸 = 𝑆𝐸total = 10log(𝑃in 𝑃out) = 𝑆𝐸A + 𝑆𝐸R + 𝑆𝐸M
(1)
Where SEA, SER, and SEM are the absorption SE, reflection SE, and multiple reflections SE, respectively.21 The SEA and SER can be obtained using eqn (2) and (3), respectively. 𝑆𝐸A = ―10log(𝑇 (1 ― 𝑅))
(2)
𝑆𝐸R = ―10log(1 ― 𝑅)
(3)
Where T and R are the power coefficients of transmissivity and reflectivity calculated by the measured scattering parameters. Tensile tests were carried out using an Instron universal testing machine (Model 5576, America) at 20 mm/min. At least five specimens with 40 mm in length and 5 mm in width were tested for each composite and the average value was used.
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Figure 1. Schematic diagram for preparation of the CNT/PLLA/PLAsc composite.
3. RESULTS AND DISCUSSION SEM
images
of
CNT/PLLA
compound,
PLAsc
granules,
and
CNT/PLLA@PLAsc complex granules are displayed in Figure 2. The CNT/PLLA compound exhibits loose networks of stretched filaments, like wisps of cotton wool. The formation of such structure is attributed to low glass transition temperature (Tg ~ 60 oC) of PLLA matrix. In smashing process, the high speed friction between CNT/PLLA powders and mixer blade would result in the high temperature exceeding the softening point of PLLA, thus the CNT/PLLA powders would soften and orientate along the rotation direction of the mixer blade. It is clear that such fluffy structure prompts CNTs to stretch as far as possible (Figure 2c), resulting in conductive networks with low contents of CNT. In addition, the loose CNT/PLLA powders with large specific area is in favor of coating on the surface of PLAsc granules in the subsequent coating process, which facilities the construction of segregated structure. Compared with CNT/PLLA compound, the PLAsc granules display larger size and
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rough surface morphology (Figure 2d), providing an ideal encased characteristic. Good coating of CNT/PLLA compound on PLAsc granules in Figure 2e and Figure 2f further verified the feasibility of the segregated structure construction.
Figure 2. SEM micrographs of CNT/PLLA compound (a, b, c), PLAsc granules (d), and CNT/PLLA@PLAsc complex granules (e, f). Figure 3 displays the OM images of the CNT/PLLA/PLAsc composites. Appearance contrast of light and shade indicates that CNTs were dispersed in local region rather than uniformly distributed in whole system. That is, the continuous CNT/PLLA phase containing CNTs was selectively located at the boundary between PLAsc regions to form typical segregated structure. During the compression molding process, since the hot compaction temperature was above the melting point of PLLA (160 ℃) and below the melting temperature of PLAsc (220 ℃), the CNTs dispersed in PLLA were impossible to penetrate into the interior of PLAsc domains which maintained solid state. Although the PLAsc domains were not melted, the plastic deformation of the PLAsc granules still occurred under high pressure and the processing temperature which is above the Tg of PLAsc, thus leading irregular
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polyhedrons formation in the composite (Figure 3b and Figure 3c). The CNT/PLLA conductive channels (black lines) surrounded the PLAsc domains (light regions) help to form conductive networks in segregated CNT/PLLA/PLAsc composite due to volume exclusion effect. Moreover, the conductive CNT networks become more perfect and compact at higher CNT contents. Although majority of CNTs are connected each other in local region, a handful of conductive networks throughout the composite are still observed at 0.2wt% CNTs loading, which means that the conductive percolation appeared at CNT content around 0.2 wt%. The entirely complete conductive CNT networks are observed in the composite with 0.4 wt% CNTs content. Despite the similar perfect networks, the composite containing 1.0 wt% CNTs exhibit more compact (darker) and more complete (thicker) conductive networks.
Figure 3. OM micrographs of the segregated CNT/PLLA/PLAsc composites with 0.2 wt% CNT (a), 0.4 wt% CNT (b), and 1.0 wt% CNT (c). To observe the detailed microstructure and the dispersion of CNTs, SEM micrographs of the segregated CNT/PLLA/PLAsc composites were also performed, as shown in Figure 4. Cracks or defects have hardly been observed at the interfaces between CNT/PLLA phase and PLAsc domains (Figure 4a ~ c), clearly indicating the excellent interfacial adherence. The improved interfacial interaction is expectedly
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beneficial for the enhancement of the mechanical performance of the segregated composite. In the magnified SEM images (Figure 4d ~ f), it is clear that CNTs were selectively distributed in the CNT/PLLA phase (the blue dotted line) without migration into PLAsc interior, revealing obvious volume exclusion effect of PLAsc domains. To get clearer understanding of the segregated structure, the PLLA region is further etched by solvent. As shown in Figure S1, macroscopic gaps are clearly observed among the adjacent PLAsc domains in the whole systems. TEM micrographs were also taken and displayed in Figure S2. CNTs are mainly located in the interior of PLLA regions to construct conducting CNT/PLLA networks between PLAsc domains.11 The combination of OM, SEM and TEM results provide solid evidences for the development of segregated structure in CNT/PLLA/PLAsc composites.
The
well-established
conductive
networks
in
the
segregated
CNT/PLLA/PLAsc composites possibly help to improve the electrical and EMI shielding performance.
Figure
4.
SEM
micrographs
of
fractured
surfaces
of
the
segregated
CNT/PLLA/PLAsc composites with 0.2 wt% CNT (a, d), 0.4 wt% CNT (b, e), and
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1.0 wt% CNT (c, f). Figure 5 shows electrical conductivity of the segregated CNT/PLLA/PLAsc composite. It is observed that the electrical conductivity increases substantially with CNT loading. The composite with 0.5 wt% CNTs achieves electrical conductivity of 0.37 S/m, almost 15 orders of magnitude higher than 1.0 × 10-15 S/m for pure PLA. When CNT contents increase to 1.0 and 2.0 wt%, the electrical conductivities rise to 3.7 and 19.7 S/m, respectively, far exceeding the required minimum value (1.0 S/m) for commercial EMI shielding application. For comparison, Figure S3 displays the electrical conductivities of the conventional CNT/PLLA composite (Supporting Information). The results reveal that CNT/PLLA composites exhibit much lower electrical conductivities than those for the segregated CNT/PLLA/PLAsc composites, with the same CNT loadings. The achieved higher electrical conductivity in the segregated CNT/PLLA/PLAsc composites could be ascribed to the well-established segregated structure, which confines the conductive CNT/PLLA phase to stay at the PLAsc region interfaces and greatly improves effective concentration of CNT in the resultant composites. The percolation theory σ = 𝜎0(𝑗 ― 𝑗𝑐)𝑡 is used to analyze the percolation threshold behavior of the segregated composites, where σ is the electrical conductivity, 𝜎0 is a constant related to the electrical conductivity of CNT, j is CNT volume fraction, jc is the percolation threshold, and t is a critical exponent used to predict the mechanism of the conductive network.45 The fitted t is 2.96, suggesting
three-dimensional
conductive
networks
in
the
segregated
CNT/PLLA/PLAsc composites.46 A low jc of 0.11 vol% is obtained, signifying
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primary conductive networks formed in the segregated composites. Such low percolation threshold is attributed to the enhanced effective concentration of CNTs in CNT/PLLA continuous phase and the dense conductive networks in the final segregated CNT/PLLA/PLAsc composites.
Figure 5. Electrical conductivity of the segregated CNT/PLLA/PLAsc composite as a function of CNT loading. The insert shows the fitting lines of the composites using the percolation theory σ = 𝜎0(𝑗 ― 𝑗𝑐)𝑡. Figure 6a shows EMI SE of the segregated CNT/PLLA/PLAsc composite in the frequency range of 8.2–12.4 GHz. It can be seen that the segregated CNT/PLLA/PLAsc composite shows satisfactory EMI SE at extremely low CNT content. EMI SE of the composite containing only 0.5 wt% CNT is higher than 20.0 dB in the frequency range from 11.0 to 12.4 GHz, already exceeding the required minimum value for commercial EMI shielding application. The EMI SE of conventional CNT/PLLA composite was also evaluated, as displayed in Figure S4 (Supporting Information). In contrast to the segregated CNT/PLLA/PLAsc composites, at least 2.0 wt% CNT is required for conventional CNT/PLLA composite
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to achieve the EMI SE standard (20.0 dB). This indicates the superiority of segregated structure in improving EMI shielding performance. Increasing the CNT contents to 1.0 and 2.0 wt%, the average EMI SE of the segregated composite over the whole frequency range rises to 26.0 and 36.0 dB. The enhanced EMI SE should be ascribed to more perfect conductive networks at higher CNT loading (as shown in Figure 2), which improves the dissipation of electromagnetic microwave. In addition, it is seen that EMI SE is dependent on frequency for the composite at low CNT loading, while the EMI SE exhibits significant independence of frequency for the composite at high CNT loading. For instance, EMI SE of 0.5 wt% CNT/PLLA/PLAsc composite changes from 12.2 dB at 8.2 GHz to 26.9 dB at 12.4 GHz, increased by as much as 120.9%. However, the EMI SE of 2.0 wt% CNT/PLLA/PLAsc composite displays good stability over the whole frequency range, fluctuated within the range of 34.0-36.0 dB. Similar phenomenon was also reported in previous work.29,41,47 The low electrical conductivity of the 0.5 wt% CNT/PLLA/PLAsc composite should be the main reason for the frequency dependent EMI shielding performance.
Figure 6. (a) EMI SE of the segregated CNT/PLLA/PLAsc composites with various CNT contents, in the frequency range from 8.2 to 12.4 GHz. (b) Comparison of SEA and SER of the segregated composites at 8.2 GHz.
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To explore the EMI shielding mechanism of the segregated CNT/PLLA/PLAsc composites, SER and SEA were calculated. Figure 6b shows the calculated SEA and SER of the segregated composites with different CNT loadings. It is obvious that SEA significantly increases as the CNT loading increases, while SER shows negligible change. Among all the CNT loadings, the contribution of SER to EMI SE is very weak. For example, the EMI SE, SEA, and SER of 0.5 wt % CNT/PLLA/PLAsc composite are 12.2, 11.1, and 1.1 dB, which means that the EMI shielding by absorption (90.9%) is much larger than reflection and demonstrates that absorption shielding is the dominated EMI shielding mechanism. To further analyze the EMI shielding mechanism, the power balance including absorbed power (A), reflected power (R), and transmitted power (T) were also calculated, as displayed in Figure S5 (Supporting Information). It is noted that A is much higher than R for the CNT/PLLA/PLAsc composites, indicating that absorption is the dominant EMI shielding mechanism again. Due to the formation of segregated structure, which produced abundant interfaces for the composite to reflect and scatter the microwaves repeatedly, it is very difficult for the incident microwaves to transmit the composite before being absorbed.21,31,32 Figure 7a shows the tensile stress-strain curves of pure PLAsc and the segregated CNT/PLLA/PLAsc composites with different CNT contents. It is clear that PLAsc fractures in a typical brittle manner, showing a low tensile strength of just 42.8 MPa and elongation at break (EB) of 4.4%. The observation of the tensile fracture surface of PLAsc in Figure 7b indicates that the whole PLAsc region is pulled out, which
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probably results from the poor adhesive interactions between adjacent PLAsc domains. With the addition of CNT/PLLA compound in PLAsc, the tensile strength and EB of the segregated CNT/PLLA/PLAsc composites are significantly enhanced when compared with pure PLAsc. The tensile strength of 2.0 wt% CNT/PLLA/PLAsc composite reaches 65.2 MPa, which is 52% higher than that of pure PLAsc. Meanwhile, the EB increases to 5.9%, exhibiting obvious toughening effect in comparison to pure PLAsc. Commonly, the ductile performance of semi-rigid polymers would seriously reduce owing to the defects at the conductive filler/polymer interfaces.48 For instance, with addition of only 1.0 wt% graphite, the EB of low-density polyethylene degraded from 1610.0% to 27.0%.49 The significantly reinforced mechanical performance in our segregated CNT/PLLA/PLAsc composites should be due to two factors: (1) enhanced adhesion between PLAsc regions and the CNT/PLLA continuous phase; (2) reinforced effect of CNT on the CNT/PLLA continuous phase. The tensile fractured surfaces of CNT/PLLA/PLAsc composites were also observed. As shown in Figure 7c and d, hardly no grooves appeared in the CNT/PLLA/PLAsc composites and plastic deformation was observed, which could be well understood by the obviously stretched and threadlike PLLA. The CNT/PLLA phase localized at the interfaces among PLAsc domains played an important role in bonding PLAsc domains and prevented the PLAsc particles being pulled out. This manifests that the introduction of PLLA indeed improves the interface adhesion of PLAsc domains via the inter-diffusion, because PLLA and PLAsc share the similar molecular structure. Excellent interfacial adhesion endows the segregated
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CNT/PLLA/PLAsc composites with better toughness by crack deflection and particle pullout mechanisms. For comparison, the stress-strain curves of CNT/PLLA composites are also presented (Figure S6 in Supporting Information), demonstrating inferior tensile strength to the segregated CNT/PLLA/PLAsc composites, which might be attributed to the enhancement effect of single PLAsc microparticle. These results demonstrates that the segregated CNT/PLLA/PLAsc composites possess comprehensive superiority in electrical, EMI shielding, and mechanical performance, in comparison to those for the CNT/PLLA composites.
Figure
7.
(a)
Stress-strain
curves
of
pure
PLAsc
and
the
segregated
CNT/PLLA/PLAsc composites. SEM micrographs of the fracture surfaces for pure PLAsc (b) and 2.0 wt% CNT/PLLA/PLAsc composite (c, d) after tensile test.
4. CONCLUSIONS The CNT/PLLA/PLAsc composites with segregated conductive networks were
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developed by compression molding method. The segregated composite display excellent EMI shielding and mechanical performance owing to formation of CNT/PLLA continuous phase as well as the enhanced adhesion between CNT/PLLA continuous phase and PLAsc domains. With only 2.0 wt% CNT, the segregated CNT/PLLA/PLAsc composite exhibits an average EMI SE high to 36.0 dB. The tensile strength reaches 65.2 MPa and the elongation at break reaches 5.9%, which are 52% and 36% enhancement in comparison to 42.8 MPa and 4.4% for pure PLAsc. Meanwhile, the high SEA and low SER demonstrate the absorption dominant shielding mechanism in the composites. It is suggested that the segregated structure fabrication approach can spread to construct functional composites with comprehensive properties by balancing the mechanical performance and EMI shielding performance.
SUPPORTING INFORMATION The Supporting Information is available free of charge on the ACS Publications website at DOI: (1) SEM images of the 1.0 wt% CNT/PLLA/PLAsc composite after being etched; (2) TEM image of the 1.0 wt% CNT/PLLA/PLAsc composite; (3) The electrical conductivity of the CNT/PLLA composites at various CNT contents; (4) The EMI SE of the CNT/PLLA composites at various CNT contents; (5) The power balance at the frequency of 8.2 GHz for the CNT/PLLA/PLAsc composites; (6) The strain-stress curves of the CNT/PLLA composites at various CNT contents (PDF)
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AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected];
[email protected] Notes The authors declare no competing financial interest.
ACKNOWLEDGEMENTS This work was financial supported by National Natural Science Foundation of China (51673134, 21706208, 21704070) and the Fundamental Research Funds for the central Universities (2012017yjsy102,2017SCU04A03).
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