Ultralow Electrical Percolation in Graphene ... - ACS Publications

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Ultralow Electrical Percolation in Graphene Aerogel/Epoxy Composites Zhenyu Wang, Xi Shen, Ne Myo Han, Xu Liu, Ying Wu, Wenjing Ye, and Jang-Kyo Kim* Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong S Supporting Information *

ABSTRACT: Graphene aerogels (GAs) with a highly aligned, porous structure are prepared using a novel unidirectional freeze casting method, followed by thermal reduction. The unique graphene orientation in a preferred direction is achieved due to the large temperature gradient generated during freeze casting, in which graphene oxide (GO) sheets are expelled by the rapidly advancing ice front to assemble between the aligned ice crystals. The resulting unidirectional GAs (UGAs) possess ultralow densities, high porosities, and large surface areas, as well as excellent electrical conductivities. The solid UGA/epoxy composites fabricated by vacuum-assisted infiltration of liquid epoxy present an extremely low percolation threshold of 0.007 vol %, which is the lowest value for all graphene/polymer composites reported in the literature. Besides, the anisotropic structure of UGAs gives rise to significant anisotropic electrical conductivities of UGA/epoxy composites, a potentially useful attribute for many important applications. A new analytical model is formulated on the basis of the interparticle distance concept to explain the percolation behaviors of composites with aligned anisotropic nanofillers. The prediction agrees well with experimental data, and the model validates the importance of aspect ratio and orientation state of nanofillers in controlling the percolation threshold of composites.

C

onductive polymer composites have attracted tremendous interests due to their applications in a wide range of technologically important areas, such as electromagnetic interference (EMI) shielding devices, strain/gas sensors, electronic devices, and rechargeable batteries.1−3 Conductive polymer composites are normally made by adding conducting fillers, such as metal powders, carbon black (CB), carbon nanotubes (CNTs), and graphene, into the insulating polymer matrixes to form multiple, interconnected electrical paths or conductive networks.4 As the conducting filler content gradually increases, the composite undergoes an insulator-toconductor transition due to the sharp surge in electrical conductivity by several orders of magnitude, known as a percolation phenomenon.5 Both experimental and theoretical studies have shown that the percolation threshold of a composite depends on the aspect ratio, geometry, and alignment of fillers. With very high aspect ratios and exceptional electron mobility, graphene has been extensively explored to synthesize high performance conductive polymer composites. Much effort has been directed to lower the percolation threshold while improving the electrical conductivities of composites by rationally assembling 2D graphene sheets, e.g., alignment of large, reduced graphene oxide (rGO) sheets6,7 and self-assembly of graphene sheets in the polymer matrix.8 However, their electrical conductivities were far below those expected from the inherent properties of graphene. In view of this, constructing a 3D interconnected, conductive network is seen more efficient than assembling 2D graphene sheets.9 © 2016 American Chemical Society

As an emerging 3D graphene material, graphene aerogel (GA) has attracted tremendous attention for application in various fields, especially as electrodes in electrochemical energy devices.10 The properties of GAs depend strongly on their microstructures. GAs are normally fabricated through the gelation of graphene oxide (GO) dispersion to form graphene hydrogels, followed by freeze-drying or critical point drying.11,12 Although some success of structural control has been demonstrated by utilizing the nematic liquid crystalline phase of GO,13,14 the pore morphologies of these GAs constructed through self-assembly of GO sheets remain largely random. It is an enormous challenge to precisely organize GO sheets into desired 3D architectures due to their size heterogeneity, high flexibility, and random distribution of functional groups.13 More recently, GAs were synthesized by direct freeze-drying of aqueous GO dispersions to form GO aerogels, followed by reduction.15−17 This synthesis process using ice crystals as the sacrificial template provides an ideal platform for the application of the freeze casting technique. As a wet shaping technique, freeze casting involves a few processing steps, including preparing a stable colloidal suspension, pouring the suspension into a mold, freezing the suspension within the mold, and sublimating the dispersing medium.18 Compared to Received: August 2, 2016 Revised: August 24, 2016 Published: August 29, 2016 6731

DOI: 10.1021/acs.chemmater.6b03206 Chem. Mater. 2016, 28, 6731−6741

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Chemistry of Materials the dry processing routes, it is capable of producing materials with complex shapes and structures. Under the optimized freezing temperature and freezing rate, desired morphologies can be constructed by directional growth of the ice crystals.19 Besides, because of the absence of any gelation process, the process can retain the initial volume and uniformity of GO dispersion, producing GAs with ultralow densities and, hence, GA/polymer composites with ultralow graphene contents. Herein, we report the synthesis of unidirectional GAs (UGAs) using a novel unidirectional freeze casting method, followed by thermal reduction. Unlike the GAs made by selfassembly, a tailored microstructure is achieved through a controllable and scalable assembly of the GO sheets. Apart from ultralow densities, excellent electrical conductivities, and large surface areas, the as-prepared UGAs possess an interconnected structure with the majority graphene preferentially aligned in the ice growth direction, giving rise to unique anisotropic electrical properties of UGA/epoxy composites in the orthogonal directions. Benefiting from such a long-range ordered and highly aligned graphene network of UGA, the UGA/epoxy composite presents the lowest percolation thresholds among all graphene/polymer composites. A new analytical model is formulated taking into account the orientation state of conductive fillers to predict the percolation threshold of aligned filler composites, which is verified by experimental results.

Figure 1. (a) Schematic of the apparatus used for unidirectional freeze casting of GO dispersion and the formation mechanism of aligned graphene structure by the vertically advancing ice crystals; (b) digital image of the UGA; (c) the fabrication process of the UGA/epoxy composites.

exhibited a highly anisotropic structure: the side view (Figures 2b,f and S1a,c) presents vertically aligned rGO sheets, while the top view (Figures 2c,g and S1b,d) shows closely packed circular pores. The formation mechanism of the unique aligned structure is described as follows. When the ice crystals grew directionally from the bottom to the top of the cylindrical container whose side wall was surrounded by thermal insulation, the GO sheets were expelled by the ice front and gathered between the oriented ice crystals, forming bundles of GO sheets aligned in the same direction as the ice crystals (see Figure 1a). The degree of alignment and porosity of UGAs depended on the concentration of precursor GO dispersion employed. The UGAs fabricated with GO at a low concentration of 0.5 mg/mL consisted of loosely interconnected rGO sheets with a low degree of orientation and a high porosity due to the insufficient GO sheets (Figure 2b). In contrast, the UGAs prepared using a high GO concentration of 1.0 mg/mL exhibited continuously and highly aligned rGO sheets with closely packed pores. The vertical main skeleton was bridged by ribbon-like, short ligaments in the horizontal direction to form a 3D interconnected, cellular structure (Figure 2i). A possible mechanism for the formation of these ligaments is that some GO sheets are entrapped by the rapidly advancing ice front instead of expulsion during freeze casting, connecting the adjacent aligned sheets. The detailed microstructure of UGAs was further examined using a transmission electron microscope (TEM) as shown in Figure 2d,h. The pore walls of UGAs exhibited a layered structure with rGO sheets oriented in one particular direction, indicating the rGO sheets were assembled in a nearly parallel manner during the unidirectional freeze casting process, similar to the previous study.32 To support the above observations, the degree of alignment of UGAs was quantitatively evaluated on the basis of the orientation distribution analysis of their SEM images (sideview) using the software Image Pro Plus. The orientation distribution analysis has been used to evaluate the size and orientation of fibers and embryonic stem cells,23,24 and this work is the first of its kind reporting its use for the measurements of graphene alignment. The orientation distribution function, N(θ), which specifies the fraction of

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RESULTS AND DISSCUSSION Aligned Graphene Network of UGAs. Materials with aligned hierarchical structures have great potential for a wide range of applications, such as tissue scaffolding,20 microfluidics,21 and growth of nanowires.22 The unidirectional freeze casting technique utilizes a temperature gradient to control the growth of ice crystals and particle ejection directions. It has been employed to fabricate aligned porous structures using polymers, ceramics, and metals as the precursor, with complex pore shapes and component geometries.19 The relatively simple process and easy control to create desired morphologies make it a preferred choice to fabricate an aligned graphene structure rather than using other methods, such as self-alignment7 and forced alignment by electric or magnetic field.4 In this study, liquid nitrogen was chosen to create a large temperature gradient (see Experimental Section) due to its capability to generate a high degree of supercooling in the GO dispersion. The degree of supercooling has a major impact on the morphology of the final product. A high freezing temperature, or a low degree of supercooling, requires a long freezing time for the entire dispersion. Once freezing is initiated, the growth of ice crystals in a specific direction may be disturbed as a result of the possible growth of secondary dendrites and the changing supercooling conditions, hindering the formation of perfectly aligned structure.19 The apparatus employed in this study with a large temperature gradient as illustrated in Figure 1a was the aim to create a strong driving force for unidirectional growth of the ice crystals. Unlike the GAs fabricated by simultaneous reduction and self-assembly of GO sheets,14 the GO aerogels were reduced in the subsequent thermal treatment to obtain UGAs. The two-step reduction process consisting of initial lowtemperature stabilization and final high-temperature treatment in N2 at a moderate ramp rate is considered an ideal means to preserve the aligned, porous structure in the final freestanding UGAs, as shown in Figure 1b. Typical SEM images of the UGAs prepared from different GO concentrations are shown in Figures 2 and S1. The UGAs 6732


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Chemistry of Materials

Figure 2. Filler orientation distributions, the corresponding side view SEM images, top view SEM images, and TEM images of UGAs made from two different GO concentrations of (a−d) 0.5 and (e−i) 1.0 mg/mL; (j) schematic of the aligned porous structure of UGA in (i). Scale bars are 200 μm in (b, c, f, and g), 10 μm in (i), and 2 nm in (d, h).

Figure 3. (a) Raman spectra and (b) XPS C 1s deconvoluted spectra of GO and UGA; (c) nitrogen adsorption/desorption isotherms; (d) pore size distribution curves of UGAs fabricated using 0.5 and 2.0 mg/mL GO dispersions.

rGO sheets within the angular element dθ,25 is plotted as a function of filler orientation, θ: the results shown in Figure 2a,e correspond to the SEM images in Figure 2b,f, respectively. Typically, at least 200 rGO sheets were selected from the SEM images; then, a reference line was drawn on each image, and acute angles formed between the reference line and rGO sheets were recorded. The orientation distribution of rGO sheets ranged from −90° to 90°, where 0° represents perfect alignment. The obtained orientation distribution histograms were then fitted using the GaussAmp peak function, and the details are given in Supporting Information.

It is found that the two different UGAs exhibited similar orientation distributions containing two obvious peaks, namely, a high peak centered at ∼0° representing the rGO sheets orientated along the ice growth direction designated as Group 1 and a low peak centered at ∼±90° representing the rGO bridges in the transverse direction designated as Group 2. The average orientation angle, ⟨cos2 θ⟩, was used here to quantitatively measure the degree of alignment of the rGO sheets in UGA, as defined in the Supporting Information. The average orientation angle concept has been widely used to describe the orientation distribution of fillers in composite.5 ⟨cos2 θ⟩ = 0 signifies that all the elements are perpendicular to 6733


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Figure 4. (a) Electrical conductivities measured in the orthogonal directions with a log plot in inset and densities of UGAs plotted as a function of GO concentration; (b) DC electrical conductivities of UGA/epoxy composites in the alignment direction and transverse to it. The inset shows a log−log plot of the conductivity as a function of (ρ−ρc); (c) frequency dependent AC conductivities of UGA/epoxy composites in the alignment direction; (d) polarized Raman spectra for composites containing 0.16 vol % graphene.

the preferred orientation, ⟨cos2 θ⟩ = 1/3 corresponds to 3D random distribution of fillers, whereas ⟨cos2 θ⟩ = 1 corresponds to all elements aligned along the preferred direction. Here, we defined ⟨cos2 θ1⟩ and ⟨cos2 θ2⟩ as the orientation angles of Groups 1 and 2, respectively. To calculate ⟨cos2 θ1⟩ and ⟨cos2 θ2⟩, the two peaks in Figure 2a,e were normalized using eq S4, and the resultant peaks were integrated using eq S3. It can be seen from Figure 2a,e that the UGAs made from the GO concentrations of 0.5 and 1.0 mg/mL presented slightly different ⟨cos2 θ1⟩ values of 0.78 and 0.87, respectively, both with a high degree of rGO alignment toward 0° (i.e., ice growth direction). The marginal difference in ⟨cos2 θ1⟩ reflects the amount of rGO sheets involved in the formation of the main skeleton in the alignment direction. However, the UGAs made from the two GO concentrations presented an identical ⟨cos2 θ2⟩ of 0.04, indicating similar small amounts of rGO sheets bridged along the 90° direction. In summary, the UGAs had a 3D interconnected structure which consisted of both the great majority of vertically aligned rGO sheets with tubular pores oriented along the freezing direction and a small amount of rGO ribbons bridging the vertical alignments, as illustrated in Figure 2j. Chemical Attributes and Physical Properties of UGAs. To characterize the efficiency of the thermal reduction process, the chemical attributes of GO and UGA were analyzed by Raman and X-ray photoelectron spectroscopy (XPS). The Raman G-band is active in sp2-hybridized carbon-based materials, while the D-band is activated when the defects participate in the double resonance Raman scattering near the K point of the Brillouin zone. Thus, the D- to G-band peak intensity ratios, ID/IG, are often used to estimate the sp2 domain size of carbon.26 After the thermal reduction at 900 °C, the ID/ IG ratio decreased from 2.53 to 1.73 (Figure 3a) as a consequence of the elimination of oxygenated functional groups from the GO sheets and the recovery of the sp2 conjugated carbon. It is also worth noting that the G-band peak was down-shifted from 1593 to 1586, verifying the recovery of the hexagonal carbon atoms. The XPS C 1s

deconvoluted spectra of GO and UGA (Figure 3b) further confirmed the reduction of GO. The binding energies of the C−C and −C−OH bonds in GO are centered at ∼284.8 and ∼286.9 eV, respectively, whereas three minor components arising from C−H, −CO, and −COOH functional groups are centered at 285.3, 287.7, and 289.0 eV, respectively. Due to the large chemical shift into the −CO emission, the C−O−C group is assigned with −CO at 287.7 eV. After the reduction, the vast majority of −C−OH and CO/C−O−C functional groups were eliminated. Consequently, the C/O atomic ratio surged from 2.2 to 37.5, confirming the efficiency of the reduction process used in this work. The specific surface area and pore volume of UGAs were evaluated on the basis of the nitrogen adsorption/desorption measurement. The nitrogen adsorption/desorption isotherm of UGA fabricated using 0.5 mg/mL GO (UGA−0.5) presented a typical type II characteristic, indicating a nonporous/macroporous structure, while that of UGA fabricated using 2.0 mg/mL GO (UGA−2.0) followed the type IV characteristic with a mesoporous structure (Figure 3c).27 The pore size distributions (Figure 3d) indicate the majority of pores varying in the range of 2−20 nm for both the UGAs. Both the surface area and pore volume of UGA−2.0 were much larger than those of UGA−0.5, i.e., 432 vs 133 m2/g and 2.33 vs 0.68 cm3/g, respectively, indicating negligible restacking of GO sheets even at the high GO concentration. The reduced, 3D interconnected graphene network imparted the freestanding UGAs with excellent electrical conductivities, as shown in Figure 4a, where the conductivities measured in the two orthogonal directions are plotted as a function of GO concentration. The UGAs delivered outstanding conductivities as high as 17 S/m in the alignment direction, indicating effective thermal reduction of GO sheets. The electrical conductivities in both directions increased with increasing GO concentration due to the formation of progressively denser conductive networks as confirmed by the functionally similar increasing trend of densities of UGAs. The lowest density obtained in this study was ∼0.23 mg/cm3, corresponding to 0.2 mg/mL in GO concentration. This value, to the best of authors’ 6734


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Chemistry of Materials Table 1. Comparison of Physical Properties of GAs Produced by Different Approaches aerogel density (mg/cm3)

electrical conductivity (S/m)

conductivity per density (S·cm2/mg)

hydrothermal improved hydrothermal freeze casting self-assembly using EDAa self-assembly using LAAb freeze casting unidirectional freeze casting

20 12.32 6.0 3.0 12−96 5.1 2.0

0.4 1.76 4.3 2.5 100 12 10

2 × 10−4 1.43 × 10−3 7.17 × 10−3 8.33 × 10−3 0.01−0.08 0.02 0.05

self-assembly and reduction at 2400 °C

7.0

40

0.057

method

a

specific surface area (m2/g) 370 310−490

512 432

ref 28 29 14 30 31 32 current study 33

EDA = ethylenediamine. bLAA = L-ascorbic acid.

Table 2. Comparison of Percolation Thresholds of Polymer-Based Nanocomposites with Different Nanocarbon Fillers filler

polymer

processing method

MWCNT MWCNT MWCNT MWCNT

HNBRa epoxy UHMWPEb epoxy

MWCNT

epoxy

two roll milling sonication mechanical mixing UV−ozone treatment and sonication shear-intensive mechanical stirring

CB CB/MWCNT

PEc epoxy

shear mixing shear mixing

CB/MWCNT

epoxy

shear mixing

MWCNT/GO

PPd

mechanical mixing

MWCNT/GNP

epoxy

simultaneous magnetic agitation and sonication

rGO pristine graphene GF graphene-RF cryogel UGA

epoxy epoxy epoxy epoxy

in situ polymerization freeze-drying + mixing CVD + vacuum infiltration sol-gel + infusion

epoxy

freeze casting + vacuum infiltration

a

aspect ratio of filler

percolation threshold (vol %)

CNT 30−50 500 100−1000 80−160

0.65 0.06 0.04 0.0031

2 × 10−8 10−6 10−6 2 × 10−6

41 39 42 43

0.0016

10−4

40

∼10 0.009 CB and 0.01 MWCNT

∼10−4 10−6

38 49

0.12 CB and 0.13 CNT

3 × 10−5

47

0.38 CNT and 0.11 GO

10−8

50

0.32 CNT and 0.06 GNP

2 × 10−4

48

0.12 0.088 0.028 0.012

10−5 10−6 102 10−7

45 46 9 51

0.007

10−2

current study

2904−5926 CB and Hybrid ∼1 CB: ∼1 CNT: 670 CB: ∼1 CNT: 500 CNT: 200 GNP: ∼3000 CNT: >77 GNP: 4000−5000 Graphene/rGO ∼15 000

∼16 000

conductivity near percolation (S/m)

ref

HNBR = hydrogenated butadiene-acrylonitrile. bUHMWPE = ultrahigh molecular weight polyethylene. cPE = polyethylene. dPP = polypropylene.

effectiveness of the current thermal reduction and the 3D conductive architecture with most rGO sheets aligned in one particular direction. This would make the UGAs an ideal filler for fabricating composites with fascinating functional properties at very low filler contents and low masses. Electrical Properties of UGA/Epoxy Composites. One of the major benefits of using 3D graphene structures, like UGAs, in preparing composites is to create an interconnected freestanding scaffold before infiltrating liquid polymers, thus completely eliminating the issue of uniform dispersion of GO sheets while maintaining conductive networks within the polymer matrix.14 The polymer composites prepared using 3D graphene fillers have shown superior electrical properties to those made from dispersed 2D graphene sheets, such as graphene nanoplatelets (GNPs) and rGO.9,14,34 The inherently interconnected network structure also means markedly reduced percolation thresholds of the composites. The direct-current (DC) electrical conductivities of UGA/epoxy composites

knowledge, is the lowest density among the GAs reported in the open literature. The anisotropic structure of UGA was clearly manifested by the disparity in conductivity between the two orthogonal directions,7 showing over an order of magnitude difference at graphene contents higher than 0.05 vol %. The excellent physical properties of UGAs presented in Figures 3 and 4 are compared with those of GAs reported in the literature as shown in Table 1. The electrical conductivity per density was used as a simultaneous measure of both the lightness and conductivity of GAs. Compared with other GAs, the current UGAs presented an extremely low density and a relatively high electrical conductivity, together with a very large specific surface area. The conductivity per density value of UGAs was almost an order of magnitude higher than that of GAs with randomly distributed rGO sheets made by normal freeze casting14 and even comparable with that of the GAs reduced at 2400 °C under high vacuum,33 confirming the 6735


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CNTs in the epoxy matrix.40 The percolation threshold of GNP/epoxy composites, however, was rather disappointing with a high value of 1.7 vol % even with an improved dispersion state using a single mixing step called the “room temperature ionic liquid” (RTIL) method.44 Aided by the highly aligned and uniformly dispersed rGO sheets with extremely high aspect ratio of ∼15 000, the rGO/epoxy composites produced by in situ polymerization delivered much enhanced electrical properties.45 To further lower the percolation threshold of the composites, a versatile freeze-drying/mixing method has been devised to uniformly disperse pristine graphene in the polymer matrix, achieving an impressive threshold of 0.088 vol %.46 In order to achieve synergetic effects and form more efficient conducting networks, much effort has been made to prepare composites containing hybrid fillers.47−50 For instance, a low percolation threshold was achieved by hybridizing 0.12 vol % CB with 0.13 vol % MWCNTs, which is lower than the single filler composites containing CB (0.36 vol %) or MWCNTs (0.2 vol %) acting alone.47 Similarly, a percolation threshold was realized by combining 0.32 vol % CNTs and 0.06 vol % GNPs, instead of single filler composites containing MWCNTs (0.56 vol %) or GNPs (0.48 vol %).48 The performance of 3D graphene/epoxy composites was always much better than their 2D graphene counterparts. For example, the graphene foam (GF)/epoxy composites exhibited a low percolation threshold of 0.028 vol % due to the 3D cellular, interconnected graphene network grown by CVD. A much lower threshold of 0.012 vol % was obtained by 3D interconnected graphene/resorcinol-formaldehyde (RF) cryogel as the filler,51 but the electrical conductivity measured near the transition was only on the order of 10−7 S/m. The UGA/ epoxy composites prepared in this study delivered an ultralow percolation threshold of 0.007 vol % as well as a high electrical conductivity of 10−3 S/m near the threshold. The above comparison manifests unique advantages arising from the 3D interconnected UGAs as effective reinforcements for conductive composites. (i) Constructing the prepercolated UGA network is a more efficient option to utilize conductive fillers than directly dispersing GO/rGO sheets into a polymer matrix. (ii) 3D interconnected UGAs with abundant internal pores are more uniformly and efficiently reduced by thermal treatment than individual 2D GO sheets/papers or the composites containing them. The effectively reduced graphene network imparts the low-density UGAs with high conductivities and thus an ultralow percolation to the composite. (iii) The current UGA/epoxy composites exhibited a lower percolation threshold than the other 3D graphene/polymer composites, even though some of these 3D graphenes, like GF and graphene-RF cryogel, were constructed by a 100% sp2 graphitic carbon network, confirming the unique advantage of using UGAs with a long-range ordered and highly aligned graphene network. The excellent electrical conductivities of the composites at such low graphene contents resulted from the synergy between the ameliorating geometric and physical features of UGAs. They include the preferential alignment of large-size graphene sheets by unidirectional freeze casting, the ultralow density of interconnected structure with a myriad of pores, and effective reduction of GO by thermal treatment. In particular, the large GO sheets used in this study played an important role; see Figure S2 for the sizes of GO sheets. It was demonstrated previously26,52 that large-size graphene sheets gave rise to a positive impact on electrical conductivities of graphene thin films and papers, due to the lower intersheet contact resistance

prepared using a vacuum-assisted infiltration method (Figure 1c) are plotted as a function of graphene content along the two orthogonal directions as shown in Figure 4b. The conductivity of neat epoxy was ∼10−10 S/m, which is consistent with the reported values.9 With the addition of only 0.01 vol % (∼0.019 wt %) graphene, a remarkable ∼8 orders of magnitude increase in conductivity was demonstrated. Similar to the freestanding UGAs (Figure 4a), the conductivities of composites increased with increasing graphene content and became almost saturated at graphene contents above 0.09 vol %. The highest conductivity achieved was 12 S/m at a graphene content of 0.16 vol % (or 0.29 wt %), which is considered to be sufficient for many practical applications. The percolation threshold of the composites, ρc, was calculated on the basis of the power law equation:35 ϕc = ϕf (ρ − ρc )n

(1)

where ϕc is the conductivity of composite, ϕf is the conductivity of filler, ρ is the filler content, and n is the critical exponent. The inset of Figure 4b shows a log−log plot of the conductivity as a function of (ρ−ρc), giving the percolation threshold of ρc = 0.007 vol % or 0.013 wt % in the alignment direction. To the best of the authors’ knowledge, this value is among the lowest for all graphene/polymer composites reported in the open literature. According to the classical percolation theory, the critical exponent, n, reflects the dimensionality of the system and follows a typical value of 1−1.3 and 1.6−2.0 for 2D and 3D systems, respectively.36 n ≈ 1.7 was estimated using the data in Figure 3b, signifying the presence of a 3D conductive network. The frequency-dependent alternating-current (AC) conductivities of UGA/epoxy composites (Figure 4c) confirmed the foregoing discussion on percolation threshold. For the graphene contents below the percolation threshold (i.e., 0.002 vol %), the composites displayed a typical dielectric behavior and the AC conductivity increased almost linearly with frequency. Above the percolation threshold, the AC conductivity remained constant, indicating an effective connection of the conducting networks in the composites. Thus, the percolation threshold prevails between 0.002 and 0.01 vol %, consistent with the DC conductivity measurements. To signify the above finding of UGAs as an effective nanofiller for conductive composites, the percolation thresholds of polymer-based composites with different nanostructured carbon fillers, including CB, multiwalled CNTs (MWCNTs), and graphene of various forms, as well as their hybrids, are compared with the present study, as shown in Table 2. These percolation thresholds were chosen as the representative values among the lowest from a myriad of similar reports, and the original wt % was converted to equivalent vol % by assuming the densities of CB, MWCNT, and graphene being 2.0, 1.8, and 2.2 g/cm3, respectively.37 As expected, CB/epoxy composites showed a high percolation threshold value of ∼10 vol %,38 due to the very low aspect ratio of the spherical CB particles, requiring a very high filler content to form a conducting network. For CNT/epoxy composites, the percolation thresholds varied significantly depending on the type of CNTs employed and the processing condition used to prepare the composites.39 There was no apparent consensus, and the percolation thresholds fluctuated from ∼0.001 vol % to over 0.1 vol %.39−43 An ultralow value of 0.0016 vol % was achieved for MWCNT/epoxy composites using chemical vapor deposition (CVD)-grown aligned CNTs and a shear-intensive process to maintain the uniform dispersion and the high aspect ratio of 6736


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Figure 5. (a) Schematic drawing of the new IPD model for UGA/epoxy composites containing two different groups of graphene sheets; (b) effect of DIP on percolation threshold for a constant D/t = 16 000, assuming all the fillers in Group 1 perfectly align along the z-axis while the fillers in Group 2 align perpendicular to the z-axis (⟨cos2 θ1⟩ = 1, ⟨cos2 θ2⟩ = 0) and the effects of average orientation angles, ⟨cos2 θ1⟩ and ⟨cos2 θ2⟩, on percolation threshold of UGA/epoxy composites with different volume ratios of fillers in two groups, (c) V1/V2 = 1 and (d) V1/V2 = 10.

as shown in the Supporting Information. R for the composites containing 2D disk-shaped fillers, such as graphene, is defined as

than smaller ones. The UGAs prepared in this study were thus expected to have more efficient conductive networks constructed by the large graphene sheets with resulting excellent conductivities of the composites. In addition, the large graphene sheets were able to form an interconnection with each other even in a dilute dispersion, making them much easier to form a freestanding aerogel structure with an ultralow density.53 Therefore, much fewer graphene sheets are required to assemble an interconnected conductive path in the composites, leading to the ultralow percolation threshold. It is also worth noting that the conductivity was higher in the alignment direction than that perpendicular to it. The anisotropic electrical conductivities in the two orthogonal directions arose from the anisotropic UGA structure as confirmed by the polarized Raman spectra (Figure 4d). The intensities of the Raman G- and D-bands of the composites containing 0.16 vol % graphene were ∼56% higher in the alignment direction than that transverse to it. This observation indicates that there was higher resonance in the alignment direction, confirming significant alignment of graphene sheets in the composites.14,45 Prediction of Percolation Threshold. 1. New Interparticle Distance Model. On the basis of the average interparticle distance (IPD) theory,5,39,54 a new analytical model was developed to predict the percolation threshold of conductive composites containing aligned reinforcements. According to the IPD approach, the volume fraction, Vc, required for a single type of fillers to form conductive networks is given by5,39,54 Vc =

π ⎛⎜ 1 ⎞⎟ 4⎝R⎠

R=

(D + DIP)3 ⟨cos2θ ⟩3 D2 t

(3)

where t and D are the thickness and diameter of disk-shape fillers, respectively, and DIP is the interparticle distance; DIP is assumed to be ∼10 nm when electron hopping happens.5 Figure 5a gives the schematic drawing of the new IPD model for UGA/epoxy composites containing two different groups of graphene sheets. In the conventional IPD approach, the composite is divided into cubic elements, each containing one filler in the center, and the total number of elements is equal to the total number of fillers. Similar to the system with a single type of cubic element, the percolation may occur in a system containing two different groups of fillers when its unit volume consists of two groups of cubic cells. Therefore, the percolation factor for the current UGA/epoxy composites containing two groups of graphene is given in the Supporting Information: R=

V1 R V2 1

+ R2

1+

V1 V2

(4)

where R1 and R2 are the percolation factors of Groups 1 and 2 and V1 and V2 are their volume fractions in the composite, respectively. By combining eqs 3 and 4, we have

(2)

R=

where R is defined as the “percolation factor” that measures the shape, size, and the orientation state of fillers in the composites, 6737

V1 (D1 + DIP)3 ⟨cos2θ1⟩3 V2 D12t1

+

1+

(D2 + DIP)3 ⟨cos2θ2⟩3

V1 V2

D2 2t 2

(5) DOI: 10.1021/acs.chemmater.6b03206 Chem. Mater. 2016, 28, 6731−6741

Article


Apart from the filler volume ratio and the orientation angles, another important filler parameter is the aspect ratio, D/t, to which the percolation ratio is inversely proportional. The above observations signify that the percolation threshold of composites can be reduced by optimizing the orientation state of 3D nanocarbon structures. Although a high degree of alignment is always desired, a certain amount of bridging ligaments is required in the transverse direction to maintain a stable 3D bulk structure even after the liquid polymer is infiltrated to fabricate composites. 3. Comparison between Theory and Experiments. To predict the percolation threshold of the current UGA/epoxy composites, the filler materials and geometric parameters, including the aspect ratio, mean orientation angles, and V1/V2, need to be known. The aspect ratio of fillers can be determined using techniques, such as SEM, TEM, and particle size analysis.5 The mean orientation angles and V1/V2 were determined on the basis of the orientation distribution analysis of graphene sheets, as discussed in Figure 2a,e. Because both the fillers in Groups 1 and 2 in the UGA/epoxy composites are the identical graphene sheets, their volume fractions, V1 and V2, are proportional to the number of fillers in the respective groups, N1 and N2. Therefore, V1/V2 was considered identical to N1/N2. The percolation factors thereby determined and the predicted percolation thresholds, Vc, are given in Table S2. Vc of the UGA/epoxy composites ranged from 0.0089 to 0.0129, which in general agreed well with the experimental result of 0.007 vol % although the prediction tended to be marginally higher. To further verify the applicability of the new model, the percolation thresholds of the composites containing single or hybrid carbon fillers with various orientation distributions are compared with the prediction as shown in Figure 6. The filler

where t1 and t2 D1 and D2 are the thicknesses and diameters of the fillers in Groups 1 and 2, respectively. Because both the fillers in Groups 1 and 2 in the UGA/epoxy composites are the identical graphene sheets, t1 = t2 = t and D1 = D2 = D. eq 5 is now simplified to R=

(D + DIP)3

V1 ⟨cos2θ1⟩3 V2

D2 t

+ ⟨cos2θ2⟩3

1+

V1 V2

(6)

Therefore, the corresponding percolation threshold, Vc, can be obtained by combining eqs 2 and 6: πD 2 t Vc = 4(D + DIP)3

1+ V1 ⟨cos2θ1⟩3 V2

V1 V2

+ ⟨cos2θ2⟩3

(7)

It is seen from eq 7 that the percolation threshold of UGA/ epoxy composites depends on several important materials and geometric parameters, including DIP, the aspect ratio, D/t, the ratio of volume fraction, V1/V2, and the average orientation angles, ⟨cos2 θ1⟩ and ⟨cos2 θ2⟩, of the fillers in Groups 1 and 2. The detailed derivation process of the new IPD model can be found in the Supporting Information. 2. Parametric Study. Parametric studies were conducted to evaluate the effects of the above materials and geometric parameters, including DIP, D/t, V1/V2, and ⟨cos2 θ1⟩ and ⟨cos2 θ2⟩, of fillers on the percolation threshold of the UGA/epoxy composites. Z-axis was chosen as the preferred orientation and an aspect ratio, D/t ∼ 16 000 (Figure S2), was used in all cases. Because ⟨cos2 θ1⟩, V1, and ⟨cos2 θ2⟩, V2 are interchangeable, Group 1 was assumed to have a higher volume fraction than Group 2, i.e., V1/V2 ≥ 1, to avoid redundant calculation. Figure 5b shows the effect of DIP on percolation threshold for DIP ranging from 1 to 104 and V1/V2 varying from 1 to 10. It was assumed that all the fillers in Group 1 perfectly aligned in the zaxis while the fillers in Group 2 aligned perpendicular to the zaxis, i.e., ⟨cos2 θ1⟩ = 1 and ⟨cos2 θ2⟩ = 0. It is shown that the percolation threshold increased with increasing V1/V2. When DIP was equal to or less than 10 nm, the percolation threshold remained almost a constant for a given V1/V2 but sharply dropped with further increasing DIP, confirming the applicability of the current IPD concept with an adopted DIP of 10 nm. Figure 5c,d presents the percolation thresholds calculated for ⟨cos2 θ1⟩ and ⟨cos2 θ2⟩ varying simultaneously. Points A−D are the terminal vertexes of the surface. It is seen that, for V1/V2 = 1, the percolation threshold rapidly reduced from Point C (infinity) to Point A (4.91 × 10−3 vol %) when both ⟨cos2 θ1⟩ and ⟨cos2 θ2⟩ were increased simultaneously from 0 to 1 (Figure 5c). In this case, the lowest percolation threshold can be maintained if both the orientation parameters were kept close to the unity. This means that they are equally important in determining the percolation threshold. When V1/V2 was increased to 10, similar to the UGAs developed in this study, the percolation thresholds exhibited similar declines from Point C (infinity) to Point A (4.91 × 10−3 vol %) with the same lowest percolation values when ⟨cos2 θ1⟩ was increased from 0 to 1 (Figure 5d). In this case, the orientation angle of the major filler group, ⟨cos2 θ1⟩, became increasingly predominant in determining the percolation threshold while ⟨cos2 θ2⟩ of the minor filler group was less important. To achieve an ultralow percolation threshold on the order of 10−3 vol %, ⟨cos2 θ1⟩ should be larger than 0.8 for a high V1/V2, according to eq 7.

Figure 6. Comparison of theoretical prediction with experimental results for composites containing single and hybrid nanocarbon fillers. Experimental data: current study: red ☆; carbon black: ⊙;38 graphene: blue ▽,55 blue △,56 blue ○,45 and blue ◇;57 CNT: green ▼,39 green ▲,43 green ●,41 green ◆,36 and green ■;42 hybrid: orange ◓,49 orange ◐,50 orange ◨,48 orange ◭,58 and orange ◮;47 prediction (red ).

properties, including D/t, V1/V2, and ⟨cos2 θ⟩ obtained from the corresponding reports and the percolation factor, R, as well as the percolation thresholds calculated on the basis of the IPD model are listed with the experimental results in Table S3. It is worth noting the prediction agreed well with the experimental data for composites containing 16 different nanocarbon fillers. There is an inverse relationship between R and percolation threshold. Due to the very low aspect ratio of 0D fillers, CB6738


Article

Chemistry of Materials based composites possess much higher percolation threshold than those containing graphene and CNTs. Graphene-based composites exhibited a generally lower R value and a higher percolation threshold than CNT-based composites because the 1D CNTs make them easier to form percolating networks than 2D graphene sheets and dispersing long CNTs appears to be much easier than synthesizing large-size graphene sheets for maintaining a large aspect ratio. It is also interesting to note that, although many studies claimed lower percolation thresholds with aligned fillers,41,43,57 the results here showed only a marginal difference (see the data points blue ◇, green ▲, and green ● in Figure 6). The less prominent effect of alignment on percolation stemmed likely from inevitable bundling, stacking, or agglomeration of individual fillers, as well as potential damages by wrinkling, bending, and fragmentation during the dispersion and alignment processes, effectively reducing their aspect ratios. In the current study, however, the in situ alignment by the advancing ice crystals could minimize the aforementioned issues to maintain large aspect ratios of graphene sheets in the final UGAs. Therefore, the percolation threshold achieved here was almost 2 orders of magnitude lower than the majority of graphene-based composites, and there was an expected perfect agreement between the theory and the experiment. It can be said that the above comparison sensibly confirmed the validity of the new analytical model for establishing a relationship between the percolation factor and the percolation threshold taking into account various materials and geometric parameters of fillers.

property: the conductivities measured parallel to the alignment direction were progressively higher than those measured transverse to it. The anisotropic electrical properties of UGA/epoxy composites have great potential for novel applications, such as field emission devices and electronic sensors.59 (v) A new analytical model was proposed on the basis of the IPD concept to predict the percolation threshold of composites containing highly aligned graphene sheets. It is demonstrated that the model could predict the percolation thresholds of composites containing single and hybrid nanocarbon fillers, including CB, CNTs, graphene, and the current UGAs, with various aspect ratios and orientation states. The prediction in general agreed well with the experimental results.

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EXPERIMENTAL SECTION

Fabrication of UGA and UGA/Epoxy Composites. Monolayer GO sheets with a mean area of ∼202 μm2 were exfoliated and dispersed in an aqueous solution from natural graphite flakes (supplied by Asbury Graphite Mills) using the modified Hummers method following our previous studies.14,60 UGAs were prepared by unidirectional freeze casting of GO dispersions using a custom-made apparatus illustrated in Figure 1a. Briefly, GO dispersions with concentrations ranging from 0.2 to 3.0 mg/mL were poured into a PP cylindrical container with an aluminum bottom which allowed effective thermal conduction between the GO dispersion and the underneath liquid nitrogen. The cylindrical container was tightly wrapped with thermally insulating styrofoam and placed on top of a metal scaffold, which in turn rested in a pool of liquid nitrogen. A large temperature gradient was developed between the bottom (−196 °C) and the top surface (room temperature (RT)) of GO dispersion, enforcing the vertical growth of ice crystals. The freeze cast GO dispersion was subsequently freeze-dried (SuperModulyo, Thermo Fisher) for 48 h to form a GO aerogel with an aligned porous structure. The GO aerogel was reduced to form UGA, as shown in Figure 1b, by stabilization in air at 200 °C for 2 h, followed by a treatment at 900 °C in a dry N2 environment for 2 h at a constant heating rate of 5 °C/min. Composites were prepared by direct infiltration of liquid epoxy resin into the pores of UGA under vacuum, followed by curing, as illustrated in Figure 1c. The epoxy resin (LY1556, supplied by Huntsman Advanced Materials) was diluted with acetone at 10 wt % of epoxy, and curing agent, triethylenetetramine, was added at a ratio of 12 wt % of epoxy, according to the specification. The mixture was then placed in a vacuum oven at RT for 2 h to allow evaporation of acetone, followed by heating to 60 °C for 30 min to reduce the viscosity of epoxy. UGA was slowly immersed into the epoxy/curing agent mixture which was degassed in vacuum at 60 °C for 1 h for full infiltration. The resin-infiltrated UGA was cured at 80 °C for 30 min and postcured at 110 °C for 2 h to produce a solid composite. It should be noted that 0.01 vol %, or an equivalent GO dispersion of 0.2 mg/mL, was the lowest graphene content that could form a stable, freestanding UGA in this study. Although we were able to prepare a composite with a graphene content of 0.002 vol % by vacuum infiltration of resin, the GAs prepared using such a low GO content were not able to sustain a stable 3D structure but rather easily collapsed during infiltration. Characterization. The morphologies and structures of UGAs were examined on a scanning electron microscope (SEM, JEOL 6390F) using the secondary electron beams at an acceleration voltage of 20 kV and field emission transmission electron microscopy (TEM, 2010, JEOL). The Raman spectroscopy (Reinshaw MicroRaman/Photoluminescence System) was used to characterize the degree of reduction of UGAs and the anisotropic nature of the composite. He−Ne laser with a wavelength of 632.8 nm was used in all experiments. The XPS (Axis Ultra DLD) was used to study the elemental compositions and the assignments of the carbon peaks of

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CONCLUSION Highly aligned UGAs having ultralow densities, high porosities, and large surface areas were synthesized using a unidirectional freeze casting method, followed by thermal reduction. These UGAs were infiltrated by liquid epoxy resin under vacuum to in situ fabricate solid UGA/epoxy composites. The composites delivered ultralow percolation thresholds with significant anisotropic electrical properties in two in-plane perpendicular directions. A new IPD model was formulated to predict the percolation thresholds of composites containing highly aligned conducting nanofillers like UGAs. The following can be highlighted from the experimental and theoretical studies: (i) The UGAs consisted of highly oriented large graphene sheets along the vertical direction which were bridged by ribbon-like graphene sheets in the transverse direction. The unique aligned graphene structure was formed due to the advancing ice crystals driven by a large temperature gradient between the top and bottom surfaces of GO dispersion in the unidirectional freeze casting process. (ii) The highly porous structure of UGAs obtained after thermal reduction gave rise to an ultralow density of 0.23 mg/cm3 and a large surface area of 432 m2/g, as well as a high electrical conductivity of 17 S/m. (iii) The UGA/epoxy composites exhibited an excellent electrical conductivity as high as 12 S/m, as well as an ultralow percolation threshold of 0.007 vol %, thanks to the highly aligned graphene structure with an aspect ratio of ∼16 000. This value is considered among the lowest thresholds for all graphene/polymer composites reported in the open literature. (iv) The anisotropic structure of UGAs imparted the corresponding composites with an anisotropic electrical 6739


Article

Chemistry of Materials GO and UGA. The nitrogen adsorption/desorption isotherms were obtained at 77 K on an automated adsorption device (Coulter SA3100 instrument) to measure the surface areas based on the Brunauer− Emmett−Teller (BET) method. The DC electrical conductivities of UGAs and their composites were measured using the four-point probe method (Scientific Equipment & Services). The DC electrical conductivities were confirmed by measuring the AC conductivities using an impedance/gain-phase analyzer (Hewlett-Packard 4149A) in the frequency ranging from 100 to 106 Hz.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b03206. Orientation distribution analysis of the UGAs; morphologies of UGAs; the GO size distribution; derivation process of the new IPD model; the comparison of the percolation thresholds between the model and experiments (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The project was supported by the Research Grants Council (GRF Projects: 61203415 and 12168119) of Hong Kong SAR. Z.W. and X.S. were recipients of the Hong Kong Ph.D. Fellowship. Technical assistance from the Materials Characterization and Preparation Facilities (MCPF), Advanced Engineering Materials Facilities (AEMF), and the Department of Chemical and Biomolecular Engineering at HKUST is appreciated.

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REFERENCES

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