The mechanics of graphene nanocomposites: A review

Composites Science and Technology 72 (2012) 1459–1476

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Review

The mechanics of graphene nanocomposites: A review Robert J. Young a,⇑, Ian A. Kinloch a, Lei Gong a, Kostya S. Novoselov b a b

Materials Science Centre, School of Materials, University of Manchester, Oxford Road, Manchester M13 9PL, UK School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK

a r t i c l e

i n f o

Article history: Received 20 March 2012 Received in revised form 1 May 2012 Accepted 6 May 2012 Available online 18 May 2012 Keywords: A. Nanocomposites A. Particle-reinforced composites B. Mechanical properties D. Raman spectroscopy

a b s t r a c t The preparation and characterisation of the different forms of graphene are reviewed first of all. The different techniques that have been employed to prepare graphene such as mechanical and solution exfoliation, and chemical vapour deposition are discussed briefly. Methods of production of graphene oxide by the chemical oxidation of graphite are then described. The structure and mechanical properties of both graphene and graphene oxide are reviewed and it is shown that although graphene possesses superior mechanical properties, they both have high levels of stiffness and strength. It is demonstrated how Raman spectroscopy can be used to characterise the different forms of graphene and also follow the deformation of exfoliated graphene, with different numbers of layers, in model composite systems. It is shown that continuum mechanics can be employed to analyse the behaviour of these model composites and used to predict the minimum flake dimensions and optimum number of layers for good reinforcement. The preparation of bulk nanocomposites based upon graphene and graphene oxide is described finally and the properties of these materials reviewed. It is shown that good reinforcement is only found at relatively low levels of graphene loading and that, due to difficulties with obtaining good dispersions, challenges still remain in obtaining good mechanical properties for high volume fractions of reinforcement. Ó 2012 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

4.

5.

6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Characterisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Mechanical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graphene oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Characterisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Mechanical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Nanomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Monolayer graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Bilayer, trilayer and many-layer graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bulk nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Micromechanics of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Mechanical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Assessment of reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions and prospects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

⇑ Corresponding author. Tel.: +44 161 306 3551; fax: +44 161 306 3586. E-mail address: [email protected] (R.J. Young). 0266-3538/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2012.05.005

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1. Introduction The study of graphene is one of the most exciting topics in materials science and condensed matter physics [1] and graphene has good prospects for applications in a number of different fields [2,3]. There has been a rapid rise of interest in the study of the structure and properties of graphene following the first report in 2004 of the preparation and isolation of single graphene layers in Manchester [4]. It had previously been thought that the isolation of single-layer graphene would not be possible since such 2D crystals would be unstable thermodynamically [5] and/or might roll up into scrolls if prepared as single atomic layers [6]. A large number of studies since 2004 have shown that this is certainly not the case. There was excitement about graphene initially because of its electronic properties, with its charge carriers exhibiting very high intrinsic mobility, having zero effective mass and being able to travel distances of microns at room temperature without being scattered [1,7]. Thus the majority of the original research upon graphene had concentrated upon electronic properties, aimed at applications such as using graphene in electronic devices [8,9]. Graphene is the basic building block of all graphitic forms of carbon. It consists of a single atomic layer of sp2 hybridized carbon atoms arranged in a honeycomb structure as shown in Fig. 1. Research upon the material has now broadened considerably as it was soon realised that graphene might have other in interesting and exciting physical properties such as high levels of stiffness and strength, and thermal conductivity, combined with an impermeability to gases. One obvious application of graphene is in the field of nanocomposites [10–13] and researchers working upon other forms of nanocomposites, such as those reinforced by nanotubes or nanoclays, have now refocused their efforts towards graphene nanocomposites. Additionally there was pre-existing expertise in the exfoliation of graphite (e.g. expanded graphite) and in the preparation of graphene oxide (originally termed ‘‘graphite oxide’’). We will also discuss the advantages and disadvantages of the use of graphene oxide in composite materials in comparison with pristine graphene.

2. Graphene 2.1. Preparation There has already been considerable effort put into the development of ways of preparing high-quality graphene in large quantities for both research purposes and with a view to possible

Fig. 1. A molecular model of a single layer of graphene. (Courtesy of F. Ding, Hong Kong Polytechnic University).

applications [14]. Since it was first isolated in 2004 several approaches have been employed to prepare the material. One is to break graphite down into graphene by techniques such as a mechanical cleavage or liquid phase exfoliation (sometimes termed ‘‘top-down’’). The other methods is to synthesize graphene using techniques such as chemical vapour deposition (CVD) (often known as ‘‘bottom-up’’), epitaxial growth on silicon carbide, molecular beam epitaxy, etc. Expanded graphite was developed more than 100 years as a filler for the polymer resins that were being developed at the same time and investigated extensively over the intervening period [15,16]. More recently there have been developments in the preparation of thinner forms of graphite, known as graphite nanoplatelets (GNPs) [17]. They can be produced by a number of techniques that include the exposure of acid-intercalated graphite to microwave radiation, ball-milling and ultrasonication. The addition of GNPs to polymers has been found to lead to substantial improvements in mechanical and electrical properties at lower loadings than are needed with expanded graphite [18,19]. The definition of GNPs covers all types of graphitic material from 100 nm thick platelets down to single layer graphene [17]. It is, however, the availability of single- or few-layer graphene that has caused the most excitement in recent times. The simplest way of preparing small samples of single- or fewlayer graphene is by the mechanical cleavage (i.e. the repeated peeling of graphene layers with adhesive tape) from either highly-oriented pyrolytic graphite or good-quality natural graphite [4]. Typically, this method produces a mixture of one-, two- and many-layer graphene flakes that have dimensions of the order of tens of microns. The rapid rise of interest in graphene for use in applications that require high volumes of material, such as in composites, led to investigations into methods of undertaking large-scale exfoliation [20–32]. One of the first successful methods was the exfoliation and dispersion of graphite in organic solvents such as dimethylformamide [20] or N-methylpyrrolidone [21–23]. Depending on the levels of agitation and purification suspensions with large (>50%) fractions of graphene monolayers could be prepared. The material produced by this method is relatively free of defects and is not oxidised but the lateral dimensions of the graphene layers are typically no more than a few microns. Coleman and coworkers [24,25] demonstrated that it was also possible to disperse and exfoliate graphite to give graphene suspensions in water-surfactant solutions and then showed that this approach could be extended to other inorganic layered compounds such as molybdenum disulphide, MoS2 [26,27]. As well as producing graphene by exfoliation of graphite there are a number of way in which it can be grown directly using ‘‘bottom-up’’ methods. In the surface science literature there are a number of reports, that date back more than 40 years, claiming the preparation and observation of thin graphitic layers on metallic substrates, and Wintterlin and Bocquet [33] have recently reviewed the literature upon the formation of graphene on metal surfaces. In addition, epitaxial growth of thin graphitic films on silicon carbide has been known for some time [34]. An important breakthrough has been the growth graphene films with macroscopic dimensions on the surfaces of metals. Two general approaches have been developed; (i) the precipitation of carbon from a carbon rich metal such as nickel [35] and (ii) the CVD growth of carbon on copper [36] using methane/H2 mixtures. Thick graphite crystals, rather than graphene, usually form on foils in the case of nickel and this problem has been overcome by depositing thin Ni layers of less than 300 nm on SiO2/Si substrates [35]. In the case of copper, growth takes place upon Cu foils via a surface-catalysed process and thin metal films do not have to be employed [36–38]. For both metals, it was found that the graphene

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2.2. Characterisation A single atomic layer of graphene absorbs 2.3% of visible light and its absorption is virtually independent of wavelength [42]. Thus, being significantly optically active, graphene can be observed by simple optical methods on certain substrates. In fact, it is possible to distinguish between flakes of graphene with different numbers of atomic layers relatively easily in a transmission optical microscope [49]. Ellipsometry can be used to identify graphene on substrates that do not provide sufficient contrast [50]. Atomic force microscopy (AFM) was one of the first methods used to characterised graphene and it is still employed widely. Novoselov et al. [4] noted in their original study of graphene that AFM indicated that some of their graphene layers were only 0.4 nm thick. This is a signature of single-layer graphene since the interlayer spacing in graphite is around 0.335 nm and AFM is now used routinely for estimating the number of layers present in few-layer graphene samples [14]. X-ray diffraction is another technique that can be used to characterise few-layer graphenes. This is because graphite has a sharp (0 0 2) Bragg reflection at 2h 26° (using Cu Ka radiation of wavelength 0.154 nm). This becomes broadened as the number of layers decreases and it is possible to use the Scherrer formula to estimate the number of layers contributing to the (0 0 2) reflection for few-layer graphene from this peak broadening [14]. BET surface area is particularly favoured by industry to give an indication of the average thickness of flakes in a large sample due to the relatively low cost and high accessibility of the technique. Single-layer graphene possesses a surface area of 2630 m2/g and this decreases as the layer thickness increases. Raman spectroscopy is a particularly useful technique to characterise graphene monolayers, bilayers and trilayers since, quite remarkably, Raman spectra can even be obtained from a single layer of carbon atoms (due to strong resonance Raman scattering in this material [51]). Moreover, graphene samples with different numbers of layers show significant differences in their Raman spectra as can be seen in Fig. 2. In the case of single layer graphene, the G0 (or 2D) Raman band is twice the intensity of the G band whereas in the two-layer material the G band is stronger than the 2D band. In addition, the 2D band is shifted to higher wavenumber in the two-layer graphene and has a different shape, consisting of four separate bands due to the resonance effects in the electronic structure of the 2-layer material [51]. In fact it is possible to use Raman spectroscopy to determine the stacking order in several layers of graphene (for instance to distinguish between two separate single layers overlapping and a graphene bilayer in which the original Bernal crystallographic stacking is retained [52,53]). As the number of layers is increased the 2D band moves to higher wavenumber and becomes broader and more asymmetric in shape for more than around five layers very similar to the 2D band of

40000

Intensity (arbitrary units)

films could be transferred to other substrates [39]. This process has now been scaled-up to a roll-to-roll production process in which the graphene is grown by CVD on copper-coated rolls. It can then be transferred to a thin polymer film backed with an adhesive layer to produce transparent conducting films [38,40–42]. Graphene nanoribbons can be produced by the unzipping of multi-walled carbon nanotubes. This can be done by an oxidative treatment in solution [43,44] or by an Ar plasma etching method upon nanotubes partially-embedded in a polymer substrate [45]. The approach has been extended recently to use small clusters of metals such Co or Ni as ‘‘nanoscalpels’’ that cut open nanotubes to create graphitic nanoribbons [46]. This is in fact a development of the use of these metal nanoparticles to undertake the controlled nanocutting of graphene [47,48]. The technique is capable of cutting graphene into pieces with well-defined shapes that can be used in a variety of applications.

G

Mechanically-Cleaved Graphene

30000

G' 20000

multilayer

2 Layers

10000 1 Layer

0 1500

2000

2500

3000

-1

Raman Wavenumber (cm ) Fig. 2. Raman spectra of graphene showing the difference in spectra between monolayer, bilayer and multilayer samples.

graphite. It should also be noted that in the Raman spectra shown in Fig. 2 the D band, which is normally found in different forms of graphitic carbon due the presence of defects, is not present indicating that the mechanically-exfoliated graphene used to obtain the spectra in Fig. 2 has a very high degree of perfection [51]. More prominent D bands are found in samples of imperfect or damaged graphene such as some CVD material or in the vicinity of edges of small exfoliated fragments. The atomic structure of graphene can be observed directly using transmission electron microscopy (TEM) [54–62]. It is found that both an image of the graphene lattice and well-defined electron diffraction patterns can be obtained from suspended graphene sheets in the TEM [54]. The sheets, however, are not exactly flat but have static ripples out of plane on a scale of the order of 1 nm [58]. It was also found that there was no tendency for the graphene sheets to scroll or fold in contradiction to one of the preconceptions of its behaviour [6]. 2.3. Mechanical properties Lee et al. [63] undertook the direct determination of the mechanical properties of monolayer graphene through the nanoindentation of graphene membranes, suspended over holes of 1.0–1.5 lm in diameter on a silicon substrate, in an atomic force microscope (AFM). They isolated the monolayers through the use of optical microscopy and identified them with Raman spectroscopy. They determined the variation of force with indentation depth and derived stress–strain curves by assuming that the graphene behaved mechanically as a 2D membrane of thickness 0.335 nm. It was found that failure of the graphene took place by the bursting of the single molecular layer membrane at large displacements with failure initiating at the indentation point. The stress–strain curve for the graphene derived from the analysis of the indentation experiments is shown in Fig. 3. It can be seen that the stress–strain curve becomes non-linear with increasing strain and that fracture occurs at a strain of well over 20%. Using density functional theory, Liu et al. [64] had earlier undertaken an ab initio calculation of the stress–strain curve of a graphene single layer. This is also plotted in Fig. 3 and it can be seen that there is extremely good agreement between the theoretical analysis and the experimentally-derived curve. The value of Young’s modulus determined from the indentation experiment [63] is 1000 ± 100 GPa and this compares very well with the theoretical estimate [64] of 1050 GPa. It is also similar to the value of 1020 GPa determined many years ago for the Young’s modulus of bulk graphite [65]. In addition, the strength of the graphene monolayer was determined experimentally to be up to 130 ± 10 GPa.

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2650

140

Calculated

100

Stress (GPa)

Raman wavenumber (cm-1)

Measured

120

80 60 40 20 0 0.00

G' (2D) Raman Band 633 nm laser

2645 2640 2635 2630 2625 2620 2615 2610

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0

Strain Fig. 3. Measured [63] and calculated [64] stress–strain curve for the deformation of a graphene monolayer.

This is the order of E/8, where E is the Young’s modulus, and so is close to the theoretically-predicted value of the strength of a defect-free material [66]. The theoretical failure stress can also be determined from the maximum stress in the calculated stress– strain curve in Fig. 3. Liu et al. [64] found that the behaviour of the graphene at high-strains should differ slightly depending upon the crystallographic direction in which the graphene is deformed. They predicted the strength to be in the range 107–121 GPa, which is again in very good agreement with the range of values measured experimentally. Similar measurements of the stiffness and strength of MoS2 monolayers have recently been reported by Bertolazzi et al. [67]. They determined an effective Young’s modulus of 270 ± 100 GPa and an average breaking strength of around 23 GPa, again close to the theoretical value [66]. They commented that such levels of stiffness and strength indicated that MoS2 could also be suitable for applications such as reinforcing elements in composites. It was explained earlier that Raman spectroscopy is an extremely useful technique for the identification and characterisation of different forms of graphene, and it is also a very good way of following the molecular deformation of graphene through observing stress-induced Raman band shifts. A number of high-performance materials, such as high-modulus polymer fibres [68], carbon fibres [69] and carbon nanotubes [70], also display stress-induced Raman band shifts and the experience gained from the study of these materials can be used in the study of graphene. In general, it is found that the rate of band shift per unit strain of such high-performance materials scales with their Young’s moduli [68]. For example, when carbon fibres are deformed tension the G and 2D (or G0 ) band positions shift approximately linearly with strain to lower wavenumber [69,71]. It was found by Cooper et al. [71] that the rate of shift for the 2D band per unit strain increased with increasing carbon fibre modulus. They were able to show that there was a linear dependence of the shift rate upon modulus, implying that there is a universal dependence of band shift upon stress for the 2D band in graphitic forms of carbon of 5 cm1/GPa [71]. Since both carbon nanotubes and graphene have well-defined 2D bands, then the Young’s modulus of these materials can also be estimated if it is assumed that the universal calibration for carbon fibres can be used for the same band in all forms of carbon. Recently Frank et al. [72] have undertaken a similar study of the shift of the Raman G band for carbon fibres and were able to determine a universal calibration factor for use with the G-band of graphene. Large stress-induced shifts of both the G and 2D Raman bands are found when graphene is subjected to deformation [71–85] showing that significant bond stretching and lattice distortion

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Strain (%) Fig. 4. Shift of the Raman 2D band with strain for a graphene monolayer.

takes place when the graphene is deformed. The ability of using Raman spectroscopy to probe the mechanical properties of graphene has recently been reviewed by Ferralis [86]. The simplest way of deforming the material is to deposit exfoliated graphene on a substrate which is then stretched or flexed in a Raman spectrometer. The behaviour is shown in Fig. 4 for the deformation of a graphene monolayer on a beam of poly(methyl methacrylate) [80]. There is a large shift in the position of the 2D band with strain and the slope of the line is of the order of 60 ± 5 cm1/% strain. This slope corresponds to a Young’s modulus for a graphene monolayer of 1200 ± 100 GPa using the universal calibration of 5 cm1/ GPa for carbon fibres [71]. This is similar to the values for monolayer graphene both measured directly [63] and calculated theoretically [64]. Detailed analysis of the behaviour of the G and 2D bands during deformation shows that they can broaden and split, as well as shift position [75,76,82,84]. In fact, it is possible to use the splitting to determine the orientation of the graphene crystal lattice relative to the direction of straining. The shift rate is slightly different in different directions in the plane of the crystal but in many applications, such as strain measurement in graphene, the simple universal calibrations can be employed [71,72]. 3. Graphene oxide 3.1. Preparation Long before the recent upsurge of interest in graphene-based materials, considerable expertise had been developed in the preparation of graphite oxide which is made up of individual graphene oxide sheets. Over 150 years ago, in an attempt to determine the ‘‘atomic weight’’ of graphite, Brodie [87] first reported the preparation of graphite oxide, though the oxidation of graphite using potassium chlorate and fuming nitric acid. The graphite oxide produced was found to be highly-oxidised with a C/O/H ratio of around 2.2/1/0.8 [87] which is typical of material made by these chemical routes. The Brodie method was modified by Staudenmaier [88] and then refined by Hummers and Offeman [89] who found they could treat the graphite quicker and more safely by employing a water-free mixture of concentrated sulphuric acid, sodium nitrate and potassium permanganate. Ruoff and co-workers [90– 92] have reviewed and summarised the current state-of-the-art in the preparation of graphite oxide. The interlayer spacing of the graphene oxide sheets in graphite oxide is between 0.6 nm and 1.0 nm depending upon the relative humidity [90]. Its structure is similar to that of graphite which is made up of stacks of more closely-spaced graphene sheets, but

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an important difference is that graphite oxide can be readily exfoliated by sonication to produce colloidal suspensions of graphene oxide sheets using a range of different solvents [90,91]. The ability to scale up production to produce material in large quantities for applications such as in composites has led to the present upsurge of interest in graphene oxide. The material that is produced directly from graphite oxide is, however, not particularly useful in that it is unstable thermally and a poor conductor of electricity. The properties of graphene oxide can be improved greatly through reduction, either chemically or thermally, although it has not yet been found to be possible to reduce the material fully back to graphene [93–99]. The use of hydrazine is one of the most popular methods of chemically-reducing graphene oxide [93,94] and sodium borohydride has also been employed [95]. This can lead to a significant reduction, by many orders of magnitude, in the electrical resistance of material made from chemically-reduced graphene oxide but the C/O ratio is still not much better than 6/1 [91]. Another method that has been used to reduce graphene oxide is thermal treatment and it is interesting to note that Brodie [87] found, in his original study, that heating of his graphite oxide led to a loss of mass and a significant increase in the C/O ratio. A recent study [100] has shown that graphene oxide, as produced by the Hummers method, is composed of functionalized graphene sheets decorated by strongly-bound oxidative debris, which acts as a surfactant to stabilize aqueous graphene oxide suspensions. This is similar to the way in which polycyclic aromatic acids are found to stabilize aqueous suspensions of oxidised multi-walled carbon nanotubes [101]. If a suspension of the as-produced graphene oxide (aGO) is treated with an aqueous solution of NaOH, a black aggregate separates out (base-washed, bwGO) that cannot be resuspended in water. 3.2. Characterisation There is considerable interest in the characterisation of graphene oxide particularly in view of the desire to reduce it back to graphene and also in exploiting its potential as a template to undergo chemical reactions that could be used to produce functional groups to control interfaces in composites. The structures of both graphite oxide and graphene oxide have therefore been analysed in detail by employing a large number of experimental techniques. Solid-state 13C nuclear magnetic resonance (NMR) spectroscopy was employed several years ago to probe the chemical structure of graphite oxide and hence also that for graphene oxide. The structure proposed using this technique [102,103] became the most well-known and widely-accepted model. It was suggested that graphene oxide sheets consist of aromatic ‘islands’ of variable size that have not been oxidised and are separated by a combination of aliphatic 6-membered rings containing, C–OH groups, epoxide groups and double bonds. Using wide-angle X-ray diffraction, the sharp (0 0 2) Bragg reflection of graphite at 2h  26° is found to disappear during its transformation to graphite oxide and a new peak at 2h  14° appears that corresponds to a layer spacing of around 0.7 nm [98]. Following heat treatment, this new peak disappears as the material is exfoliated into single sheets of graphene oxide [98]. AFM one of the most direct methods of quantifying the degree of exfoliation to graphene oxide and minimum sheet thicknesses of 1 nm and 1.1 nm have been measured for materials produced by chemical [94] and thermal [98] exfoliation respectively. These values are higher than the layer spacing found by X-ray diffraction, but the determination of sheet thickness for graphene oxide is complicated by issues such as adsorbed moisture or solvents, and the wrinkled sheets [10]. High-resolution TEM has also been used to study the structure of both graphene oxide [94,104,105] and reduced graphene oxide

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Fig. 5. Raman spectra of aGO and bwGO obtained using a 633 nm laser excitation (after [100]).

[105,106]. The structure of graphene oxide is remarkably similar to that of graphene at low magnification and the electron diffraction patterns are virtually identical. This means that the sheets of graphene oxide are not completely amorphous, and that the structure has both short- and long-range order and there is also no order in the oxygen-containing functional groups [96]. In the case of reduced graphene oxide [106], it is found that the structure consists of graphene islands of between 3 nm and 6 nm in size, surrounded by holes and defect clusters forming quasi-amorphous sp2 bonded areas. This again was consistent with the generally-accepted structural model for the sheets of reduced graphene oxide. The Raman spectrum of graphene oxide is quite different from that of graphene [96,100] as can be seen from Fig. 5. The G band is considerably broadened in graphene oxide and there is also a strong D band that is not present in exfoliated graphene. The appearance of the D band is a clear indication of the presence of sp3 bonding in the graphene oxide although other features of the spectrum indicate defects in the structure [107]. The relative intensities of the G and D bands can be used to follow structural changes that occur during the reduction of graphene oxide [93,107]. Fig. 5 shows Raman spectra in this region for as-produced (aGO) and based-washed (bwGO) graphene oxide using a 633 nm laser excitation [100]. The aGO material shows broad D and G peaks, with a ratio of integrated peak intensities of D/G = 1.9. The bwGO shows an almost identical response with D/G = 1.9. In contrast Raman spectra from the oxidative debris show no evidence of D or G peaks [100]. Together with the XPS and TEM results, this confirms that the bwGO consists of oxidatively functionalized graphene-like sheets, similar to those envisaged in the original model [102,103], and suggests that the sheets themselves are not altered significantly by the base wash process. The latest model proposed for the structure of graphene oxide is summarised in Fig. 6 [100]. Graphene oxide produced using the Hummers method [89] is found to be a stable complex of oxidative debris adhering strongly to functionalized graphene-like sheets. Under basic conditions the oxidative debris is stripped from the graphene-like sheets. The base-washed graphene oxide is electrically conducting and cannot easily be resuspended in water. 3.3. Mechanical properties The mechanical properties of graphene oxide are inferior to those of graphene due to the disruption of the structure through oxidation and the presence of sp3 rather than sp2 bonding. Dikin et al. [108] first investigated the mechanical properties of micron thick samples of graphene oxide paper and found it to have a stiff-

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Hummers' method "graphene oxide"

HO2C

O HO

CO2H

O HO

CO2H

OH

OH

O

OH

O

O

OH O

OH

O

O

HO2C

CO2H O

CO2H

O

C:0 ~ 2:1 Brown Water soluble Insulating

OH

Base wash removes oxidative debris

HO2C

O HO

CO2H

O HO

CO2H

OH

OH OH

O

O OH

O HO2C

OH

O

O

O

O CO2H

CO2H

O

C:0 ~ 4:1 Black Water insoluble Conducting

OH

Fig. 6. The structure of graphene oxide produced by Hummers’ method and the modification to the structure produced base washing [100] (reproduced with permission).

ness of up to 40 GPa but a strength of only 120 MPa. Subsequent studies [109–111] upon graphene oxide paper have not produced material with significantly better mechanical properties. The elastic deformation of monolayers of chemically-reduced graphene oxide was investigated by Gomez-Navarro et al. [112] using a similar AFM indentation technique on a suspended film of material to that used previously for exfoliated graphene [63]. They suspended single layers of graphene oxide up to 1 lm2 in size over a trench in a SiO2/Si wafer and monitored force–displacement curves as the AFM tip was pushed into the graphene oxide film. Although there was considerable scatter in their data, they determined a Young’s modulus of 250 ± 150 GPa. In addition they noted that graphene oxide sheets consisting of three or more layers appeared to have a Young’s modulus an order of magnitude lower. Suk et al. [113] undertook a similar study of the AFM indentation graphene oxide that had not been reduced and measured a Young’s modulus of 208 ± 23 GPa when an effective thickness of the graphene of 0.7 nm was used. A theoretical study to compare the stress–strain behaviour of graphene and graphene oxide containing both epoxide and hydroxyl groups was undertaken by Paci et al. [114]. They again predicted a modulus in excess of 1000 GPa for pristine graphene. Its structural modification, however, leads to the graphene oxide being predicted to have a modulus of only 750 GPa, for a sheet of graphene oxide of the same thickness as a graphene monolayer (0.34 nm). The effective thickness of the graphene oxide is, in reality, at least twice this value and this leads to a predicted modulus of less than 400 GPa and so closer to the measured values [112,113]. The effect of the oxidation of graphene upon its fracture behaviour was also calculated [114]. Changes in chemical bonding due to oxidation were found to halve the strength compared to pure graphene (again assuming the same sheet thickness). The presence of holes, due to missing carbon atoms, was found to drop the strength even further. It was concluded that it may be the presence of these holes that limits the strength of graphene oxide. Gao et al. [115] have recently undertaken a study of the mechanical properties of graphene oxide paper and also followed its deformation using Raman spectroscopy, enabling its Young’s modulus to be estimated. In particular they show that they were able to tailor the adhesion between the interfaces in the paper and so improve the mechanical properties by introducing small molecules, such as glutaraldehyde and water molecules, into the gallery regions. The Young’s modulus of the graphene oxide paper was found to increase by a factor of three following this chemical treatment. Gao et al. [115] were also able to follow molecular deformation in the graphene oxide sheet from shifts of the Raman

G band. They found that there was a significant increase in the rate of band shift per unit strain, again by a factor of about 3, following the chemical treatment. The rate of shift of the G component of the band for the treated material was found to be about 15 cm1/% strain which can be compared to 32 cm1/% strain for the same band in exfoliated graphene [76]. This figure allows the effective Young’s modulus of the graphene oxide in the paper to be estimated. If the Young’s modulus of the graphene is 1020 GPa then the equivalent modulus of the graphene oxide will be 1020  15/32 = 480 GPa. In the case of graphene oxide the carbon atoms have to support a sheet of material that is 0.7 nm thick rather than 0.34 nm for the graphene [113]. Hence the effective Young’s modulus of the graphene oxide will be 480  0.34/ 0.7 = 230 GPa which is within the range of values determined in the AFM indentation experiments on individual graphene oxide sheets [112,113].

4. Model nanocomposites The transfer of stress from a low modulus matrix to a highmodulus reinforcing fibre is the fundamental issue in fibre reinforcement. For the axial deformation of composites with long aligned fibres with high aspect ratios the strain in the fibre is usually the same as that in the matrix. Hence the high modulus fibre takes the majority of the load and so gives rise to the reinforcement. In the case of short fibres, the situation is more complex and the stress builds up from the ends of the fibres through a shear stress at the fibre–matrix interface. This phenomenon was first analysed by employing the shear-lag theory of Cox [116] which is now the foundation stone of composites micromechanics [66,117]. For the reinforcement of a composite by platelets, such as graphene, the starting point is to consider it to be a two-dimensional version of fibre reinforcement. The shear lag approach has also been used by a number of groups to analyse reinforcement by platelets in the context of clays [118] and biological systems such as bone [119] and shells [120] that have microstructures that rely upon platelet reinforcement. Gong et al. [80] investigated the problem of the mechanics of reinforcement by a graphene platelet both theoretically and experimentally. They pointed out that being a one-atom thick crystalline material, graphene poses several fundamental questions in the field of composite mechanics that needed to be addressed:  Could the decades of research upon carbon-based composites be applied to an atomically-thin crystalline material?

R.J. Young et al. / Composites Science and Technology 72 (2012) 1459–1476

  coshðns xlÞ ef ¼ em 1  coshðns=2Þ

 Is continuum mechanics that is used traditionally with composites still valid at the atomic level?  How does a polymer matrix interact with the graphene crystals and what type of theoretical description is appropriate?

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ð1Þ

where

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2Gm t n¼ Eg T

It will now be demonstrated how these issues have so far been addressed using model nanocomposites specimens.

ð2Þ

and Gm is the matrix shear modulus, Eg is the Young’s modulus of the graphene monolayer, l is the length of the graphene monolayer in the x direction, t is the thickness of the graphene, T is the total resin thickness and s is the aspect ratio of the graphene (l/t) in the x direction. The parameter n is widely accepted in composite micromechanics [117] to be an effective measure of the interfacial stress transfer efficiency, so ns depends on both the morphology of the graphene monolayer and the degree of interaction it has with the matrix. In addition, the variation of shear stress, si, at the polymergraphene interface is given by [80]

4.1. Nanomechanics Shear lag theory can be using to model the mechanical behaviour of a graphene monolayer in a matrix. In this case it is assumed that the graphene is a mechanical continuum and surrounded by a layer of elastic polymer resin as shown in Fig. 7. For a given level of matrix strain, em, it is predicted [80] from shear-lag analysis that the variation of strain in the graphene monolayer, ef, with position, x, across the monolayer will be of the form

si ¼ nEg em

  sinh ns xl cosh ðns=2Þ

ð3Þ

Inspection of these equations shows that the graphene monolayer is subjected to the highest level of stress, i.e. the most efficient level of platelet reinforcement is obtained, when the value of the product ns is high. This implies that for good reinforcement a high aspect ratio, s, is desirable along with a high value of n. It should be pointed out that this analysis relies on the assumption that both the graphene monolayer and polymer behave as linear elastic continua. The extent to which it is appropriate to make this assumption will be addressed next. 4.2. Monolayer graphene Gong et al. [80] used the sensitivity of the graphene 2D Raman band to strain [73,75,76,81,83,86] to monitor stress transfer in a model graphene composite consisting of a mechanically-cleaved single graphene monolayer in a thin polymer matrix. Following the discovery of strain-dependent Raman bands shifts in carbon fibres [121], subsequent studies have demonstrated that using Raman spectroscopy to determine the variation of the local strain

Fig. 7. The model of a graphene flake within a resin used in shear-lag theory. The shear stress, s, acts at a distance z from the centre of the monolayer.

Polymer

(a) 0.6

(b)

ns = 10, 20, 50

0.4%

Strain (%)

0.5 0.4 0.3 0.2 0.1 0.0 0

2

4

6

8

10

12

Position, x (µm) Fig. 8. (a) Schematic diagram (not to scale) of a section through a single monolayer graphene composite. (b) Distribution of strain in the graphene in the direction of the tensile axis across a single monolayer at 0.4% strain. The curves were calculated from Eq. (1) using different values of ns.

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along a carbon fibre in a polymer matrix allows the level of adhesion between the fibre and matrix to be evaluated [122–128]. In a similar way, Gong et al. [80] showed that determining the variation of the local strain across a graphene monolayer enables stress transfer from the polymer to the graphene to be followed [80]. Fig. 8a shows a schematic diagram of their specimen in which the graphene monolayer is sandwiched between thin layers of transparent polymer. Fig. 8b shows the local variation of strain across the graphene monolayer in the direction, x, parallel to the strain axis determined from the stress-induced Raman band shifts at 0.4% matrix strain. It is found that the strain builds up from the edges of the monolayer and is constant across the middle where the strain in the monolayer equals the applied matrix strain (0.4%). This behaviour is analogous to the situation of a single discontinuous fibre in a model composite in which there is good bonding between the fibre and matrix [122–128]. Using shearlag theory [66,116,117], the experimental data in Fig. 8b were fitted to Eq. (1). It can be seen that the fits of the theoretical shear-lag curves to the strain distribution are sensitive to the value of ns chosen with the best fit being for ns = 20. For fibre-reinforced composites, the quality of reinforcement is often described in terms of the ‘critical length’, lc. This parameter is defined as 2 the distance over which the strain rises from the fibre ends to the plateau level and is smaller for stronger interfaces [66,117]. It can be seen from Fig. 8a that the strain rises to about 90% of the plateau value over about 1.5 lm from the edge of the flake making the critical length to be of the order of 3 lm for the graphene reinforcement in this specimen. In order to obtain good fibre reinforcement, it is generally thought that the fibre length should be 10lc. Hence, relatively large graphene flakes (>30 lm) are needed for efficient reinforcement to take place. Processes for

exfoliating graphene into a high yield of single layers reported recently produce monolayers of less than one micron across [21,22]. Deformation of the graphene monolayer composite to an axial strain higher than 0.4% led to breakdown of the graphene polymer interface at an interfacial shear stress of the order of around 1 MPa and a different shape of strain distribution [80]. This means that the level of adhesion between the graphene and polymer matrix is relatively poor. It can be contrasted with the level of interfacial shear stress, si  20–40 MPa, determined for carbon fibre composites, which is an order of magnitude higher [122–128]. The efficiency of reinforcement by the graphene monolayer is also reflected in the value of the parameter ns (=20) in the shear lag analysis needed to fit the experimental data. Since the graphene is atomically thin, the aspect ratio s will be large (in this case, 12 lm/0.35 nm = 3.5  104) making the parameter n small (6  104) compared with carbon fibres. The findings from the study of Gong et al. [80] have important implications for the use of graphene as a reinforcement for composites. It appears that the continuum mechanics approach is valid at the atomic level – answering a question widely asked in the field of nanocomposites – and that the composite micromechanics developed for the analysis of fibre reinforcement is also valid at the atomic level for graphene. In a further study, Young et al. [129] showed that the strain distribution in a single graphene atomic layer sandwiched between two thin layers of polymer on the surface of a poly(methyl methacrylate) beam (Fig. 8a) could be mapped in two dimensions with a high degree of precision from Raman band shifts. They found that the distribution of strain across the graphene monolayer was relatively uniform at levels of matrix strain up to 0.6% but that it became highly non-uniform above this strain as shown in Fig. 9.

Fig. 9. Contour maps of strain mapped over the graphene monolayer in a model composite. Maps are shown for the original flake before coating with the top polymer layer and then after coating with the top polymer layer at different levels of matrix strain indicated (after [129]).

R.J. Young et al. / Composites Science and Technology 72 (2012) 1459–1476

The change in the strain distributions was shown [129] to be due to a fragmentation process as a result of the development of cracks, probably in the polymer coating layers, with the graphene appearing to remain intact. The strain distributions in the graphene between the cracks were approximately triangular in shape and the interfacial shear stress, si, in the fragments was found to be only about 0.25 MPa, an order of magnitude lower than the interfacial shear stress before fragmentation. This relatively poor level of adhesion between the graphene and polymer layers again has important implications for the use of graphene in nanocomposites. A study of the graphene in a model composite subjected to compression has been undertaken using Raman spectroscopy by Galiotis and co-workers [77,130] who employed a specimen geometry, consisting of a graphene monolayer on a beam sandwiched between two polymer films, similar to that shown in Fig. 8a. It is well known that composites are often subjected to complex stress fields in practical applications and they are particularly prone to failure under compressive loading by buckling [131,132]. It was found that in tension the (2D) band shifted to lower wavenumber with a slope of around 60 cm1/% and in compression it shifted to higher wavenumber initially at a similar rate with strain. However, as the compressive strain was increased, the band shift rate decreased until at a critical compressive strain, which depended upon the geometry of the monolayer, there was no further band shift due to the onset of an Euler-type buckling process [77,130]. In contrast, the compressive behaviour of free-standing graphene films on a surface, without a top covering polymer film, were found to stop taking up axial stress at lower strains due to rippling. It was concluded [130] that the presence of the top polymer film gives lateral support to the graphene monolayer and makes it much more resistant to buckling-type failure. 4.3. Bilayer, trilayer and many-layer graphene It was shown in the previous section that efficient composite reinforcement with monolayer graphene will only be realised if the in-plane dimensions of the flakes are sufficiently large (>30 lm). The best geometry for reinforcement in terms of the lateral dimensions of the flakes has therefore been established but the optimum number of graphene layers needed in the flakes is not yet clear. It was shown earlier that considerable effort has been expended in processing graphite to produce exfoliated graphene with high proportions of monolayer material [21–32] with a view to using it in composites and it is worth exploring the assumptions behind this approach. It is well known the relatively-weak van der Waals bonding between the individual graphene layers of graphite allows sliding between the layers to take place relatively easily, like the shearing of a deck of cards. This is the classical explanation of the low-friction properties of graphite [133]. More recently the frictional characteristics of graphene have also been investigated using AFM-related techniques. One of first investigations showed using friction force microscopy that the friction on SiC is greatly reduced by the presence of a graphene monolayer and that this is reduced by a further factor of two for bilayer graphene [134]. In a systematic investigation upon different graphene samples with up to four layers it was found that the friction decreased monotonically as the number of graphene layers increased [135], and tended towards the value for the bulk material value. Since easy shear between the graphene layers will reduce the efficiency of stress transfer and hence the level of reinforcement in composites, it would appear therefore that monolayer graphene might be the optimal form of the material for reinforcement in nanocomposites. A similar issue arises in the case of multiwalled carbon nanotubes where, even if the interface with the matrix is strong, sliding between the inner and outer walls could reduce the level of rein-

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forcement. Cui et al. [136] studied interlayer stress transfer in MWNTs using an epoxy matrix composite reinforced with peapod-based double-walled nanotubes [137] as a model material. By deforming the composite using a four-point bending rig, the higher-frequency component of the 2D-band which corresponds to the outer wall, shifted at a rate of 9.2 cm1/%strain, whereas the lower-frequency component that corresponds to the inner wall shifted at a much lower rate, of 1.1 cm1/% strain. This indicated the efficiency of stress transfer from the outer wall to the inner wall was rather poor such that the inner wall does not carry load, consistent with the theoretical predictions of Zalamea et al. [138]. Cui et al. [136] also demonstrated the effective modulus of MWNTs in composites decreases as the number of walls increases, and that cross-linking the walls may possibly increase the resistance of the walls to the easy shear process [139,140]. The question that arises is how far this experience upon stress transfer in multiwalled nanotubes can be extended to reinforcement by bilayer, trilayer and many-layer graphene. It was shown earlier that large stress-induced shifts of the G and 2D Raman bands are found when graphene is subjected to deformation [72–85] and that the rate of band shifts per unit strain could be related to the Young’s modulus of the material. Most of these investigations were concerned with the deformation of monolayer graphene but a number also followed the deformation of graphene flakes with more than one layer. In one of the first investigations of the deformation of exfoliated graphene flakes, Ni et al. [73] found that the shift rate of trilayer graphene upon a polyester film was less than that of the monolayer material. Tsoukleri and coworkers [77] followed the deformation of polymercoated graphene flakes upon a PMMA beam and found that the shift rate of the 2D band for many-layer material (that they termed ‘‘graphite’’) was lower than that for monolayer graphene. Moreover, they found that the band-shift rate for the many-layer graphene without a top coat was very low. Proctor et al. [78] followed the shifts of the G and 2D bands of graphene, with different numbers of layers, supported uncoated upon the surface of 100 lm thick silicon wafers subjected to hydrostatic pressure. Since the thickness of the graphene was very much less than that of the silicon, the graphene followed the biaxial compression of the surface of the silicon wafer during the pressurisation. Proctor et al. [78] found that the highest rate of band shift (per unit pressure) was for a graphene monolayer. This band shift rate for bilayer graphene on the silicon substrate was slightly lower than that of the monolayer, whereas the shift rate of their ‘‘few-layer’’ graphene was only half that of the monolayer material. It was suggested [78] that this lower rate for few-layer material could be due to poor adhesion with the substrate but considering the other observations discussed above it is more likely that this behaviour could be a result of easy shear between the graphene layers. A systematic study of the deformation of bilayer, trilayer and many-layer graphene has been undertaken recently by Gong et al. [141] with a view to determining the optimum number of layers for the reinforcement of nanocomposites. They found that the rate of 2D band shift for uncoated bilayer graphene on a PMMA beam was lower than that for a monolayer, implying relatively poor stress transfer between the two layers. The effect of coating the graphene was then also investigated. Fig. 10 shows the shifts of the 2D Raman bands from the middle of adjacent monolayer, bilayer and trilayer regions of a coated graphene flake up to 0.4% strain. Doing this on the same flake ensured that the orientation of the graphene is identical in each region (A–B Bernal stacking could be confirmed from the forms of the 2D bands [142]). The shift with strain of the four components of the bilayer graphene 2D band [51] is shown in Fig. 10a along with the shift of the adjacent monolayer region for comparison. The slopes of the two strong components 2D1A and 2D2A, are similar to each other,

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Bilayer loaded to 0.4%

2720

Raman wavenumber (cm-1)

2700

Fitted to a Single 2D Peak

2700 2D1B 2D1A 2D2A 2D2B

Many layer

2690 2680

Trilayer

2680

2670 Bilayer

2660

2660

2650

2640 Monolayer

2640 2620

Monolayer

2630 2600 0.0

(a)

2620 0.1

0.2

0.3

0.4

(b) 0.0

0.1

0.2

Strain (%)

0.3

0.4

0.5

Strain (%)

Fig. 10. (a) Shift with strain of the four components of the 2D Raman band of bilayer graphene along with the shift of the 2D band in an adjacent monolayer region on the same flake. (b) Shifts with strain of the 2D band for adjacent monolayer, bilayer and trilayer regions along with the shift with strain for the 2D band of a multilayer flake on the same specimen [141] (reproduced with permission).

and also similar to the slope of the adjacent monolayer region implying that bilayer graphene will give reinforcement equally as good as monolayer graphene. Similar behaviour has been reported by Frank et al. [143] although they did find evidence of a local Bernal to non-Bernal transition due possibly to cohesive failure of the bilayer graphene. The 2D band shifts with strain of the four different coated graphene structures are given in Fig. 10b for comparison. It can also be seen that the slopes of the plots are similar for the monolayer and bilayer material but somewhat lower for the trilayer. In contrast, the slope for the many-layer graphene is significantly lower at only around 8 cm1/% strain. Gong et al. [141] interpreted these findings as indicating good stress transfer at the polymer–graphene interface but poorer levels of stress transfer between the graphene layers. Gong et al. [141] went onto model the behaviour by adapting the theory of Zalamea et al. [138] for multiwalled nanotubes to quantify the efficiency of stress transfer between the individual layers within graphene. First of all, they considered the relative advantages of using bilayer graphene compared with the monolayer material. For two monolayer flakes dispersed well in a polymer matrix, the closest separation they can have will be of the order of the dimensions of a polymer coil, i.e. at least several nm [117]. In contrast the separation between the two atomic layers in bilayer graphene is only around 0.34 nm and so it will be easier to achieve higher loadings of the bilayer material in a polymer nanocomposite, leading to an improvement in reinforcement ability by up to a factor of two over the monolayer material. They went onto determine the optimum number of layers needed in manylayer graphene flakes for the best levels of reinforcement in polymer-based nanocomposites [141]. They showed that the effective Young’s modulus of monolayer and bilayer graphene is similar and decreases as the number of layers decreases. In high volume fraction nanocomposites, however, it is necessary to accommodate the polymer coils between the graphene flake and the separation of the flakes will be limited by the coil dimensions as shown in Fig. 11. The minimum separation of the graphene flakes will depend upon the type of polymer and its interaction with the graphene. This minimum separation is unlikely to be less than 1 nm and probably more like several nm but the separation of the layers in multilayer graphene is only of the order of 0.34 nm. The nanocom-

Fig. 11. Schematic diagram of the microstructure of graphene-based nanocomposites based upon either monolayer or trilayer reinforcements. The interlayer spacing of the graphene is 0.34 nm and the effective thickness of the polymer coils is assumed to be to be around 2 nm [141] (reproduced with permission).

posite can be assumed to be made up of parallel graphene flakes separated by thin polymer layer of the same uniform thickness as shown in Fig. 11 for monolayer and trilayer graphene nanocomposites. For a given polymer layer thickness, the maximum volume fraction of graphene in the nanocomposite will increase with the number of layers in the graphene, as shown in Fig. 12a. The Young’s modulus, Ec, of such as nanocomposite can be determined using the simple ‘‘rule-of-mixtures’’ model such as [117]

Ec ¼ Eeff V g þ Em V m

ð4Þ

where Eeff is the effective Young’s modulus of the multilayer graphene, Em is the Young’s modulus of the polymer matrix (3 GPa), and Vg and Vm are the volume fractions of the graphene and matrix respectively. The maximum nanocomposite Young’s modulus was determined using this equation along with experimental data [141] and is shown in Fig. 12b as a function of nl for polymer layers of different thickness. The modulus peaks at nl = 3 for a 1 nm polymer layer thickness and then decreases and the number of graphene layer in the flakes and polymer thickness increase. For a 4 nm layer thickness the maximum nanocomposite Young’s modulus is virtually constant for nl > 5. To summarise, it appears that monolayer material will not necessarily give the best reinforcement. The optimum graphene layers

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500

1 nm

900

0.7

(b)

2 nm

800

0.6

700

0.5

4 nm

0.4

600

0.3 500

0.2

400

Maximum Composite Modulus (GPa)

(a)

0.8

Maximum Graphene Volume Fraction

Effective Graphene Young's Modulus (GPa)

0.9 1000

400 1 nm

300

2 nm 4 nm

200 100

0.1

300

0.0 0

2

4

6

8

10

0 0

Number of Layers, nl

2

4

6

8

10

Number of Layers, nl

Fig. 12. (a) Effective graphene Young’s modulus, Eeff, and maximum graphene volume fraction for different indicated polymer layer thicknesses, as a function of the number of layers, nl, in the graphene flakes. (b) The maximum nanocomposite modulus predicted for different indicated polymer layer thicknesses as a function of the number of layers, nl, in the graphene flakes [141] (reproduced with permission).

for the best reinforcement will depend upon the polymer layer thickness and the efficiency of stress transfer between the graphene layers. It should also be pointed out that this analysis assumes that the graphene flakes are infinitely long and there is good stress transfer at the graphene–polymer matrix interface. The maximum Young’s modulus will be reduced for flakes of finite length because of shear-lag effects at the flake edges (Fig. 8b) and also if there is failure of the graphene–polymer interface.

5. Bulk nanocomposites There are a number of reasons for developing graphene-based composites. The first and most obvious reason is that addition of a filler with such impressive mechanical properties would be expected to lead to a significant improvement in the mechanical properties of the host polymer matrix. It is also found, however, that changes to the mechanical properties are also accompanied by modification of functional properties such as electrical conductivity, thermal conductivity and barrier behaviour. This presentation will be concerned principally with mechanical properties but a brief discussion of the effect of graphene upon the functional properties of a polymer matrix is also included. The preparation and properties of bulk graphene composites has been recently reviewed in detail by a number of researchers [10–12,144–146]. The vast majority of work in this area has been undertaken using graphene oxide, often in the reduced form, although some research has also been undertaken upon composites containing graphite nanoplatelets (GNPs). It is often difficult to tell the form of graphene that has been used just from the title of a paper, since the word ‘‘graphene’’ is often used to describe work upon graphene oxide, and careful reading of the original papers is often necessary to determine exactly the type of graphene that was employed. It will be shown that the number of reports of research undertaken on bulk composites based upon fully-exfoliated graphene is currently limited. Graphene oxide has many attractions over graphene since it is readily obtainable in large quantities, much easier to exfoliate and disperse in a polymer matrix, and has built-in functional groups available for bonding to form a strong interface with a polymer matrix. The individual nanoplatelets of graphene oxide are, however, often wrinkled and it was shown earlier that graphene oxide has significantly inferior mechanical properties to graphene. Graphene nanoplatelets have also been employed but are often poorly exfoliated and so do not lead to very high levels of reinforcement. In the following discussion care will be taken to distinguish between work upon the different forms of graphene.

5.1. Preparation Obtaining a good distribution of the nano-reinforcement is one of the greatest challenges in the preparation of polymer-based nanocomposites [147] since it will be demonstrated that the properties of the nanocomposites can be compromised by a poor dispersion. Experience has shown that carbon nanotubes have a tendency to form bundles that can be difficult to break down and so much of the effort in the area of nanotube-based composites has focussed upon developing methods of obtaining good distributions of nanotubes using techniques such as chemical functionalization of the nanotubes [148]. In the case of graphene or graphene oxide, however, the formation of bundles is not an issue although there can still be a tendency for incomplete exfoliation to be obtained and restacking to occur. Graphene oxide has one major advantages for processing in that it can be exfoliated in water and so nanocomposites can readily be prepared with the use of water-soluble polymers such as poly(vinyl alcohol) [149] and poly(ethylene oxide) [150] or using water-based latex technology [151]. Nanocomposites can also be prepared using solution-based methods with non-water-soluble polymers such as poly(methyl methacrylate) [152] and polyurethanes [153] by modifying the graphene oxide chemically. An attractive method of preparing graphene-based composites is in situ polymerisation of the polymer matrix although solvents are often employed to reduce the viscosity of the dispersions. For example, intercalative polymerisation of methyl methacrylate [111,154] and epoxy resins [155–157] has been achieved with graphene oxide to produce nanocomposites with enhanced properties. In situ polymerisation has been employed to successfully produce polyethylene- [158] and polypropylene-matrix graphene oxide nanocomposites [159]. Grafting of poly(methyl methacrylate) chains onto graphene oxide has also been employed to compatibilize the filler with the polymer matrix [160,161]. Melt blending offers a simple way of dispersing nanoparticles in a polymer matrix and it has been used to disperse thermally-reduced graphene oxide in a number of polymers that include polycarbonate [162] and poly(ethylene-2,6-naphthalate) [163]. It has also been employed to disperse expanded graphite into a biodegradable polylactide [164]. Reasonable levels of dispersion can be obtained in these systems but the addition of the nanoparticles increases the viscosity of the polymer melt significantly and clearly makes processing more difficult. Solid-state shear dispersion, using a modified twin-screw extruder, has been employed as a simple method to produce nanocomposites of unmodified, as-received graphite dispersed in polypropylene [165]. Significant property improvements were reported although it was found by X-ray dif-

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fraction and electron microscopy that the composites contained graphite nanoplatelets ranging from a few to 10 nm thick and so containing up to 30 graphene layers, rather than individual graphene platelets. Graphene-based nanocomposites have now been prepared with a wide range of other different matrix materials including silicone foams [166], large aromatic molecules [167], nanofibrillated cellulose [168] and poly(vinylidene fluoride) (PVDF) [169].

of an aligned reinforcement, the ratio of the Young’s modulus of the composite to that of the matrix is

Ec 1 þ ngV p ¼ Em 1  gV p where the parameter, g, is given by Ep

g ¼ EEmp Em

5.2. Micromechanics of reinforcement The reinforcement of polymers by rigid particles and the effect of particulate reinforcement upon the mechanical properties have been discussed in detail by Young and Lovell [117]. The Young’s modulus of particulate-reinforced polymers can be predicted relatively easily, although in practice only upper and lower bounds can be determined rather than single values. To determine the Young’s modulus it is necessary to undertake the analysis in two distinct situations where the particles and matrix (and hence the nanocomposite) are subjected to either uniform strain or uniform stress. For a particulate composite, in the case of uniform strain, it is found that the Young’s modulus Ec of the composites is given by the rule of mixtures (c.f. Eq. (4)) as

Ec ¼ V p Ep þ V m Em

ð5Þ

ð9Þ

1 þn

ð10Þ

In this equation, the parameter n is a measure of reinforcement geometry that depends upon the loading conditions and it is a parameter that is essentially controlled by the aspect ratio of the reinforcement. The limiting values of n are n = 0 and n = 1 and for the prediction of the longitudinal modulus of reinforcement by a ribbon of length l and thickness t, the value of n can be taken as 2l/t [170]. Eq. (9) tends to the lower, uniform stress, bound (Eq. (8)) as n ? 0 and to the upper, uniform strain, bound (Eq. (6)) as the aspect ratio of the reinforcement increases and n ? 1. A number of other approaches have been employed to model the reinforcement by nanoparticles [171,172] but the Halpin–Tsai approach for aligned reinforcement [170], that produces relatively-simple equations, has been employed widely for the analysis of graphene-based nanocomposites. It will be used next in the assessment of the measured levels of reinforcement reported for graphene-based nanocomposites.

or

Ec Ep ¼ Vp þ Vm Em Em

5.3. Mechanical properties

ð6Þ

where Ep is the Young’s modulus of the particles, Em is the Young’s modulus of the matrix and Vp and Vm are the volume fraction of particles and matrix respectively, within the composite (where Vp + Vm = 1). The other situation that must be considered is the case of uniform stress where the Young’s modulus of the composite is given by

1 Vp Vm ¼ þ Ec Ep Em

ð7Þ

and this can be rearranged to give

Ec Ep ¼ Em V m Ep þ V p Em

ð8Þ

It is found that these equations give very large differences in the prediction of the Young’s modulus of particulate composites, especially in cases where Ep  Em, and they are normally taken as upper and lower bounds of the properties. There is normally a distribution of stress in the reinforcement in which case that the particles are subjected to neither uniform stress nor uniform strain. The Young’s modulus normally lies between the two predictions that can be considered to be upper (uniform strain) and lower (uniform stress) bounds of composite Young’s modulus. Having such widely-separated bounds of modulus prediction has given rise to significant uncertainty about properties and over the years there have been a number of attempts to produce more appropriate predictions of the Young’s modulus of particulate reinforced composites, without having such widely-separated bounds [170–173]. Halpin and Tsai developed an approach based upon the self-consistent micromechanics method of Hill that enabled them to predict the elastic behaviour of a composite for a variety of both fibre and particulate geometries (see [170]). This approach was employed by Halpin and Thomas [173] to predict the behaviour of ribbon-shaped reinforcements which is clearly relevant to graphene-based composites. Their theory predicts that in the case

The simplest way of assessing the reinforcement of polymers upon the addition of graphene is through stress–strain curves as shown in Fig. 13 which shows results upon poly(vinyl alcohol) reinforced with reduced graphene oxide [174]. It can be seen that the there is large effect upon the stress–strain curve with a loading of only 0.3% by volume of reduced graphene oxide but the addition 10 more material (up to 3.0%) leads to a less spectacular effect upon properties. Both the Young’s modulus and tensile strength of the polymer are found to increase with the loading of reduced graphene oxide but the elongation at break decreases. This behaviour is typical of many graphene/polymer systems of which there are a number of reports in the literature. For example, Song et al. investigated the stress–strain behaviour of polypropylene reinforced with reduced graphene oxide [175]. Again a significant improvement was found for a loading of only 0.1% by weight of reduced graphene oxide but the elongation a break then decreased with further loading and the tensile strength and Young’s modulus peaked at a loading of around 0.5–1.0% by weight of reduced graphene oxide. These two reports [174,175] are typical of many in the literature where the formulations are produced by weighing materials and so data are often given in terms of weight fraction. Most theories, however, are formulated in terms of filler volume fraction and so data are often converted into volume fractions. Since most polymers have a density of around 1000 kg/m3 and graphene-based fillers have a density of about 2000 kg/m3, for a given loading, the volume fraction will be approximately half the weight fraction. Hence the addition of 2% of filler by weight will give rise to a volume fraction of 1%. The two reports [174,175] are also similar in that they refer to ‘‘graphene’’ in the title but careful reading reveals that they used reduced graphene oxide which was shown earlier to be quite different from graphene, with a different structure and mechanical properties. Coleman and coworkers [176] investigated the reinforcement of a polyurethane by pristine graphene (characterised by Raman spectroscopy) produced by solvent exfoliation and therefore not reduced graphene oxide. Fig. 14 shows a series of stress–strain curves for different loadings of the graphene by weight. It can be

R.J. Young et al. / Composites Science and Technology 72 (2012) 1459–1476

Fig. 13. Mechanical properties of nanocomposites consisting of reduced graphene oxide in PVA at various loadings (vol%). (a) Stress–strain curves, (b) tensile strength and elongation at break versus graphene loadings (after [174]).

Fig. 14. Stress–strain curves for nanocomposites consisting of solvent-exfoliated graphene in a polyurethane matrix with different loadings of graphene (wt%) (after [176]).

seen that there is a large increase in the slope of the stress–strain curve (the Young’s modulus increases by a factor of around 102 for their highest loadings) and the strain to failure decreases with graphene loading. They also found that for a given loading of graphene, the reinforcement effect decreased as the graphene flake size decreased [176], which they pointed out was consistent with the findings of Gong et al. [80] upon the need to have large lateral graphene flake dimensions for good reinforcement. Another aspect

1471

of their work is that they were looking at the reinforcement of a flexible polyurethane with a Young’s modulus of only around 10 MPa. It will be shown that much higher levels of reinforcement are generally found with low-modulus polymers than with more rigid matrix materials. Recent studies have started to look at mechanical properties other than the simple stress–strain behaviour of graphene-based nanocomposites. Bortz et al. [177] undertook a detailed study of the effect of the addition of graphene oxide to an epoxy resin upon its fracture toughness and fatigue behaviour. They found that even though the addition of the graphene oxide gave only a modest increase in Young’s modulus, it led to the fracture energy GIc being more than doubled and the fatigue resistance being increased by several orders of magnitude. Comparisons have also been made been the relative improvements in mechanical properties with the addition of either carbon nanotubes or graphene. It has been found multi-walled carbon nanotubes give rise to a nanocomposite with better mechanical and electrical properties than graphene nanoplatelets upon melt blending with nylon 12 [178]. Since it is possible to have a number of different forms of both nanotubes and graphene processed in different ways in a number of different polymer matrices, it remains to be seen if this observation a holds generally. A recent study has looked at the properties of hybrid poly(vinyl alcohol) nanocomposite fibres reinforced with both reduced graphene oxide and single-walled carbon nanotubes [179]. Significant improvement in mechanical properties were obtained and it was found that a 50/50 mixture of the two reinforcements gave rise to fibres with a surprising degree of toughness, comparable with spider silk or aramid fibres. It was suggested that this high level of toughness could be the result of the formation of and interconnected network of partially-aligned reduced graphene oxide flakes and carbon nanotubes. Direct evidence of stress transfer to a graphene-oxide-based reinforcement has recently been demonstrated by Gao et al. [115] who followed the deformation of graphene oxide paper with and without impregnation by glutaraldehyde. The monitored the deformation of the graphene oxide sheets from stress-induced shifts of the Raman G band. They found that during deformation of the graphene oxide paper, the G component of the band shifted by around 4.2 cm1/% strain but that this increase considerably up to 14.6 cm1/% strain upon treatment with glutaraldehyde which appears to greatly improve the interlayer adhesion. They then compared this behaviour with the shift rate with strain of 31.7 cm1/% strain for the Raman G-band of monolayer graphene found by Mohiuddin et al. [76] and deduced that the stress transfer efficiency increased from 0.13 in the as-received graphene oxide paper to 0.46 in the glutaraldehyde-treated paper. They also reported an increase in the macroscopic Young’s modulus of the graphene oxide paper from around 10 GPa to 30 GPa upon treatment with glutaraldehyde and went onto use the Raman bands shift data to model the mechanical properties of the paper, using the simple rule of mixtures (c.f. Eq. (4)). They showed that when they took into account the volume fraction of graphene oxide in the paper (0.3 in the as-received paper to 0.23 in the treated material), the stress transfer efficiency factors (0.13 for the as-received paper and 0.26 for the treated material) and the effective modulus of the graphene oxide (which they took as 400 GPa [112]), they were able to derive Young’s modulus values similar to the measured ones for both materials as long as they included a factor of the order of 0.6–0.8 to account for misalignment of the sheets (which they were unable to measure directly). It was explained earlier that the Young’s modulus of graphene oxide is probably lower than 400 GPa and so it may be possible to model the behaviour without the need to invoke sheet misalignment. It was shown earlier that stress transfer from a polymer matrix to graphene reinforcement can be demonstrated in model nanocomposites but is

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clear that this approach of Gao et al. [115] points the way forward in allowing us to also correlate the bulk mechanical properties of graphene-based nanocomposites with stress-induced Raman bands shifts, and hence deformation, of the reinforcement. 5.4. Assessment of reinforcement The classical way of assessing the level of reinforcement imparted upon a polymer matrix by a filler is to plot the ratio of the Young’s modulus of the composites to that of the matrix, Ec/ Em against the volume fraction of filler particles, Vp as shown in Fig. 15. It can be seen that the upper and lower bounds given by Eqs. (6) and (8) for uniform strain and uniform stress respectively are widely-spaced. Eq. (9) gives the expected behaviour for a ribbon-shaped reinforcement but the form of this relationship depends upon both the aspect ratio n and the ratio of the Young’s modulus of the filler to that of the matrix, Ep/Em through the parameter, g (Eq. (10)). It is necessary therefore to make different plots for families of materials with different ratios of Ep/Em and values of n in order to compare the behaviour of different systems. The majority of the published research upon the mechanical properties of graphene-reinforced polymers is concerned with the reinforcement of either rigid polymers (both glassy and semicrystalline) for which Ep/Em  103, taking the Young’s modulus of graphene as around 1 TPa or elastomers for which Ep/Em  106, since most elastomers have a Young’s modulus of the order of 1 MPa. General plots for the two types of matrix materials with a series of lines for different values of n can therefore be produced. Values of Ep/Em determined experimentally as a function of Vp for

3 Eqn. 6

ξ = 1000 ξ = 100

Ec /Em

References - 180 - 182 - 154 - 181

(a) Rigid Polymers 3 Ep/Em = 10

2

ξ = 10

Eqn. n 8

1

0

1

2

3

4

⊕-

187 188 152 189 184 164 183 156 163 185 186 159 173 174 175 160

Vp (%) 20 Eqn q .6

(b)

ξ = 10000 ξ = 1000

Ec /Em

15

Elastomers 6 Ep/Em = 10

References - 10 - 153 - 193 - 194 - 195 - 196 - 197

10

5

ξ = 100

0

Eqn. 8

ξ = 10

0

1

2

3

4

Vp (%) Fig. 15. Predicted and measured variation of Ec/Em with the volume fraction, Vp, of graphene-based filler particles for (a) rigid polymers and (b) elastomers.

nanocomposites with either rigid [152,154,156,160,163,164,173– 175,180–192] or elastomeric [10,153,193–196] matrices are also given on these plots. Since some of the literature data were presented in terms of the weight fraction of filler, it has been necessary to convert this to volume fraction using the density of the filler and matrix. Where only weight fraction data are given in the original publication, a filler density of 2280 kg/m3 has been assumed for the data in Fig. 15. This is by no means a complete review of the published data but it serves to give a general picture of the behaviour. There are also reports of the reinforcement of polyurethanes using functionalized graphene sheets [198,199]. These data are not included in the plots in Fig. 15 as the Young’s modulus values of the polyurethane matrices tend to lie between those of rigid and elastomeric polymers. It is instructive to examine the relationship between the experimental data and theoretical predictions. It would be expected that the parameter n (=2l/t) would be of the order of at least 1000 in the case of fully-exfoliated graphene or graphene oxide and that if the particles were providing good reinforcement, the experimental data should therefore lie above the line for n = 1000. It can be seen that in the case of the rigid reinforcement (Fig. 15a) the data generally lie close to the line for n = 1000 only at very low volume fractions (<0.1%) and then fall away in the range 1000 < n < 100 for volume fractions up to around 0.5%. Above volume fractions of 1% the data points lie in the region in for which 100 < n < 10. In the case of the fewer data available for elastomeric matrices it can be seen in Fig. 15b that the data are all in the range 1000 < n < 100. It appears therefore that, except at very low volume fractions, the level of reinforcement measured experimentally is less than what would be expected from the theoretical Young’s modulus value for graphene. There are a number of possible reasons why this might be the case: (1) Eqs. (9) and (10) are only strictly valid for aligned platelets and the predicted values of Ep/Em will be lower in the case of randomly-oriented platelets [156,200,201]. The waviness of the reinforcing flakes that is found particularly in the case of thermally-reduced graphite oxide and this will contribute to the further reduction of modulus [156,187]. The persistence length of graphene within polymers is also currently unclear and it is plausibly that the larger mono- or few-layer graphene sheets roll and fold up during processing [111]. (2) Most of the data in Fig. 15 are for composites reinforced with graphene oxide rather than pristine graphene and it was shown earlier that defects and holes in the material will reduce the Young’s modulus of the reinforcement to around 250 GPa [112,113]. (3) The interface between the platelets and the matrix may not be particularly strong and this will lead to poor stress transfer. There may be some advantage of using graphene oxide, despite its lower Young’s modulus, since the presence of the functional groups on the surface of may help to provide a stronger interface with a polymer matrix than in the case of pristine graphene or graphite nanoplatelets. It has also been shown that an improvement in Young’s modulus of the nanocomposites can be obtained through the use of coupling agents [202]. (4) In many cases the length of the flakes is relatively short and reinforcing material is not completely exfoliated [163]. This will have the effect of making the appropriate value of n significantly less than 1000. (5) The dispersion of the reinforcement may be poor, particularly at higher volume fractions, leading to clustering. This is a similar problem to that encountered with nanotubes [147]. There may also be a tendency of the graphene platelets to re-aggregate.

R.J. Young et al. / Composites Science and Technology 72 (2012) 1459–1476

Although the levels of reinforcement achieved so far in graphene-based composites have generally been disappointing more impressive mechanical are now being reported [176,190] as a better understanding of the mechanisms of reinforcement [80, 129,141] is being gained. It is clear, however, that there is considerable scope to overcome some of the issues listed above and produce nanocomposites with even better mechanical properties.

[20] [21]

[22]

[23]

6. Conclusions and prospects It is clear that both graphene and graphene oxide show promise as reinforcements in high-performance nanocomposites. They have high levels of stiffness and strength and this means that the nanocomposites ought to have outstanding mechanical properties. There are problems, however, in obtaining good dispersions and there are challenges in obtaining the full exfoliation of graphene into single- or few-layer material with reasonable lateral dimensions or producing graphene oxide without imparting significant damage upon the flakes. It is also necessary to ensure that there is a strong interface between the reinforcement and the polymer matrix to obtain the optimum mechanical properties. It should also be remembered that in addition to offering good prospects of mechanical reinforcement there are also possibilities of using graphene to control functional properties such as electrical conductivity, gas barrier behaviour and thermal conductivity, expansion and stability. Acknowledgements

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