Mechanical, Thermal, and Electrical Properties of Graphene-Epoxy Nanocomposites—A Review

Monolithic epoxy, because of its brittleness, cannot prevent crack propagation and is vulnerable to fracture. However, it is well established that when reinforced—especially by nano-fillers, such as metallic oxides, clays, carbon nanotubes, and other carbonaceous materials—its ability to withstand crack propagation is propitiously improved. Among various nano-fillers, graphene has recently been employed as reinforcement in epoxy to enhance the fracture related properties of the produced epoxy–graphene nanocomposites. In this review, mechanical, thermal, and electrical properties of graphene reinforced epoxy nanocomposites will be correlated with the topographical features, morphology, weight fraction, dispersion state, and surface functionalization of graphene. The factors in which contrasting results were reported in the literature are highlighted, such as the influence of graphene on the mechanical properties of epoxy nanocomposites. Furthermore, the challenges to achieving the desired performance of polymer nanocomposites are also suggested throughout the article.


Introduction
Polymer Matrix Composites (PMCs) have found extensive applications in aerospace, automotive, and construction, owing to ease of processing and high strength-to-weight ratio, which is an important property required for aerospace applications [1]. Among different polymers, epoxy is the most commonly used thermosetting polymer matrix in PMCs [2]. The damage tolerance and fracture toughness of epoxy can be enhanced with the incorporation of (nano-) reinforcement, such as metallic oxides [3][4][5], clays [6][7][8], carbon nanotubes (CNTs) [9][10][11], and other carbonaceous materials [12][13][14]. After the groundbreaking experiments on the two-dimensional material graphene by Nobel Laureates Sir Andre Geim and Konstantin Novoselov [15] from the University of Manchester, graphene came into the limelight in the research community, mainly because of its excellent electrical [16], thermal [17], and mechanical properties [18]. Graphene found widespread applications in electronics [19], bio-electric sensors [20], energy technology [21], lithium batteries [22], aerospace [23], bio-engineering [24], and various other fields of nanotechnology [25]. There is an exponential rise in the use of graphene in different research areas, mainly because of the properties inherited in, and transferred by, graphene to the processed graphene-based materials.
To summarize the research trends related to graphene-based nanocomposites, multiple review articles were recently published in which various aspects of graphene-based nanocomposites were discussed. There are numerous ways to produce and characterize graphene-based materials [26]. Graphene-based materials were studied for different properties, such as thermal properties [27], the properties of other carbonaceous materials such as fullerenes, graphite, Single-Walled Carbon Nanotubes (SWNTs), and Multi-Walled Carbon Nanotubes (MWNTs). It was believed that the real existence of stand-alone single layer graphene would not be possible because of thermal fluctuations, as the stability of long-range crystalline order found in graphene was considered impossible at finite (room) temperatures. This perception was turned into belief by experiments when the stability of thin films was found to have direct relation with the film thickness; i.e., film stability decreases with a decrease in film thickness [52]. However, graphene can currently be found on a silicon substrate or suspended in a liquid and ready for processing. Although its industrial applications are not ubiquitous, it is widely used for research purposes (e.g., as reinforcement in PMCs) and has shown significant improvement in different (mechanical, thermal, electrical etc.) properties of produced nanocomposites [52][53][54][55][56].
The ability of a material to resist the propagation of an advancing crack is vital to the prevention of failure/fracture [57]. Graphene can significantly improve fracture toughness of epoxy at very low volume fraction by deflecting the advancing crack in the matrix. The details of the influence of various kinds of graphene/graphite nanoplatelets (GNPs) on the fracture toughness of epoxy nanocomposites are listed in Table 1. In all the composite systems mentioned in Table 1, epoxy was used as matrix and the nanocomposites were produced using solution casting technique, except [58] where the resin infiltration method was employed. The incorporation of graphene in epoxy can increase its fracture toughness by as much as 131% [59]. It can also be observed that graphene size, weight fraction, surface modification, and dispersion mode have strong influence on the improvement in fracture toughness values of the produced epoxy-graphene nanocomposites. Monolithic epoxy shows brittle fracture and beeline crack propagates, which results in straight fracture surfaces. The advancing crack in epoxy interacts with the graphene sheets. Initially, the crack propagates through the epoxy matrix as there are no significant intrinsic mechanisms available in monolithic epoxy to restrict crack propagation. However, no sooner than the crack faces strong graphene sheets ahead, it surrenders and subdues. Nevertheless, the extent of matrix strengthening and crack bridging provided by graphene strongly depends upon its dispersion state and interfacial interactions with the epoxy matrix [60,61].

Fracture Toughness
The successful employment of epoxy-based nanocomposites relies on the ability of the composite system to meet design and service requirements. The epoxy-based nanocomposites have found applications in aerospace, automotive, and construction due to ease of processing and high strength-to-weight ratio. In many applications, the composite system undergoes external loadings. The relationship between loads acting on a system and the response of the system towards the applied loads is studied in terms of mechanical properties. Therefore, epoxy-based nanocomposites are supposed to have superior mechanical properties. There are various tests to measure mechanical properties, such as tensile testing, bend testing, creep testing, fatigue testing, and hardness testing, to name a few. These tests usually take specimens of specific geometries and subject to loading at certain rate. In general, the industrial scale samples contain porosity and notches which act as stress concentrators and are deleterious to the mechanical properties of nanocomposites. Sometimes, it becomes difficult to control the maximum flaw size. The shape of the flaw is another very important parameter, as pointed notch (V-notch) is more detrimental than round notch (U-shaped) [62]. Due to the pronounced effect of defects on nanocomposite properties, it is important to understand how a system will tolerate external loading in the presence of a flaw under operating conditions, and how a system will resist the propagation of cracks from these flaws. Therefore, how the material will behave in reality will only be determined when the test specimen contains possible flaws, such as a notch. To deal with this issue in a pragmatic way, an intentional notch is produced in the specimen, and resistance to fracture is measured and is termed fracture toughness. Different specimens are used for fracture toughness, such as notched tension, three-point bending, and compact tension specimen, as shown in Figure 1. The toughness is usually measured in three different modes namely (1) Mode-I (tensile mode); (2) Mode-II (shearing mode); and (3) Mode-III (tearing mode), as shown in Figure 2. Most of the literature on epoxy nanocomposites reported Mode-I fracture toughness. Mode-I is preferred in contrast to Mode-II, because shear yielding is the dominant mechanism of failure that is acting under Mode-II, delivering higher values than in Mode-I. Mode-III is never practiced. Due to the pronounced effect of defects on nanocomposite properties, it is important to understand how a system will tolerate external loading in the presence of a flaw under operating conditions, and how a system will resist the propagation of cracks from these flaws. Therefore, how the material will behave in reality will only be determined when the test specimen contains possible flaws, such as a notch. To deal with this issue in a pragmatic way, an intentional notch is produced in the specimen, and resistance to fracture is measured and is termed fracture toughness. Different specimens are used for fracture toughness, such as notched tension, three-point bending, and compact tension specimen, as shown in Figure 1. The toughness is usually measured in three different modes namely (1) Mode-I (tensile mode); (2) Mode-II (shearing mode); and (3) Mode-III (tearing mode), as shown in Figure 2. Most of the literature on epoxy nanocomposites reported Mode-I fracture toughness. Mode-I is preferred in contrast to Mode-II, because shear yielding is the dominant mechanism of failure that is acting under Mode-II, delivering higher values than in Mode-I. Mode-III is never practiced.  Some of the fracture toughness tests include double torsion, indentation, double cantilever tests, and Chevron notch method. Chevron notch method is popular, as it uses a relatively small amount of material and no material constants are needed for the calculations. The technique is also suitable Due to the pronounced effect of defects on nanocomposite properties, it is important to understand how a system will tolerate external loading in the presence of a flaw under operating conditions, and how a system will resist the propagation of cracks from these flaws. Therefore, how the material will behave in reality will only be determined when the test specimen contains possible flaws, such as a notch. To deal with this issue in a pragmatic way, an intentional notch is produced in the specimen, and resistance to fracture is measured and is termed fracture toughness. Different specimens are used for fracture toughness, such as notched tension, three-point bending, and compact tension specimen, as shown in Figure 1. The toughness is usually measured in three different modes namely (1) Mode-I (tensile mode); (2) Mode-II (shearing mode); and (3) Mode-III (tearing mode), as shown in Figure 2. Most of the literature on epoxy nanocomposites reported Mode-I fracture toughness. Mode-I is preferred in contrast to Mode-II, because shear yielding is the dominant mechanism of failure that is acting under Mode-II, delivering higher values than in Mode-I. Mode-III is never practiced.  Some of the fracture toughness tests include double torsion, indentation, double cantilever tests, and Chevron notch method. Chevron notch method is popular, as it uses a relatively small amount of material and no material constants are needed for the calculations. The technique is also suitable material and no material constants are needed for the calculations. The technique is also suitable for high-temperature testing, as flaw healing is not a concern. However, it requires a complex specimen shape that incurs an extra machining cost. The most commonly used specimen is a single-edge notched beam subjected to three or four-point bending. Unfortunately, it has been reported that the results of this test are very sensitive to the notch width and depth. Therefore, a pre-notched or molded beam is preferred. As polymers and polymer nanocomposites can be molded into a desired shape, a specific kind of notch can be replicated in multiple specimens. Due to the reproducibility of notch dimensions, the single-edge notched beam test can give reproducible values of fracture toughness in polymers and polymer nanocomposites. These are the reasons that most of the literature published on polymers and polymer nanocomposites used single-edge notch beams (subjected to three-point bend loading) to determine fracture toughness values (K 1C ). Impact loading methods, such as Charpy and Izod impact tests, are also used to determine impact fracture toughness. Fracture toughness values obtained through different techniques cannot be directly compared [91].
Fracture can be defined as the mechanical separation of a solid owing to the application of stress. Ductile and brittle are the two broad modes of fracture, and fracture toughness is related to the amount of energy required to create fracture surfaces. In ideally-brittle materials (such as glass), the energy required for fracture is simply the intrinsic surface energy of the materials, as demonstrated by Griffith [92]. For structural alloys at room temperature, considerably more energy is required for fracture, because plastic deformation accompanies the fracture process. In polymer nanocomposites, the fracture path becomes more tortuous as cracks detour around strong reinforcement. This increase in crack tortuosity provides additional work to fracture and, therefore, an increase in fracture toughness. In polymers, the fracture process is usually dominated by crazing or the nucleation of small cracks and their subsequent growth [93].
Toughness is defined as the ability of a material to absorb energy before fracture takes place. It is usually characterized by the area under a stress-strain curve for a smooth (un-notched) tension specimen loaded slowly to fracture. The term fracture toughness is usually associated with the fracture mechanics methods that deal with the effect of defects on the load-bearing capacity of structural components. The fracture toughness of materials is of great significance in engineering design because of the high probability of flaws being present. Defined another way, it is the critical stress intensity at which final fracture occurs. The plane strain fracture toughness (critical stress intensity factor, K 1C ) can be calculated for a single-edge notched three-point bending specimen using Equation (1), where P max is the maximum load of the load-displacement curve (N), f (a/w) is a constant related to the geometry of the sample and is calculated using Equation (2), B is sample thickness (mm), W is sample width (mm), and a is crack length (a should be kept between 0.45 W and 0.55 W, according to ASTM D5045) [72]. The critical strain energy release rate (G 1C ) can be calculated using Equation (3), where E is the Young's modulus obtained from the tensile tests (MPa), and ν is the Poisson's ratio of the polymer. The geometric function f(a/W) strongly depends on the a/W ratio [94].
The fracture toughness is dependent on many factors, such as type of loading and environment in which the system will be loaded [95]. However, the key defining factor is the microstructure as summed up in Figure 3 [96]. The properties of nanocomposites are also significantly dependent on filler shape and size [51]. The graphene size, shape, and topography can be controlled simultaneously [97].

Structure and Fracture Toughness
Graphene has a honeycomb lattice having sp 2 bonding, which is much stronger than the sp 3 bonding found in diamond [98]. There is sp 2 orbital hybridization between Px and Py that forms a σbond [52]. The orbital Pz forms a π-bond with half-filled band that allows free motion of electrons. When bombarded with pure carbon atoms, hydrocarbons, or other carbon-containing molecules, the graphene directs the carbon atoms into vacant seats, thereby self-repairing the holes in the graphene sheet. Through their crack deflection modeling, Faber and Evans showed that maximum improvement in fracture toughness, among all other nano-reinforcements, can be obtained using graphene-mainly because of its better capability of deflecting the propagating cracks [99,100].

Structure and Fracture Toughness
Graphene has a honeycomb lattice having sp 2 bonding, which is much stronger than the sp 3 bonding found in diamond [98]. There is sp 2 orbital hybridization between P x and P y that forms a σ-bond [52]. The orbital P z forms a π-bond with half-filled band that allows free motion of electrons. When bombarded with pure carbon atoms, hydrocarbons, or other carbon-containing molecules, the graphene directs the carbon atoms into vacant seats, thereby self-repairing the holes in the graphene sheet. Through their crack deflection modeling, Faber and Evans showed that maximum improvement in fracture toughness, among all other nano-reinforcements, can be obtained using graphene-mainly because of its better capability of deflecting the propagating cracks [99,100].
As graphene is a 2D structure, each carbon atom can undergo chemical reaction from the sides, resulting in high chemical reactivity. The carbon atoms on the edge of graphene sheet have three incomplete bonds (in single layer graphene) that impart especially high chemical reactivity to edge carbon atoms. In addition, defects within a graphene sheet are high energy sites and preferable sites for chemical reactants. All these factors make graphene a very highly chemical reactive entity. The graphene oxide can be reduced by using Al particles and potassium hydroxide [101]. The graphene structure can be studied using Transmission Electron Microscopy (TEM) and other high-resolution tools. Wrinkles were observed in graphene flat sheet, which were due to the instability of the 2D lattice structure [72,102].
Wrinkling is a large and out-of-plane deflection caused by compression (in-plane) or shear. Wrinkling is usually found in thin and flexible materials, such as cloth fabric [103]. Graphene nanosheets (GNSs) were also found to undergo a wrinkling phenomenon [104]. When wrinkling takes place, strain energy is stored within GNSs which is not sufficient to allow the GNSs to regain their shape. Wrinkling can be found on GNSs as well as on exfoliated graphite. The wrinkles in GNSs are sundering apart at different locations while getting closer at other regions. As GNSs do not store sufficient elastic strain energy, wrinkling is an irreversible phenomenon, but can be altered by external agency [105]. The surface roughness varies depending on graphene sheets, owing to their dissimilar topographical features, such as wrinkles' size and shape. Therefore, the ability of sheets to mechanically interlock with other sheets and polymer chains is dissimilar. Wang et al. showed that a wrinkle's wavelength and amplitude are directly proportional to sheet size (length, width, and thickness), as is clear from Equations (4) and (5), where λ is wrinkle wavelength, ν is Poisson's ratio, L is graphene sheet size, t is thickness of graphene sheet, ε is edge contraction on a suspended graphene sheet, and A is wrinkle amplitude [57].
Palmeri et al. showed that the graphene sheets have a coiled structure that helps them to store a sufficient amount of energy [106]. The individual sheet and chunk of sheets together are subjected to plastic deformation at the application of external load. The applied energy is utilized in undertaking plastic work that enhances the material's ability to absorb more energy. It is believed that large graphene sheets have large size wrinkles [107]. These wrinkles twist, bend, and fold the graphene sheets. The wrinkles and other induced defects remain intact while curing of polymer matrix. This reduces the geometric continuity and regularity of graphene and lowers load transfer efficiency, and can cause severe localized stress concentration.

Surface Area and Fracture Toughness
K 1C strongly depends upon the surface area of the reinforcement, as it influences the matrix-reinforcement interfacial interactions. When the reinforcement has a large surface area, the interfacial area increases, which increases the number of routes for the transport of load from matrix to reinforcement [87]. On the contrary, when agglomeration takes place, not only the agglomerates act as stress raisers, but the net surface area is also decreased, which further drops the fracture toughness and other mechanical properties of nanocomposites [108]. One reason that graphene supersedes other reinforcements is its high surface area [109]. The surface area of graphene is even higher than that of CNTs [110]. To make a comparison, the surface areas of short carbon fiber and graphene are calculated. The surface area of carbon fiber is calculated using the formula for a solid cylinder, while the surface area of graphene is calculated using the formula for a rectangular sheet. The thickness of graphene is considered variable, so the same relation can be used for multiple layers of graphene sheets stacked together in the form of graphene nanosheets. The length of short carbon fiber is taken to be 1 µm and the diameter 0.1 µm. The dimensions of graphene are ˆwˆt = 1 µmˆ0.1 µmˆ10 nm. The density of both short carbon fiber and graphene is taken to be 2.26 to make comparison based on dimensions only. The surface area of 1 g of carbon fibers is 19 m 2 and that of graphene is 98 m 2 . It can be observed that although the lengths of both reinforcements are the same and the width of graphene is equal to the diameter of a short carbon fiber, there is a large difference in surface areas when the thickness of graphene is kept 10 nm. This difference will further increase if graphene dimensions are reduced. The specific surface area of graphene is as high as 2600 m 2 /g [111,112]. It shows that graphene, having a much larger surface area, can significantly improve the fracture toughness of the epoxy nanocomposites [113,114]. There is also improved thermal conduction among graphene-graphene links that significantly improves the overall thermal conductivity of the nanocomposites [115,116]. The electrical conductivity also increases with graphene as graphene sheets form links and provide a passageway for electrical conduction [117].
Zhao and Hoa used a theoretical computer simulation approach to study the improvement in toughness when epoxy is reinforced with 2D nano-reinforcements of different particle size [118,119]. The simulation results showed that there is a direct relation between particle size and stress concentration factor up to 1 µm, after which point the stress concentration factor was impervious to any further size increase. However, Chatterjee et al. [82] showed that fracture toughness was improved by increasing the graphene size, which is in negation with simulation results by Zhao and Hoa [120,121].
The relationship between graphene size and stress concentration factor can be correlated with the facile analogy of substitutional solid solution. The extent of strain field produced by a foreign atom depends upon the difference in atomic sizes of the foreign and parent atoms. When there is a large difference between foreign and parent atoms, a large strain field around the atom is generated. On the contrary, when the difference in atomic sizes of parent and foreign atoms is small, the strain field is limited. As both atomic and GNPs sizes are in the nano-meter range, the analogy can arguably be applied to an epoxy-graphene system where large sheet size will cause higher stress concentration factor than that produced by small sheet size. Therefore, graphene with smaller sheet size can be more efficient in improving the fracture toughness than the larger graphene sheets.
The increase in the fracture toughness of epoxy was found to be strongly dependent upon the graphene sheet size [57]. For the nanocomposites, an inverse relation was found between sheet size and fracture toughness in most cases. The increase in fracture toughness with a decrease in sheet size can be explained on the basis of stress concentration factor, as discussed above. Although graphene acts as reinforcement, however, it has associated stress and strain fields which arise from the distortion of the structure of polymer matrix. When sheet size, weight fraction, or both are increased beyond a certain value, the stress concentration factor dominates the reinforcing character. As a result, fracture toughness and other mechanical properties-such as tensile and flexural strength and stiffness-start decreasing, which is in accordance with Zhao and Hoa's simulation results [118].
Wang et al. used Graphene Oxide (GO) of three different sizes, namely GO-1, GO-2, GO-3, having average diameters 10.79, 1.72, and 0.70 µm, respectively, to produce nanocomposites using an epoxy matrix [57]. They observed that fracture toughness was strongly dependent on GO sheet size. The maximum increase in fracture toughness was achieved with the smallest GO sheet size. The K 1C values dropped when weight fraction was increased beyond 0.1 wt %. This decrease in K 1C with increasing weight fraction can be correlated with crack generation and dispersion state.

Weight Fraction and Fracture Toughness
The K 1C first increases with GO and then starts decreasing in all three of the cases. The increase in K 1C is due to the reinforcing effect of GO, while the drop in K 1C is due to crack generation and agglomeration. The addition of a high GO weight fraction generates cracks that reduce the fracture toughness of the nanocomposite [57]. The other reason for such behavior is due to the high probability of agglomeration at higher weight fractions due to Van der Waals forces [57].
The weight fractions of reinforcements at which maximum K 1C was achieved for different epoxy-graphene nanocomposites are shown in Figure 4. All the published research articles stated that the maximum K 1C values were achieved at or below 1 wt % of graphene, and K 1C dropped when the weight fraction of graphene was raised beyond 1 wt %. The decrease in K 1C with a higher weight fraction of graphene can be correlated with the dispersion state of graphene. As graphene weight fraction increases beyond 1 wt %, the dispersion state becomes inferior. The maximum increase in K 1C was 131%, which is achieved at 1 wt % graphene [59]. However, the dispersion mode adopted is worth discussing. The graphene was dispersed using a combination of sonication and mechanical stirring. This combination provides an efficient means of dispersing the graphene into epoxy. In addition to that, sonication causes exfoliation, delayering, and length shortening of graphene sheets. These aspects help alleviate the stress concentration factor and cracks associated with large graphene sheets. These factors result in K 1C improvement up to 131%, which is the maximum among the improvements in K 1C values reported in epoxy-graphene nanocomposites. the weight fraction of graphene was raised beyond 1 wt %. The decrease in K1C with a higher weight fraction of graphene can be correlated with the dispersion state of graphene. As graphene weight fraction increases beyond 1 wt %, the dispersion state becomes inferior. The maximum increase in K1C was 131%, which is achieved at 1 wt % graphene [59]. However, the dispersion mode adopted is worth discussing. The graphene was dispersed using a combination of sonication and mechanical stirring. This combination provides an efficient means of dispersing the graphene into epoxy. In addition to that, sonication causes exfoliation, delayering, and length shortening of graphene sheets. These aspects help alleviate the stress concentration factor and cracks associated with large graphene sheets. These factors result in K1C improvement up to 131%, which is the maximum among the improvements in K1C values reported in epoxy-graphene nanocomposites.  Table 1).
It can be observed from Figure 4 that there is no fixed value of GNPs wt % at which a maximum increase in K1C is achieved. In addition, the increase in K1C at fixed GNP wt % is not the same. For example, at 0.5 wt %, the % increase in K1C is reported to be up to 45% by Chandrasekaran et al. [67], and about 110% by Ma et al. [80]. Therefore, it can be concluded that the wt % of GNPs is not the sole factor defining the influence of GNPs on the mechanical properties of nanocomposites. There are other influential factors as well, such as dispersion method, use of dispersant, and functionalization. In addition, the use of organic solvent is another important parameter in defining the improvement in mechanical properties. It was observed that a lower improvement in K1C was observed when dispersion was carried out with only sonication, and a higher improvement in K1C was observed when sonication was assisted with a secondary dispersion method, especially mechanical stirring.

Dispersion State and Fracture Toughness
The end product of most of the graphene synthesis methods is agglomerated graphene [33]. In addition, graphene tends to agglomerate due to weak intermolecular Van der Waals forces [113]. Therefore, dispersing graphene in epoxy matrix is always a challenge. The relationship between dispersion state and the nature of crack advancement is shown schematically in Figure 5. The advancing cracks can be best barricaded by uniformly dispersed graphene. Tang et al. produced  Table 1).
It can be observed from Figure 4 that there is no fixed value of GNPs wt % at which a maximum increase in K 1C is achieved. In addition, the increase in K 1C at fixed GNP wt % is not the same. For example, at 0.5 wt %, the % increase in K 1C is reported to be up to 45% by Chandrasekaran et al. [67], and about 110% by Ma et al. [80]. Therefore, it can be concluded that the wt % of GNPs is not the sole factor defining the influence of GNPs on the mechanical properties of nanocomposites. There are other influential factors as well, such as dispersion method, use of dispersant, and functionalization. In addition, the use of organic solvent is another important parameter in defining the improvement in mechanical properties. It was observed that a lower improvement in K 1C was observed when dispersion was carried out with only sonication, and a higher improvement in K 1C was observed when sonication was assisted with a secondary dispersion method, especially mechanical stirring.

Dispersion State and Fracture Toughness
The end product of most of the graphene synthesis methods is agglomerated graphene [33]. In addition, graphene tends to agglomerate due to weak intermolecular Van der Waals forces [113]. Therefore, dispersing graphene in epoxy matrix is always a challenge. The relationship between dispersion state and the nature of crack advancement is shown schematically in Figure 5. The advancing cracks can be best barricaded by uniformly dispersed graphene. Tang et al. produced highly dispersed and poorly dispersed RGO-epoxy nanocomposites using solution casting technique. The high dispersion of RGO in epoxy was achieved using a ball milling process [72]. The RGO dispersed in epoxy using sonication process and not subjected to ball milling was termed poorly dispersed. They studied the influence of graphene dispersion on the mechanical properties of the produced nanocomposite. The highly dispersed RGO-epoxy showed a 52% improvement in K 1C , while the poorly dispersed RGO-epoxy showed only a 24% improvement in K 1C . It shows that better dispersion of graphene can significantly improve the fracture toughness of epoxy nanocomposites [72]. dispersed in epoxy using sonication process and not subjected to ball milling was termed poorly dispersed. They studied the influence of graphene dispersion on the mechanical properties of the produced nanocomposite. The highly dispersed RGO-epoxy showed a 52% improvement in K1C, while the poorly dispersed RGO-epoxy showed only a 24% improvement in K1C. It shows that better dispersion of graphene can significantly improve the fracture toughness of epoxy nanocomposites [72]. Several dispersion modes to disperse reinforcement into epoxy matrix were successfully adopted (see references in Table 1). The maximum % increase in K1C as a function of dispersion mode is shown in Figure 6. In most of these articles, sonication is the main mode of dispersing reinforcement in epoxy matrix. It can be observed that when sonication is assisted by a supplementary dispersion technique (such as mechanical stirring and magnetic stirring), the K1C values were significantly Several dispersion modes to disperse reinforcement into epoxy matrix were successfully adopted (see references in Table 1). The maximum % increase in K 1C as a function of dispersion mode is shown in Figure 6. In most of these articles, sonication is the main mode of dispersing reinforcement in epoxy matrix. It can be observed that when sonication is assisted by a supplementary dispersion technique (such as mechanical stirring and magnetic stirring), the K 1C values were significantly increased. The maximum improvement of 131% in K 1C was achieved when a combination of sonication and mechanical stirring was employed [59]. The second highest improvement in K 1C was achieved with a combination of sonication and magnetic stirring, an increase in K 1C of 109% [80]. The minimum values in K 1C improvements are achieved when sonication is coupled with ball milling [60,64,100]. Since both the sonication and ball milling processes reduce the sheet size and produce surface defects [120][121][122][123][124][125][126][127][128][129][130][131][132][133][134], we believe that the surface defects significantly increased and sheet size was reduced below the threshold value, and therefore a greater improvement in K 1C was not achieved. Although three roll milling (3RM, calendering process) is an efficient way of dispersing the reinforcement into the polymer matrix due to high shear forces, the maximum improvement in K 1C using three roll mill was reported as 86% [77], which is far below that achieved with a combination of sonication and mechanical stirring (131% [59]). sonication and mechanical stirring was employed [59]. The second highest improvement in K1C was achieved with a combination of sonication and magnetic stirring, an increase in K1C of 109% [80]. The minimum values in K1C improvements are achieved when sonication is coupled with ball milling [60,64,100]. Since both the sonication and ball milling processes reduce the sheet size and produce surface defects [120][121][122][123][124][125][126][127][128][129][130][131][132][133][134], we believe that the surface defects significantly increased and sheet size was reduced below the threshold value, and therefore a greater improvement in K1C was not achieved. Although three roll milling (3RM, calendering process) is an efficient way of dispersing the reinforcement into the polymer matrix due to high shear forces, the maximum improvement in K1C using three roll mill was reported as 86% [77], which is far below that achieved with a combination of sonication and mechanical stirring (131% [59]).  Table  1).

Functionalization and Fracture Toughness
Achieving maximum improvement in fracture toughness of polymers by using graphene depends on the ability to optimize the dispersibility of graphene and the interfacial interactions with the epoxy matrix. As described previously, graphene tends to agglomerate due to the weak Van der Waals interactions, and its smoother surface texture inhibits strong interfacial interactions. To tackle the limited dispersibility and interfacial bonding of graphene, surface modifications are carried out [135][136][137][138][139]. In fact, the introduction of functional groups on the graphene surface can induce novel properties [140][141][142][143][144]. Various methods to modify the graphene surface have been employed, and can be categorized into two main groups, namely: (1) chemical functionalization; and (2) physical functionalization.
In chemical functionalization, chemical entities are typically attached covalently. For example, in defect functionalization, functional groups are attached at the defect sites of graphene, such as -COOH (carboxylic acid) and -OH (hydroxyl) groups. Defects can be any departure from regularity, including pentagons and heptagons in the hexagonal structure of graphene. Defects may also be produced by reaction with strong acids such as HNO3, H2SO4, or their mixture, or strong oxidants including KMnO4, ozone, and reactive plasma [145]. The functional groups attached at the defect sites of graphene can undergo further chemical reactions, including but not limited to silanation, thiolation, and esterification [146]. Unlike chemical functionalization, physical functionalization has non-covalent functionalization, where the supermolecular complexes of graphene are formed as a result of the wrapping of graphene by surrounding polymers [33]. Surfactants lower the surface tension of graphene, thereby diminishing the driving force for the   Table 1).

Functionalization and Fracture Toughness
Achieving maximum improvement in fracture toughness of polymers by using graphene depends on the ability to optimize the dispersibility of graphene and the interfacial interactions with the epoxy matrix. As described previously, graphene tends to agglomerate due to the weak Van der Waals interactions, and its smoother surface texture inhibits strong interfacial interactions. To tackle the limited dispersibility and interfacial bonding of graphene, surface modifications are carried out [135][136][137][138][139]. In fact, the introduction of functional groups on the graphene surface can induce novel properties [140][141][142][143][144]. Various methods to modify the graphene surface have been employed, and can be categorized into two main groups, namely: (1) chemical functionalization; and (2) physical functionalization.
In chemical functionalization, chemical entities are typically attached covalently. For example, in defect functionalization, functional groups are attached at the defect sites of graphene, such as -COOH (carboxylic acid) and -OH (hydroxyl) groups. Defects can be any departure from regularity, including pentagons and heptagons in the hexagonal structure of graphene. Defects may also be produced by reaction with strong acids such as HNO 3 , H 2 SO 4 , or their mixture, or strong oxidants including KMnO 4 , ozone, and reactive plasma [145]. The functional groups attached at the defect sites of graphene can undergo further chemical reactions, including but not limited to silanation, thiolation, and esterification [146]. Unlike chemical functionalization, physical functionalization has non-covalent functionalization, where the supermolecular complexes of graphene are formed as a result of the wrapping of graphene by surrounding polymers [33]. Surfactants lower the surface tension of graphene, thereby diminishing the driving force for the formation of aggregates. The graphene dispersion can be enhanced by non-ionic surfactants in case of water-soluble polymers [33].
The different functionalization methods adopted to study their influence on K 1C values with corresponding improvements (%) in K 1C values are shown in Figure 7. The minimum improvement was achieved for amino-functionalized graphene oxide (APTS-GO) [74], while the maximum improvement was recorded for surfactant-modified graphene nanoplatelets [59]. This could be attributed to the improvement in the dispersion state of graphene in the epoxy matrix when surfactants were used, in addition to improving interactions without causing a reduction in graphene sheet size or imparting surface defects on graphene sheets. The different functionalization methods adopted to study their influence on K1C values with corresponding improvements (%) in K1C values are shown in Figure 7. The minimum improvement was achieved for amino-functionalized graphene oxide (APTS-GO) [74], while the maximum improvement was recorded for surfactant-modified graphene nanoplatelets [59]. This could be attributed to the improvement in the dispersion state of graphene in the epoxy matrix when surfactants were used, in addition to improving interactions without causing a reduction in graphene sheet size or imparting surface defects on graphene sheets.  Table 1).

Crosslink Density and Fracture Toughness
In thermosetting materials, such as epoxy, high crosslink density is desirable for the improvement of mechanical properties. However, high crosslink density has a detrimental effect on fracture toughness [57]. Therefore, a crosslink density threshold is required in order to achieve optimal properties [147,148]. During the curing of thermoset polymers, while phase transformation takes place, graphene sheets tend to agglomerate in order to reduce configurational entropy [57]. Additionally, the viscosity initially reduces when the temperature is increased during curing, which makes the movement of the graphene sheets relatively easy, supporting their agglomeration. Due to the wrinkle-like structure and high specific surface area of graphene, strong interfacial interactions are possible with epoxy chains. It may also affect the overall curing reaction by changing the maximum exothermic heat flow. Molecular dynamics studies conducted by Smith et al. also showed that there was a change in polymer chain mobility caused by geometric constraints at the surface of nano-reinforcement [149].
The graphene affects the crosslink density of epoxy [65]. When graphene is dispersed in epoxy, the polymer chains are restricted, and crosslinking is decreased. The decrease in crosslinking lowers the heat release rate. It was reported that both graphene platelets (GnPs) and polybenzimidazole functionalized GnPs (fGnPs) decreased the heat release rate of the curing reaction and increased the curing temperature [65]. It can also be attributed to the dispersion state of the reinforcement. Uniformly dispersed reinforcement will have a more pronounced effect on heat release rate and curing temperature than poorly dispersed reinforcement. Therefore, fGnPs have a better dispersion  Table 1).

Crosslink Density and Fracture Toughness
In thermosetting materials, such as epoxy, high crosslink density is desirable for the improvement of mechanical properties. However, high crosslink density has a detrimental effect on fracture toughness [57]. Therefore, a crosslink density threshold is required in order to achieve optimal properties [147,148]. During the curing of thermoset polymers, while phase transformation takes place, graphene sheets tend to agglomerate in order to reduce configurational entropy [57]. Additionally, the viscosity initially reduces when the temperature is increased during curing, which makes the movement of the graphene sheets relatively easy, supporting their agglomeration. Due to the wrinkle-like structure and high specific surface area of graphene, strong interfacial interactions are possible with epoxy chains. It may also affect the overall curing reaction by changing the maximum exothermic heat flow. Molecular dynamics studies conducted by Smith et al. also showed that there was a change in polymer chain mobility caused by geometric constraints at the surface of nano-reinforcement [149].
The graphene affects the crosslink density of epoxy [65]. When graphene is dispersed in epoxy, the polymer chains are restricted, and crosslinking is decreased. The decrease in crosslinking lowers the heat release rate. It was reported that both graphene platelets (GnPs) and polybenzimidazole functionalized GnPs (fGnPs) decreased the heat release rate of the curing reaction and increased the curing temperature [65]. It can also be attributed to the dispersion state of the reinforcement. Uniformly dispersed reinforcement will have a more pronounced effect on heat release rate and curing temperature than poorly dispersed reinforcement. Therefore, fGnPs have a better dispersion state than GnPs [65]. There are two opposite effects of filler in the matrix: (1) the fillers could restrict the polymer chains, which should increase T g ; (2) the reactive fillers could lower the crosslinking density of epoxy, which should decrease T g . An increase in T g shows that interfacial interactions dominate the crosslinking density effect [65].

Fracture Patterns
Monolithic epoxy exhibits a bamboo-like brittle fracture pattern [105]. However, with the incorporation of graphene, the cracks are deflected, resulting in parabolic and non-linear fracture patterns [105]. The change in graphene structure and shape upon the application of external stress also affects the overall fracture pattern of the nanocomposite, due to changes in mechanical interlocking and interfacial interactions [105]. It was recorded that bending behavior of GNSs when wrapping around a corner resulted in the sliding of layers over one another, and was termed "sliding mode" [105]. In sliding mode, angular change (γ) was observed. This γ was produced when layers slid over one another. If the state of stress is relatively high, the inner layers undergo splitting and buckling that further results in kinking, by which the bending stress is alleviated [105]. GNSs size and edge morphology control the type of fracture mode. In the case of smaller GNSs (smaller refers to volume of individual GNSs), where the sliding surface is smaller, the resistance to sliding is lower, and hence sliding mode will be preferred. On the contrary, if GNSs are of larger size and the sides are longer, the resistance to sliding would be higher, and hence buckling mode will be preferred over sliding mode [105]. The tearing step subdivides into multiple steps. Consequently, the initial crack branches into multiple small cracks [105]. However, the extent of subdivision of the advancing cracks depends on the dispersion state of the filler and interfacial interactions.

Other Mechanical Properties
The literature shows an absence of consensus on the role of graphene in improving other mechanical properties of nanocomposites. Some authors reported significant improvement in the mechanical properties of nanocomposites reinforced with GNPs [150][151][152][153][154]. On the other hand, there was no significant effect due to the incorporation of GNPs into epoxy matrix [155][156][157][158], and even worse, the mechanical properties deteriorated by the addition of GNPs [159][160][161][162][163]. In general, a major portion of the literature has shown that GNPs can significantly improve the mechanical properties of epoxy nanocomposites. The percent improvements in tensile strength and tensile modulus are shown in Figure 8. The maximum improvement in tensile strength is as high as 108% [164] and in the tensile modulus up to 103% [165]. GNPs were also found to improve flexural properties of nanocomposites. Naebe et al. produced covalent functionalized epoxy-graphene nanocomposites, and reported 18% and 23% increase in flexural strength and modulus, respectively [166]. Qi et al. produced graphene oxide-epoxy nanocomposites and reported an increase of up to 53% in flexural strength [167]. The impact strength and hardness were also significantly improved by graphene in epoxy nanocomposites. For example, Ren et al. applied a combination of bath sonication, mechanical mixing, and shear mixing to disperse GO in cyanate ester-epoxy and produced nanocomposites using in situ polymerization [168]. They reported an increase of 31% in impact strength. Qi  The G 1C also improved with the incorporation of graphene in epoxy nanocomposites. Meng et al. produced epoxy-graphene nanocomposites and reported an increase in G 1C of up to 597% [173].

Thermal Properties
Due to the superior thermal conductivity of graphene, graphene-based polymer nanocomposites are promising candidates for high-performance thermal interface materials [174]. The dissipation of heat from electronic devices may also be barricaded when the high thermal conductivity of graphene is efficiently utilized. The graphene has shown higher efficiency in increasing the thermal conductivity of polymers than CNTs [175]. It has been found experimentally that the Effective Thermal Conductivity (K eff ) of graphene-based polymer nanocomposites has a non-linear dependence on graphene weight fraction [176][177][178]. Xie et al. proposed an analytical model to determine the K eff of graphene-based nanocomposites [179]. Their model proposed very high thermal conductivity values, as the model did not take into account the interfacial thermal resistance. Lin et al. developed a model based on Maxwell-Garnett effective medium approximation theory to determine the effective thermal conductivity of graphene-based nanocomposites [180,181]. They showed that the enhancement in thermal conductivity is strongly influenced by the aspect ratio and orientation of graphene. conductivity of polymers than CNTs [175]. It has been found experimentally that the Effective Thermal Conductivity (Keff) of graphene-based polymer nanocomposites has a non-linear dependence on graphene weight fraction [176][177][178]. Xie et al. proposed an analytical model to determine the Keff of graphene-based nanocomposites [179]. Their model proposed very high thermal conductivity values, as the model did not take into account the interfacial thermal resistance. Lin et al. developed a model based on Maxwell-Garnett effective medium approximation theory to determine the effective thermal conductivity of graphene-based nanocomposites [180,181]. They showed that the enhancement in thermal conductivity is strongly influenced by the aspect ratio and orientation of graphene. Hu et al. used a molecular dynamics approach to show that the agglomeration of graphene is of major concern in increasing the thermal conductivity of the system [192]. The variation in thermal conductivity with various forms of graphene and graphite nanocomposites is summarized in Table  2, and the influence of dispersion mode on the improvement of thermal conductivity is shown in Figure 9. The maximum improvement in thermal conductivity was observed in the case of mechanical stirring. In general, sonication caused a lower improvement in thermal conductivity. However, maximum improvement in thermal conductivity (not shown in Figure 9) was observed in the case of sonication, 1.6 × 10 4 % [193]. Hu et al. used a molecular dynamics approach to show that the agglomeration of graphene is of major concern in increasing the thermal conductivity of the system [192]. The variation in thermal conductivity with various forms of graphene and graphite nanocomposites is summarized in Table 2, and the influence of dispersion mode on the improvement of thermal conductivity is shown in Figure 9. The maximum improvement in thermal conductivity was observed in the case of mechanical stirring. In general, sonication caused a lower improvement in thermal conductivity. However, maximum improvement in thermal conductivity (not shown in Figure 9) was observed in the case of sonication, 1.6ˆ10 4 % [193]. major concern in increasing the thermal conductivity of the system [192]. The variation in thermal conductivity with various forms of graphene and graphite nanocomposites is summarized in Table  2, and the influence of dispersion mode on the improvement of thermal conductivity is shown in Figure 9. The maximum improvement in thermal conductivity was observed in the case of mechanical stirring. In general, sonication caused a lower improvement in thermal conductivity. However, maximum improvement in thermal conductivity (not shown in Figure 9) was observed in the case of sonication, 1.6 × 10 4 % [193].  Table 2).  Table 2).

Electrical Properties
Tailoring the electrical properties of graphene can unlock its many potential electronic applications [194,195]. For example, effective gauge fields are introduced when graphene lattice deformation takes place. Like the effective magnetic field, the produced effective gauge fields influence the Dirac fermions [196]. The Fermi level in undoped graphene lies at the Dirac point, where the minimum conductivity values are achieved [197]. By adding free charge carriers (i.e., dopants), the electrical properties of graphene can be improved, and conductivity increases linearly with carrier density [198,199]. For example, boron as dopant can contribute~0.5 carriers per dopant in a graphene sheet [200]. Dopants can be introduced during the synthesis of graphene using chemical vapor deposition (CVD) [201]. The variation in electrical conductivity with various forms of graphene and graphite nanocomposites is summarized in Table 3, and the influence of dispersion mode on the improvement of thermal conductivity is shown in Figure 10. The maximum improvement in electrical conductivity was observed in the case of a combination of ball milling and mechanical stirring. Therefore, both thermal and electrical conductivities improved in the case of mechanical stirring.

Electrical Properties
Tailoring the electrical properties of graphene can unlock its many potential electronic applications [194,195]. For example, effective gauge fields are introduced when graphene lattice deformation takes place. Like the effective magnetic field, the produced effective gauge fields influence the Dirac fermions [196]. The Fermi level in undoped graphene lies at the Dirac point, where the minimum conductivity values are achieved [197]. By adding free charge carriers (i.e., dopants), the electrical properties of graphene can be improved, and conductivity increases linearly with carrier density [198,199]. For example, boron as dopant can contribute ~0.5 carriers per dopant in a graphene sheet [200]. Dopants can be introduced during the synthesis of graphene using chemical vapor deposition (CVD) [201]. The variation in electrical conductivity with various forms of graphene and graphite nanocomposites is summarized in Table 3, and the influence of dispersion mode on the improvement of thermal conductivity is shown in Figure 10. The maximum improvement in electrical conductivity was observed in the case of a combination of ball milling and mechanical stirring. Therefore, both thermal and electrical conductivities improved in the case of mechanical stirring.  Table 3).  Table 3). The simultaneous inclusion of GnPs and SnP/SnW at a combined loading of 1 vol % resulted in about 40% enhancement in the through-thickness thermal conductivity, while the inclusion of GnP at the same loading resulted in only 9% improvement. A higher increment with simultaneous addition of GnP and SnP/SnW can be attributed to synergistic effects. Three-dimensional graphene network (3DGNs) (30 wt %) None 1,900 (Composites produced using layer-by-layer dropping method.) The filler with large size is more effective in increasing the thermal conductivity of epoxy because of continuous transmission of acoustic phonons and minimum scattering at the interface due to reduced interfacial area. High intrinsic thermal conductivity of graphene is the major reason for the obtained high thermal conductivity of nanocomposites. Sn + MgSr

237.5
As the filler/matrix interfaces increase, the thermal resistance increases due to phonon scattering. In order to improve the thermal conductivity of a composite, it is better to structure a sample with an adapted morphology than trying to have the best dispersion. A 3D-network was first prepared with graphite foils oriented through the thickness of the sample and then stabilized with DGEBA/DDS resin. The produced composite sample was called as "Network". In "fibers", all the graphite flakes were aligned through the thickness of sample. When a DGEBA interface layer was applied in "fiber", the sample was called "Fiber + 1 interface". When two DGEBA interface layers was applied in "fiber" the sample was called as "Fiber + 2 interfaces". The increase in thermal conductivity is higher in the case of larger particle size than smaller particle size. [  The thermal conductivity increases with increasing particle size. The particle size distribution significantly influences the thermal conductivity. GNPs with a broad particle size distribution gave higher thermal conductivity than the particles with a narrow particle size distribution, due to the availability of smaller particles that can bridge gaps between larger particles. [221] GNPs  GNPs showed a significantly greater increase in thermal conductivity than MWNTs. The maximum improvement in thermal conductivity is shown by non-covalent functionalized GNS, which can be attributed to high surface area and uniform dispersion of GNS. The layered structure of MWNTs enables an efficient phonon transport through the inner layers, while SWNTs present a higher resistance to heat flow at the interface, due to its higher surface area. The f-MWNTs have functional groups on their surface, acting as scattering points for the phonon transport.
[226]   The conductivity was measured before post-curing.
GO (0.5 wt %) Two phase extraction 240 The system was not fully cured during curing process.
GO (0.5 wt %) 7.80ˆ10 3 The conductivity significantly increased after post-curing. The increase in electrical conductivity with Al(OH) 3 functionalization decreased. The electrically insulating Al(OH) 3 on the graphene oxide nanosheet can prevent electron tunneling and act as ion traps which block ion mobility, resulting in a decrease in the electrical properties of nanocomposites.

Conclusions
The following are the key points related to epoxy/graphene nanocomposites:

1.
Epoxy is an excellent matrix for graphene composites because of its efficient properties such as enhancement in composite mechanical properties, processing flexibility, and acceptable cost [2].

2.
Graphene can significantly enhance the fracture toughness of epoxy nanocomposites-i.e., up to 131% [59]. When epoxy is reinforced with graphene, the carbonaceous sheets shackle the crack and restrict its advancement. This obstruction and deflection of the crack by the graphene at the interface is the foremost mechanism of raising the fracture toughness of nanocomposites. 3.
The graphene sheets with smaller length, width, and thickness are more efficient in improving the fracture toughness than those with larger dimensions [57]. Large graphene sheets have a high stress concentration factor, because of which crack generation becomes easy in the epoxy matrix [118,119]. The cracks deteriorate the efficiency of graphene in enhancing the fracture toughness of epoxy/graphene nanocomposites.

4.
Uniformly dispersed graphene improves fracture toughness significantly as compared to the poorly dispersed graphene [72]. It is evident from the published literature that the fracture toughness dropped when graphene weight fraction was increased beyond 1 wt %. The decrease in fracture toughness with higher weight fraction of graphene can be correlated with the dispersion state of graphene. As graphene weight fraction increases beyond 1 wt %, the dispersion state becomes inferior.

5.
Three roll milling or calendering process is an efficient way of dispersing the reinforcement into a polymer matrix, as it involves high shear forces [244][245][246][247][248]. However, the maximum enhancement in fracture toughness was achieved with a combination of sonication and mechanical stirring [59]. 6.
In thermosetting materials such as epoxy, high crosslink density is desirable for improved mechanical properties. However, fracture toughness is dropped with high crosslinking [57]. 7.
The main factors that dictate graphene's influence on the mechanical properties of epoxy nanocomposites include topographical features, morphology, weight fraction, dispersion state, surface modifications, and interfacial interactions.