Flexible polyimide nanocomposites with DC bias induced excellent

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Applications of Polymer, Composite, and Coating Materials

Flexible polyimide nanocomposites with DC bias induced excellent dielectric tunability and unique nonpercolative negative-k towards intrinsic metamaterials Chao Zhang, Zhi-Cheng Shi, Fan Mao, Chaoqiang Yang, Xiao-tong Zhu, Jie Yang, Heng Zuo, and Runhua Fan ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b09063 • Publication Date (Web): 13 Jul 2018 Downloaded from http://pubs.acs.org on July 14, 2018

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ACS Applied Materials & Interfaces

Flexible polyimide nanocomposites with DC bias induced excellent dielectric tunability and unique non-percolative negative-k towards intrinsic metamaterials Chao Zhang,1 Zhicheng Shi,1* Fan Mao, Chaoqiang Yang, 1 Xiaotong Zhu, 1 Jie Yang, Heng Zuo, 1 Runhua Fan 2*

C. Zhang, F. Mao, C. Q. Yang, X. T. Zhu, J. Yang, H. Zuo, Prof. Z. C. Shi 1

School of Materials Science and Engineering

Ocean University of China Qingdao 266100, China E-mail: [email protected] Prof. R. H. Fan 2

Institute of Marine Materials Science and Engineering

Shanghai Maritime University Shanghai 201306, China E-mail: [email protected]

Keywords Metamaterials; Negative-k; Non-percolative; Multilayer films; DC bias. 1 ACS Paragon Plus Environment

ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Abstract Intrinsic metamaterials with negative-k that originated from random-structured materials have drawn increasing attention. Currently, intrinsic negative-k was mainly achieved in percolative composites by tailoring the compositions and microstructures. Herein, plasma-like negative-k was successfully achieved in MWCNT/PI nanocomposites via applying external DC bias which exhibited excellent capability in conveniently and accurately adjusting negative-k. Mechanism analysis indicated that the localized charges at the interfaces between MWCNT and PI became delocalized after gaining energy from DC bias, resulting in elevated concentration of delocalized charges, hence the enhanced negative-k. Furthermore, it is surprising to observe that negative-k also appeared in multilayer nanocomposites consisting of alternating BaTiO3/PI and PI layers, in which there was no percolative conducting network. On the basis of systematic analysis, it is proposed that the unique non-percolative negative-k was resulted from the mutual competition between plasma oscillations of delocalized charges and polarizations of localized charges. Negative-k appeared once the polarizations were overwhelmed by plasma oscillations. This work demonstrated that applying DC bias is a promising way to achieve highly tailorable negative-k. Meanwhile, the observation of unique non-percolative negative-k and the clarification of underlying mechanisms offer new insight into

negative-k

metamaterials,

which

will

greatly

facilitate

the

exploration

of

high-performance electromagnetic metamaterials.

1. Introduction Metamaterials with negative permittivity (negative-k) and (or) negative permeability (negative-µ) have drawn increasing attention worldwide owing to their fascinating 2 ACS Paragon Plus Environment

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electromagnetic properties1-3 and huge potential applications in antennas,4 electromagnetic cloaking,5, 6 perfect lens7 and holography,8 etc. Since the first experimental observation of negative parameter phenomenon in an artificial medium consisting of periodic split ring resonators and wires,9 various artificial structures with periodic unit cells were constructed to achieve negative electromagnetic parameters. In these artificial metamaterials, the negative parameters are usually originated from the Fano resonances and Mie resonances of periodic building blocks, and the negative parameters can be easily controlled via adjusting the arrangement as well as the geometry and dimension of the building blocks. 10-15 In the early development stage of metamaterials, it is generally accepted that negative-k and negative-µ could only be achieved in artificial medium of periodic structures rather than natural materials

with

random

structures.

Interestingly,

recent

researches

experimentally

demonstrated that negative electromagnetic parameters can also be achieved in random composites without periodic structures, i.e., intrinsic metamaterials.16 Furthermore, the negative parameters could be effectively adjusted via tailoring the composition and microstructure of the composites.17-20 Similarly, negative electromagnetic parameters were also further reported in other natural materials, such as spinel ferrites,21, La1−xSrxMnO3,23 granular composites24,

25

22

and conductor/polymer composites,26,

perovskite 27

etc. In

these intrinsic metamaterials, negative-k and negative-µ are commonly generated by the collective oscillations of a large number of delocalized electrons,28 i.e., plasma oscillations, and the magnetic resonances, respectively. Moreover, the magnitude and frequency band of negative-k can be tailored by varying the concentration of delocalized electrons,16-20 while tunable negative-µ can be achieved by adjusting the spin and domain wall resonances, as well 3 ACS Paragon Plus Environment


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as by exerting external magnetic fields.21-23 Currently, the magnitudes of negative-µ (< 5.0) were usually much lower than negative-k (> 103), resulting in the impedance mismatch in intrinsic metamaterials. To solve this problem, the realization of tailorable negative-µ and negative-k becomes particularly important. Basically, negative-µ could be generated in magnetic materials via magnetic resonances, and the magnitude and frequency band of negative-µ could be effectively tuned by the composition and microstructure of materials,29 as well as external magnetic fields.30 As for negative-k, it is usually originated from the plasma oscillation of delocalized electrons in percolative conductor/insulator composites according to Drude model.31 Thus, the concentration of delocalized charges, which is greatly associated with the composition and microstructure of the composites, is the key factor needs to be controlled to achieve tunable negative-k. In recent years, extensive researches have been carried out to achieve tunable negative-k in conductor/insulator composites via tailoring the compositions and microstructures,

including

metal/polymer,32

metal/ceramic,33

carbon/polymer34 and

carbon/ceramic composites,35 etc. Although tunable negative-k has been obtained, the tunability is limited due to the fact that the composition and microstructure of composites are difficult to be precisely adjusted. As discussed above, controlling the loading fractions and spatial distributions of conductors in the conductor/insulator composites is an effective way to adjust the concentration of delocalized charges, hence the negative-k. It should be noted that the concentration of delocalized electrons could also be adjusted via applying external DC bias, which may provide an alternative way to achieve tailorable negative-k. Following this idea, 4 ACS Paragon Plus Environment

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the dielectric responses of a series of single-layer multi-walled carbon nanotubes/polyimide (MWCNT/PI) and barium titanate/polyimide (BaTiO3/PI) composites, as well as multilayer polyimide based nanocomposites as a function of external DC bias were investigated in detail in this work. Interestingly, plasma-like negative-k was observed in the multi-walled carbon nanotubes/polyimide (MWCNT/PI) nanocomposites when the DC bias reached some critical values and the negative-k could be easily and precisely tailored via adjusting the DC bias. Furthermore, the underlying mechanism of the DC bias induced plasma-like negative-k was explored. Subsequently, the dielectric responses of multilayer polyimide nanocomposites as a function of DC bias were explored. Surprisingly, negative-k was also realized in BaTiO3/PI-PI multilayer nanocomposites consisting of alternately stacked BaTiO3/PI and PI layers, in which there was no percolative conducting network which was thought to be indispensable to the realization of intrinsic negative-k.16-27 Then the mechanism behind the unique non-percolative negative-k phenomenon was explored. The realization of unique non-percolative negative-k and the clarification of underlying mechanisms offer new insight into

negative-k

metamaterials,

which

will

greatly

facilitate

the

exploration

of

high-performance electromagnetic metamaterials.

2. Results and discussion 2.1 Morphologies and Compositions. Figure 1 presents the schematic architecture, SEM morphologies and EDS of the multilayer composite films. In this work, multilayer films consisting of 3, 5, 7 and 9 layers of alternating MWCNT/PI and BT/PI layers were designed and fabricated via a layer-by-layer casting process. As expected, layered structures were formed (Figure 1b-e) and the fillers were homogeneously distributed in the matrix 5 ACS Paragon Plus Environment


Figure 1. Schematic layer-by-layer casting process (a); microstructure and optical images of multilayer films (b); SEM and EDS spectra of multilayer films (c-j). 6 ACS Paragon Plus Environment

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without obvious sedimentation and agglomeration even in composites with high filler loading fractions (Figures S1b-f, Supporting Information) because of the surface modification of fillers and the in-situ polymerization process. As we know, multilayer

composites, particularly those prepared by simple hot pressing process, commonly suffer from delamination phenomenon, which has been generally proved to be harmful to the dielectric and mechanical performances of multilayer materials.36-38 Herein, the multilayer films were prepared via a layer-by-layer casting process, which will help the

adjacent layers make sufficient contact with each other, resulting in well unified interfacial regions. Therefore, although there exist distinct “composition” contrast between adjacent layers as demonstrated by the EDS, there is no sharp physical layer boundary. In addition, since the evaporation of solvents is fast during the preparation process of multilayer films, when another layer is cast on top of the dried PAA film, the diffusion of solvents into the dried PAA film is very limited and the solvents only slightly soften rather than dissolve the formed fillers/PAA composite films. So the original structure of the PAA film was not destroyed. As shown in Figure S2a-d (Supporting Information), distinct multilayer structures without obvious mutual dissolution between adjacent layers are observed, and there is no bubbles or voids at the layer/layer interfaces. Furthermore, the compositions of the composites were verified by XRD and FTIR. As shown in Figure S3a, there is no vibration absorption peak at 2900-3200 cm-1, indicating no surplus monomer is present in the polymer. The formation of pristine PI can be further demonstrated by the absorption peaks at 1715 cm-1 (symmetrical stretching of C=O), 1785 cm-1 (asymmetric stretching of C=O) and 1367 cm-1 (symmetrical stretching of C-N),39 as shown in Figure S3b. 7 ACS Paragon Plus Environment


The pristine PI exhibits a broad peak at 2θ = 18° representing a typical amorphous structure which is mainly attributed to the irregularity of the polymer chains. In addition, characteristic peaks at 2θ = 27° representing the carbon appear in the XRD patterns. No significant change of the broad peak position was observed in MWCNT/PI composites, implying that the averaged interplanar distance of PI is not changed by the addition of carbon nanotubes.40

Figure 2. Dielectric spectra of MWCNT/PI composites under different external DC bias (a-e) and schematic influence of external DC bias on the energy level of electrons (f). 8 ACS Paragon Plus Environment

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Furthermore, no additional peaks can be observed, indicating that the fillers and PI matrix are physically mixed together without the occurrence of unexpected mutual chemical reactions.

2.2 Dielectric performances of single layer composites. The dielectric specta of MWCNT/PI composites under different external DC bias were displayed in Figure 3. For the pristine PI and MWCNT/PI composite containing 2 wt% MWCNT, the dielectric permittivities show slight dependence on frequency and the dielectric specta exhibit no obvious change with external DC bias. However, when the DC bias exceeds 15 V, the dielectric permittivities become strongly dependent on frequency (Figures 2a and 3b) and higher DC bias results in lower dielectric permittivity. In the MWCNT/PI composites, the polarizations of accumulated electrons at the interfaces between MWCNT and PI contribute greatly to the dielectric permittivity. Therefore, the concentration of localized electrons on MWCNT-PI interfaces plays significant roles in dermining the magnitude of dielectric permittivity. In this work, the energy status of localzied electrons at MWCNT-PI interfaces could be changed by the DC bias. As illustrated in Figure2f, when there is no DC bias, the enegy level of the trapped electrons is low and they can not escape from the MWCNT-PI interfaces, forming localized charges.41 When the external DC bias is applied, the trapped electrons will gain energy from the DC bias and reach a higher energy level. Once the applied DC bias is high enough, a fraction of trapped electrons will get rid of the MWCNT-PI interfaces and be capable of hopping between trapped positons along the electric filed direction, becoming delocalized charges.42 Consequently, the concetration of accumualted charges at MWCNT-PI interfaces will be lowered and the dielectric permittivity becomes suppressed. Moreover, the external DC bias will also influence the polarization processes. 9 ACS Paragon Plus Environment


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When an external DC bias is exerted on a MWCNT/PI composite, the polarization units, such as localzied charges and dipoles, tend to arrange along the direction of DC bias. Therefore, the orientation of polarizaition units will be greatly affected by the DC bias, leading to the appearance of addional relaxiation processes in dielectric specta (Figures 2a and b). It should be noted that, when the MWCNT content exceeds 4 wt%, plasma-like negtive-k appeared when the external DC bias is high enough (Figures 2c-e). In addition, the switching frequency at which the permittivity turns from negative to positive shifts to higher frequency with increasing DC bias. Meanwhile, increasing DC bias also brings about the enhanced magnitude of negative-k. In recent years, negative-k has been reported in various materials via adjusting materials’ microstructures and compositions.21-27 However, there is rare literature about the realization of negative-k via applying DC bias and no detailed investigations on how the DC bias affect the frequency dispersion behaviors of negative-k was reported. Theoretically, the frequency dispersion behviour of plasma-like negative-k follows the Drude model, which describes the dielectric responses of delocalized electrons:31

ε r′ (ω ) = 1 −

ωΡ =

ωΡ2 ω 2 + ωτ 2

(1)

neff e 2 meff ε 0

(2)

where ωp (ωp=2πfp) is the plasma frequency, ω is frequency of electric field, ωτ is damping parameter, ε0 is permittivity of vacuum (8.85×10-12 F/m ), neff is effective concentration of delocalized electrons, meff is effective weight of electron, and e is electron charge (1.6×10-19 C). In the Drude model, the value of ωτ is usually 3 or 4 orders of magnitude lower than ωp. Thus, when the frequey ω is close to ωp, the permittiivty becomes close to zero according to 10 ACS Paragon Plus Environment

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equaiton (1). In other words, the plasma frequency ωp corresponds to the swithching frequency at which the permittiivty turns from negative to positive. Furthermore, ωp is proportional to neff

1/2

according to equation (2). Therefore, higher concentration of

delocalized electrons that induced by applying DC bias will results in higher switching frequency and enhanced magnitude of negative-k. In previous studies, the magnitude of negative-k was usually very high (> 104),16-27 which was detrimental to the matching between negative-µ and negative-k in double negative metamaterials. Herein, the nanocomposites with dramatically suppressed negative-k are promising candidates for electromagnetic metamaterials. As discussed above, appling external DC bias has been demonstrated to be an effective way to obtain highly tunable negative-k in MWCNT/PI nanocomposites. In order to compare the negative-k regulation effects between adjusting materials’ compositions and applying external DC bias, the variation of switching frequency and magnitude of negative-k as a function of MWCNT content and DC bias were presented in Figure 3. As depicted in Figure 3a, as the MWCNT content increases slightly from 6 wt% to 8 wt%, the switching frequency shifts are as high as 245 kHz (UDC=2 V), 390 kHz (UDC=3 V) and 255 kHz(UDC=4 V), respectively. However, as the DC bias increases from 1 V to 2 V, the switching frequency shift of 6 wt% MWCNT/PI composite is merely 20 kHz (Figures 2d and 3a). Particularly, the switching frequency shift of 4 wt% MWCNT/PI composite appears to be as small as 1 kHz as the DC bias increases from 20 V to 25 V (Figure 2d). Similarly, the magnitude of negative-k is also more sensitive to the composition variation of MWCNT/PI composites than to the variation of DC bias (Figure 3b). 11 ACS Paragon Plus Environment


Consequently, it is difficult for us to finely adjust the frequency band and magnitude of negative-k via merely varying the composition of materials due to the fact that the precise control of materials' compositions is challenging. As an alternative, DC bias exhibit excellent capability in finely regulating negative-k. In addition, applying DC bias also possess other advantages, in particular its accuracy, repeatability and convenience, over adjusting materials’ compositions. For instance, it is commonly accepted that the distribution of fillers in a composite cannot be absolutely homogeneous owing to the agglomeration of fillers, especially nanoscale fillers with high specific surface areas. Therefore, two composites with the same composition usually do not exhibit exactly the same dielectric

Figure 3. Variation of switching frequency (a) and magnitude of dielectric permittivity (b) with MWCNT content and DC bias. 12 ACS Paragon Plus Environment

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response, even if the preparation conditions for the composites were strictly controlled. On the contrary, the strength and direction of DC bias can be accurately and conveniently controlled. Moreover, the DC bias can be easily superimposed with external AC electric fields in the practical applications. As discussed above, although adjusting materials’ composition and applying external DC bias are both effective ways to obtain and adjust negative-k, applying DC bias appears to perform better than adjusting materials' compositions.

Figure 4. Frequency dependences of reactance for MWCNT/PI composites with 2 wt% (a), 4 wt% (b), 6 wt% (c) and 8 wt% (d) MWCNT under different DC bias. As we know, reactance Z'' is the opposition of a circuit element to a change of current or voltage due to that element's inductance or capacitance. Generally, materials under electric fields can be regarded as equivalent electric circuits, in which the frequency dispersion 13 ACS Paragon Plus Environment


behaviour of reactance may provide some important clues associated with the underlying mechanism of electrical responses. The reactance can be commonly expressed as Z''=ωL−1/(ωC), where ωL and −1/(ωC) represent inductive reactance and capacitive reactance, respectively. As shown in the inset of Figure 4a, the Z'' of MWCNT/PI composites containing 2 wt% MWCNT under 0 V, 5 V and 10 V DC bias exhibit strict linear dependence on 1/f, representing typical capacitive characteristic. However, when the DC bias was further elevated to 15 V, 20 V and 25 V, the correlations between Z'' and frequency display distinct monotonic behaviors. With increasing frequency, Z'' show a trend of first increase and then decrease. Such non-monotonic Z''~f relationship should be attributed to the competition between inductive reactance and capacitive reactance. As discussed earlier, increasing DC bias could generate more delocalized electrons which should be regarded as inductive unit cells under electric fields. As a consequence, the contribution of inductive reactance to the overall reactance will be intensified by increasing DC bias. Similar non-monotonic Z''~f relationships were also observed in MWCNT/PI composites with 4 wt% MWCNT, as shown in Figure 4b. The difference is that the absolute values of Z'' for 4 wt% MWCNT/PI composites are approximately two orders of magnitude lower than that of 2 wt% MWCNT/PI composites. Such a distinct magnitude difference indicates the drastically enhanced contribution of inductive reactance as a result of increased concentration of delocalized charge carriers. When the MWNCT content was further increased to 6 wt%, the absolute value of Z'' show a further dramatic decrease of about 4 orders of magnitude compared with 4 wt% MWCNT/PI composites, indicating the dramatically enhanced contribution of inductive reactance to the overall reactance. It is interesting to point out that, 14 ACS Paragon Plus Environment

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although the Z''~f curves of the 8 wt% MWCNT/PI composite feature behaviors similar to that found in the 6 wt% MWCNT/PI composite, unique positive Z'' were observed at low frequencies when the DC bias exceeded 2 V, and the magnitude of Z'' increased slightly with higher DC bias. The positive Z'' implied the phase lag of current behind voltage, i.e., inductive characteristic, which contributes to the appearance of plasma-like negative-k.16-20 The dielectric specta of the 30 wt% BaTiO3/PI composite under different external DC bias were depicted in Figure 5. Similar to the MWCNT/PI composites, the dielectric permittivity of 30 wt% BaTiO3/PI composite exhibits no obvious variation with frequency

Figure 5. Frequency dependences of dielectric permittivity (a) and loss tangent (b) for BaTiO3/PI composite containing 30 wt% BaTiO3 under different external DC bias; Variation of dielectric permittivity (c) and loss tangent (d) as a function of DC bias for BaTiO3/PI composites with different BaTiO3 loading fractions. 15 ACS Paragon Plus Environment


when the DC bias is below 15 V and becomes strongly dependent on frequency when the DC bias exceeds 15 V. Meanwhile, the magnitudes of permittivities decrease with higher DC bias (Figures 5a and c). As shown in Figure S4, when the BaTiO3 loading fractions were further increased to 10 wt%, 20 wt%, 40 wt% and 50 wt%, the BaTiO3/PI composites also display the same dielectric spectra variation trend as 30 wt% BaTiO3/PI compoiste as a function of DC bias. The reduced permittivities should be ascribed to the suppression or even gradual vanish of original dipolar and interfacial polarizations, while the strong relaxiation behaviors should be attirbuted to the appearance of new types of polarizations, in particular the interfacial polarizations at the interfaces between BaTiO3 and PI. Although the BaTiO3/PI composites display similar dielectric spectra variation with DC bias, no plasma-like negative-k was obseved even though the DC bias was strengthened up to 25 V. As mentioned earlier, negative-k was always generated by the plasma oscillaiton of free electrons in percolative conduting networks in negatve-k metacomposites. In the BaTiO3/PI composites, there is no conducting component. For that reason, it is very difficult to form percolative conduting network even under high DC bias. Thus, it is reasonable that no negative-k phnomenon took place in the BaTiO3/PI composites. Figures 5 b and d present the variation of loss tangent as a function of frequeny and DC bias. It can be seen that the loss tangent increases as the DC bias becomes higher, which should be mainly contributed by the leakage conduction of untrapped charge carriers generated by high DC bias.

2.3 Dielectric performances of multilayer composites. Figure 6 depicts the frequency dispersion behaviors of dielectric permittivity for multilayer composites.

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Figure 6. Frequency dependences of permittivity for multilayer composites (a-d); Variation of dielectric permittivity with DC bias for multilayer composites (e, f). Compared with single layer composites, there exist much more interfaces, in particular layer-layer interfaces, in the multilayer composites. Charge accumulations, polarizations and electric field redistributions, which may give rise to plenty of interesting dielectric responses, could occur at the numerous interfaces. As shown in Figures 6a and b, the multilayer composites consisting of alternating 6 wt% MWCNT/PI layers and 30 wt% BT/PI layers 17 ACS Paragon Plus Environment


manifest similar dielectric permittivity variation tendencies with single layer MWCNT/PI composites as a function of DC bias, i.e., the reduction of dielectric permittivity with increasing DC bias. Moreover, the 5-layer composites possess obviously enhanced permittivity (~ 30 @10 kHz, 0 V) in comparison with 3-layer composites (~ 17 @10 kHz, 0 V). As the number of layers were further increased to 7 and 9 layers, the permittivities of the composites without applying DC bias reached ~ 45 @10 kHz and ~ 60 @10 kHz (Figures S5a and b, Supporting Information), respectively. Such permittivity boost phenomena should be ascribed to the strong interfacial polarizations on the enlarged interfaces between adjacent layers. As expected, no negative-k was achieved in the 30-6-30 multilayer composites because percolative conducting networks, which were believed to be necessary for the realization of negative-k in intrinsic metacomposites, are very difficult to form in these multilayer composites owing to the existence of the insulating BT/PI layers. Surprisingly, negative-k was observed in multilayer composites consisting of alternately stacked 30 wt% BT/PI and PI layers (Figures 6c and d). To confirm the reliability of this unique negative-k phenomenon, a series of multilayer composites were further prepared and their dielectric responses were investigated. It is interesting to see that negative-k were also obtained in 30-0-30 composites with 7 and 9 layers (Figures S5c and d, Supporting Information), as well as trilayered 10-0-10 and 20-0-20 composites (Figures S6c and d, Supporting Information). The variation of dielectric permittivity εr' (@ 30 kHz) as a function of DC bias for multilayer composites with different architectures were depicted in Figure 6e. Clearly, all of the 30-6-30 and 30-0-30 multilayer composites display gradual decreases of εr' with elevated DC bias. Particularly, negative-k appears in the 30-0-30 multilayer composites once 18 ACS Paragon Plus Environment

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the DC bias reaches some critical values (e.g., 15 V in this work), whereas the εr' of 30-6-30 multilayer composites stay positive even though the DC bias is raised to 25 V. As shown in Figure S7, the dielectric Weibull breakdown strengths of the 30-6-30 multilayer composites (< 76.13 MV/m) are much lower than those of the 30-0-30 multilayer composites(> 90.29 MV/m), indicating that the 30-6-30 multilayer composites that containing conducting MWCNT fillers are much more prone to form percolative conducting networks in comparison with 30-0-30 multilayer composites. Accordingly, it was supposed to be easier to achieve negative-k in 30-6-30 multilayer composites than in 30-0-30 multilayer composites under the same DC bias because negative-k was commonly believed to be resulted from the plasma oscillation of delocalized charges in percolative conducting networks. However, negative-k was evidently achieved in 10-0-10, 20-0-20 and 30-0-30 composites rather than 10-6-10, 20-6-20 and 30-6-30 composites, indicating that the negative-k achieved in these multilayer composites should not be simply originated from percolative conducting networks. This unique phenomenon should be resulted from the competitions between the polarizations of localized charges and plasma oscillations of delocalized charges. In the following section, the detailed underlying mechanisms will be discussed. On the basis of systematic investigations, the following mechanism for this unique non-percolative negative-k phenomenon is proposed. As illustrated in Figure 6f, the positive-k of the multilayer composites was mainly contributed by dipolar polarizations (i.e., rotation of dipoles in polymer matrix and fillers under external ac electric field) and interfacial polarizations (i.e., forced oscillations of trapped carriers at the filler-matrix and layer-layer interfaces which usually need long time to be established and occur at low 19 ACS Paragon Plus Environment


Figure 7. Frequency dependences of loss tangent for 30-6-30 (a, b) and 30-0-30 (c, d) multilayer composites. frequencies). When a DC bias is applied, the rotation of dipoles will be stiffened along the direction of DC bias, leading to longer relaxation time. For that reason, the dipolar polarization strength will be gradually weakened by increasing DC bias, resulting in the decrease of positive-k. Meanwhile, the DC bias will also bring about the redistribution of mobile charge carriers in the composites, giving rise to enhanced charge accumulations and interfacial polarizations at the interfaces, in particular layer-layer interfaces because of the distinct mismatch of conductivity and permittivity between adjacent layers. The dramatically boosted permittivity at low frequencies under 15 V DC bias should be attributed to the enhanced interfacial polarizations. It is worth noting that, the charge carriers accumulated at 20 ACS Paragon Plus Environment

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the interfaces will become delocalized once the DC bias strength exceeds some critical values. As mentioned earlier, the oscillation of localized (or trapped) charge carriers (i.e., polarizations) contribute to the positive-k. Meanwhile, the delocalized charge carriers will also oscillate under external ac electric fields (i.e., plasma oscillations), resulting in negative-k as described by Drude model. As we know, the concentration variation of localized or delocalized charge carriers in the composites can be reflected, to some extent, by the frequency dispersion behaviors of dielectric loss. For instance, the dielectric loss describes the energy dissipation in a dielectric material because of leakage DC current conduction, dipole polarizations, and interfacial polarizations, which can be described by ᇱᇱ ᇱᇱ ߝ ᇱᇱ = ߝdc + ߝMW + ߝDᇱᇱ , where ε''dc, ε''MW and ε''D are DC conduction loss, interfacial

polarization loss and dipole loss, respectively.37 As displayed in Figure 7, the 30-0-30 composites exhibit distinct relaxation peaks which were not observed in the loss spectra of 30-6-30 composites. In addition, the 30-6-30 composites exhibit much higher loss than 30-0-30 composites. The relaxation peaks should be attributed to the interfacial polarizations occurred at the filler-matrix and layer-layer interfaces. Undoubtedly, there exist both polarizations loss and DC conduction loss in the 30-6-30 and 30-0-30 composites. The difference is that the loss of 30-6-30 composites is mainly originated from the conduction loss while the loss of 30-0-30 composites is dominated by polarization loss. In other words, the concentrations of delocalized charge carriers, which contribute to the conduction loss, in 30-6-30 composites are higher than those in 30-0-30 composites. Thereby, the 30-6-30 composites were supposed to be able to generate stronger negative-k than 30-0-30 composites. However, it should also be taken into account that the polarizations which generate positive-k, 21 ACS Paragon Plus Environment


as discussed earlier, are much stronger in 30-6-30 composites than that in 30-0-30 composites. In this case, the permittivities of these multilayer composites were determined by two competing processes: polarizations that contribute to positive-k and plasma oscillations that contribute to negative-k. The composites will manifest negative-k once the polarizations are overwhelmed by plasma oscillations. For the 30-6-30 multilayer composites, the initial permittivities are too high (> 15 @30 kHz) to be counteracted by the plasma oscillations induced negative-k, thus no negative-k appeared. According to above analysis, it can be conclude that percolative conducting networks are not indispensable to the realization of negative-k. Actually, negative-k should appear while two conditions are satisfied: (a) DC bias or other external energy sources (e.g., magnetic fields, heating sources, electromagnetic waves, etc) that can deliver energy to the trapped charges at interfaces and delocalize them are applied; (b) the dipole polarizations and interface polarizations of localized charges are overwhelmed by plasma oscillations of delocalized charges. The realization of unique non-percolative negative-k and the exploration of underlying mechanisms offer new insight into negative-k metamaterials, which will be of great significance for the development of electromagnetic metamaterials. Furthermore, these multilayer composites with highly tunable dielectric properties could be promising candidates not only for electromagnetic metamaterials, but also for capacitive sensors,43 energy-storage capacitors44 and field-effect transistors (FETs),45 etc.

3. Conclusions In summary, the dielectric responses of a series of polyimide based single-layer and multilayer nanocomposites under external DC bias were investigated. Interestingly, 22 ACS Paragon Plus Environment

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plasma-like negative-k with highly tailorable magnitudes and frequency bands were achieved via adjusting DC bias. It is indicated that the localized charges at the filler-matrix interfaces will become delocalized after absorbing energy from the DC bias, leading to elevated concentration of delocalized charges, hence the intensified negative-k magnitude and higher plasma frequencies. In addition, DC bias exhibit superior capability in finely adjusting the negative-k, in particular its convenience and accuracy, over conventionally adjusting materials' compositions. Thus applying DC bias is demonstrated to be a promising strategy to obtain negative-k metamaterials with excellent dielectric tunability. It is commonly believed that percolative conducting networks are indispensable for the occurrence of plasma-like negative-k in intrinsic metamaterials. Surprisingly, negative-k was achieved in BaTiO3/PI-PI multilayer nanocomposites consisting of alternating BaTiO3/PI and PI layers, in which there was no percolative conducting networks. Based on systematic analysis, it is proposed that the unique non-percolative negative-k of multilayer nanocomposites should be attributed to the dominating contribution of the oscillations of delocalized charges, in comparison with polarizations of localized charges, to the overall dielectric responses. The realization of unique non-percolative negative-k and the clarification of underlying mechanisms offer new insight into negative-k metamaterials, which is quite beneficial to the exploration of high-performance electromagnetic metamaterials.

4. Experimental section Surface modification of multi-walled carbon nanotubes (MWCNT): The dispersion of fillers in the matrix has an important effect on the capacitance of the composites, thus affecting the permittivity of the polymer composites. The surfactant (KH560 silane coupling 23 ACS Paragon Plus Environment


agent) was introduced in this work to functionalize the surface of MWCNT to enhance the interfacial affinity of MWCNT in matrix to obtain composites with highly stable and repeatable dielectric performances. Typically, 1 g MWCNT (>95 %, inner diameter of 5-15 nm, outer diameter of >50 nm, and the length of 10-20 μm.) was added into 31.2 ml solution of anhydrous ethanol and deionized water (9:1). Then 46.9 μl KH560 was added to this solution and continuously stirred at 60 °C for 30 min. Finally, the precipitate was washed three times with absolute ethanol and heated in an oven at 120 °C for 6 h, and cooled down to room temperature. Preparation of single-layer multi-walled carbon nanotubes/polyimide (MWCNT/PI) composite films: Typically, 0.0105 g carbon nanotubes and 0.5 g 4, 4-oxydianiline (ODA, AR) was dispersed in 10 ml N, N-dimethyl-acetamide (DMAc, AR) with ultrasonication for 30 min, and a stable dispersion was obtained. Then 0.545 g pyromellitic dianhydride (PMDA, 99%) was divided into 3 portions and added within 1 h. Then MWCNT/polyamic acid (PAA) suspension was magnetically stirred for 5 h at room temperature. Last, the suspension was put on a glass plate to form a uniform film and placed in an oven through temperature programmed progress at 60 °C for 2 h, 120 °C for 1 h, 150 °C for 1 h, and 190 °C for 1 h, respectively, to complete imidization, forming the MWCNT/PI composite films. The MWCNT loading fractions in the composite films are 0 wt%, 2 wt%, 4 wt%, 6 wt% and 8 wt%, respectively. Preparation of single-layer barium titanate/polyimide (BaTiO3/PI) composite films: Firstly, 0.1045 g barium titanate (with radius of about 0.3 µm) and 0.5 g 4, 4-oxydianiline (ODA, AR) were dispersed in 10 ml N, N-dimethyl-acetamide (DMAc, AR) with ultrasonication 24 ACS Paragon Plus Environment

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for 30 min, forming a stable dispersion. Then 0.545 g pyromellitic dianhydride (PMDA, 99%) was divided into 3 portions and added within 1 h. Then BT/polyamic acid (PAA) suspension was magnetically stirred for 5 h at room temperature. Subsequently, the suspension was put on a glass plate to form a uniform film. Finally, the films were placed in an oven through temperature programmed progress at 60 °C for 2 h, 120 °C for 1 h, 150 °C for 1 h, and 190 °C for 1 h, to complete imidization and obtain the BT/PI composite films. The BT loading fractions in the composite films are 10 wt%, 20 wt%, 30 wt%, 40 wt% and 50 wt%, respectively. Preparation of multilayer films: A series of multilayer films were prepared using layer-by-layer solution casting process. First of all, BT/PAA solution and CNT/PAA solution were prepared. The BT/PAA solution was casted onto a glass plate as the first layer and then transferred to an oven at 60 °C for 2 h. Subsequently, the MWCNT/PAA solution was casted on the top of the first BT/PAA film, then cured at 60 °C for 2 h in an oven until the second layer was totally dried. Afterwards, BT/PAA solution was casted on the top of the MWCNT/PAA layer to obtain the trilayer structured BT/PI-CNT/PI-BT/PI composite film. Furthermore, the MWCNT/PAA solution was casted on the top of BT/PAA layer of trialyer BT/PI-MWCNT/PI-BT/PI film followed by curing at 60 °C for 2 h to form the fourth layer. Hereafter, the BT/PAA solution was casted on the top of the MWCNT/PAA layer as the fifth layer to obtain the 5-layer BT/PI-MWCNT/PI-BT/PI-MWCNT/PI-BT/PI composite film was obtained. Following the fabrication process described above, 3-layer (BT/PI-MWCNT/PI-BT/PI) film, 5-layer (BT/PI-MWCNT/PI-BT/PI-MWCNT/PI-BT/PI) film, 7-layer (BT/PI-MWCNT/PI-BT/PIMWCNT/PI-BT/PI-MWCNT/PI-BT/PI) film and 9-layer (BT/PI-MWCNT/PI-BT/PI-MWCNT/PI25 ACS Paragon Plus Environment


BT/PI-MWCNT/PI-BT/PI-MWCNT/PI-BT/PI) composite films with alternately stacked BT/PI and MWCNT/PI layers were prepared. The multilayer films were placed in an oven through temperature programmed progress at 60 °C for 2 h, 120 °C for 1 h, 150 °C for 1 h, and 190 °C for 1 h, to complete imidization. In the multilayer films, the thickness of every single layer was controlled to be about 22-25 μm. The succinct symbol of “30-6-30(3 layers)” represents the trilayer composite with 30 wt% BT in BT/PI layers and 6 wt% MWCNT in the MWCNT/PI layers. Similarly, the corresponding multilayer composites with 5, 7 and 9 layers were reported as “30-6-30(5 layers)”, “30-6-30(7 layers)” and “30-6-30(9 layers)”, respectively. Characterization: Attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) was conducted with a NICOLET 5700 FT-IR Spectrometer over the range of 4000-400 cm-1. The fracture morphologies and EDS spectra of the composites were presented by scanning electron microscopy (SEM, S-4800, Hitachi, Ltd.). The compositions of the composites were analyzed by using an X-ray diffractometer (XRD, D8 Advance, Bruker, Ltd.). Dielectric measurements: Gold electrodes were sputtered on both sides of the films for the dielectric measurements. One side was entirely sputtered with the gold electrode, while the other side is sputtered using a ceramic mask with a 2.98 mm diameter ring, respectively. Tonghui Electronics TH2828S Automatic Component Analyzer with Electrode-d of a TH26008A dielectric test fixture was used to test the dielectric properties of the composites within the frequency range from 1 kHz to 1 MHz at room temperature under DC bias from 0 V to 25 V. The dielectric constant can be described as εr =Cd/ε0S, where C is the capacitance, d is the thickness of the material, ε0 is the absolute permittivity of free space and S is the 26 ACS Paragon Plus Environment

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area of the electrode.

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements The authors acknowledge the financial support of this work by National Natural Science Foundation of China (51773187, 51402271), Foundation for Outstanding Young Scientist in Shandong Province (BS2014CL003).

Conflict of Interest The authors declare no conflict of interest.

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Negative Capacitance Field-Effect Transistor. Nano Lett. 2018, 18, 3682−3687.

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Flexible polyimide nanocomposites with DC bias induced excellent

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