The role of filler aspect ratio in the reinforcement of an epoxy resin with graphene nanoplatelets

The mechanisms of reinforcement of an epoxy resin by the addition of graphene nanoplatelets (GNPs) has been studied in detail. It is found that the addition of GNPs increases both the stiffness and fracture toughness of the epoxy resin. The dependence of the flexural modulus upon the volume fraction of the GNPs has been modelled using a combination of the rule of mixtures and shear lag analysis and it is shown that the reinforcement is controlled principally by the aspect ratio (length/thickness) of the GNPs. The dependence of the fracture energy upon the GNP volume fraction has been modelled assuming failure takes place through the debonding of the GNP particles followed by their pull-out and it is again shown that the aspect ratio of the GNPs is a vital parameter in controlling the level of toughening. It is found that the behaviour can be modelled using a similar value of GNP aspect ratio to model both the flexural stiffness and fracture behaviour, demonstrating the importance of this parameter in controlling the mechanical properties of GNP/epoxy resin nanocomposites.


GRAPHICAL ABSTRACT Introduction
Polymers such as epoxy resins are commonly used in a number of different applications such as the matrix material within composites or as adhesives [1]. The properties of epoxy based composite materials [2] that make them attractive for particular applications are that they have a high strength-to-weight ratio, offer high creep resistance and display good resistance to corrosion. Composite materials are becoming increasing popular for their integration as primary and secondary structural materials within the commercial and military aerospace products and composites are also now used widely in the automotive [3] and energy sectors [4].
Although there are many advantages of epoxy resins such as mechanical strength and stiffness, one of their principal downsides is that they are relatively brittle making them susceptible to crack initiation and propagation [5,6]. To overcome this shortcoming, a practical approach is to add a secondary phase to help toughen the material. Successful toughening has been achieved through the use of both elastomeric [6,7] and rigid filler materials [6,8,9]. Over recent years interest has grown in the use of different forms of nanomaterials such as silica particles [10] or nanocarbons such as nanotubes [11,12] and graphene [12][13][14][15][16][17][18][19][20][21][22] to reinforce a wide variety of polymers including epoxy resins.
Graphene [23] was first isolated in the form of a monolayer in Manchester in 2004 and has been studied widely as a result of its outstanding mechanical and electronic properties. It is now available in bulk quantities in the form of graphene nanoplatelets, GNPs [24] and a large number of studies have been undertaken upon the properties of polymer-based nanocomposites reinforced with GNPs [25]. It is well established that the addition of graphene nanoplatelets to epoxy resins leads to nanocomposites with improved of stiffness and toughness, although the detailed mechanisms of reinforcement are not yet fully understood.
Detailed analysis of the extensive literature data for a wide variety of matrix materials [25]indicated that the increase in stiffness upon the addition of nanoplatelets to a polymer matrix is controlled by the aspect ratio of the filler. Following this observation we developed a theory recently that has confirmed that for polymer nanocomposites for which the stiffness of the nanoplatelet reinforcement is very much higher than that of the matrix, the level of reinforcement depends principally upon the aspect ratio, (s = length/thickness) of the nanoplatelets and is independent of the filler Young's modulus [21]. Chong et al. [20] also undertook an extensive investigation into the mechanical properties and toughening mechanisms of a GNP-modified epoxy resin. They demonstrated that the principal toughing mechanisms are particle debonding and pull-out [2,26], controlled by the aspect ratio of the GNPs.
Other workers [12][13][14][15][16]19] have also indicated that pull-out is a major process involved in the toughening of epoxy resins by different forms of graphene. In particular, Mouritz, Kinloch and coworkers [27,28] have been able to investigate the pull-out process in detail by controlling the alignment of the GNPs through the use of an electric field during processing of the nanocomposite.
We have recently undertaken a detailed study of the deformation and tearing of a fluoroelastomer (FKM) reinforced with GNPs [29]. We found that the Young's modulus of the FKM increased upon the addition of the GNPs and that the tearing resistance is increased by a factor of three due to a combination of nanoparticle debonding and pull-out, with the debonding process being the principal energy-absorbing mechanism. The increase in stiffness and toughness were both analysed using micromechanical models and it was again shown that the aspect ratio was the main feature of the GNP filler controlling the mechanisms of both stiffening and toughening. It was found that similar values of aspect ratio could be could be used for the interpretation of both processes [29] unifying our understanding of the different deformation processes in these materials.
The aim of this present study is to study the effect to the addition of GNPs to an epoxy resin system upon its stiffness, strength and fracture energy. It contrasts with our previous study in that epoxy resins are brittle glassy polymers with a Young's modulus three orders of magnitude higher than that of elastomers. In this study, the role of the aspect ratio of GNP particles is explored from both an experimental and modelling viewpoint with a view seeing if it possible to also unify our understanding of the different deformation processes in GNP-reinforced epoxy resins and polymers in general.

Epoxy resin and hardener
The epoxy resin used was P-(2,3-epoxypropoxy)-N,N-bis(2,3-epoxypropyl)aniline (Araldite MY 0510) supplied by Huntsman Advanced Materials. This epoxy resin system is trifunctional and used in applications such as adhesives, coatings and composites. Advantages of this epoxy resin are that it has a low viscosity (550-850 mPa -s at 25°C), is fast reacting, has excellent chemical and corrosion resistance and has good mechanical strength. The epoxy resin was stored in a sealed glass jar at room temperature.
Aradur 9664-1, (4,4 0 -diaminodiphenylsulphone), was chosen as the hardener in this study and is commonly used with Araldite epoxy resins. It is supplied by Huntsman Advanced Materials in the form of a powder with a particle size of less than 50 lm. This hardener is typically used in adhesives, prepregs and advanced composites and provides good chemical resistance and excellent high temperature properties in cured composite systems. The curing agent was stored in a sealed tin to prevent moisture ingress.

Graphene nanoplatelets
Unfunctionalised GNPs, grades M5 and M25, were purchased from XG Sciences and the numbers denote the nominal particle diameters in microns [24]. They are produced by an intercalation/exfoliation process and have a specific surface area of 120 to 150 m 2 g -1 with a nominal average thickness of between 2 to 15 nm [30]. The manufacturer states that the oxygen content of grade M materials is less than 1% which indicates a high level of purity [30]. The GNPs were stored in a sealed container to prevent moisture ingress and are termed GNP-5 and GNP-25 in this present study.

Preparation of the nanocomposites
The epoxy resin nanocomposites were prepared using a range of GNPs loadings using the procedure given in the Supplementary Material. In brief, after mixing the resin and hardener with the GNPs at room temperature, the mixture was heated up in a mould to 180°C. It was held at this temperature for 180 min and then cooled slowly to room temperature. Samples were prepared of the neat resin and loading by weight of 1%, 3% and 5% of each type of the GNPs.

Characterisation
Differential scanning calorimetry DSC tests during this study were performed using a TA Instruments Q2000 calorimeter. Samples of approximately 10 mg were analysed using aluminium hermetic sample pans. The program used for experimental DSC tests was a temperature ramp from -50 to 300°C at a heating rate of 10°C per min in a furnace purged with nitrogen gas at a purge rate of 50 mL per min. All thermograms were analysed as a function of temperature versus heat flow using the TA Universal Analysis software package.

Dynamic mechanical thermal analysis
DMTA tests were performed using a TA Instruments Q800. The nominal dimensions of the specimens were 25 mm in length, 10 mm in width and 4 mm in thickness with the actual specimen dimensions determined using a digital calliper prior to the test. Tests were carried out in single cantilever bending mode at a fixed frequency of 1 Hz. The temperature program used was 50 to 300°C at a ramp rate of 5°C per minute. The curves obtained from the experiments are presented as a function of temperature versus storage modulus, loss modulus and damping factor. The T g was determined from the maximum in the variation of tand with temperature.

Scanning electron microscopy
Specimens viewed in conventional SEMs must be electrically conductive in order to achieve a good signal to noise ratio for image quality and thus a thin layer of gold was deposited on the surface of the specimen to ensure that the specimen was conductive. Fractured test specimens were gold coated using a sputter coater (Edward S150B) and the GNP powder samples were adhered to a silicon stub using conductive tape. Micrographs of each sample were obtained using a Philips XL 30 scanning electron microscope with a 10 kV electron acceleration voltage.

Mechanical testing Flexural testing
Mechanical property investigations in this project were carried out using a 3-point bend procedure. Specimens were conditioned within the testing laboratory at a temperature of 23 ± 2°C and 50 ± 5% relative humidity for a period of 72 h before commencing tests. Flexural modulus and strength tests were performed on rectangular specimens according to ASTM D790-03 using an Instron 5982 universal test machine. The values of flexural modulus were calculated using a chord slope between 0.25% and 1% flexural strain. The capacity of the machine load cell was 100 kN. Both the loading nose radius (upper support span) and support radii (lower support span) were 5 mm. The nominal dimensions of the test specimens were 13 mm in width and 4 mm in thickness. At least 5 specimens were tested for each sample batch.

Fracture mechanics testing
The fracture toughness of the materials was evaluated using a single edge notched bend test [6]. Specimens were prepared with a 'v-notch' at the centre. A pre-crack was created in the notch using a sharp blade applied using a drop weight for consistency in the crack depth created. They were then subjected to force displacement in a 3-point bend arrangement until failure. Specimens were conditioned within the testing laboratory at a temperature of 23 ± 2°C and 50 ± 5% relative humidity for a period of 72 h before commencing tests. Specimens were tested using an MTS Insight universal test frame in accordance with ASTM D5045-99 using a 0.1 kN load cell and a test speed of 10 mm per minute. The loading nose radius (upper support span) and support radii (lower support span) were 3.2 mm. The span between the supports was 50.8 mm. The nominal dimensions of the tests specimens were 12.7 mm in width and 3 mm in depth. Both the critical strain energy release rate K IC and fracture energy, G IC were determined for all the specimens.

Characterisation
Scanning electron micrographs of the two types of GNPs are shown in Figure S1 of the Supplementary Material. Histograms of the lateral dimension of the GNPs are also presented in Figure S2 showing that the average flake lengths are 5.2 ± 3.2 lm for GNP-5 and 7.7 ± 4.2 lm for GNP-25. The length for GNP-25 is smaller than the nominal dimensions given by the manufacturer and inspection of the histogram in Figure S2 shows that this nominal value may be influenced by the presence of a few large flakes [31]. Raman spectra of the two types of GNPs are presented in Figure S3 of the Supplementary Material. The spectra are similar and show the presence of D, G and 2D bands typical of GNPs of similar shape and intensity for both materials.
The degree of conversion of the neat epoxy resin and nanocomposites was determined using differential scanning calorimetry. The results are shown in Table S1 of the Supplementary Material and it can be seen that the degree of conversion was over 95% for all formulations. Dynamic mechanical thermal analysis was employed to determine the glass transition temperatures, T g , of the cured materials as shown in Table S2 of the Supplementary Material. The T g of the neat epoxy was found from the peak in tand to be 264.8 ± 0.1°C and increase slightly by * 1°C upon the addition of up to 5 wt% of the GNPs for both types of GNPs. It is unlikely that this small increase will have any significant effect upon the properties of the nanocomposites.

Mechanical properties of the GNP composites
The results of the flexural testing of the neat resin and GNP modified composites are presented in Fig. 1 and in Table S3 of the Supplementary Material. It can be seen that the addition of both the GNP-5 and GNP-25 GNPs leads to a monotonic increase in the Young's modulus of the nanocomposites. In contrast, the addition of these nanofillers causes a drop in the fracture strength which is most marked for the larger GNP-25 filler. These findings are similar to those of previous investigations [20,32] with the high modulus GNPs leading to a significant increase in stiffness but a reduction in strength as the result of the introduction of defects into the system which are larger for the GNP-25 flakes.

Fracture mechanics
Plots of the critical stress intensity factors (K IC ) and critical strain energy release rates (G IC ) for the neat resin and GNP modified composites are presented in Fig. 2 Table S4 of the Supplementary Material. It can be seen that, although the fracture mechanics data are more scattered than the flexural testing data in Fig. 1, the values of both K IC and G IC both increase steadily with the addition of both types of GNP nanofiller.

Flexural modulus
The data in Fig. 1 show that the addition of the GNPs to the epoxy resin leads to an increase in flexural modulus. Our previous study [21] suggested that the relationship between the Young's modulus of the composites, E c and the GNP loading could be analysed using the ''rule of mixtures'' where E f is the Young's modulus of the GNP filler, E m is the Young's modulus of the matrix, V f is the volume fraction of the filler, V m is the volume fraction of the matrix, g o is the Krenchel orientation factor and g l is the length factor determined from shear lag analysis [21]. This analysis assumes that the GNPs are well dispersed in the matrix. The micrographs in Figures S4&S5 Table S5 in the Supplementary Materials shows the variation of E c -E m V m with the volume fraction for the two type of GNP filler. The volume fraction of the GNPs V f , was determined from the wt% (Table S1) using a density for the GNPs of 2.00 g/cm 3 and 1.2 g/cm 3 as the corresponding value for the density of the epoxy matrix. A linear dependence of E c -E m V m upon V f is predicted by Eq. (2), but although the orientation factor g o is known (between 8/15 for random flakes and 1 for aligned flakes) the value of g l depends upon the aspect ratio of nanoplatelets [21]. Only the product g l 9 E f can be calculated from the slope of a plot of E c -E m V m versus V f , and not the two parameters independently.
In our previous study we suggested an alternative approach [21] in the case of a high modulus filler in a low modulus matrix, for which E f [ [ E m as for the materials used in this present study. In this situation the filler modulus is given approximately by where s is the aspect ratio of the GNPs, t is their thickness, m m is the matrix Poisson ratio. In a nanocomposite containing an array of nanoplatelets, the ratio t/T is related to the proximity of neighbouring particles and hence the volume fraction of filler, V f . The exact relationship will depend upon the geometry of the arrangement of the nanoplatelets and for the simple case of a stack of nanoplatelets sandwiched between layers of polymer matrix, it can be assumed that t/T * V f . Using this relationship and substituting Eq. (3) back into the rule of mixtures Eq. (1) gives This can be rearranged to give This equation predicts that E c -E m V m depends linearly upon V f 2 and the particle aspect ratio s can be determined from the slope of the line. Moreover it also follows that modulus of the composite E c is independent of E f (only in the case where E f [ [ E m ) and is controlled principally by the aspect ratio of the nanoplatelets [21]. There is accumulated evidence of the importance of nanoparticle aspect ratio in controlling the mechanical properties nanocomposites reinforced with GNPs [20] and other 2D materials such as hBN nanosheets [33]. Moreover, a recent study upon multiwall carbon nanotubes (MWCNTs) in ethylene-a-octene block copolymer nanocomposites also demonstrated that the level of reinforcement depends strongly upon the aspect ratio of the MWCNTs [34]. Both of these aspect ratios are considerable lower than the nominal values of the order of 1000 based upon the manufacturer's specification. In practice, the values of aspect ratios will be reduced by restacking of the nanoplatelets and agglomeration of the GNPs within the nanocomposites. Moreover the aspect ratio of the two types of GNPs appears to be similar implying that although the lateral dimensions of GNP-25 is higher than that of GNP-5, this may be compensated for by GNP-25 having a higher level of thickness.

Crack propagation in GNP nanocomposites
Based upon the facture surfaces of the nanocomposites in Figs. 4&5 we have modelled the toughening of the epoxy resin by the GNPs in terms of the debonding and pull-out of a single GNP across a crack as shown in Fig. 6. This follows the analysis of the pull-out of a single fibre from a matrix developed by Hull and Clyne [2] for which two important parameters are the aspect ratio of the GNPs, s = L/t and the debonding distance, x 0 L/2 (Fig. 6). If the volume fraction of flakes = V f then the number of flakes per unit area, N = V f /(cross-sectional area of one flake) = V f /Lt.

Debonding
The work done for the interfacial debonding of a single flake is where G ic is the fracture energy of the interface (per unit area of the interface). The total number of flakes with an embedded length of between x 0 and (x 0 ? dx 0 ) = Ndx 0 /(L/ 2) = 2Ndx 0 /L. The total work of debonding, the fracture energy for debonding, G cd , is given by ðnumber of flakesÞ Â ðwork for debonding a single flakeÞ ð 7Þ Since Hence, the fracture energy for debonding is predicted to be proportional to both the aspect ratio and the volume fraction of flakes.

Frictional sliding/pull-out
We need to also calculate the energy required to pull the flakes out of the holes after debonding, the pullout energy, G cp .
Work done on a single flake = (force acting on the interface) 9 (distance moved) where s Ã i is the interfacial shear stress Work done in pulling out the flake completely is therefore Integrating over all flakes being pulled out, the pull-out energy is given by Figure 6 Model GNP flake and debonding geometry.
Âðwork done pulling out a single flakeÞ The fracture energy for sliding/pull-out, G cp , is predicted to also be proportional to both the aspect ratio and the volume fraction of flakes. Moreover, it is shown in Eq. (17) to be proportional to the lateral dimensions of the flakes, L, as well.

Overall behaviour
Assuming that fracture of the flakes does not take place then failure of the nanocomposites will involve a combination of debonding followed by pull-out as shown in the SEM micrographs in Figs. 4, 5 in which there is strong evidence of the pull-out of flakes leaving cavities in the fracture surfaces for all the materials. The contribution from the two different processes will depend upon the system being studied. For example Hull and Clyne [2] suggested that for typical fibre-reinforced composites, the pull-out energy is much more significant than the debonding energy. In contrast, Liu et al. [29] found that for an FKM elastomer reinforced with GNPs debonding was the main energy absorbing process rather than frictional sliding. Chong et al. [20] suggested for a GNP modified epoxy resin that the main toughening mechanisms are combination of debonding followed by pull-out. They suggested, based upon the analysis of the fracture mechanics of nanotube-reinforced nanocomposites, that the value of G ic for debonding should be around 25 J/m 2 with a value of s Ã i * 100 MPa for pull-out, similar to the tensile strength of the epoxy polymer.
Our data for the dependence of fracture energy upon the volume fraction of GNPs are plotted in Fig. 7 and they show a linear dependence of the fracture energy G IC upon V f . The theoretical analyses of debonding and pull-out above predict that for both mechanisms fracture energy is proportional to the flake volume fraction, V f (Eqs. 10 & 17). Similar behaviour has been reported in the literature forgraphene-based nanocomposites [20], which indicates that the fracture behaviour might be explained by composite micromechanics through Eqs. 10 & 17. These two equations also predict a linear dependence of G IC upon s, the aspect ratio. A value of the effective aspect ratio s & 70 for the system has been estimated from the flexural modulus data fitted using micromechancial modelling. We have also measured the diameter of the flakes as around 5-7 lm and a thickness of 6-8 nm is reported by the manufacturer which would give aspect ratios s & 1000. In practice the effective aspect ratio of the nanoplatelets in the nanocomposites will be reduced by aggregation and Chong et al. [20] suggested that an aspect ratio of the order of 100 is more appropriate for the XG Sciences GNPs employed in this present study.
We have fitted the data in Fig. 7 to Eqs. 10 & 17 using the aspect ratios determined from the flexural modulus data (s = 73 for GNP-5 and s = 70 for GNP-25). It was assumed that both debonding and pull-out contribute to the toughening process in an additive manner and the relative contributions of the two processes were adjusted to give appropriate values of G ic and s Ã i : It was found that the best fit to the data was for a contribution of 1/3 of the fracture energy from the debonding process and 2/3 of the fracture energy from the pull-out process. The predicted values of G ic and s Ã i are given in Fig. 7 and they are similar to the suggested values of * 25 J/m 2 and * 100 MPa respectively, suggested by Chong et al. [20]. Other mechanism such as voiding, crack pinning and crack deflection might also contribute to the fracture energy but there is little evidence from the fracture surfaces for them taking place. Moreover it appears that the fracture behaviour can be accounted for completely by the energy absorbed from the two mechanisms of debonding and pull-out without invoking any other processes.

Conclusion
The deformation and fracture of an epoxy resin reinforced by GNPs has been studied in detail and it has been found that the mechanical behaviour is controlled principally by the aspect ratio (length/ thickness) of the GNPs. Other properties of the GNPs such as their Young's modulus or fracture strength do not appear to influence the mechanical properties of the GNP/epoxy nanocomposites. This finding is consistent with recent studies upon nanocomposites reinforced with another 2D material such as hBN [33] and with carbon nanotubes [34]. It has been demonstrated that dependence of the flexural modulus upon the volume fraction of the GNPs can modelled using a combination of the rule of mixtures and shear lag analysis, and the fitting the data the theoretical equation generates an aspect ratio of the GNPs of the order of 70. It has also been found that fracture energy of the GNP/epoxy nanocomposites is proportional to the volume fraction of the GNPs and combined with SEM observations this behaviour has been modelled in terms of a combination of flake debonding followed by pull-out. Using the same value of aspect ratio as that determined from the flexural modulus it is shown that the debonding process contributes to one third of the fracture energy with the remaining two-thirds resulting coming from flake pull-out. These finding have important implications for our understanding of the mechanical properties of brittle polymers reinforced with 2D materials.

Declarations
Conflicts of Interest The authors have no conflicts of interest to declare that are relevant to the content of this article.
Ethical Approval Not applicable.

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