Graphene Core 1 Graphene-Based Disruptive Technologies ...graphene-flagship.eu/Lists/Deliverables/Core 1 D14... · In this report, we review the progress in the understanding of charge

Project funded by the European Commission under Grant Agreement n°696656

Graphene Core 1 Graphene-Based Disruptive Technologies

Horizon 2020 RIA

WP14 Nanocomposites Deliverable 14.3 “Report on electrical percolation of

2D materials in 3D composites”

Main Author(s):

Dimitrios Papageorgiou, UNIMAN

Alex Marsden, UNIMAN

Christina Valles, UNIMAN

Robert Young, UNIMAN

Ian Kinloch, UNIMAN

Julio Gomez, AVA

Jonathon Coleman, TCD

Andrea Liscio, CNR

Vincenzo Palermo, CNR

Due date of deliverable: M12

Actual submission date: M12

Dissemination level: Public

Graphene Core 1 D14.3 31 March 2017 2/ 22

List of Contributors

Partner Acronym Partner Name Name of the contact

2 CNR Consiglio Nazionale delle Ricerche Vincenzo Palermo

6 UMAN University of Manchester Ian Kinloch

31 AVA AVANZARE Julio Gomez

46 TCD Trinity College Dublin Jonathon Coleman


TABLE OF CONTENTS

List of Contributors ................................................................................................... 2

Summary .................................................................................................................... 4

1. Intrinsic Electrical Conductivity of Graphene Derivatives ........................... 4

2. Fundamental Aspects of Electrical Conductivity .......................................... 61.1. Percolation Theory .................................................................................................... 61.2. Conduction Mechanisms in Single Sheets ............................................................. 71.3. Conduction Mechanisms in 2D multilayered systems .......................................... 7

3. Influence of Graphene Morphology on Composite Properties .................... 81.4. Model graphene composites .................................................................................... 81.5. Graphene nanoplatelets ........................................................................................... 91.6. Thermally Reduced Graphene Oxide (TrGO) Composites .................................. 111.7. Chemically Reduced Graphene Oxide Composites ............................................. 12

4. Comparison with other carbonaceous particles ......................................... 13

5. Effect of strain on percolated networks ....................................................... 13

Conclusions ............................................................................................................. 14

References ............................................................................................................... 15


Summary Composites are one of the most promising applications for graphene, where graphene can

be used to the give increase performance of the host matrix, including mechanical stiffness

and strength, thermal stability, thermal conductivity, barrier properties, and sensing abilities.

Graphene could be particularly useful when added to insulating materials such as polymers:

polymers are extremely versatile, but their insulating nature (apart from a few exceptions1)

limits their application in a range applications for conductive adhesives, electrostatic painted

components, lightning strike protection, earthed products, EM shielding and materials for

anti-static applications. However, adding materials to a matrix can also alter other properties,

and these can be potentially degrading. Thus, careful balance is required between addition

and the resulting performance. To further the development of conducting composites, a

detailed understanding of the way charge percolates through the composite is essential.

In this report, we review the progress in the understanding of charge percolation in

composites and how this has led to an improvement in conducting, graphene-based

composites. The conductive properties of intrinsic graphene are discussed initially,

highlighting the importance of production route and morphology on the resulting physical and

electrical properties. The fundamentals of electrical percolation are presented, with a focus

on percolation and hopping transport. We then review recent results on the electrical

properties of graphene-based composites, with Table 1 (Appendix) summarising the reported

composite conductivities as a function of production method and graphene type highlighted.

Finally, the effect of strain on the conducting composites is discussed.

1. Intrinsic Electrical Conductivity of Graphene Derivatives The extremely high conductivity of graphene is one of its most attractive properties. This

conductivity arises from the combination of the high charge carrier mobility and the high

charge carrier concentration present in doped graphene. The conductivity, however, is very

sensitive to the material’s environment and quality. For example, the interaction of graphene

with its substrate has an significant influence with the highest conductivity (6×105 S/m) being

measured on suspended sheets 1. Furthermore, these measurements were performed on

high quality, mechanically exfoliated graphene; a method that is not suitable for industrial

scale production. There are, of course more technologically viable production routes, but

each of these comes with some deterioration of graphene’s properties.

Chemical vapour deposition (CVD) can produce large areas of monolayer 2 or multilayer

graphene depending on the growth conditions used. The measured conductivities of CVD

graphene are less than that of mechanically exfoliated graphene mainly due to its


polycrystalline nature leading to grain boundaries that scatter charges 3. However, recent

developments have opened up the possibility of growing CVD crystal graphene 4,5.

A more relevant choice for composites is graphene nanoplatelets (GNPs) which are typically

much cheaper than other GRMs and available at the tonne scale. Production methods vary,

but most exfoliate bulk graphite using thermal expansion and/or mechanical agitation. The

dimensions, primarily the thickness, of GNPs dictate their intrinsic conductivity, with thinner

GNPs having the highest values; GNPs with a thickness of 50, 5 and 3 nm have conductivity

of 7×104 S/m, 1×105 S/m and 1.5×105 S/m respectively 6. The reason for this thickness effect

is thought to be in the poor between plane conductivity of graphite. Thus, producing thin

flakes remains a priority for conductive composites. The lateral dimensions of GNPs also

play a role, however, less towards their intrinsic conductivity but more to achieving the

percolation threshold at lower contents and minimising flake-to-flake resistance.

Graphite oxide (GO) is produced by the Hummers method 7 or modern modified versions that

are less polluting/safer 8. These routes are scalable and result in monolayer GO 9. The

covalent functionalization of GO has a dramatic impact on its conductivity with reported

values generally around 2×10-2 S/m 9, significantly lower than those of graphene, and this

renders GO unusable for most electrical applications. The covalent functionalization of GO,

however, is reversible to a certain extent, and some electrical conductivity can be recovered.

Reduction routes (yielding reduced graphene oxide, rGO) generally follow thermal routes

(thermally reduced GO, TrGO), or chemical routes (chemically reduced, CrGO).

Chemical reduction involves the exposure of GO to aggressive reduction agents, most

commonly hydrazine. A bulk powder of rGO formed after exposure of hydrazine recovered a

conductivity of 200 S/m 9. Similar values were also obtained from individual monolayers (50-

200 S/m) 10. Another chemical treatment was with immersion in FeI2 at 95°C, which

recovered a conductivity to 6×104 S/m 11.

Thermal treatments have also been applied successfully, and generally perform better at

recovering conductivity. rGO thin films displayed conductivities of ≈5×104 S/m after being

heated to 1100°C whilst still maintaining 80% transmittance 12. As a comparison, the same

study found a hydrazine treatment with annealing at 400°C gave ≈5000 S/m. More recently,

thin films of rGO have reached 9×104 S/m, after annealing at 1000°C in a Ar/H2

atmosphere13. Finally, heating to very high temperatures >2000°C using arc discharge can

recover conductivities of 2x105 S/m 14. Despite success, these reduction methods have not

been able to recover the pristine conductivity of graphene (~9×104 S/m from an rGO thin film

after Ar/H2 heating to 1000°C 13 c.f. free standing graphene 6×105 S/m 1). This difference is

thought to be because only isolated conductive regions of graphene are recovered, and

electrons are required to hop between these regions, reducing the conductivity 10. Further,

even full removal of oxygen containing groups does not recover graphene’s properties, as


defects in the graphene lattice remain, reducing the conductivity. For this reason, covalently

functionalized graphene may not be a suitable material for high-end electrical applications,

and flakes that remain unmodified are likely to be more advantageous 15.

Coleman et al. exfoliated graphene in a liquid using surfactants, rather than functionalization

to stabilise the sheets16. Flakes typically 1-10 layers thick and with lateral size of 500-1000

nm were produced17,18. This route is yields large volumes of graphene that is solution

processeable and high quality with very little defects, and thus should be an excellent

conductor. Indeed, inkjet-printed thin films had conductivities of 3000 S/m 19.

2. Fundamental Aspects of Electrical Conductivity

1.1. Percolation Theory

The versatility and multifunctionality of

polymers make them attractive for several

applications, however the majority of

polymers are classified as insulating and

cannot be used in applications where

electrical conductivity is the main target. A

common strategy for the enhancement of

the conductivity (σ) of polymers is the

addition of a conductive filler which can

form a network at a specific loading, named

percolation threshold (pc). When the filler

loading reaches the percolation threshold, the conductivity of the composite rises suddenly

and the conductivity-loading plot takes the characteristic S-shaped form, demonstrating the

three zones of conduction: insulating, percolating and conductive. In order for a composite to

conduct electricity, the fillers must form a network within the volume of the composite, so the

flow of electrons is not obstructed by the insulating areas of the matrix. Aggregated

structures that are interconnected with individual filler particles can also promote percolation,

along with the existence of a phase-separated, co-continuous morphology comprising of

graphene-rich and poor phases within the composite volume (volume-exclusion theory) 20, 21.

Therefore, reaching the percolation threshold in a composite depends on several

parameters: processing methods, state of dispersion, filer-matrix interactions, filler-filler

interactions, interphase, filler functionalization, crystallinity, defects and others. Graphene is

one of the most efficient fillers for the preparation of conductive composites due to its large

specific surface area, which leads to smaller percolation threshold 22, 23 and the existence of

the highly mobile electrons in graphene. The majority of the graphene field use classical

Figure 1. Electrical conductivity versus filler content for PET/graphene and PET/graphite composites. Solid lines are fits to the percolation theory. Inset:

log-log plot of volume electrical conductivity versus (φ-φc)


percolation theory 24 to rationalize the conductive behaviour of composites:

𝜎" = 𝜎$ 𝜑&' − 𝜑"), where φgr is the volume fraction of graphene and φc is the percolation

volume fraction, while σc and σ0 are the conductivity of the composite and the intrinsic

conductivity of the filler respectively. t is the critical power law exponent and depends on the

system dimensionality, taking values of ~1.33 for 2D systems 25 and ~2 for 3D systems 26.

One example of the application of this theory is Zhang et al. who prepared PET/graphene

composites by melt compounding. They observed a pc of only 0.47 vol% graphene, while an

ultimate conductivity of 2.1 S/m was achieved with only 3 vol% graphene. The use of the

percolation theory was in good agreement with the experimental results (Fig. 1).

1.2. Conduction Mechanisms in Single Sheets

When there is disorder in an insulator-conductor composite, charge will percolate via a

hopping conduction mechanism 27. This involves the activation of charge carriers into free,

delocalized states 28. Electrons then hop between the available states to transport charge.

Hopping conduction mechanisms are split into two main mechanisms: nearest neighbour

hopping and variable range hopping. Both mechanisms normally proceed simultaneously,

but only one is usually the dominant mechanism. The general equation for hopping

conduction is 29: 𝜎 𝑇 = 𝜎$𝑒- ./

.

0

, where T is temperature, s0 and T0 are constants (although

they do have some a much weaker T dependence, it is much weaker effect) gamma is

hopping exponent. The hopping exponent depends on the dominant conduction mechanism,

which itself depends on the temperature of the system. At low temperatures, variable range

hopping is dominant. The hopping exponent then depends on the available dimensions of the

hopping as 𝛾 = 1𝐷 + 1 where D is the dimensionality. Mott law corresponds to 3D case, in

which p=1/4 30.

1.3. Conduction Mechanisms in 2D multilayered systems

In general, although various detailed studies on charge transport properties have been

published for single RGO sheets 31-34 clearly showing the Variable Rang Hopping (VRH)

regimes, a systematic study on more complex, multi-sheet systems is still lacking. To this

aim, CNR performed a systematic study of charge-transport mechanisms measuring

resistivity vs temperature curves (i.e. 𝜌 𝑇 ) of the macroscopic films of RGO. In such 3D

materials transport is highly anisotropic, taking place mostly intra-sheet (i.e. along single

RGO sheets, which are all oriented along the plane of the film), with however a significant

role of inter-sheet charge hopping (see Fig. 2).


Figure 2. a) Resistivity vs temperature and b) corresponding activation energy W(T) measured on RGO films of thickness: (square) 2.4 nm, (circle) 3.1 nm, (triangle) 4.5 nm, (rhomb) 7.1nm, (star) 14.1 nm. Orange dotted line indicates the Tt temperature separating the two charge transport regimes. c) Scheme of the charge transport on (a) single RGO sheet and (b) thin film. The single sheet is represented as a long line of sp2, red points the inter-domain border composed of voids, C-O functionalities or other defects; the green arrow is the metallic like transport (no hopping) and the red arrow next to the border defects is the ES-VRH hopping. The extension of the localization length is approximately reported as crystal domains in RGO sheets and several crystal domains for thin films.

Unambiguous selection between hopping conduction mechanisms is a challenge due to an

intrinsic problem related to the fitting procedure. The Levenberg-Marquardt algorithm

typically used cannot be considered a robust approach for reproducing exponential or power-

law curves 35. The ambiguities can be avoided by exploiting the logarithmic derivative and

defining the activation energy as follow: 𝑊 = −𝜕𝑙𝑛𝜌 𝜕𝑙𝑛𝑇 36. Using this approach, the fitting

procedure results to be more “robust” and the VRH regime can be determined in a self-

consistent way: 𝜌 𝑇 = 𝜌$ ∙ 𝑒𝑥𝑝=/=

> Þ 𝑙𝑛𝑊 𝑇 = 𝐴 − 𝑝𝑙𝑛𝑇, where A is constant, p = 1/3,

1/4, 1/2 in the case of 2D-, 3D-Mott or Efros-Shklovskii VRH regimes. The W(T) curves

corresponding to the𝜌 𝑇 measurements are reported in fig. 2b clearly indicate the presence

of two regimes at different temperatures. At T lower than a transition temperature Tt the

linear behavior of W(T) clearly indicates the transport regime described by the regime ES-VRH for all the thicknesses (p = 0.5). The localization length (ξ), i.e. the spatial localization of

the charge involved in the hopping process, increases with the film thickness passing from

60±10 nm to 2.5±0.2 µm which results larger than one order of magnitude with respect to the

single RGO sheet. For higher T (T>Tt), the achieved plateau regime of W(T) corresponds to

a power-law dependence of𝜌 𝑇 due to the increasingly metallic properties of the system,

caused by an insulator to-metal transition.

3. Influence of Graphene Morphology on Composite Properties

1.4. Model graphene composites

An ideal graphene-based composite system would include continuous graphene sheets with

large lateral size, which would allow efficient load transfer from the matrix, perfect dispersion


of the filler in the matrix and controllable electrical and thermal conductivities. The CVD

method offers the opportunity to make an experimental model of such an “ideal” system as it

produces high-quality graphene with large lateral dimensions. Vlassiouk et al. 37 prepared flat

laminates and scrolls of laminates by using a layer-by-layer approach between poly(methyl

methacrylate) (PMMA) and CVD graphene. The graphene loading in the flat laminate

composite was only 0.13 vol%, however the conductivity was amongst the highest reported

for graphene-based nanocomposites, at 810 S/m. This is a result of the ideal composite

architecture which allows enhanced electrical conduction and perfect orientation of the

graphene layers, without attributing heavy crumbling or even rolling of the graphene.

Moreover, CVD graphene does not require any reduction processes compared to the

majority of graphene flakes used in composites, which leads to high conductivity values.

Strano and co-workers subsequently prepared similar polycarbonate/CVD graphene layered

composites with a conductivity of S= 420 S/m at a filler content of 0.19 vol%, and a

percolation threshold as low as 0.003 vol% 38.

1.5. Graphene nanoplatelets

Graphene nanoplatelets (GNPs) are among the most popular materials used for reinforcing

polymer matrices because of their inherent tensile strength, and electrical and thermal

conductivity. However, the introduction of GNPs to improve electrical properties is not

straightforward, as several factors in material selection and preparation procedure govern the

resulting properties. Preparation method is particularly important in the case of GNPs as they

are prone to crumple, wrinkle and roll during composite processing. This is particularly

important when using GNPs in high-shear processes such as melt mixing. In contrast,

solution blending can help preserve the ideal form of the GNPs. Pang et al. 39 used a solvent-

assisted dispersion method followed by hot compression during the production of

UHMWPE/GNP composites and they achieved a percolation threshold at only 0.07 vol% filler

content. Another preparation method is in situ polymerization. This is known to produce

composites with a higher degree of dispersion; however it should be kept in mind that post-

processing methods such as hot pressing or injection moulding can also affect the dispersion

of the fillers and the ultimate conductivity of the composite. The different effect of solution

blending, in situ polymerization, and melt compounding on the conductivity of

polyurethane/graphene nanocomposites was investigated by Macosko and coworkers 40.

They found that the highest conductivity values were obtained from composites prepared via

solution blending. Melt mixing lead to particle reaggregation and particle attrition, which

reduced the lateral size of the graphene. For in situ polymerization, covalent bonds formed

between the matrix and the filler, which hindered direct contact between the fillers and

reduced the effective aspect ratio. Similar results were recently reported in the work of Xu et


al. 41. Apart from the formation of a conductive filler network, the volume-exclusion principle

may also govern the conductivity of GNP-based composites. In this case, graphene is

selectively localized in specific areas in the volume of the composite, reducing the conductive

pathway and the respective percolation threshold.

Figure 3. Electrical conductivity for PS and nanocomposites, TEM image of PS/PLA (60:40) composite with 0.46 vol% graphene. The selective localization of graphene can be seen 42.

Koraktar and coworkers prepared conductive graphene/polystyrene and

MWCNT/polystyrene composites by solution mixing and reached percolation at a graphene

content of 0.33 vol% 42. The ultimate conductivity values of the graphene composites were

also 2-4 orders of magnitude higher than the MWCNT composites. When poly(lactic acid)

was incorporated in the graphene/PS composite, graphene was selectively localized in the

PS-rich regions, formed favourable π-π interactions and resulted in a network structure at

lower graphene contents, reducing the threshold 4.5 times, from 0.33 to 0.075 vol% (Fig. 3).

Moreover, functionalization of the filler can help towards the improvement of solubility and

processability, enhance the interactions between the filler and the matrix, and enable a

homogeneous dispersion. On the other hand, the covalent interactions between the fillers

and the matrix can sometimes disrupt the sp2 hybridized C atom conductive pathways and

reduce the electrical conductivity as in the work of Arzac et al. 43, 44. The composite

conductivity is also dependent on the contact type between the GNP flakes; plane to plane

contact is most effective rather than edge to edge or edge to plane, as a result of high

electron mobility and higher contact area between the different flakes. Therefore, forcing an

orientation on the filler during the preparation procedure can enhance the conductivity of the

composite. The correlations between all these parameters are quite difficult to establish. The

results of different preparation methods and graphene types in recent studies is summarised

in table 1 (Appendix) in an attempt to understand these correlations. The majority of the

works listed in the table are post-2010 as other reviews cover the literature up to 2011 45, 46.


1.6. Thermally Reduced Graphene Oxide (TrGO) Composites

Thermally reduced graphene oxide flakes (TrGO) with specific surface areas of 600 to 950

m2/g have been prepared by oxidation of graphite followed by thermal expansion at

temperatures between 600 and 1000 °C 47. These thermal post-treatments increased the

carbon content of the GO materials up to 97 wt.% and lowered their resistivity to values from

1600 to 50 Ω×cm (depending on the reduction temperature), which are comparable to those

of compressed carbon black (CB) and natural graphite 47. The electrical conductivity of both

TrGO and the respective TrGO nanocomposites increases with increasing carbon content.

The presence of the remaining functional groups still promotes dispersion and interfacial

adhesion in many polymer matrices and that is the reason why TrGO is very promising to be

melt compounded in polymers of greatly different polarity. Several research groups have

employed TrGO materials to prepare thermoplastic nanocomposites based upon

polyethylene 48, maleic-anhydride grafted poly(propylene) 49, polystyrene 50 and

ethylene/methyl acrylate/acrylic acid copolymers 51. In comparison to conventional GO, TrGO

with its much higher degree of exfoliation, high specific surface area and higher carbon

content gave improved electrical properties at lower graphene content. Mulhaupt’s group

melt-compounded isotactic poly(propylene) (iPP), poly(styrene-co-acrylonitrile) (SAN),

polyamide 6 (PA6), and polycarbonate (PC) in a twin-screw mini-extruder together with TrGO 47. They showed that after melt extrusion the TrGO is uniformly dispersed and maintains

aspect ratios > 200. When loading TrGO into SAN, percolation was observed at 4 wt.%,

yielding a resistivity of 2.7×109 Ω×cm. By adding 12 wt.% of TrGO an ultimate specific

resistivity of 820 Ω·cm was obtained. For TrGO in PC-based nanocomposites, the authors

obtained a resistivity of 1.3×107 Ω·cm at 2.5 wt.% content, where the percolation threshold

was observed. By comparison, the conductivity of carbon-black filled composites was

considerably lower at the same filler contents. The incorporation of GO materials into

elastomers has also been reported. For example, natural rubber (NR) latex nanocomposites

have been reinforced with TrGO materials, showing an electrical percolation threshold at 3

phr of TrGO with values around 10-4 S/m 52. In addition, a comparative study on

carbon/styrene butadiene rubber (SBR) 53,54 has recently shown that TrGO exhibits superior

electrical performance with respect to other carbon nanofillers (including carbon black and

carbon nanotubes). This is in accordance with reports by other groups on enhanced

electrical conductivity on SBR/TrGO composites 54 and natural rubber composites found by

Ruoff and coworkers 55,56. In all the cases, TrGO has shown a very efficient formation of

percolation network. Compared to MWNTs, TrGO composites showed lower percolation

thresholds, which is attributed to the higher aspect ratio of TrGO 47,57. The low percolation

threshold of these graphene-based materials is of particular interest when aiming to improve


the electrical conductivity of polymer nanocomposites at very low carbon content. The

maximum conductivity achieved with TrGO materials is however slightly lower (by about an

order of magnitude), compared to the equivalent MWCNT-based composites, probably due

to the presence of residual oxygen in TrGO. Random alignment of the flakes during melt

extrusion and presence of considerable amounts of defects could also play a role.

Some works report chemical compatibilisation strategies to achieve improved interfacial

adhesion between the TrGO and the polymer, as better adhesion leads to better dispersions.

An example is the work reported by Shim et al., where they coagulated SBR together with

raw, carboxylated and cetyltrimethylammonium bromide stabilized TrGO, and reported

improvements on the electrical conductivity showing percolation thresholds as low as 0.5

wt.% 54,58. Another example is the addition of TrGO to maleated linear low-density

polyethylene LLDPE and to its derivatives with pyridine aromatic groups by melt

compounding 57. In this report, very low electrical percolation thresholds (between 0.5 and

0.9 vol.%) depending on the matrix viscosity and the type of functional groups were found for

LLDPE/TrGO composites 57. However, due to the low density and very high surface area of

TrGO, the simple melt mixing procedure for the preparation of nanocomposites is challenging

and requires special handling and safety procedures. As a result, the alternative approach of

chemical reduction of GO materials is often selected, as described below.

1.7. Chemically Reduced Graphene Oxide Composites

Stable graphene dispersions are produced by chemical reduction of aqueous GO dispersions

using chemical reducing agents like hydrazine, sodium borohydride, hydroquinone, hydrogen

plasma, various alcohols, sulfur-containing compounds, or even vitamin C 59,60. These

treatments yield materials with less oxygen containing functionalities, more restored sp2

network, and higher electrical conductivity. The oxygen content of CRGO materials is similar

to that of TrGO produced at 400 ºC (~15% oxygen). Agglomeration during chemical

reduction can be prevented either by using very low concentrations or by adding surfactants

or polymers, during the reduction step 61-66. Approaches in which aqueous CRGO dispersions

were blended together with polymer latex to produce graphene containing composites with

good mechanical and electrical properties (~15 S/m at 1.6-2 wt.%) and very low percolation

thresholds (~0.8-0.9 wt.%) have been reported 66, 67. Ruoff and coworkers reported enhanced

electrical properties for both natural rubber (NR)/TrGO and NR/CrGO composites55, 56. They

found similar electrical performances for CrGO and TrGO materials, which were superior in

respect to CB. TrGO and CRGO nanofillers were also incorporated into styrene-butadiene

rubber (SBR) 53. When processed under identical conditions, CNT, multilayer graphene

(MLG) and TRGO show similar electrical conductivities and percolation thresholds, which

were all superior to other carbon fillers. In general, the ranking of carbon filler performance


parallels their ability to form a percolating network. Furthermore, because TrGO is more

effectively exfoliated into single sheets, it often yields better electrical conductivity in

composites than other carbon nanofillers.

4. Comparison with other carbonaceous particles Avanzare has conducted extensive trials with a range of different GRMs and processing

conditions to obtain the highest possible conductivity at the lowest possible pc. They have

also benchmarked their GRMs against

other fillers, including multi-walled

nanotubes MWNTs (Figure 4). TrGO with a

very low content of oxygen (<1.5%at) and

large lateral size (40 μm) was found to

have a low pc in an epoxy matrix with a

high electrical conductivity at moderate

concentrations (0.5%v). It outperformed

both MWCNTs and relatively thin GNPs (6

nm thickness. By comparison, the

industrial-standard conductive filler, carbon

black, has a pc >10 wt%.

5. Effect of strain on percolated networks For some applications, composites are required to be flexible as well as conducting, e.g.

piezoelectric sensors and smart textiles. Graphene-based polymer composites have shown

excellent promise as strain sensors, functioning up to strains of 800% and monitoring signals

at 160 Hz 17. Combining graphene in a similar way with highly viscoelastic silicone polymer

(commonly found as Silly Putty) yielded a composite material with variable conductivity as

described by classic percolation theory (Fig. 5A) 68. More interestingly, the resistance varied

with strain in a controllable way with extremely high sensitivities of up to 500 (Fig. 5 B-C).

This level of dynamic sensing allowed them to monitor breathing and pulse, as well as the

movement of a spider (Fig. 5D). The mechanism for the change in resistance is still being

developed but is thought to be a combination of two processes, both of which lie in the

structure of the conducting network. The first is that as the composite stretches the number

of conductive pathways is reduced as graphene flakes become separated 69. A second

mechanism involves disconnected but closely spaced graphene sheets which the charge

carriers tunnel across; as these sheets become more separated, the tunnelling diminishes 69.

Both of these processes are reversible and hence the graphene-polymer composites are

able to perform many strain cycles (400 cycles with 60% strain 70) before failure. As well as

Figure 4. Electrical conductivity for chemically reduced and thermally expanded RGOx (1.4% at of Oxygen); GNP and MWCNT epoxy nanocomposites.


strain sensors, graphene loaded composites could also be used for wearable heaters. These

are popular for the treatment of pain disorders and muscle strain. In contrast to strain

sensors, in this application a consistent resistance upon deformation is required. Without

this, localized heating could cause burns. Recent reports have shown that an addition of rGO

to a WPU/PEDOT:PSS composite did not alter the electrical conductivity of the network, but

did improve the thermal conductivity, yielding better thermal management 71.

0 2 4

0

2

4

6

8

10D

R/R

0

Strain, e (%)

7.9 vol%

G=350

B5 10 15

0

200

400

600

Sens

itivi

ty, G

f (%)

C

5 10 1510-11

10-9

10-7

10-5

10-3

10-1

s (S

/m)

f (%)

A

0 10 20 30 40-10

-5

0

5

10fc,e=1.75 vol%ne=11.9

DR

/R0 (

%)

t (s)

D

Figure 5: A) Conductivity as a function of volume fraction for polysilicone/graphene composites with the solid line representing percolation theory. B) Resistance change as a function of strain for a 7.9 vol% composite. C) In B), the slope represents the sensor sensitivity which is plotted versus graphene volume fraction. D) The polysilicone/graphene composite employed as an impact sensor, monitoring the footsteps of a small spider.

Conclusions The intrinsic conduction of GRMs depends on their thickness, grain structure, and degree of

defects/functionality. The majority of GRMs display conductivities that make them perfect

candidates for use as conductive reinforcements in polymer composites. The conductivity-

loading relationship is found to be described by classic percolation threshold, meaning that

the conductivity of a bulk composite is sensitive to flake morphology and processing history

of the composite. The values of the conductivities are sufficiently high for applications and

out-perform nanotubes processed under similar conditions. Finally, the percolated networks

are shown to be piezoelectric, providing a route to strain sensors capable of detecting a

spider’s footsteps.


Appendix - References Table 1: Summary of electrical properties of graphene-based composites

Matrix Filler Preparation Method

Percolation Threshold

Ultimate DC Conductivity

(S.m-1)

Reference

PS GNP Solution blending 0.1 vol% 13.8 72 PS GNP Solution blending 0.33 vol% 3.5 42

PS GNP Electrostatic self-assembly 0.09 vol% 25.2 73

PS GNP Electrostatic assembly 0.054 vol% 46.3 74

PS CRGO Solution mixing + freeze-drying < 1 wt.% 15 67

sPS GNP Solution blending 0.46 vol% 4.7 75 PS/PLA GNP Solution blending 0.075 vol% 3 42 PMMA f-TRG Self-assembly 0.06 vol% 1.2 76 PMMA f-GNP Solution blending 0.8 vol% 20 77

PC TrGO

CB MWNT

Melt mixing 2.5 wt.% 2.5 wt.% 2.5 wt.%

0.001 0.1

0.006

47

PVC GNP Solution blending 0.1 vol% 5.8 78 PE f-GNP Melt mixing 0.83 vol% 0.01 79

UHMWPE

rGO Solution blending and hydrazinereduction

0.028 vol% 5 80

LLDPE TrGO Melt compounding 0.5-0.9 vol.% 10-4 57

PP

TrGO MLG CB

CNT EG

Melt compounding

< 5 wt.% 5 wt.%

7.5 wt.% 7.5 wt.%

--

1 x 10-2 3 x 10-3 3 x 10-5 4 x 10-6

--

81

iPP TrGO

CB MWNT Melt mixing

5 wt.% 5 wt.% 5 wt.%

0.02 3.3

3.1

47

PA6 TrGO

CB MWNT

7.5 wt.% 7.5 wt.%

--

7.1 x 10-3 2.2 x 10-8

-- 47

PA12 TrGO

N-TrGO Melt compounding 1-2.5 wt.%

1 wt.% 5.2 x 10-10

10-8 82

PA12

TrGO MLG350

EG CNTs

CB

Melt compounding

2.5 wt.%

2.5 wt.% 10 wt.% 5 wt.% 5 wt.%

8.9 x 10-6

1.2 x 10-6 6.6 x 10-12 1.6 x 10-5 1.3 x 10-5

83

Epoxy GNP Solution blending 0.52 vol% 0.05 84 Epoxy f-GNP Solution blending 0.16 vol% 10 85

EP TrGO Solvent free mixing method

1 wt.% 1 wt.%

2.0 x 10-10 1.0 x 10-9

86


N-TrGO DMG

5 wt.% 8 x 10-9

PU rGO Solution blending 0.078 vol% 0.001 87

PU f-TrGO

CB CNT

In-situ polymerization 0.5-2 wt.%

2 wt.% 2 wt.%

1.4 x 10-11 1.3 x 10-11 1.9 x 10-11

88

TPU/PP f-rGO Solution-flocculation and

melt mixing 0.054 vol% ~ 10-6 89

NR GNP Latex self-assembly 0.62 vol% 0.03 90 NR rGO Solution blending 0.21 vol% 0.23 91 NR TrGO Latex technology 3 phr 10-8 52 NR CRGO Coagulation method 3 wt.% 10-4 55 NR TEGO Two-roll mill 0.02 vol.% 3.41 x 10-9 56

SBR Surface modified

MLGs

Hetero-coagulation method 0.5 wt.% 8.24 x 10-6 92

SBR f-3D-GO Latex coagulation 0.39 vol% ~ 10-2 93

SAN TrGO

CB MWNT

Melt compounding 4 wt.% 4 wt.%

12 wt.%

0.1 9

7 x 10-4

47


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