Micromechanics of reinforcement of a graphene-based thermoplastic elastomer nanocomposite

In this work, a series of graphene-reinforced thermoplastic elastomers were prepared, with the introduction of graphene nanoplatelets (GNPs) of different particle diameter. Their microstructures were characterised by SEM and quantified by polarised Raman spectroscopy. Τhe GNPs were well-dispersed and their orientation across the cross-section of the injection moulded samples was consistent with the shear rate profile of fountain flow mechanism. The mechanical properties of the nanocomposites were evaluated by tensile testing and it was found that the GNPs contributed to significant improvements in both the stiffness and strength. A micromechanical model based on the combination of shear-lag theory and the rule-of-mixtures was introduced to analyse the stiffening mechanisms. Τhe effective aspect ratio of GNPs was in the order of 100 and decreased with increasing filler loading due to agglomeration. Finally, the stress transfer efficiency from the matrix to GNPs was evaluated by observing the Raman band shifts under tension.


Introduction
Thermoplastic elastomers (TPEs) based on thermoplastic vulcanizate blends are considered an interesting class of materials since they combine the melt processability of thermoplastics with the properties of conventional thermoset rubbers [1]. The TPEs usually have excellent weatherability, ozone resistance, chemical resistance to oils and abrasion resistance; however, their applications are limited by their relatively poor mechanical properties [2]. In this context, inorganic fillers have been incorporated within the TPEs and enhancements in their mechanical performances have been reported in the literature [3][4][5][6][7]. More recently, since the isolation of monolayer graphene [8] and the discovery of its unique properties, graphene and graphene-related nanomaterials have been employed extensively as reinforcement in elastomers [9].
It has been reported previously that although the intrinsic Young's modulus of monolayer graphene has been found to be very high (~1 TPa) [10,11], it cannot be fully utilized in bulk nanocomposites, especially in soft materials such as elastomers due to inefficient stress transfer from the low modulus matrix to the high modulus filler by shear at the filler/matrix interface [9,[12][13][14][15][16][17]. In addition, we showed recently that classical micromechanics can be applied for the study of the mechanisms of stress transfer in polymeric matrices with varying stiffness and a theory was developed, which can predict the modulus of bulk nanocomposites based on the characteristics of the nanoplatelets [15,17]. The reinforcing mechanism of elastomers reinforced by graphene is different from that of stiff polymers: the normalized modulus of an elastomer/graphene nanocomposite is dependent upon the graphene orientation, the aspect ratio and volume fraction of the filler, while it is independent of the filler modulus [17]. This result suggests that the filler geometry and the processing methods (which in turn affect the nanoscale filler distribution [9,18]) will eventually determine the mechanical properties of the elastomeric nanocomposites.
In the present work, we have undertaken a comprehensive study of the mechanisms of reinforcement of a TPE by GNPs. The composite samples based on a thermoplastic elastomer 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 3 (Alcryn ® ) and GNPs with three different flake sizes were prepared by melt mixing. The microstructure of the injection moulded specimen was studied by quantifying the orientation factor of the fillers with polarised Raman spectroscopy. The mechanical properties of the nanocomposites with different filler loadings were evaluated by tensile testing followed by stress transfer measurements by observing the 2D Raman band shifts of the fillers during in situ deformation. Moreover, we applied our recently developed theory [17] to the experimental results from tensile testing and correlated the fittings with important geometrical characteristics of the filler, such as the effective aspect ratio. Through the experimental and theoretical analysis, we can conclude that the enhancement of thermoplastic elastomers with graphene nanoplatelets is effective, and gives considerable potential to develop high-performance engineering plastics, with tuned, application-specific properties.

Materials and preparation
Graphene nanoplatelets (GNPs) with nominal lateral diameters of 5, 10, 25 µm (dimensions claimed by the supplier) and average thicknesses in the range of 6-8 nanometres were purchased from XG Sciences, Inc. Lansing, Michigan, USA and used as received. Three grades of xGnP ® M5, M15 and M25 were used. The thermoplastic elastomer, Alcryn  2265 UT (Unfilled Translucent), which is based on a partially crosslinked chlorinated olefin interpolymer alloy, was purchased from A. Schulman, Inc.
The dumbbell-shaped tensile specimens were prepared by injection moulding in a HAAKE Minijet Piston Injection Moulding System. The temperatures of the barrel and the mould were set as 185 o C and 30 o C. The injection pressures were 500 bar, 550 bar, 600 bar, 700 bar and 800 bar for the neat polymer and the nanocomposites filled with 1 wt%, 5 wt%, 10 wt% and 20 wt% of GNPs, respectively. The injection pressure was held for 10 seconds followed by post-injection pressure of 200 bar, held for 5 seconds, for all specimens.

Characterization of the nanocomposites
The actual loadings of GNPs in the nanocomposites were obtained by thermogravimetric analysis (TGA) using a TA Q500 TGA instrument. The samples were heated from room temperature up to 600 o C under a 50 mL/min flow of N 2 at 10 o C/min. Three samples were tested for each material in order to ensure reproducibility of the results.
The morphologies of the fillers, neat polymer and the microstructure of the nanocomposites were examined using scanning electron microscopy (SEM). The samples (GNP powders and cryofractured dumbbells) were placed on conductive carbon tapes, which were stuck on aluminium stubs. Subsequently, the coating process was carried out using Au-Pd alloy in order to provide satisfactory conductivity to the samples. The images were acquired using a high-resolution XL30 Field Emission Gun Scanning Electron Microscope (FEGSEM) at 6 kV.
The XRD diffractograms were obtained from a PANalytical X'Pert3 diffractometer with Cu K radiation. The 2-theta angle range was selected from 5° to 90° with a step size of 0.03 o and a step time of 180 s operated at 40 kV and 40 mA.
Stress-strain curves were obtained using dumbbell-shaped specimens in an Instron 4301 machine, under a tensile rate of 50 mm·min −1 with a load cell of 5 kN. 5 Raman spectra were obtained using a Renishaw InVia Raman spectrometer with a laser wavelength of 633 nm and an objective of ×50, which produces a spot size of 1-2 µm. The Raman 2D band shift of the injection moulded samples (gauge length ~ 55 mm) was studied following the application of strain on the nanocomposites with the highest loading of GNPs (20 wt%). The tests were carried out using a mini-tensile rig. The strain was determined by measuring the extension of the two grips with a digital caliper. The Raman laser spot was in the order of 1-2 µm and it was focused on the same point of a single flake on each sample surface. The results were based on 5 composite samples for each type of GNPs, at the highest loading. All the spectra were fitted with a single Lorentzian curve.
The spatial orientation of the GNPs in the composites was determined using the method reported in previous studies from our group [13,14,19]. The equipment employed was a 514 nm Raman spectrometer by Renishaw with 'VV' (vertical-vertical) polarisation, in which the incident and scattered radiation were polarised in the same direction. In the test, the laser, was aligned perpendicular to the surface of the materials either along X or Z axis, as shown in Fig. S1-Supplementary Material. The Raman G bands were recorded as a function of rotation angle (Φ X, Φ Z ) and the rotation angles were used to estimate the orientation distribution function (ODF) [14,19]. Regarding the X-axis tests, the orientation factor may vary throughout different regions, since the samples were injection moulded [20]. Hence, the tests were carried out on a number of regions across the cryo-fractured cross-sections of the samples (red dash lines in Fig. S1) to give the variation of the orientation parameter values.

Characterisation of the filler and matrix
The three types of GNPs were examined by scanning electron microscopy as shown in Figs. S2(ac). It can be seen that the flake size increases from M5 to M15 to M25. However, the M15 and   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 6 M25 GNPs batches seem to include a number of smaller flakes, which will decrease the average lateral size quoted by the manufacturer. Another important observation is that folded and looped structures can be found particularly in larger flake samples ( Fig .S2 d and e). Overall, the three types of fillers display the stacked and agglomerated structure of many-layer graphene. The cryofractured cross-section of the neat elastomer can be also seen in Fig. S2(f). Two distinct morphologies can be observed, revealing the two components in the matrix and indicating that the polymer blend is not completely miscible, as expected from earlier reports [1].
The Raman spectra of the GNPs are shown in the Fig. S3(a). The G (~1580 cm -1 ) and 2D bands (~2680 cm -1 ) are well defined for all types of the nanoplatelets, consistent with the signature of graphitic structures. The 2D bands are broad and asymmetric suggesting that the nanoplatelets consist of many layers of graphene [11,21,22]. Moreover, broad and weak D bands can be observed at ~ 1360 cm -1 which is an indication of defects that are present in the structure. The XRD patterns of GNPs are also shown in Fig. S3(b), which display the sharp and strong peaks at 2θ ≈ 26° consistent with reflections from the (002) plane of graphite, while weak peaks can be seen at 2θ ≈ 42.1, 44.3 and 54.4° corresponding to reflections from (100), (010) and (004) planes, respectively.

Characterisation of the composites
Thermogravimetric analysis was employed initially to determine the actual volume fractions of the fillers after the preparation procedure. The mass residue and volume fractions of the filler in the prepared composites are given in Table S1. It can be seen that the final mass fractions were very close to the nominal mass fractions of the nanocomposites.
The cross-sectional surfaces of cryo-fractured dumbbell samples were investigated by SEM as shown in Fig. 1. The low magnification images of the composites with highest loading (20 wt%) Figs. 1 (a-c) indicate that a uniform distribution of the fillers was achieved even at high filler 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65   7 contents. The observation of different regions of the cross-section, reveals a distinct alignment of the fillers, which was induced by the shear rate distribution during the injection moulding procedure, known as a fountain flow mechanism [20,23]. The orientation of nanoplatelets due to the fountain flow mechanism in the case of our samples can be seen in Fig S4. There are regions within the samples with different degrees of orientation of the fillers, due to the variation of shear rate generated by the combination of the injection pressure and the slightly lower temperature of the mould walls [20,23].
The high magnification SEM images (Figs. 1 c-f) demonstrate the morphologies of the individual flakes within the matrix. Generally, the interface between the matrix and the nanoplatelets is intact, without voids or gaps, which is expected to contribute to higher reinforcement efficiency.
Interestingly, the shorter flakes tend to maintain their shape after processing, as shown in Fig.1 (d), while on the other hand, the larger ones can be seen bent or form looped-folded morphologies as shown in Figs.5 (e, f). It can be also seen that the flakes tend to restack and form agglomerates, particularly at higher loadings, which will reduce the reinforcing efficiency.

Polarised Raman spectroscopy
Since it is obvious from SEM that the flakes have a preferred alignment, it is possible to quantify the orientation factor using polarised Raman spectroscopy [14]. Different regions across the cryofractured cross-sections of the samples were studied by using a rotation stage. Because the sample was ~5 mm in width and ~1.5 mm in thickness, the tests were carried out stepwise, every 0.25 mm from the edge to the centre of the cross-sections in the perpendicular direction of the dumbbell surfaces and the test track lines are equidistant and parallel to the two parallel sides of the rectangular cross-sections (red dash lines in both Figs. S1 and S5).  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 8 From the results shown in Fig. 2(a), it can be seen that when the laser is polarised parallel to the Z axis, there is no change in G band intensity with the rotation of Φ Z , indicating no preferred orientation. In contrast, the G band intensity decreases from 0° to 90° and subsequently increases from 90° to 180° when the sample is rotated around the X axis (shown in Fig. 2b for the M5 GNP sample), which is an indication that the flakes tend to be oriented along the X axis. The calculated average orientation factor can be used to evaluate the effect of orientation on the reinforcing efficiency of the filler [14,19]. The <P 2 (cosθ)> and <P 4 (cosθ)> values described in detail in Refs. [14,19] are obtained by the X axis tests along with the curve fitting using equation (1).
where I o is the amplitude and assuming the surface normals are uniformly distributed around the Z-axis.

Mechanical testing
Tensile testing was used to evaluate the mechanical properties of the materials. The stress-strain behaviour of all injection moulded samples is presented in Fig. 4(a). It can be seen that the addition of GNPs up to ~10 vol% increases the stiffness and tensile strength of the thermoplastic elastomer significantly. Overall, larger flakes are more efficient in increasing the modulus, whereas the smaller flakes contribute to better tensile strength enhancements. It is also apparent that the addition of GNPs results in a reduction of strain at failure.
The initial Young's modulus values are plotted against the volume fractions of the fillers in Fig.4 (b). As expected, in all cases, the modulus increases significantly with increasing GNP content.
The modulus values of the composites are up to ~6 times higher (at 20 wt% filler loading) compared with the matrix, indicating the stiffening effect of the fillers. The reinforcement mechanism of graphene in composites is attributed to the interfacial stress transfer from the matrix to the flakes; larger platelets resulting in larger aspect ratio are beneficial for stress transfer on the basis of the well-established shear-lag theory [11,24].
Tensile strength and strain at failure values are also plotted against GNP volume fractions in Figs.

(c-d). The tensile strength increases with increasing GNP loading, indicating a strong interaction
between the fillers and the matrix. It has been reported that the wrinkled structure of graphene flakes can improve the tensile strength by acting as a crack propagation barrier and improve the mechanical interlocking between the matrix and the filler [25]. It can be clearly seen that the tensile strength enhancement is dependent significantly upon the flake size, particularly at high filler loadings. Tensile strength is known to depend heavily on the dispersion characteristics [15]; therefore these results indicate higher degree of aggregation of larger flakes at higher loadings and 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 10 looped/folded flake morphologies similar to the ones seen in Fig. 1(e,f). The strain at failure declines significantly with increasing filler fraction. Similar results have been observed not only for elastomeric nanocomposites but almost all polymer nanocomposites where agglomerated fillers act as failure points during elongation [9].

Raman 2D band shifts
Raman spectroscopy has been proven to be a very effective technique in assessing the stress transfer efficiency from the matrix to any type of carbon-based reinforcement [11-13, 15, 17, 26-34]. The samples the highest amount of filler (20 wt%) were strained in situ under a Raman spectrometer and the characteristic shifts of the Raman bands were recorded with increasing strain.
A representative example of the shift of the 2D band for the composite filled with M15 flakes, can be seen in Fig. S6. The slope of the band shifts versus strain represents the stress transfer efficiency between the matrix and the filler. For each composite reinforced by M5, M15 and M25 nanoplatelets, 5 samples were tested, in order to give the average values shown in Fig. 5. It was shown that the flakes display very low 2D band shifts, with obvious scattering on the linear curve fitting, indicating the significantly lower stress transfer efficiency of this elastomeric material than the stiffer matrices of previous studies [12,14,28] but higher than softer matrices such as natural rubber [13]. The small values of the slope indicate the low effective modulus of GNPs within the TPE matrix, compared with pristine graphene (-60 cm -1 /% strain for the 2D band that corresponds to a modulus of 1050 GPa) [10,11]. This is because the interfacial stress transfer efficiency in graphene nanocomposites depends upon the stiffness of the matrix (the effective modulus of graphene increases with increasing stiffness of the matrix), as discussed in our previous study [17].  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65   11 4. Discussion

Micromechanics of reinforcement
The effect of the addition of GNPs upon the stiffness of the elastomer can be evaluated by an equation we recently developed, which is the result of the simultaneous use of the rule-of-mixtures along with the well-accepted shear-lag theory [17]. The modulus of the composite is given by:  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 12 previous study [17]. The reason for the relatively small values of aspect ratio can be attributed to the restacking and agglomeration of the flakes that is unavoidable, especially at higher filler loading and to the additional presence of looped and folded flakes in the composites, that can preexist in the batches of the nanoplatelets or can also originate from the shear forces applied to the flakes during melt mixing/injection moulding. As shown in Fig. 5(f), the looped/folded flakes can even form hollow structures, resulting in significant reductions of the aspect ratio values.
( Figure 6) The fitted values of the effective aspect ratio for both equations can be used to evaluate the reinforcing efficiency of the GNPs. Nevertheless, the Guth-Gold-Smallwood theory is based on the effect of pairs of spherical fillers [35,36], which is an analogy of rod-like fillers, rather than relatively thin nanoplatelets. This is why the fitted aspect ratio f, obtained from the GGS equation is significantly lower than that of the GNP flakes. Moreover, from Fig.6 it can be seen that the normalized modulus of the nanocomposites filled with 5 wt% and 10 wt% lie above the expected theoretical values. This observation indicates a more homogeneous dispersion of the filler at lower GNP loadings [12,15,37]. The phenomenon can be also inspected from Fig. 7, where the experimental data have been fitted for every specimen individually. In order to obtain the effective aspect ratio at each filler content, we noted that s eff decreases with increasing filler fractions, which reduces the reinforcing efficiency. The respective effective aspect ratios can be seen on Fig. 7 for each sample. The reduction of s eff with increasing loading was expected, as larger loadings can lead to pronounced agglomeration, restacking and folding of the flakes, which obviously reduce their ultimate aspect ratio.  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 13

Stress-induced 2D Raman band shifts
In our previous work, we showed that on the basis of the shear-lag theory, for soft matrices reinforced by graphene nanoplatelets, the Young's modulus of the flakes obtained from Raman experiments (E R ) is higher than the filler modulus (E f ) acquired from tensile testing [17]. The Raman modulus of the graphene flakes is given by: Pa (5) where -dω 2D /dε is the 2D Raman band shift rate per % composite strain for any type of graphene.
The filler modulus from tensile tests, according to the simple rule of mixtures can be calculated by where t is the thickness of the flake and T is the thickness of the polymer layer surrounding the flake in the model nanocomposite. Equations (7) and (8) predict that the Raman modulus is higher than the filler modulus obtained from tensile testing. If we take the E R /E f ratio from the two equations, then E R ≈1.5E f . The experimental data of E R and E f from the samples with the highest filler contents are all listed in Table 1. The experimentally obtained values of E R and E f reveal that the effective modulus of graphene within this quite soft TPE matrix (E m ≈10 MPa) is in the order of hundreds of MPa, which is three to four orders of magnitude lower than the intrinsic modulus of monolayer graphene (1050 GPa) [10,11]. The reason for the low E f and E R values is that the shear modulus of the elastomeric matrix is very low; therefore, the shear stress transferred from the 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 14 matrix to the flakes through the TPE/GNP interface, according to the shear lag theory, is relatively low [13,17]. Based on this, even though the absolute enhancement of the mechanical properties of soft materials in terms of percentage is almost always impressive, the superlative mechanical properties of graphene and graphene nanoplatelets are not realised in these systems.
It should also be stated that the Raman band shift experiments were carried out probing flakes axially aligned on the sample surface. This means that the flakes that were tested should be considered nearly perfectly orientated (η o ≈1), whereas the calculated filler modulus E f values have actually taken the orientation factors of the bulk composites into account. Therefore, the actual relationship between experimental E R and E f should be given by where η o is the overall orientation factor of the bulk composites.
( Table 1) The results from the use of the E R ≈1.5E f /η o relationship show good consistency with the measured E R values (Table 1) especially for smaller flakes and the differences between the data can originate either from disoriented flakes that have been tested or due to the rough and wrinkled surface of the nanoplatelets [38]. Another factor of discrepancy can be the length effects that are known to reduce the efficiency of reinforcement from the nanoplatelets. The agreement between the theoretical and experimental values is another indication that the orientation factor calculated from the polarized Raman experiments are very close to reality, for the bulk composites.

Conclusions
A series of GNP-reinforced thermoplastic elastomers have been successfully prepared by melt mixing. The SEM images suggest that the dispersion of the GNPs is quite homogeneous, while the alignment of the fillers is induced by shear during the injection moulding procedure. The interface   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 15 between the nanoplatelets and the matrix is most of the times intact, while looped and folded morphologies can be found for larger flakes, which are expected to reduce their intrinsic properties. Polarised Raman spectroscopy has been employed to quantify the orientation factor of the injection moulded samples and we showed that the orientation profile throughout the crosssection was consistent with the trend of the shear rate profile from injection moulding. Larger flakes have lower degree of orientation, again as a result of looped or folded structures.
The mechanical properties from tensile tests revealed that the introduction of GNPs into the TPE gave rise to significant improvements in its stiffness (6 times higher, up to 10 vol% loading) and strength compared to the matrix. Overall, the larger flakes contribute to better enhancements in the stiffness while smaller flakes lead to a better increase of strength. The modulus values were studied with an equation derived by analytical methods and described in detail in our previous work, by combining the shear lag theory with the well-accepted rule-of-mixtures [17]. It was revealed that the composite modulus has a quadratic relationship with the volume fraction of the filler and depends heavily on the aspect ratio of the filler, which is similar as the classical Guth-Gold theory. The effective aspect ratio is found to be of the order of 100. With increasing loading, the average effective aspect ratio of the GNPs is reasonably reduced as a result of restacking, agglomeration and folding of the GNPs, which can explain the effect of reduced reinforcing efficiency on both stiffness and strength. Finally, both the filler modulus from the tensile testing and Raman modulus of the bulk composites measured by 2D band shifts were found to be lower compared to composites based on stiff polymers but higher than those based on very soft matrices (ie. silicon rubber) due to different shear modulus of the materials. The experimental data have also been analysed and show a good consistency with theory.