Conductive network formation in bacterial cellulose-based nanocomposite aerogels

Composites Part B 174 (2019) 106981

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Conductive network formation in bacterial cellulose-based nanocomposite aerogels Hadi Hosseini a, Mehrdad Kokabi a, *, Seyyed Mohammad Mousavi b a b

Department of Polymer Engineering, Faculty of Chemical Engineering, Tarbiat Modares University, P.O. Box 14115-114, Tehran, Islamic Republic of Iran Department of Biotechnology, Faculty of Chemical Engineering, Tarbiat Modares University, P.O. Box 14115-114, Tehran, Islamic Republic of Iran

A R T I C L E I N F O

A B S T R A C T

Keywords: Nano-structures Porosity Computational modeling Fractal dimension

In this work, the network formation of reduced graphene oxide (rGO) in comparison with multiwall carbon nanotubes (MWCNTs) in the in-situ biosynthesized bacterial cellulose (BC) matrix-based nanocomposite aerogels was investigated. A modified model was proposed for predicting the overall broadband dielectric properties (AC conductivity and dielectric permittivity) of BC-based nanocomposite aerogels that had a good agreement with experimental data. Broadband dielectric properties indicated higher percolation values for both BC/MWCNTs (0.7 wt%) and BC/rGO (0.9 wt%) nanocomposite aerogels in comparison to Dynamic mechanical thermal analysis (DMTA) findings. Fractal dimensions of 2.6 and 1.86 were obtained for rGO and MWCNTs networks, respectively.

1. Introduction Aerogels as highly porous materials have attracted significant attention to be employed in the high temperature insulating and acoustic materials [1]. However, the low mechanical strength and fragility, specifically in the mineral aerogels, hinder their applications wherein the flexibility is required such as strain sensors or energy storage devices. Therefore, the reinforcement of the aerogel structure is immensely challenging. In this regard, the utilization of a flexible matrix as well as the incorporation of promising nanofillers including nano­ tubes and nanoplatelets with high aspect ratio, considerably enhance or even eliminate the aforementioned limitations. Accordingly, BC as a renewable and natural biodegradable polymer, due to its unique fea­ tures such as interconnected three dimensional nanofibrous and porous network associated with the desired flexibility and high modulus, is a favorable candidate to support different nanostructures [2]. It has been reported that the pivotal problem on the fabrication of BC-based nanocomposites is how to integrate and distribute the various nanofillers in BC frameworks. However, the addition of MWCNTs or rGO into BC structure via filtration or immersing method is challenging owing to the lack of homogeneous dispersion of nanofillers in pristine BC [3]. To tackle this, the in-situ biosynthesis approach was proposed in which the hybridization of BC and nanofillers achieved simultaneously with growth and synthesis of BC. This method possessed the

advantageous of the facility, versatility, cost-effectively and eco-friendly as well as preserving BC three-dimensional nanostructure. There are some researches devote to the in-situ biosynthesis of BC in the presence of MWCNTs or graphene oxide (GO). Most of the work in the literature has focused on the characterization of resultant nanocomposites. The fabrication of BC in the presence of graphene and its characterization by Luo et al. [4], Si et al. [6] and Kiziltas et al. [5] have been reported. In addition, evaluating of the GO reduction in the culture medium of BC [6] along with an assessment of cytotoxicity test [7] or utilization as a free-standing film for monitoring of the cellular response [8] were car­ ried out. Moreover, the integration of MWCNTs into the BC culture medium and characterization of fabricated nanocomposites [9–11] or their application as scaffolds for bone regeneration [12] and enzymatic biofuel cell [13] were expressed. In the light of literature, there is a dearth of study about dielectric properties, comparison of CNT and GO network structure and differ­ ences of fractal dimensions for both of them, creating a percolated network in BC aerogel framework. Fractal geometry originates from random displacements of fillers associated with their aggregating diffusion. It is a statistical process that has been extensively discussed by Kluppel et al. [14–16] for carbon back based composites. They well found that the fractal dimensions of carbon black as spherical fillers was 2.8 [14]. However, the fractal dimension analysis of formed network for carbon nanotubes and graphene sheets have not been described else­ where. The using of fractal dimension is a favorable tool for evaluating

* Corresponding author. E-mail address: [email protected] (M. Kokabi). https://doi.org/10.1016/j.compositesb.2019.106981 Received 3 February 2019; Received in revised form 26 May 2019; Accepted 27 May 2019 Available online 31 May 2019 1359-8368/© 2019 Elsevier Ltd. All rights reserved.

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Nomenclature Aspect ratio Eshelby tensor Electrical conductivity Complex electrical conductivity Real part of complex conductivity Imaginary part of complex conductivity Conductivity tensor Scattered tensor Volume concentration Electrical conductivity of interface Thickness of rGO nanosheets Diameter of MWCNT Scale parameter Cauchy’s cumulative probabilistic function

α S

σ *σ ‘(ω)σ “σ (ω) L T φ

σint t r λ F

C

σ (ω) τσ τε σc εc R dw θ

percolated networks. It is the first report about dielectric properties in terms of modeling and experimental associated with network formation in details for nanocomposite aerogels.

the kinetics of the formed network the. The network formation has great importance in aspects related to the reinforcement of nanocomposite systems. For this reason, dielectric spectroscopy is a powerful tool for investigating the network formation and fractal analysis in nano­ composite materials. It has found that the investigation and design of dielectric materials with high permittivity value are important because of their importance in energy storage devices. Nevertheless, there are a few research about modeling or theoretical aspects of dielectric prop­ erties of nanocomposites in AC loading. Early works in this field are related to AC hopping conductivity of Dyre [17] and dielectric relaxa­ tion that has been defined by Debye [18]. Recently, effective-medium theory has been treated by Xia et al. [19] to predict AC conductivity and dielectric permittivity graphene-polymer nanocomposites upon AC field. In this regard, they considered electron tunneling effect along with Maxwell-Wagner-Sillars (MWS) phenomenon at two conditions: static interface effects and frequency-dependent interface effects for consid­ ering interface contribution. For this reason, their presentation was applied as a basic model to calculate and predict the dielectric properties of nanocomposite aerogel systems. The derivation of the mentioned model will describe in the next section. In our previous works [20,21], the characterization of the in-situ biosynthesized BC/rGO and BC/MWCNT nanocomposite aerogels along with their electrical conductivity and strain sensing behavior were discussed. In addition, a modified model was proposed in order to pre­ dict the overall electrical conductivity of nanocomposite aerogels in DC setting. In this work, a comparable work is carried out on the network

2

A self-consistent effective medium theory was used for prediction of AC electrical conductivity and dielectric properties of nanocomposite aerogels, which it composed of randomly oriented and distributed rGO or MWCNTs in BC matrix. This approach is according to the model that has been proposed by Wang et al. [22,23] as follows; (1)

Te ¼ ϕ0 T0 þ ϕ1 T1 h Ti ¼ ðLi

Lr Þ

1

i þ Si Lr 1

1

(2)

where, Te is the effective medium scattered tensor. As expressed by Weng [24], the effective medium can be generalized to multiphase systems: h ðLe

L0 Þ

1

i þ SL0 1

N X

1

¼

h φi ðLi

L0 Þ

1

i þ SL0 1

1

(3)

i¼1

In this regard, Xia and coworkers [19] proposed a frequency-dependent theory for predicting electrical conductivity and dielectric permittivity nanocomposite containing graphene:

3

σ

�

* 0

13

=

σ *e þ

2. Theoretical

�

σ

* e

�

σ*0

" # � � 7 2 σ*1 σ *e σ *3 σ*e 7 þ 1 3ϕ1 � � ¼0 þ * �5 σ*e þ S11 σ*1 σ *e σ e þ S33 σ *3 σ*e *

(4)

=

ð1

6 ϕ1 Þ6 4

Dielectric permittivity vacuum permittivity Complex dielectric permittivity Broadening parameter Angular frequency Interfacial capacitance Symmetric hopping function Characteristic time of electron tunneling Relaxation time Conductivity of thinly coated filler Permittivity of thinly coated filler Interfacial resistivity Fractal dimensions

ε εvac ε* ν ω

σe

formation of MWCNTs and rGO in BC-matrix using AC conductivity, dielectric permittivity and dynamic mechanical thermal analysis (DMTA) techniques. These techniques provide useful information about network formation, also fractal dimensions in percolated systems to reveal underlying differences between MWCNTs and rGO networks. Additionally, a modification performs on the effective medium theory for predicting overall dielectric properties (AC conductivity and dielectric permittivity) of nanocomposite aerogels and confirms with experimental data. Furthermore, gap distances between two adjacent nanofillers were determined in both of the electrical and mechanical

The properties of matrix and nanofillers are denoted with subscripts, 0 and 1(or 3), respectively. Furthermore, σ* as the complex conductivity is represented as follows:

σ * ðωÞ ¼ σ ðωÞ þ iσ00 ðωÞ ¼ iωεvac ε* 0

(5)

With preserving their model, a modification, based on the general­ ization of effective medium theory, is performed in order to develop Equation (4) for prediction of AC electrical conductivity in nano­ 0 composite aerogels. Based on Maxwell equations,σ ðωÞ and σ00 ðωÞ are 2

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related to imaginary (ε00 ) and the real part of dielectric permittivity (ε ) using the following formulas: 0

0

0

00

σ ðωÞ ¼ σ ac ðωÞ ¼ ωεvac ε 0 σ00 ðωÞ ¼ ωεvac ε

σ ðωÞ ¼ h

(6)

�i2

(15)

þ ðarctan ωτσ Þ2

(16)

ðcÞ σ ðcÞ frequency ðωÞ ¼ σ i σ ðωÞ

3

2 � 13

σe þ

7 � 7 5þ εe Þ ω

ðσ σe Þ þ iðε0 εe Þω � � � � 0 ðσ 0 σe Þ þ i εe þ 1 3 ðε0 =

6 ϕP Þ6 4

ϕ1

0:5Lnð1 þ ðωτσ Þ2

In which,τσ is defined as the characteristic time of electron tunneling (10 4 s). Therefore electrical conductivity of interface along with tunneling mechanism in the frequency dependent loading is:

In this way, in order to predict electrical conductivity and dielectric permittivity of nanocomposite aerogels at AC settings, the final form of the modified model is rewritten as follows:

ð1

ωτσ ðarctan ωτσ Þ

=

�

� 2½ðσ 1 σe Þ þ iðε1 εe Þω� þ 1 σ e þ S11 ðσ 1 σe Þ þ i½εe þ S11 ðε1 εe Þ�ω 2 � � 6 ðσ3 σ e Þ þ iðε3 εe Þω þ ϕP 6 4 σe þ S33 ðσ3 σ e Þ þ i½εe þ S33 ðε3 εe Þ�ω

(7)

1 3ϕ

=

�

�

13

σp

�

σe þ i εp σe

�

� � � þ i εe þ 1 3 εp

=

σ

¼

εðcÞ i ¼

σi εi

εðcÞ i ¼

(9)

σ

σ þ1

3. Materials and methods

εi

(11)

1 þ Sii ð2 þ 1=αÞεi =rC

3.1. In-situ biosynthesis of BC/rGO and BC/MWCNTs hydrogels converting to nanocomposite aerogels

In which:

C ¼ Cðϕ1 Þ ¼ C0

�

F ϕ1 ; ϕ*1 ; λ

Fð1; ϕ*1 ; λÞ

F ϕ1 ; ϕ*1 ; γ

�

Fð1; ϕ*1 ; γÞ

BC/rGO and BC/MWCNTs nanocomposite hydrogels were prepared using in-situ biosynthesis protocol similar to our previous works [20, 21]. Briefly, according to obtained percolation threshold, (0.9 wt% for rGO and 0.7 wt% for MWCNT), two concentrations beneath and beyond percolation threshold with an interval of 0.2 wt% was chosen. The specified concentration values of rGO or MWCNT, added to the culture medium solution, containing (2 g glucose, 0.5 g yeast, 0.5 g peptone, 0.115 g citric acid, and 0.27 g Na2HPO4⋅12H2O). The pH of all culture mediums adjusted at 6.5. All the culture medium materials acquired from Merck, Germany. Then, culture mediums containing the various fraction of nanofillers were autoclaved and subsequently ultrasonicated again to fully dispersion. Seed culture broth with Gluconacetobacter xylinus (PTCC 1734, purchased from the Iranian Research Organization for Science and Technology (IROST)), was inoculated to latter culture mediums and transferred into a rotary shaker incubator operating at a rotational speed of 100 rpm at 28 � C for 7 days to prevent the settling of rGO during incubation process. Finally, the biosynthesized nano­ composite hydrogels were washed with 1% (w/v) sodium hydroxide (NaOH) solution for 1 h at 85 � C to remove bacterial cell debris and purified and cleansed using distilled water several times to reach a neutralize pH. Then, the harvested products were converted to the aerogels by supercritical CO2 method. In order to convert weight

� (12)

Fð0; ϕ*1 ; λÞ F 0; ϕ*1 ; γ

�

Fð0; ϕ*1 ; γÞ

(13)

Moreover, F is: � � 1 ϕ F ϕ1 ; ϕ*1 ; λ ¼ arctan 1

π

(17)

respectively in Equation (7) for prediction of frequency dependent overall electrical conductivity and dielectric permittivity by considering the interface effects.

R S r ii i

F 1; ϕ*1 ; λ

εðcÞ inf 1 þ ðωτε Þ2

ðcÞ σ ðcÞ frequency ðωÞ and εfrequency ðωÞ are replaced with (σ 1 ; σ 3 ) and (ε1 ; ε3 ),

(10)

�i

R ¼ Rðϕ1 Þ ¼ R0

εðcÞ i

where,τε is known as the relaxation time and εinf is the dielectric permittivity of the interface at infinite frequency.

For MWCNT: 2 þ 1=α

εe ω

ðcÞ

1 þ Sii ð2 þ 4αÞεi =tC

σ ðcÞ i ¼ �

7 � 7 5¼0

ðcÞ εðcÞ frequency ðωÞ ¼ εinf þ

(8)

ð2 þ 4αÞ RtSii σi þ 1

�

On the other hand, the variation of interfacial dielectric permittivity with frequency can be written by:

To consider interface effects associated with tunneling and micro­ scale capacitors phenomena, Equations (8) and (9) can be defined for electrical conductivity and dielectric permittivity [22,25]: ðcÞ i

�

εe ω =

σe þ

3

σp

ϕ*1 λ

� þ

1 2

(14)

where, α, t and r are the aspect ratio, thickness of rGO nanosheets and diameter of MWCNTs, respectively. Sii is Eshelby tensor, R and C are the interfacial resistivity and capacitance and λ(0.001) is the scaling parameter [22,25]. In addition, by using the Dyre’s hopping model that was introduced for disordered solids [26], and Debye’s theory of dielectric relaxation [19], the interfacial effects for AC setting could be proposed. Dyre’s hopping function is based on random free-energy barrier model which also refers to the symmetric hopping model for AC conductivity [27]:

3

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percentage (wt %) to volume percentage (vol %), one can use the following formula: �� � �� 1 vol% ¼ ρBC (18) 1 ρBC þ ρfiller wt% Where ρBC and ρfiller denote BC (1.5 g/cm3) and nanofiller (1.9 g/cm3) density, respectively [20]. 3.2. Aerogels characterization The Field Emission Scanning Electron Microscope (FESEM) images were taken by a TESCAN MIRA 3-XMU (Republic of Czech) at operating voltage of 5–15 kV to evaluate the morphology of products. All the aerogel samples were sputter coated with a thin layer of gold under high vacuum conditions before imaging (20 mA, 100 s). A PHI Quantera X-ray photoelectron spectroscopy (XPS, ULVAC-PHI, Inc., Japan) was utilized to study the variation of surface chemical states of BC aerogels and nanocomposite aerogels, also the binding energy was calibrated with C1s ¼ 284.8 eV. The dynamic mechanical thermal analysis was conducted using the NETZCH-242C (Germany) instrument in a tension mode for nano­ composite and neat aerogels. The specimens were thin rectangular strips with dimensions of 25 mm � 5 mm � 0.1 mm. The experiments were carried out in a temperature range of 80 to 250 � C with a heating rate of 5 � C/min at four different frequencies, i.e., 1, 10, 20 and 50 Hz. For prediction of the viscoelastic behavior of neat aerogel and nanocomposites aerogels at low and high frequency ranges, the timetemperature superposition equation (TTS) and the Wil­ liams–Landel–Ferry (WLF) equation were used. The time shift factor connects the temperature with frequency, can be calculated according to the following equation [28]: logaT ¼

C1 ðT C2 þ ðT

T0 Þ T0 Þ

(19)

To is the reference temperature, which is an arbitrary temperature between Tg and Tgþ100 � C and it is different for BC and nanocomposite aerogels. The parameters C1 and C2 are material dependent constants which were determined by: C1 ¼

Cg1 Cg2 ; C2 ¼ Cg2 þ T0 Cg1 þ T0 Tg

Tg

Fig. 1. Theoretical results for AC conductivity of (A) BC/rGO and (B) BC/ MWCNT nanocomposites and aerogel counterparts.

(20)

nanocomposite aerogels is lower than that of corresponding porosityfree nanocomposites at the whole of the frequency range. This is in a good agreement with the corresponding aforementioned theoretical results at a constant frequency (Figs. S1 and S2). By increasing of nanofiller contents, at percolation threshold, there is no difference be­ tween nanocomposite aerogels and porosity-free nanocomposites, indi­ cating that the impact of filler network formation is dominant in comparison with porosity in the nanocomposite aerogel systems. Similar results were found for the dielectric permittivity of nanocomposite aerogels in comparison with porosity-free nanocomposites, Fig. 2. In Fig. 1, linear trends of AC electrical conductivity versus frequency for BC/rGO and BC/MWCNTs nanocomposite aerogels, at a volume concentration of 0.0040 for rGO and 0.0035 for MWCNTs, represent the insulating behavior of nanocomposite aerogels that originates from normal diffusion of charge carrier with a slope of 1. By increasing both of rGO and MWCNTs loading levels, at the low-frequency range, a plateau region is observed which indicates the formation of filler conductive network and percolation threshold. By passing the critical frequency, the trend of electrical conductivity curves alters to the exponential state with a power lower than 1.This value obtained from the slope of the curve with linear fitting, indicating the dispersion region. Further rising of nanofiller contents, for both of rGO and MWCNTs nanocomposite aerogels, led to the critical frequency (the transition from plateau region to dispersion region) shifted to the higher frequency. At the low-frequency range, the differences between all curves (the

The dielectric properties (AC electrical conductivity and dielectric permittivity) of BC aerogels and resultant nanocomposite aerogels were performed using a broadband dielectric spectrometer, GW Instek, LCR8101G LCR meter, Taiwan. AC setting was carried out in the fre­ quency interval 10 Hz to 10 MHz at room temperature. In order to reduce the contact resistance between aerogels and probes, the surfaces of samples were coated by silver paste. 4. Results and discussion 4.1. Model prediction In this section, the model predictions for electrical conductivity and dielectric permittivity are discussed for nanocomposite aerogels (at a range of frequency). The outcomes of the model, at a constant frequency, have been presented in Supplementary information (Figs. S1–S4). The variations of electrical conductivity and dielectric permittivity for nanocomposite aerogels in comparison to porosity-free nano­ composite counterparts are exhibited over a frequency range. Three levels for nanofiller loading are considered including beneath, at, and beyond the percolation threshold. The predicted results are illustrated in Figs. 1 and 2. In Fig. 1, beneath the percolation threshold, porosity has a dramatic effect on the electrical conductivity. The electrical conductivity of 4

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possesses large relaxation time, thus it diminishes with the increment of frequency. Besides, with the further rising of nanofiller contents, step-like behavior and transition to the plateau range, shift to higher frequency domains. The validation of theoretical results will examine later. 4.2. Aerogels morphology and microstructure Fig. 3 shows the FESEM micrographs of BC neat aerogel and nano­ composite aerogel counterparts. Generally, BC aerogel has a 3D porous and nanofibrous structure, Fig. 3(A). Moreover, as can be seen in FESEM micrographs of bare MWCNTs (Fig. 3(B)), partially U-shaped MWCNTs along with entanglement of them are the pivotal characteristic that significantly alter the network formation and its related properties. The flexibility of MWCNTs results in U-shaped morphology that can remarkably enhance the chance of elastic interlocking of MWCNTs [30]. On the contrary, the FESEM image of rGO exhibits a long straight nanoplates morphology, Fig. 3(C). Fig. 3(D) and (E), depict the FESEM micrographs of the in-situ bio­ synthesized BC aerogels in the presence of MWCNTs and rGO at the percolation threshold, respectively. After incorporation of MWCNTs into BC culture media and in-situ biosynthesis process, the BC nanofibers and MWCNTs intertwine together and MWCNTs adhere strongly on the surfaces of BC nanofibers, Fig. 3(D). The white points in the FESEM micrographs of BC/MWCNTs are due to the high conductivity of MWCNTs, as they distribute uni­ formly in the BC structure without aggregation. On the other hand, it is observed that for BC/rGO nanocomposite aerogel, the rGO nanosheets were interpenetrating within the BC nanofibers and bound by them in a spider web-like manner for creating uniform nanocomposite network [4,31]. Thus, according to the FESEM micrographs, it can be claimed that despite some differences between BC/MWCNTs with BC/rGO nanocomposite aerogels microstructures, the dispersion state of both nanofillers are comparatively similar, thereby revealing good dispersion of them in BC matrix that is shown schematically in Fig. 3(F) and (G). To confirm the chemical bonding in BC aerogel, BC/MWCNTs and BC/rGO nanocomposite aerogels, the XPS analysis performed. (Fig. S5 shows the XPS results).

Fig. 2. Comparison between theoretical results of nanocomposites and aerogels for (A) BC/rGO and (B) BC/MWCNT.

4.3. Dynamic mechanical properties of aerogels

curves related to the beneath, at, and beyond the percolation threshold) are significant. It is due to the dominance of the static effects of interface that are controlled by nanofiller content. At the high-frequency ranges, all curves merge to each other, due to extra electron hopping effect according to Dyre’s formula (Equation (15)). In this regard, at the highfrequency range, the influence of frequency dependent interface is dominant in comparison with that of static effect [19]. Therefore, at the low-frequency range, the content of nanofiller is pivotal on the electrical conductivity, although the influence of frequency is decisive at higher frequency regime. On the contrary, as shown in Fig. 2(A) and (B), a frequency inde­ pendent behavior is observed for dielectric permittivity at a low content of rGO (0.0040) and MWCNTs (0.0035), owing to the absence of a nanofiller network. Then, by increasing of nanofillers (up to 0.0049 for rGO and 0.0042 for MWCNTs), around percolation threshold, a step-like behavior can be observed for both of BC/rGO and BC/MWCNT nano­ composite aerogels. Generally, upon establishment of the nanofiller network, the immobilization of accumulated charge carriers occurs in the interface due to the high discrepancy between the conductivity of nanofiller and polymer matrix, leading to the formation of many nanocapacitors along with the impressive increment of dielectric permittivity at low-frequency range. This phenomenon is recognized as Maxwell-Wagner-Sillars (MWS) polarization effect [29]. The accumu­ lated charge carriers decline with increasing of frequency, resulting in the substantial drop of dielectric permittivity. MWS polarization

Fig. S6 presents the storage modulus and tanδ curves for BC aerogel. Additionally, the same curves for BC/rGO and BC/MWCNTs nano­ composite aerogels are demonstrated in Figs. 4 and 5, respectively. Moreover, it is observed from Figs. 4(A)–5(A) that upon introducing the rGO and MWCNTs into BC framework, the storage modulus signif­ icantly increases in the whole temperature range, indicating that incorporation of nanofillers has a strong impact on the improvement of elastic properties of the BC-based matrix aerogels. It reveals that strong interactions are formed between functional groups of BC (hydroxyl groups) with those of rGO and MWCNTs during the in-situ biosynthesis formation of BC microfibrillar in the early stages. Therefore, it results in the formation of the interphase region, i.e. immobilized polymer chains coated on the nanofillers. In addition, the uniform distribution of MWCNTs and rGO in the culture medium and BC structure, along with their high specific surface area are the main con­ tributors for a drastic increment of storage modulus of both BC/ MWCNTs and BC/rGO nanocomposite aerogels in comparison with neat BC aerogel. From Fig. 4, it can be seen that the storage modulus values of the BC/rGO nanocomposite aerogels are higher than those of the BC/ MWCNTs nanocomposite aerogels. This is attributed to the 2D geometry of rGO nanosheets compared with 1D MWCNTs, which induces much denser and rougher surfaces with many tortuous paths for load trans­ ferring between filler and matrix [32]. Unlike MWCNTs, the rGO nanosheets are straight and have lower flexibility in comparison with 5

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Fig. 3. FESEM micrographs of (A) BC aerogels, (B) as received MWCNT, (C) rGO, (D) BC/MWCNT (0.7 wt%) and (E) BC/rGO (0.9 wt%) nanocomposite aerogels, schematic images about dispersion of (F) MWCNT and (G) rGO in BC structure.

MWCNTs. Thus, rGO nanosheets increase the storage modulus higher than MWCNTs in nanocomposite aerogels. These findings are in line with morphological results obtained by FESEM. However, in Fig. 4(A) the storage modulus drop for BC/rGO nano­ composite aerogels is more than those of BC aerogel and BC/MWCNTs nanocomposite aerogels. This observation originates from a higher de­ gree of oxidation for rGO nanosheets due to the formation of abundant edges in the rGO structures, thus facilitating their reaction with oxygen at the elevated temperature [30]. On the contrary, tanδ curves for BC/rGO and BC/MWCNTs nano­ composite aerogels (Figs. 4(B) and 5(B)), show the addition of MWCNTs and rGO to the culture medium and resulting BC, as mentioned earlier, clearly improve the elasticity of the systems, and hence reduce the en­ ergy losses. The reduction in the intensity of tanδ curves is consistent with the increase of rGO and MWCNTs contents. This is ascribed to the addition of rGO and MWCNTs in the culture medium, preventing the mobility of the G. xylinus bacteria that is responsible for the production of BC microfibrillar. Besides, rGO and MWCNTs adhere to the BC nanofibers due to the interaction between OH functional groups of BC and carboxylic acid groups of rGO and MWCNTs, giving rise to the creation of coated filler regions. This indicates that the movements of BC

microfibrils chains are restricted to a certain degree. However, the in­ fluence of rGO nanosheets in the decrease of tanδ intensity is more distinct over MWCNTs. This suggests that rGO nanosheets, due to their 2D dimensional structure and the higher specific surface area in com­ parison with MWCNTs, absorb more BC nanofibers macromolecules on their surface, hence leading to the formation of a larger transition zone surrounding nanosheets. Thus, this results in the severe reduction of the mobility of BC chain segments. Moreover, as the MWCNTs and rGO nanosheets are embedded into BC framework, the Tg shifts to the higher temperature, owing to the restriction of microfibrillar chains. Therefore, according to tanδ curves, the Tg values for BC/rGO (0.7 wt%), BC/rGO (0.9 wt%) and BC/rGO (1.1 wt%) aerogels are in the 15–25 � C, 20–35 � C, and 35–50 � C ranges, respectively. Additionally, for BC/ MWCNTs nanocomposite aerogels containing 0.5 wt%, 0.7 wt% and 0.9 wt% MWCNTs, the Tg values are observed in the 23–28 � C, 32–38 � C, and 38–45 � C ranges, respectively. Therefore, the strong interfacial in­ teractions are evident from the increases in Tg of BC-based nano­ composite aerogels in the various content of nanofillers. To further elucidate the impact of MWCNTs and rGO on the visco­ elastic properties of BC-based aerogels and interpretation of structureproperty relationships, the frequency dependent behavior of BC neat 6

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Fig. 4. Variations of (A) storage modulus and (B) Tan δ, versus temperature for BC/rGO nanocomposite aerogels containing (1) 0.7 %wt, (2) 0.9 %wt and (3) 1.1% wt rGO.

aerogel, BC/MWCNTs, and BC/rGO nanocomposite aerogels, like the master curve, was obtained from experimental data using timetemperature superposition principle. The master curve illustrates the variation of molecular mobility and structure-property relationships. To obtain a master curve, the storage modulus curves at different temperatures shift horizontally along the frequency range using transfer coefficient, and by taking the isotherm at 50 � C as the reference tem­ perature for all samples. 0 Fig. 6(A) represents the master curves of storage modulus (E ) for BCbased aerogels. At very low frequency, the storage modulus is low, but as the frequency increases, modulus rises gradually. This observation is related to relaxation of BC chains, which is limited at high frequency,

leading to an increase in the storage modulus and vice versa. The tem­ perature and frequency have a reverse effect on the modulus. The storage modulus changes linearly with frequency. This trend resembles liquid-like rheological behavior. Moreover, by introducing rGO (0.7%) and MWCNTs (0.5%) into BC, the storage modulus increases significantly. It is apparent from Fig. 6(C) that MWCNTs bundles and rGO nano­ sheets have a dramatic effect on the viscoelastic properties of BC. For BC/MWCNTs (0.5%) similar to BC/rGO (0.7%), a plateau region at the low frequency range is clear. It indicates solid-like behavior which it can be attributed to the formation of the network at percolation threshold for both of MWCNTs and rGO in BC framework. It is observed that 7

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Fig. 5. Variations of (A) storage modulus and (B) Tan δ versus temperature for BC/MWCNT nanocomposite aerogels containing (1) 0.5 wt %, (2) 0.7 wt % and (3) 0.9 wt % MWCNT.

percolation threshold in BC/MWCNTs nanocomposite aerogel occurs at relatively lower concentrations compared to BC/rGO counterpart. This is attributed to MWCNTs geometrical features and range of interparticle attractive interactions. It has a marked effect on network formation. Additionally, the elastic interlocking of MWCNTs is an important feature. It can extremely affect the percolation threshold value reduc­ tion. On the contrary, the higher percolation threshold value for rGO can be ascribed to the lower flexibility and inferior interlacing ability of rGO nanosheets in the formation of the network compared to their MWCNTs counterpart. At the high-frequency range, due to polymer relaxation domination [33], the influence of nanoparticles for both BC-based nanocomposite aerogels becomes weaker. By further increasing of MWCNTs and rGO loading levels (Fig. 6(D-G)), it seems that the plateau

region extends. Thus, the DMTA findings disclose that despite higher storage modulus of BC/rGO nanocomposite aerogel in comparison with BC/MWCNTs nanocomposite aerogel, the latter aerogel has a lower percolation threshold over former aerogel. 4.4. Electrical conductivity and dielectric permittivity of aerogels Fig. 7 compares the theoretical and experimental variation of the AC electrical conductivity as a function of frequency for harvested BC/rGO and BC/MWCNTs nanocomposite aerogels. An ascending trend in the whole frequency domain is obviously observed for both of BC/rGO and BC/MWCNTs nanocomposite aerogels. The slope of AC conductivity curve for both samples is around 1. This is ascribed the insulated nature 8

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Fig. 6. Storage modulus master curves for (A) BC aerogels, (B, D and F) BC/MWCNT and (C, E and G) BC/rGO nanocomposite aerogels containing various loading levels of nanofillers.

of nanocomposite aerogels at low contents of nanofillers, arising from a lack of substantial in-phase current flow [34]. Upon integrating 0.9 wt% rGO and 0.7 wt% MWCNTs into BC, electrical conductivity increases for both BC/rGO and BC/MWCNTs nanocomposite aerogels. In addition, beneath a critical frequency, a plateau region is clearly perceived, followed by a rising trend with a frequency beyond it. This behavior indicates the formation of conduc­ tive nanofiller network and establishment of percolation threshold. The plateau domains correspond to the normal diffusion of charge carriers, where DC current of in-phase charges is dominant. Although, frequency dependent region originates from anomalous diffusion of charge car­ riers, indicating dispersion region beyond critical frequency [15]. In this region, the slope of AC conductivity curves (equal to the exponent in σ AC∝ ωn) for BC/rGO and BC/MWCNTs nanocomposite aerogels, ob­ tained 0.58 and 0.73, respectively. By the establishment of the perco­ lation threshold an infinite cluster is created, which could be described by the fractal concept. This concept is very useful in order to further insights into the distinction between rGO and MWCNT conductive net­ works. Generally, fractals are known as complex patterns with self-similarity across various scales. A fractal dimension is defined as a statistical index showing how the alteration of schema in detail varies

with the scale of its calculation. On the other hand, there are two different mechanisms for network formation: firstly, percolation that is based on geometrical features and second one is kinetical aggregation that considers the movement of the nanofiller within the matrix over the mixing process. Both of aforementioned implications result in network formation with self-similarity in small length scales. This length scale is related to the fractal dimension, thus different structures (nanofiller networking) possess various fractal dimensions. Hence, random struc­ ture or network of nanofillers follows fractal structure [35,36]. Accordingly, using scaling laws, the exponent of AC conductivity curve (n) beyond critical frequency (ωc), can be related to the fractal di­ mensions (df) and anomalous diffusion exponent on the infinite cluster (dw) using following formula: n ¼ (dw-df þ 1)/dw, where dw value for percolated system is around 3.8 [15]. The fractal dimensions for rGO and carbon nanotubes networks obtained 2.6 and 1.86, respectively. This clearly confirms the different constructed networks by rGO and MWCNTs within BC. The df value for rGO is similar to that of reported for carbon black (2.8) [14], which indicates the similarity of rGO fractal dimensions to a sphere (df ¼ 3). The lower df value for MWCNTs ascribes to the spatial interpenetration of nanofiller cluster arms [14], somehow proves our claim about the interlocking ability of carbon nanotubes. 9

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Fig. 8. Comparison between the predicted dielectric permittivity and experi­ mental data for (A) BC/rGO and (B) BC/MWCNT nanocomposite aerogels.

Fig. 7. Comparison between the predicted AC electrical conductivity and experimental data for (A) BC/rGO and (B) BC/MWCNT nano­ composite aerogels.

that required distance of filler-filler to form mechanical or electrical percolation threshold is distinct. For this purpose, the minimum dis­ tances between nanotube-nanotube (or platelet-platelet) for initiating of electron hopping/tunneling phenomena must be 5 nm for making conductive systems [37]. The main reason for observing different values of these two types of percolation threshold, as proposed previously in the literature, is originated from this fact, as long as the average radius of gyration of a polymer chain is larger than the interparticle distance of two nanofillers (the filler-filler gap distance), the polymer chain motion can be impeded via nanofillers network, thus the interparticle distance of mechanical percolation is larger than that of electrical percolation, as a result more nanofillers are needed for the construction of electrical percolated network. Meanwhile, it should be noted that the parameters such as nanofiller defects or nonmetallic parts of nanofillers (especially nanotubes) do not remarkably influence to the electrical behavior of systems, however they may restrain polymer mobility. Thereby, it could be concluded that a denser nanofiller network is accounted to attain the electrical percolation than that for the mechanical percolation [37–39]. Besides, it is an acceptable claim that the interparticle distance in electrical percolated system is lower than 5 nm in order to occur the quantum tunneling of electron between two adjacent fillers. It is worthwhile to note that the average radius of gyration has been esti­ mated 27 nm for cellulose [40]. Based on above-mentioned statement, these explanations confirm our claim. Thus, higher contents of nano­ fillers demand the creation of an electrical percolation threshold in

Moreover, by further increasing of nanofiller levels the plateau regime, for both of BC/rGO and BC/MWCNTs nanocomposite aerogels, extends. In other words, as shown in Fig. 7, in the crossover frequency (ωc), the transition from plateau regime to dispersion regime shifts to higher frequencies. On the contrary, from Fig. 8, at a low content of nanofiller, dielectric permittivity for both of BC/rGO (0.7 wt %) and BC/MWCNTs (0.5 wt %) nanocomposite aerogels is independent of frequency. This clearly in­ dicates the dominance of BC dipolar polarization at low contents of rGO or MWCNTs. In addition, dielectric permittivity significantly increases at low frequencies, by an increment of MWCNTs and rGO up to 0.9 wt % and 0.7 wt %, respectively. In this regard, the dielectric permittivity reached the value of 105 and 106 for BC/rGO and BC/MWCNTs nano­ composite aerogels, respectively. This behavior is attributed to the for­ mation of the nanocapacitors, originating from the creation of the conductive network in both of nanocomposite aerogels. Furthermore, with a comparison between theoretical results and experimental data, for AC electrical conductivity as well as dielectric permittivity, a broad agreement is observable, confirms the efficacy of the proposed modified model. Meanwhile, a discrepancy is observed between mechanical and electrical determined percolation threshold for both BC/rGO and BC/ MWCNTs nanocomposite aerogels (Figs. 6 and 7). This explains the fact 10

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Fig. 9. Schematic images indicating (A) electrical and (B) mechanical percolation threshold.

comparison to that of mechanical. This diversity schematically demon­ strates in Fig. 9. Nevertheless, we applied dielectric spectra with Cole–Cole function as well as three phase J-model in order to further quantify the values of gap distance in electrical and mechanical percolated systems that are described as follows. Cole–Cole function is presented in Equation (20):

εðωÞ ¼ εinf þ

X m

Δεm σ þ 1 þ ðiωτε Þνm iωεvac

(23): �

εðωÞ ¼ εinf þ

(21)

ωgap

adjacent nanofillers (δ) is determined by introducing Equation (21): 3e2 κ0 expð 16π2 hεvac ε

κ0 δÞ

�

�

� Δεωτε σ þ i 1 þ ω2 τ2ε ωεvac

(24)

According to the above descriptions, the outcome of fitting proced­ ure is shown in Fig. 10. As can be observed, the fitting parameter of ωgap is obtained 2 � 104 and 3.7 � 105 Hz, for BC/rGO and BC/MWCNT, respectively. By substituting these values within Equation (21), gap distance between two adjacent nanofillers is determined 4.5 nm and 3 nm for BC/rGO and BC/MWCNT, respectively, which is smaller than 5 nm. In order to find the value of filler-filler distances in mechanical percolated system, Ji model as a three-phase model, which presumes the interphase in the nanocomposite polymer systems is regarded as: 2 3 1

For m ¼ 1 and ν ¼ 1, the relaxation time of gap obtains by using the fitting procedure on the ε0 and ε’’ (in the percolation threshold). This relaxation time exhibits the high relaxation phenomena, which occurs due to tunneling upon gaps between adjacent nanofillers. Therefore, τε is � recognized τgap (τgap ¼ 1 ). Subsequently, the gap distance of two

ωgap ¼

Δε 1 þ ω2 τ2ε

Ec 6 ¼ 6ð1 Em 4

(22)

θÞ þ

θ ð1

β

θÞ þ

θðk 1Þ lnðkÞ

7 � � 7 5 � βÞðkþ1Þ þ Ef E β 2 β

þ ð1

θÞ þ ðθ

m

(25)

Here, e, h and κ0 are the electron charge, the Planck constant and a constant parameter, respectively. κ0 depends on the mean potential barrier (V ¼ 5 eV) and the mass of electron (me) according to the following formula: pffiffiffiffiffiffiffiffi 2 2me pffiffiffi V (23) κ0 ¼ h

sffi�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffiffiffiffiffiffi rffihffiffiffiffi� ffiffiffiffiffiffiffiffiffi�ffiffiffiffiffiffiffiffiffiffiffiiffiffiffiffiffi 2 Whereθ ¼ 2 δ=t þ 1 φ and θ ¼ ðr þ δÞ=r φ are considered for nanosheets and nanotubes, respectively. The parameters β and κ are volume fraction and interface modulus ratio to matrix modulus that are pffiffiffi denoted by β ¼ φ; k ¼ Ei ð0Þ=E , respectively [41]. The parameters of m

δ and κ are gained by fitting of Ji model with experimental data. In the present study, the modulus of specimens is determined based on DMTA storage modulus data at 25 � C. The modulus of rGO and the modulus of CNT are considered 186 GPa [42] and 1 TPa [43], respectively. Fig. 11

In this regard, ωgap is ascertained using curve fitting, followed by calculating of gap distance [14,15]. Furthermore, note that the real and imaginary parts of Equation (22) can be separated via algebraic method to reach a final form as Equation

Fig. 10. Cole–Cole fit of (A) BC/rGO and (B) BC/MWCNT nanocomposite aerogels. 11

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Composites Part B 174 (2019) 106981

Fig. 11. Fitting of Ji model with experimental data for (A) BC/rGO and (B) BC/MWCNT nanocomposite aerogels.

illustrates the results of experimental modulus that fitted by Ji model for prepared nanocomposite aerogels at different content of nanofillers. As shown in Fig. 11, by curve fitting of Ji model with experimental data, the values of filler-filler distances for BC/rGO and BC/MWCNT are determined 15 nm and 12 nm, respectively. The latter value is compa­ rable with that of reported for MWCNT inter particle distance (10 nm) in polycarbonate matrix that was obtained by an AFM tip [42]. These outcomes obviously confirm, the smaller interparticle distances required to form conductive percolated network in comparison with that of me­ chanical percolation.

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5. Conclusions A series of BC-based nanocomposite hydrogels containing rGO or MWCNTs were prepared using facile and cost-effective in-situ biosyn­ thesis strategy, and then converted to the aerogels by ScCO2 protocol. A modification was performed on the effective medium theory to predict the overall broadband dielectric properties of the aforementioned nanocomposite aerogels. Theoretical findings indicated beneath the percolation threshold, a discrepancy can be observed between nano­ composite aerogels with that of corresponding porosity-free nano­ composite counterparts, due to the lack of the conductive network of nanofillers. The experimental results confirmed the modeling outcomes. The DMTA findings showed that despite higher storage modulus of BC/ rGO nanocomposite aerogel in comparison with BC/MWCNTs nano­ composite aerogel, it had higher percolation threshold (0.7 wt%) than BC/MWCNTs nanocomposite aerogel (0.5 wt%). This attributed to the elastic interlocking of carbon nanotubes that clearly declined the percolation threshold. In addition, the dielectric properties revealed that by integrating 0.9 wt% of rGO and 0.7 wt% of MWCNTs into BC, nanofiller networks established for both of nanocomposite aerogels. However, a distinction was detected between mechanical and electrical percolation threshold, that was related to the different required dis­ tances of filler-filler to form mechanical or electrical percolation threshold. Moreover, by analysis of AC electrical conductivity curves, at percolation threshold, the fractal dimensions for rGO networks and MWCNTs network were obtained 2.6 and 1.86, respectively. Acknowledgments The authors wish to thank Tarbiat Modares University and the Iran Nanotechnology Initiative Council for their support. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.compositesb.2019.106981. 12

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