The samples for XRD analysis were prepared by pressing thin films of each sample 3G-PMC, 30G-PMC, and 90G-PMC at 23 0o C and 5,500 psi over a 2 minute time period. Each sample was positioned between aluminum sheets prior to pressing using a Carver Uniaxial Press with heated platens.

Diffraction patterns of the pressed films were acquired using a Philips XPert powder Diffractometer with sample changer (Xpert) at 40kV and 45mA with an incident slit thickness of 0.3 mm from 4-70 0 20 and a step size of 0.02 ° 20. 21 Substitute Specification_Marked-Up 3. Diffraction patterns were uploaded into WinPLOTR Powder diffraction graphics tool, without background editing or profile adjustments prior to peak fitting. Single peak fitting was applied at a 2 0 range of 26 °-27.5, using a pseudo-Voigt function and taking into account a global FWHM, global eta (proportion of Lorentz), and linear background. Single peak fitting of the profile provides the full width at half maximum (FWHM) of the relevant peak. The average out-of-plane crystallite size (D) (sometimes referred to as along the c-axis, and proportional to the number of graphene layers which are stacked) is calculated using the Debye-Scherrer Equation and the (002) FWHM values, for which X is the X-ray wavelength, coefficient K = 0.89, R is the FWHM in radians, and 0 is the diffraction angle. The d-spacing is also calculated. Equation 2 D SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.21.14.1207.1418.1391.1533.svg 0.383 0.613 Chemistry Black and white Morphology Results The morphology of each sample, 3G-PMC, 30G-PMC, and 90G-PMC, at three different scales (magnification) is shown in FIG. 1. In (a-c), a p m scale and 1,000 X magnification shows good distribution of multi-layer graphene or graphene within the PSU matrix at each mixing time. In (d-f), a 1 p m scale and 1 0,000 X magnification and (g-i), a 1 p m scale and 50,000X magnification shows mechanically exfoliated graphite within the PSU matrix. In (d-i), micro- folding of the multi-layer graphene or graphene is evident, as well as good bonding between the graphene nanoparticles and the polymer mat rix. The 90G-PMC sample, the sample mixed for the longest time and exposed to the most repetitive shearing, exhibits superior mechanical exfoliation and the smallest crystal size. As shown in FIG. 2, mechanical exfoliation has reduced the graphene nanoparticle thickness in the 90G-PMC sample to 8.29 nm. X-ray Diffraction Results The Debye-Scherrer equation was applied to the FWHM and d-spacing results obtained from the X-ray diffraction patterns for 3G-PMC, 30G-PMC, and 90G-PMC to provide the crystal thickness (D) of the multi-layer graphene or graphene nanoparticles. The XRD results and 22 Substitute Specification_Marked-Up crystal thickness appear in Table 1. For the 3G-PMC, 30G-PMC, and 90G-PMC samples, the crystal thickness is 40 nm, 31 nm, and 23 nm; the FWHM is 0.202 0, 0.257 °, and 0.353 0; and the d-spacing is 3.361 nm, 3.353 nm, and 3.387 nm, respectively. The FWHM increases with mixing time, and crystal thickness decreases with mixing time, which indicates that mechanical exfoliation of the graphite to multi-layer graphene or graphene is occurring and is enhanced over longer mixing times. The decrease in crystal size is a function of FWHM. TABLE 1. Debye-Scherrer Equation applied to the average XRD results from each 2 % Graphite Exfoliated in PSU sample mixed for 3 m in, 30 m in, and 90 m in SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.22.10.276.1045.2273.1515.svg 1.567 6.657 Chemistry Black and white Graphene Modification Mechanical exfoliation of the graphite into multi-layer graphene or graphene as a result of the repetitive shear strain action in the polymer processing equipment generates dangling primary and secondary bonds that provide the opportunity for various chemical reactions to occur, which can be exploited to obtain property enhancement of the G-PMC. This represents an advance over prior art conventional methods forming graphene oxides, where the dangling primary and secondary bonds covalently bond with oxygen, which typically remain in these positions even after the graphene oxide is reduced. For example, chemical reactions that covalently attach these dangling bonds from the multi-layer graphene or graphene nanoparticles to the polymer matrix would provide superior mechanical properties of the G-PMC. Alternatively, electrical conductivity may be enhanced by chemically linking appropriate band gap materials at the graphene nano-particle edges or by coordinating with conductive metals such as gold, silver, copper, and the like. The graphene-reinforced polymer may then be added to polymers or other compositions to provide or increase electrical conductivity. The bonds may also be coordinated to metals, such as platinum and palladium, to provide a catalyst, with the graphene-reinforced polymer serving as a catalyst support. Other 23 Substitute Specification_Marked-Up forms of f u nctionalized graphene are disclosed in U.S. Patent No. 8,096,353, the disclosure of which is incorporated herein by reference. The method of the present invention is particularly advantageous because in situ functionalization reactions may be performed during the exfoliation process via one-pot reactive compounding. The graphene-reinforced polymers may be used as electrodes for lightweight batteries. Other uses include composite boat hulls, aircraft, aerospace systems, transportation vehicles, lightweight armor (vehicular or personnel armor), pressure vessels, reactor chambers, spray coatings, polymer powders for 3-D printing, transparent electrodes for electronic device touch screens, and the like. Addition of 1-2 wt % graphene to a polymer matrix imparts electrical conductivity, while maintaining optical transparency, thus enabling applications in solar panels, flat-panel displays, and for static-discharge control in hospitals. Mechanical exfoliation successfully converted 2 % graphite melt-blended with PSU into a G- PMC using a repetitive shearing action in the Small Scale Extension Mixer by Randcastle Extrusion Systems, Inc. ("Randcastle"). Results may be improved by machine modification to increase shear; for example, by using a larger diameter mixing element to increase rotational speed and/or by minimizing the spacing between the mixing element and the cylinder wall. Modified Randcastle Extrusion System's Small Scale Extension Mixer: The design of the existing small batch mixer may be modified to provide higher shear rate, which in turn provides superior mechanical exfoliation of graphite within the polymer matrix. The shear rate, j, is calculated according to Equation 1, where r is the tooling radius and A r is the clearance for compounding. Machine modifications are listed in Table 2, along with the maximum achievable shear rate. The newly designed mixer has a maximum shear rate 22 times that of the current mixer, which will provide enhanced mechanical exfoliation of graphite within a polymer matrix at shorter lengths of time. In other words, the crystal size, D, may be reduced to smaller dimensions in a more efficient length of time. 24 Substitute Specification_Marked-Up TABLE 2. Modifications of the Randcastle Extrusion System's Small Scale Extension Mi x er to provide enhanced mechanical exfoliation SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.24.4.276.465.2273.825.svg 1.20 6.657 Chemistry Black and white Modified Single Screw Extrusion: Randcastle has made modifications to the extruder screw that will better enable mechanical exfoliation of the graphite into multi-layer graphene or graphene in a polymer matrix to fabricate a G-PMC. MATERIALS Raw graphite was extracted from the ground, crushed to powder, and float separated to obtain Separated Mineral Graphite ("SMG"). PEEK has a specific gravity of 1.3, a melt flow of 3 g/10 min (400 °C, 2.16 kg), a glass transition temperature at 150 °C, and a melting point at 340 °C. The tensile modulus and strength are 3.5 GPa and 95 MPa, respectively. Prior to the creation of the xG-PMC in this example, SMG and PEEK were dried for approximately 12 hours at 100 °C and 150 °C, respectively. In this example, SMG was blended with PEEK using a Randcastle micro-batch mixer with a 10-gram capacity at 360 °C (680 °F) and 100 RPM under a nitrogen blanket, according to the following steps: PEEK₃ -- To create a control sample, 10 grams of PEEK was added to the mixer. After three minutes of mixing time, the port was opened to allow PEEK to flow out as extrudate and 2.6 grams were extruded out until no more material was able to flow. SMG-PEEK₃ -- To create a weight composition ratio of 2-98 % SMG-PEEK, 2.4 g of PEEK and 0.2 g of SMG were added to the mixer. After three minutes 25 Substitute Specification_Marked-Up of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 1.96 g were extruded out until no more material was able to flow. SMG-PEEK₃0 -- To maintain the 2-98 wt % composition ratio, 1.92 g of PEEK and 0.04 g of SMG were added to the mixer. After 30 minutes of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 0.94 g were extruded out until no more material was able to flow. SMG-PEEK₉0 -- To maintain the 2-98 wt % composition ratio, 0.92 g of PEEK and 0.02 g of SMG were added to the mixer. After 90 minutes of mixing time, the port was opened to allow G-PMC to flow out as extrudate, however, no more material was able to flow. The experiment was terminated and the mixer opened. Under visual observation, the G-PMC did not appear as a standard molten polymer, but rather was in a rubber-like, fibrous form. In this next example, SMG and PEEK were processed in a Randcastle micro-batch mixer with a 100-gram capacity at 360 ° C (680 ° F) and 30 RPM under a nitrogen blanket, according to the following steps: PEEK₉0 -- To create a control sample, 100 g of PEEK was added to the mixer. After 90 minutes of mixing time, the port was opened to allow PEEK to flow out as extrudate and 28.5 g were extruded out until no more material was able to flow. SMG-PEEK₂5 -- To create a weight composition ratio of 2-98 % SMG-PEEK, 98 g of PEEK and 2 g of SMG were added to the mixer. After 25 minutes, of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 5.1 g were extruded out until no more material was able to flow. Characterization The samples used for characterization appear in Table 3, as follows: 26 Substitute Specification_Marked-Up Table 3: Samples Used for Characterization SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.26.3.276.415.2273.1004.svg 1.963 6.657 Chemistry Black and white Morphology The morphology of the xG-PMC was examined using a Zeiss Sigma Field Emission Scanning Electron Microscope ("FESEM") with Oxford EDS. An accelerating voltage of 3kV and working distance of approximately 8.5 mm was used during viewing. Prior to viewing, specimens were notched, cryogenically fractured to produce a flat fracture surface, placed under vacuum for at least 24 hours, gold coated, and stored under vacuum. As illustrated in Fig. 3, the morphology of SMG-PEEK₉0 is shown in (a) 10 pm scale and 1,000 magnification (b) 10 pm scale and 5,000 magnification, (c) 1p m scale and 10,000 magnification, and (d) 1 pm scale and 50,000 magnification. Thermal Analysis The thermal properties of the samples were characterized using a TA Instruments Q 1000 Differential Scanning Calorimeter (DSC). Each sample was subject to a heat/cool/heat cycle from 0-400 °C at 10 °C/min. The glass transition temperature (Tg) and melting temperature (Tm) for the initial heat scan are illustrated in Fig. 3. The Tg increases from 152 °C for PEEK₃ to 154 for SMG-PEEK₉0, however, this increase is not significant. The Tm is consistent for samples PEEK₃, SMG-PEEK₃, and SMG-PEEK₃0 at almost 338 °C but decreases significantly to 331.7 °C for SMG-PEEK₉0. The delta H is similar for samples PEEK₃, SMG-PEEK₃, and SMG-PEEK₃0, and varies between the initial, cool, and reheat scans, and ranges between 116-140 J/g. However, the delta H for SMG-PEEK₉0 is much lower and consistent at approximately 100 J/g for the initial, cool, and reheat scans. The observable difference in the heat of fusion of PEEK for the SMG-PEEK₉0 sample, as compared with the 27 Substitute Specification_Marked-Up other samples, indicates a major difference in the morphology. Furthermore, the constant heat of fusion between the initial, cool, and reheat scans of the SMG-PEEK₉0 sample supports the existence of cross links between the graphene and PEEK matrix. Parallel Plate Rheology A frequency sweep from 100-0.01 Hz at 1.0 % strain and at a temperature of 360 ° C was performed using a TA Instruments AR 2000 in parallel plate mode. Samples SMG-PEEK₃0, SMG-PEEK₃, and PEEK₃ were tested. The G' and G" and the tan delta for samples SMG- PEEK ₃0, SMG-PEEK₃, and PEEK₃ were recorded. Tan delta is equal to the G"/G'. This rheology data provides information regarding the morphology of the sample, according to Table 4, as shown below. The so l/gel transition point, or "gel point", of a thermoset resin occurs when tan delta = 1, or rather when G'=G". For samples SMG-PEEK₃ and PEEK ₃, the G" is greater than the G', indicating liquid-like behavior. Contrastingly for sample SMG-PEEK₃0, the G' is greater than G", indicating more elasti c -like or solid-like behavior. Furthermore, tan delta is less than 1 and remains nearly constant across the entire frequency range for SMG-PEEK₃0, indicating that SMG-PEEK₃0 has undergone some degree of cross-linking. Table 4. Rheology data and the so l/gel transition point SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.27.18.276.1808.2273.2309.svg 1.67 6.657 Chemistry Black and white Dissolution Lightly gelled thermosetting resins when placed in solvents swell through imbibition to a degree depending on the solvent and the structure of the polymer. The original shape is preserved, and the swollen gel exhibits elastic rather than plastic properties. Cross-linking in thermoplastic polymers is commonly accomplished by 1) peroxides, 2) a grafted silane process cross-linked by water, 3) electron beam radiation, and 4) UV light. 28 Substitute Specification_Marked-Up In this example, cross-linking was induced between SMG and PEEK during a mechanical exfoliation process due to the cleavage of graphene flakes that results in dangling free radicals. To confirm the presence of cross-linking in the SMG-PEEK XG-PMC, a dissolution method was used by placing neat PEEK, PEEK ₃, PEEK ₉0, SMG-PEEK₃, SMG-PEEK ₃0, and SMG- PEEK₉0 samples in sulfuric acid, according to the following steps. A 10 mg specimen from each sample was prepared; Each specimen was placed in a test tube with 20 mL of 95 -98% w/w sulfuric acid (A₃₀₀ S 500 Fisher Scientific); The solution was shaken for 5 minutes; Each test tube was capped with Teflon ® tape to form a seal; Photographs of each sample were taken at times 0, 24, 48, and 72 hours. Upon visual observation, the PEEK samples all dissolve within the sulfuric acid before 24 hours, and the SMG-PEEK₉0 sample is the only one that remains in the sulfuric acid after 72 hours. The SMG-PEEK₉0 sample was cross-linked and swelled when placed in the solvent similar to a thermoset resin. The SMG-PEEK₃0 sample remained in the sulfuric acid after 24 hours but dissolved before 48 hours. SMG-PEEK₃0 required further testing to determine if cross-linking was induced, since the other data suggests that SMG-PEEK₃0 was cross-linked. The foregoing examples and description of the preferred embodiments should be taken as illustrating, rather than as limiting the present invention as defined by the claims. As will be readily appreciated, numerous variations and combinations of the features set forth above can be utilized without departing from the present invention as set forth in the claims. Such variations are not regarded as a departure from the spirit and scope of the invention, and all such variations are intended to be included within the scope of the following claims. Claims What is claimed is:

A graphene-reinforced polymer matrix composite prepared according to the method of Claim

A thermoplastic polymer composite comprising thermoplastic polymer chains intermolecularly cross-linked by torn single- and/or multi-layer graphene sheets having carbon atoms with reactive bonding sites on the torn edges of said sheets. Withdrawn

The samples for XRD analysis were prepared by pressing thin films of each sample 3G-PMC, 30G-PMC, and 90G-PMC at 23 0o C and 5,500 psi over a 2 minute time period. Each sample was positioned between aluminum sheets prior to pressing using a Carver Uniaxial Press with heated platens.

Diffraction patterns of the pressed films were acquired using a Philips XPert powder Diffractometer with sample changer (Xpert) at 40kV and 45mA with an incident slit thickness of 0.3 mm from 4-70 0 20 and a step size of 0.02 ° 20. 21 Substitute Specification_Marked-Up 3. Diffraction patterns were uploaded into WinPLOTR Powder diffraction graphics tool, without background editing or profile adjustments prior to peak fitting. Single peak fitting was applied at a 2 0 range of 26 °-27.5, using a pseudo-Voigt function and taking into account a global FWHM, global eta (proportion of Lorentz), and linear background. Single peak fitting of the profile provides the full width at half maximum (FWHM) of the relevant peak. The average out-of-plane crystallite size (D) (sometimes referred to as along the c-axis, and proportional to the number of graphene layers which are stacked) is calculated using the Debye-Scherrer Equation and the (002) FWHM values, for which X is the X-ray wavelength, coefficient K = 0.89, R is the FWHM in radians, and 0 is the diffraction angle. The d-spacing is also calculated. Equation 2 D SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.21.14.1207.1418.1391.1533.svg 0.383 0.613 Chemistry Black and white Morphology Results The morphology of each sample, 3G-PMC, 30G-PMC, and 90G-PMC, at three different scales (magnification) is shown in FIG. 1. In (a-c), a p m scale and 1,000 X magnification shows good distribution of multi-layer graphene or graphene within the PSU matrix at each mixing time. In (d-f), a 1 p m scale and 1 0,000 X magnification and (g-i), a 1 p m scale and 50,000X magnification shows mechanically exfoliated graphite within the PSU matrix. In (d-i), micro- folding of the multi-layer graphene or graphene is evident, as well as good bonding between the graphene nanoparticles and the polymer mat rix. The 90G-PMC sample, the sample mixed for the longest time and exposed to the most repetitive shearing, exhibits superior mechanical exfoliation and the smallest crystal size. As shown in FIG. 2, mechanical exfoliation has reduced the graphene nanoparticle thickness in the 90G-PMC sample to 8.29 nm. X-ray Diffraction Results The Debye-Scherrer equation was applied to the FWHM and d-spacing results obtained from the X-ray diffraction patterns for 3G-PMC, 30G-PMC, and 90G-PMC to provide the crystal thickness (D) of the multi-layer graphene or graphene nanoparticles. The XRD results and 22 Substitute Specification_Marked-Up crystal thickness appear in Table 1. For the 3G-PMC, 30G-PMC, and 90G-PMC samples, the crystal thickness is 40 nm, 31 nm, and 23 nm; the FWHM is 0.202 0, 0.257 °, and 0.353 0; and the d-spacing is 3.361 nm, 3.353 nm, and 3.387 nm, respectively. The FWHM increases with mixing time, and crystal thickness decreases with mixing time, which indicates that mechanical exfoliation of the graphite to multi-layer graphene or graphene is occurring and is enhanced over longer mixing times. The decrease in crystal size is a function of FWHM. TABLE 1. Debye-Scherrer Equation applied to the average XRD results from each 2 % Graphite Exfoliated in PSU sample mixed for 3 m in, 30 m in, and 90 m in SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.22.10.276.1045.2273.1515.svg 1.567 6.657 Chemistry Black and white Graphene Modification Mechanical exfoliation of the graphite into multi-layer graphene or graphene as a result of the repetitive shear strain action in the polymer processing equipment generates dangling primary and secondary bonds that provide the opportunity for various chemical reactions to occur, which can be exploited to obtain property enhancement of the G-PMC. This represents an advance over prior art conventional methods forming graphene oxides, where the dangling primary and secondary bonds covalently bond with oxygen, which typically remain in these positions even after the graphene oxide is reduced. For example, chemical reactions that covalently attach these dangling bonds from the multi-layer graphene or graphene nanoparticles to the polymer matrix would provide superior mechanical properties of the G-PMC. Alternatively, electrical conductivity may be enhanced by chemically linking appropriate band gap materials at the graphene nano-particle edges or by coordinating with conductive metals such as gold, silver, copper, and the like. The graphene-reinforced polymer may then be added to polymers or other compositions to provide or increase electrical conductivity. The bonds may also be coordinated to metals, such as platinum and palladium, to provide a catalyst, with the graphene-reinforced polymer serving as a catalyst support. Other 23 Substitute Specification_Marked-Up forms of f u nctionalized graphene are disclosed in U.S. Patent No. 8,096,353, the disclosure of which is incorporated herein by reference. The method of the present invention is particularly advantageous because in situ functionalization reactions may be performed during the exfoliation process via one-pot reactive compounding. The graphene-reinforced polymers may be used as electrodes for lightweight batteries. Other uses include composite boat hulls, aircraft, aerospace systems, transportation vehicles, lightweight armor (vehicular or personnel armor), pressure vessels, reactor chambers, spray coatings, polymer powders for 3-D printing, transparent electrodes for electronic device touch screens, and the like. Addition of 1-2 wt % graphene to a polymer matrix imparts electrical conductivity, while maintaining optical transparency, thus enabling applications in solar panels, flat-panel displays, and for static-discharge control in hospitals. Mechanical exfoliation successfully converted 2 % graphite melt-blended with PSU into a G- PMC using a repetitive shearing action in the Small Scale Extension Mixer by Randcastle Extrusion Systems, Inc. ("Randcastle"). Results may be improved by machine modification to increase shear; for example, by using a larger diameter mixing element to increase rotational speed and/or by minimizing the spacing between the mixing element and the cylinder wall. Modified Randcastle Extrusion System's Small Scale Extension Mixer: The design of the existing small batch mixer may be modified to provide higher shear rate, which in turn provides superior mechanical exfoliation of graphite within the polymer matrix. The shear rate, j, is calculated according to Equation 1, where r is the tooling radius and A r is the clearance for compounding. Machine modifications are listed in Table 2, along with the maximum achievable shear rate. The newly designed mixer has a maximum shear rate 22 times that of the current mixer, which will provide enhanced mechanical exfoliation of graphite within a polymer matrix at shorter lengths of time. In other words, the crystal size, D, may be reduced to smaller dimensions in a more efficient length of time. 24 Substitute Specification_Marked-Up TABLE 2. Modifications of the Randcastle Extrusion System's Small Scale Extension Mi x er to provide enhanced mechanical exfoliation SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.24.4.276.465.2273.825.svg 1.20 6.657 Chemistry Black and white Modified Single Screw Extrusion: Randcastle has made modifications to the extruder screw that will better enable mechanical exfoliation of the graphite into multi-layer graphene or graphene in a polymer matrix to fabricate a G-PMC. MATERIALS Raw graphite was extracted from the ground, crushed to powder, and float separated to obtain Separated Mineral Graphite ("SMG"). PEEK has a specific gravity of 1.3, a melt flow of 3 g/10 min (400 °C, 2.16 kg), a glass transition temperature at 150 °C, and a melting point at 340 °C. The tensile modulus and strength are 3.5 GPa and 95 MPa, respectively. Prior to the creation of the xG-PMC in this example, SMG and PEEK were dried for approximately 12 hours at 100 °C and 150 °C, respectively. In this example, SMG was blended with PEEK using a Randcastle micro-batch mixer with a 10-gram capacity at 360 °C (680 °F) and 100 RPM under a nitrogen blanket, according to the following steps: PEEK₃ -- To create a control sample, 10 grams of PEEK was added to the mixer. After three minutes of mixing time, the port was opened to allow PEEK to flow out as extrudate and 2.6 grams were extruded out until no more material was able to flow. SMG-PEEK₃ -- To create a weight composition ratio of 2-98 % SMG-PEEK, 2.4 g of PEEK and 0.2 g of SMG were added to the mixer. After three minutes 25 Substitute Specification_Marked-Up of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 1.96 g were extruded out until no more material was able to flow. SMG-PEEK₃0 -- To maintain the 2-98 wt % composition ratio, 1.92 g of PEEK and 0.04 g of SMG were added to the mixer. After 30 minutes of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 0.94 g were extruded out until no more material was able to flow. SMG-PEEK₉0 -- To maintain the 2-98 wt % composition ratio, 0.92 g of PEEK and 0.02 g of SMG were added to the mixer. After 90 minutes of mixing time, the port was opened to allow G-PMC to flow out as extrudate, however, no more material was able to flow. The experiment was terminated and the mixer opened. Under visual observation, the G-PMC did not appear as a standard molten polymer, but rather was in a rubber-like, fibrous form. In this next example, SMG and PEEK were processed in a Randcastle micro-batch mixer with a 100-gram capacity at 360 ° C (680 ° F) and 30 RPM under a nitrogen blanket, according to the following steps: PEEK₉0 -- To create a control sample, 100 g of PEEK was added to the mixer. After 90 minutes of mixing time, the port was opened to allow PEEK to flow out as extrudate and 28.5 g were extruded out until no more material was able to flow. SMG-PEEK₂5 -- To create a weight composition ratio of 2-98 % SMG-PEEK, 98 g of PEEK and 2 g of SMG were added to the mixer. After 25 minutes, of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 5.1 g were extruded out until no more material was able to flow. Characterization The samples used for characterization appear in Table 3, as follows: 26 Substitute Specification_Marked-Up Table 3: Samples Used for Characterization SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.26.3.276.415.2273.1004.svg 1.963 6.657 Chemistry Black and white Morphology The morphology of the xG-PMC was examined using a Zeiss Sigma Field Emission Scanning Electron Microscope ("FESEM") with Oxford EDS. An accelerating voltage of 3kV and working distance of approximately 8.5 mm was used during viewing. Prior to viewing, specimens were notched, cryogenically fractured to produce a flat fracture surface, placed under vacuum for at least 24 hours, gold coated, and stored under vacuum. As illustrated in Fig. 3, the morphology of SMG-PEEK₉0 is shown in (a) 10 pm scale and 1,000 magnification (b) 10 pm scale and 5,000 magnification, (c) 1p m scale and 10,000 magnification, and (d) 1 pm scale and 50,000 magnification. Thermal Analysis The thermal properties of the samples were characterized using a TA Instruments Q 1000 Differential Scanning Calorimeter (DSC). Each sample was subject to a heat/cool/heat cycle from 0-400 °C at 10 °C/min. The glass transition temperature (Tg) and melting temperature (Tm) for the initial heat scan are illustrated in Fig. 3. The Tg increases from 152 °C for PEEK₃ to 154 for SMG-PEEK₉0, however, this increase is not significant. The Tm is consistent for samples PEEK₃, SMG-PEEK₃, and SMG-PEEK₃0 at almost 338 °C but decreases significantly to 331.7 °C for SMG-PEEK₉0. The delta H is similar for samples PEEK₃, SMG-PEEK₃, and SMG-PEEK₃0, and varies between the initial, cool, and reheat scans, and ranges between 116-140 J/g. However, the delta H for SMG-PEEK₉0 is much lower and consistent at approximately 100 J/g for the initial, cool, and reheat scans. The observable difference in the heat of fusion of PEEK for the SMG-PEEK₉0 sample, as compared with the 27 Substitute Specification_Marked-Up other samples, indicates a major difference in the morphology. Furthermore, the constant heat of fusion between the initial, cool, and reheat scans of the SMG-PEEK₉0 sample supports the existence of cross links between the graphene and PEEK matrix. Parallel Plate Rheology A frequency sweep from 100-0.01 Hz at 1.0 % strain and at a temperature of 360 ° C was performed using a TA Instruments AR 2000 in parallel plate mode. Samples SMG-PEEK₃0, SMG-PEEK₃, and PEEK₃ were tested. The G' and G" and the tan delta for samples SMG- PEEK ₃0, SMG-PEEK₃, and PEEK₃ were recorded. Tan delta is equal to the G"/G'. This rheology data provides information regarding the morphology of the sample, according to Table 4, as shown below. The so l/gel transition point, or "gel point", of a thermoset resin occurs when tan delta = 1, or rather when G'=G". For samples SMG-PEEK₃ and PEEK ₃, the G" is greater than the G', indicating liquid-like behavior. Contrastingly for sample SMG-PEEK₃0, the G' is greater than G", indicating more elasti c -like or solid-like behavior. Furthermore, tan delta is less than 1 and remains nearly constant across the entire frequency range for SMG-PEEK₃0, indicating that SMG-PEEK₃0 has undergone some degree of cross-linking. Table 4. Rheology data and the so l/gel transition point SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.27.18.276.1808.2273.2309.svg 1.67 6.657 Chemistry Black and white Dissolution Lightly gelled thermosetting resins when placed in solvents swell through imbibition to a degree depending on the solvent and the structure of the polymer. The original shape is preserved, and the swollen gel exhibits elastic rather than plastic properties. Cross-linking in thermoplastic polymers is commonly accomplished by 1) peroxides, 2) a grafted silane process cross-linked by water, 3) electron beam radiation, and 4) UV light. 28 Substitute Specification_Marked-Up In this example, cross-linking was induced between SMG and PEEK during a mechanical exfoliation process due to the cleavage of graphene flakes that results in dangling free radicals. To confirm the presence of cross-linking in the SMG-PEEK XG-PMC, a dissolution method was used by placing neat PEEK, PEEK ₃, PEEK ₉0, SMG-PEEK₃, SMG-PEEK ₃0, and SMG- PEEK₉0 samples in sulfuric acid, according to the following steps. A 10 mg specimen from each sample was prepared; Each specimen was placed in a test tube with 20 mL of 95 -98% w/w sulfuric acid (A₃₀₀ S 500 Fisher Scientific); The solution was shaken for 5 minutes; Each test tube was capped with Teflon ® tape to form a seal; Photographs of each sample were taken at times 0, 24, 48, and 72 hours. Upon visual observation, the PEEK samples all dissolve within the sulfuric acid before 24 hours, and the SMG-PEEK₉0 sample is the only one that remains in the sulfuric acid after 72 hours. The SMG-PEEK₉0 sample was cross-linked and swelled when placed in the solvent similar to a thermoset resin. The SMG-PEEK₃0 sample remained in the sulfuric acid after 24 hours but dissolved before 48 hours. SMG-PEEK₃0 required further testing to determine if cross-linking was induced, since the other data suggests that SMG-PEEK₃0 was cross-linked. The foregoing examples and description of the preferred embodiments should be taken as illustrating, rather than as limiting the present invention as defined by the claims. As will be readily appreciated, numerous variations and combinations of the features set forth above can be utilized without departing from the present invention as set forth in the claims. Such variations are not regarded as a departure from the spirit and scope of the invention, and all such variations are intended to be included within the scope of the following claims. Claims What is claimed is:

A graphene-reinforced polymer matrix composite prepared according to the method of Claim

A thermoplastic polymer composite comprising thermoplastic polymer chains intermolecularly cross-linked by torn single- and/or multi-layer graphene sheets having carbon atoms with reactive bonding sites on the torn edges of said sheets. Withdrawn

The samples for XRD analysis were prepared by pressing thin films of each sample 3G-PMC, 30G-PMC, and 90G-PMC at 23 0o C and 5,500 psi over a 2 minute time period. Each sample was positioned between aluminum sheets prior to pressing using a Carver Uniaxial Press with heated platens.

Diffraction patterns of the pressed films were acquired using a Philips XPert powder Diffractometer with sample changer (Xpert) at 40kV and 45mA with an incident slit thickness of 0.3 mm from 4-70 0 20 and a step size of 0.02 ° 20. 21 Substitute Specification_Marked-Up 3. Diffraction patterns were uploaded into WinPLOTR Powder diffraction graphics tool, without background editing or profile adjustments prior to peak fitting. Single peak fitting was applied at a 2 0 range of 26 °-27.5, using a pseudo-Voigt function and taking into account a global FWHM, global eta (proportion of Lorentz), and linear background. Single peak fitting of the profile provides the full width at half maximum (FWHM) of the relevant peak. The average out-of-plane crystallite size (D) (sometimes referred to as along the c-axis, and proportional to the number of graphene layers which are stacked) is calculated using the Debye-Scherrer Equation and the (002) FWHM values, for which X is the X-ray wavelength, coefficient K = 0.89, R is the FWHM in radians, and 0 is the diffraction angle. The d-spacing is also calculated. Equation 2 D SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.21.14.1207.1418.1391.1533.svg 0.383 0.613 Chemistry Black and white Morphology Results The morphology of each sample, 3G-PMC, 30G-PMC, and 90G-PMC, at three different scales (magnification) is shown in FIG. 1. In (a-c), a p m scale and 1,000 X magnification shows good distribution of multi-layer graphene or graphene within the PSU matrix at each mixing time. In (d-f), a 1 p m scale and 1 0,000 X magnification and (g-i), a 1 p m scale and 50,000X magnification shows mechanically exfoliated graphite within the PSU matrix. In (d-i), micro- folding of the multi-layer graphene or graphene is evident, as well as good bonding between the graphene nanoparticles and the polymer mat rix. The 90G-PMC sample, the sample mixed for the longest time and exposed to the most repetitive shearing, exhibits superior mechanical exfoliation and the smallest crystal size. As shown in FIG. 2, mechanical exfoliation has reduced the graphene nanoparticle thickness in the 90G-PMC sample to 8.29 nm. X-ray Diffraction Results The Debye-Scherrer equation was applied to the FWHM and d-spacing results obtained from the X-ray diffraction patterns for 3G-PMC, 30G-PMC, and 90G-PMC to provide the crystal thickness (D) of the multi-layer graphene or graphene nanoparticles. The XRD results and 22 Substitute Specification_Marked-Up crystal thickness appear in Table 1. For the 3G-PMC, 30G-PMC, and 90G-PMC samples, the crystal thickness is 40 nm, 31 nm, and 23 nm; the FWHM is 0.202 0, 0.257 °, and 0.353 0; and the d-spacing is 3.361 nm, 3.353 nm, and 3.387 nm, respectively. The FWHM increases with mixing time, and crystal thickness decreases with mixing time, which indicates that mechanical exfoliation of the graphite to multi-layer graphene or graphene is occurring and is enhanced over longer mixing times. The decrease in crystal size is a function of FWHM. TABLE 1. Debye-Scherrer Equation applied to the average XRD results from each 2 % Graphite Exfoliated in PSU sample mixed for 3 m in, 30 m in, and 90 m in SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.22.10.276.1045.2273.1515.svg 1.567 6.657 Chemistry Black and white Graphene Modification Mechanical exfoliation of the graphite into multi-layer graphene or graphene as a result of the repetitive shear strain action in the polymer processing equipment generates dangling primary and secondary bonds that provide the opportunity for various chemical reactions to occur, which can be exploited to obtain property enhancement of the G-PMC. This represents an advance over prior art conventional methods forming graphene oxides, where the dangling primary and secondary bonds covalently bond with oxygen, which typically remain in these positions even after the graphene oxide is reduced. For example, chemical reactions that covalently attach these dangling bonds from the multi-layer graphene or graphene nanoparticles to the polymer matrix would provide superior mechanical properties of the G-PMC. Alternatively, electrical conductivity may be enhanced by chemically linking appropriate band gap materials at the graphene nano-particle edges or by coordinating with conductive metals such as gold, silver, copper, and the like. The graphene-reinforced polymer may then be added to polymers or other compositions to provide or increase electrical conductivity. The bonds may also be coordinated to metals, such as platinum and palladium, to provide a catalyst, with the graphene-reinforced polymer serving as a catalyst support. Other 23 Substitute Specification_Marked-Up forms of f u nctionalized graphene are disclosed in U.S. Patent No. 8,096,353, the disclosure of which is incorporated herein by reference. The method of the present invention is particularly advantageous because in situ functionalization reactions may be performed during the exfoliation process via one-pot reactive compounding. The graphene-reinforced polymers may be used as electrodes for lightweight batteries. Other uses include composite boat hulls, aircraft, aerospace systems, transportation vehicles, lightweight armor (vehicular or personnel armor), pressure vessels, reactor chambers, spray coatings, polymer powders for 3-D printing, transparent electrodes for electronic device touch screens, and the like. Addition of 1-2 wt % graphene to a polymer matrix imparts electrical conductivity, while maintaining optical transparency, thus enabling applications in solar panels, flat-panel displays, and for static-discharge control in hospitals. Mechanical exfoliation successfully converted 2 % graphite melt-blended with PSU into a G- PMC using a repetitive shearing action in the Small Scale Extension Mixer by Randcastle Extrusion Systems, Inc. ("Randcastle"). Results may be improved by machine modification to increase shear; for example, by using a larger diameter mixing element to increase rotational speed and/or by minimizing the spacing between the mixing element and the cylinder wall. Modified Randcastle Extrusion System's Small Scale Extension Mixer: The design of the existing small batch mixer may be modified to provide higher shear rate, which in turn provides superior mechanical exfoliation of graphite within the polymer matrix. The shear rate, j, is calculated according to Equation 1, where r is the tooling radius and A r is the clearance for compounding. Machine modifications are listed in Table 2, along with the maximum achievable shear rate. The newly designed mixer has a maximum shear rate 22 times that of the current mixer, which will provide enhanced mechanical exfoliation of graphite within a polymer matrix at shorter lengths of time. In other words, the crystal size, D, may be reduced to smaller dimensions in a more efficient length of time. 24 Substitute Specification_Marked-Up TABLE 2. Modifications of the Randcastle Extrusion System's Small Scale Extension Mi x er to provide enhanced mechanical exfoliation SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.24.4.276.465.2273.825.svg 1.20 6.657 Chemistry Black and white Modified Single Screw Extrusion: Randcastle has made modifications to the extruder screw that will better enable mechanical exfoliation of the graphite into multi-layer graphene or graphene in a polymer matrix to fabricate a G-PMC. MATERIALS Raw graphite was extracted from the ground, crushed to powder, and float separated to obtain Separated Mineral Graphite ("SMG"). PEEK has a specific gravity of 1.3, a melt flow of 3 g/10 min (400 °C, 2.16 kg), a glass transition temperature at 150 °C, and a melting point at 340 °C. The tensile modulus and strength are 3.5 GPa and 95 MPa, respectively. Prior to the creation of the xG-PMC in this example, SMG and PEEK were dried for approximately 12 hours at 100 °C and 150 °C, respectively. In this example, SMG was blended with PEEK using a Randcastle micro-batch mixer with a 10-gram capacity at 360 °C (680 °F) and 100 RPM under a nitrogen blanket, according to the following steps: PEEK₃ -- To create a control sample, 10 grams of PEEK was added to the mixer. After three minutes of mixing time, the port was opened to allow PEEK to flow out as extrudate and 2.6 grams were extruded out until no more material was able to flow. SMG-PEEK₃ -- To create a weight composition ratio of 2-98 % SMG-PEEK, 2.4 g of PEEK and 0.2 g of SMG were added to the mixer. After three minutes 25 Substitute Specification_Marked-Up of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 1.96 g were extruded out until no more material was able to flow. SMG-PEEK₃0 -- To maintain the 2-98 wt % composition ratio, 1.92 g of PEEK and 0.04 g of SMG were added to the mixer. After 30 minutes of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 0.94 g were extruded out until no more material was able to flow. SMG-PEEK₉0 -- To maintain the 2-98 wt % composition ratio, 0.92 g of PEEK and 0.02 g of SMG were added to the mixer. After 90 minutes of mixing time, the port was opened to allow G-PMC to flow out as extrudate, however, no more material was able to flow. The experiment was terminated and the mixer opened. Under visual observation, the G-PMC did not appear as a standard molten polymer, but rather was in a rubber-like, fibrous form. In this next example, SMG and PEEK were processed in a Randcastle micro-batch mixer with a 100-gram capacity at 360 ° C (680 ° F) and 30 RPM under a nitrogen blanket, according to the following steps: PEEK₉0 -- To create a control sample, 100 g of PEEK was added to the mixer. After 90 minutes of mixing time, the port was opened to allow PEEK to flow out as extrudate and 28.5 g were extruded out until no more material was able to flow. SMG-PEEK₂5 -- To create a weight composition ratio of 2-98 % SMG-PEEK, 98 g of PEEK and 2 g of SMG were added to the mixer. After 25 minutes, of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 5.1 g were extruded out until no more material was able to flow. Characterization The samples used for characterization appear in Table 3, as follows: 26 Substitute Specification_Marked-Up Table 3: Samples Used for Characterization SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.26.3.276.415.2273.1004.svg 1.963 6.657 Chemistry Black and white Morphology The morphology of the xG-PMC was examined using a Zeiss Sigma Field Emission Scanning Electron Microscope ("FESEM") with Oxford EDS. An accelerating voltage of 3kV and working distance of approximately 8.5 mm was used during viewing. Prior to viewing, specimens were notched, cryogenically fractured to produce a flat fracture surface, placed under vacuum for at least 24 hours, gold coated, and stored under vacuum. As illustrated in Fig. 3, the morphology of SMG-PEEK₉0 is shown in (a) 10 pm scale and 1,000 magnification (b) 10 pm scale and 5,000 magnification, (c) 1p m scale and 10,000 magnification, and (d) 1 pm scale and 50,000 magnification. Thermal Analysis The thermal properties of the samples were characterized using a TA Instruments Q 1000 Differential Scanning Calorimeter (DSC). Each sample was subject to a heat/cool/heat cycle from 0-400 °C at 10 °C/min. The glass transition temperature (Tg) and melting temperature (Tm) for the initial heat scan are illustrated in Fig. 3. The Tg increases from 152 °C for PEEK₃ to 154 for SMG-PEEK₉0, however, this increase is not significant. The Tm is consistent for samples PEEK₃, SMG-PEEK₃, and SMG-PEEK₃0 at almost 338 °C but decreases significantly to 331.7 °C for SMG-PEEK₉0. The delta H is similar for samples PEEK₃, SMG-PEEK₃, and SMG-PEEK₃0, and varies between the initial, cool, and reheat scans, and ranges between 116-140 J/g. However, the delta H for SMG-PEEK₉0 is much lower and consistent at approximately 100 J/g for the initial, cool, and reheat scans. The observable difference in the heat of fusion of PEEK for the SMG-PEEK₉0 sample, as compared with the 27 Substitute Specification_Marked-Up other samples, indicates a major difference in the morphology. Furthermore, the constant heat of fusion between the initial, cool, and reheat scans of the SMG-PEEK₉0 sample supports the existence of cross links between the graphene and PEEK matrix. Parallel Plate Rheology A frequency sweep from 100-0.01 Hz at 1.0 % strain and at a temperature of 360 ° C was performed using a TA Instruments AR 2000 in parallel plate mode. Samples SMG-PEEK₃0, SMG-PEEK₃, and PEEK₃ were tested. The G' and G" and the tan delta for samples SMG- PEEK ₃0, SMG-PEEK₃, and PEEK₃ were recorded. Tan delta is equal to the G"/G'. This rheology data provides information regarding the morphology of the sample, according to Table 4, as shown below. The so l/gel transition point, or "gel point", of a thermoset resin occurs when tan delta = 1, or rather when G'=G". For samples SMG-PEEK₃ and PEEK ₃, the G" is greater than the G', indicating liquid-like behavior. Contrastingly for sample SMG-PEEK₃0, the G' is greater than G", indicating more elasti c -like or solid-like behavior. Furthermore, tan delta is less than 1 and remains nearly constant across the entire frequency range for SMG-PEEK₃0, indicating that SMG-PEEK₃0 has undergone some degree of cross-linking. Table 4. Rheology data and the so l/gel transition point SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.27.18.276.1808.2273.2309.svg 1.67 6.657 Chemistry Black and white Dissolution Lightly gelled thermosetting resins when placed in solvents swell through imbibition to a degree depending on the solvent and the structure of the polymer. The original shape is preserved, and the swollen gel exhibits elastic rather than plastic properties. Cross-linking in thermoplastic polymers is commonly accomplished by 1) peroxides, 2) a grafted silane process cross-linked by water, 3) electron beam radiation, and 4) UV light. 28 Substitute Specification_Marked-Up In this example, cross-linking was induced between SMG and PEEK during a mechanical exfoliation process due to the cleavage of graphene flakes that results in dangling free radicals. To confirm the presence of cross-linking in the SMG-PEEK XG-PMC, a dissolution method was used by placing neat PEEK, PEEK ₃, PEEK ₉0, SMG-PEEK₃, SMG-PEEK ₃0, and SMG- PEEK₉0 samples in sulfuric acid, according to the following steps. A 10 mg specimen from each sample was prepared; Each specimen was placed in a test tube with 20 mL of 95 -98% w/w sulfuric acid (A₃₀₀ S 500 Fisher Scientific); The solution was shaken for 5 minutes; Each test tube was capped with Teflon ® tape to form a seal; Photographs of each sample were taken at times 0, 24, 48, and 72 hours. Upon visual observation, the PEEK samples all dissolve within the sulfuric acid before 24 hours, and the SMG-PEEK₉0 sample is the only one that remains in the sulfuric acid after 72 hours. The SMG-PEEK₉0 sample was cross-linked and swelled when placed in the solvent similar to a thermoset resin. The SMG-PEEK₃0 sample remained in the sulfuric acid after 24 hours but dissolved before 48 hours. SMG-PEEK₃0 required further testing to determine if cross-linking was induced, since the other data suggests that SMG-PEEK₃0 was cross-linked. The foregoing examples and description of the preferred embodiments should be taken as illustrating, rather than as limiting the present invention as defined by the claims. As will be readily appreciated, numerous variations and combinations of the features set forth above can be utilized without departing from the present invention as set forth in the claims. Such variations are not regarded as a departure from the spirit and scope of the invention, and all such variations are intended to be included within the scope of the following claims. Claims What is claimed is:

A graphene-reinforced polymer matrix composite prepared according to the method of Claim

A thermoplastic polymer composite comprising thermoplastic polymer chains intermolecularly cross-linked by torn single- and/or multi-layer graphene sheets having carbon atoms with reactive bonding sites on the torn edges of said sheets. Withdrawn

The samples for XRD analysis were prepared by pressing thin films of each sample 3G-PMC, 30G-PMC, and 90G-PMC at 23 0o C and 5,500 psi over a 2 minute time period. Each sample was positioned between aluminum sheets prior to pressing using a Carver Uniaxial Press with heated platens.

Diffraction patterns of the pressed films were acquired using a Philips XPert powder Diffractometer with sample changer (Xpert) at 40kV and 45mA with an incident slit thickness of 0.3 mm from 4-70 0 20 and a step size of 0.02 ° 20. 21 Substitute Specification_Marked-Up 3. Diffraction patterns were uploaded into WinPLOTR Powder diffraction graphics tool, without background editing or profile adjustments prior to peak fitting. Single peak fitting was applied at a 2 0 range of 26 °-27.5, using a pseudo-Voigt function and taking into account a global FWHM, global eta (proportion of Lorentz), and linear background. Single peak fitting of the profile provides the full width at half maximum (FWHM) of the relevant peak. The average out-of-plane crystallite size (D) (sometimes referred to as along the c-axis, and proportional to the number of graphene layers which are stacked) is calculated using the Debye-Scherrer Equation and the (002) FWHM values, for which X is the X-ray wavelength, coefficient K = 0.89, R is the FWHM in radians, and 0 is the diffraction angle. The d-spacing is also calculated. Equation 2 D SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.21.14.1207.1418.1391.1533.svg 0.383 0.613 Chemistry Black and white Morphology Results The morphology of each sample, 3G-PMC, 30G-PMC, and 90G-PMC, at three different scales (magnification) is shown in FIG. 1. In (a-c), a p m scale and 1,000 X magnification shows good distribution of multi-layer graphene or graphene within the PSU matrix at each mixing time. In (d-f), a 1 p m scale and 1 0,000 X magnification and (g-i), a 1 p m scale and 50,000X magnification shows mechanically exfoliated graphite within the PSU matrix. In (d-i), micro- folding of the multi-layer graphene or graphene is evident, as well as good bonding between the graphene nanoparticles and the polymer mat rix. The 90G-PMC sample, the sample mixed for the longest time and exposed to the most repetitive shearing, exhibits superior mechanical exfoliation and the smallest crystal size. As shown in FIG. 2, mechanical exfoliation has reduced the graphene nanoparticle thickness in the 90G-PMC sample to 8.29 nm. X-ray Diffraction Results The Debye-Scherrer equation was applied to the FWHM and d-spacing results obtained from the X-ray diffraction patterns for 3G-PMC, 30G-PMC, and 90G-PMC to provide the crystal thickness (D) of the multi-layer graphene or graphene nanoparticles. The XRD results and 22 Substitute Specification_Marked-Up crystal thickness appear in Table 1. For the 3G-PMC, 30G-PMC, and 90G-PMC samples, the crystal thickness is 40 nm, 31 nm, and 23 nm; the FWHM is 0.202 0, 0.257 °, and 0.353 0; and the d-spacing is 3.361 nm, 3.353 nm, and 3.387 nm, respectively. The FWHM increases with mixing time, and crystal thickness decreases with mixing time, which indicates that mechanical exfoliation of the graphite to multi-layer graphene or graphene is occurring and is enhanced over longer mixing times. The decrease in crystal size is a function of FWHM. TABLE 1. Debye-Scherrer Equation applied to the average XRD results from each 2 % Graphite Exfoliated in PSU sample mixed for 3 m in, 30 m in, and 90 m in SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.22.10.276.1045.2273.1515.svg 1.567 6.657 Chemistry Black and white Graphene Modification Mechanical exfoliation of the graphite into multi-layer graphene or graphene as a result of the repetitive shear strain action in the polymer processing equipment generates dangling primary and secondary bonds that provide the opportunity for various chemical reactions to occur, which can be exploited to obtain property enhancement of the G-PMC. This represents an advance over prior art conventional methods forming graphene oxides, where the dangling primary and secondary bonds covalently bond with oxygen, which typically remain in these positions even after the graphene oxide is reduced. For example, chemical reactions that covalently attach these dangling bonds from the multi-layer graphene or graphene nanoparticles to the polymer matrix would provide superior mechanical properties of the G-PMC. Alternatively, electrical conductivity may be enhanced by chemically linking appropriate band gap materials at the graphene nano-particle edges or by coordinating with conductive metals such as gold, silver, copper, and the like. The graphene-reinforced polymer may then be added to polymers or other compositions to provide or increase electrical conductivity. The bonds may also be coordinated to metals, such as platinum and palladium, to provide a catalyst, with the graphene-reinforced polymer serving as a catalyst support. Other 23 Substitute Specification_Marked-Up forms of f u nctionalized graphene are disclosed in U.S. Patent No. 8,096,353, the disclosure of which is incorporated herein by reference. The method of the present invention is particularly advantageous because in situ functionalization reactions may be performed during the exfoliation process via one-pot reactive compounding. The graphene-reinforced polymers may be used as electrodes for lightweight batteries. Other uses include composite boat hulls, aircraft, aerospace systems, transportation vehicles, lightweight armor (vehicular or personnel armor), pressure vessels, reactor chambers, spray coatings, polymer powders for 3-D printing, transparent electrodes for electronic device touch screens, and the like. Addition of 1-2 wt % graphene to a polymer matrix imparts electrical conductivity, while maintaining optical transparency, thus enabling applications in solar panels, flat-panel displays, and for static-discharge control in hospitals. Mechanical exfoliation successfully converted 2 % graphite melt-blended with PSU into a G- PMC using a repetitive shearing action in the Small Scale Extension Mixer by Randcastle Extrusion Systems, Inc. ("Randcastle"). Results may be improved by machine modification to increase shear; for example, by using a larger diameter mixing element to increase rotational speed and/or by minimizing the spacing between the mixing element and the cylinder wall. Modified Randcastle Extrusion System's Small Scale Extension Mixer: The design of the existing small batch mixer may be modified to provide higher shear rate, which in turn provides superior mechanical exfoliation of graphite within the polymer matrix. The shear rate, j, is calculated according to Equation 1, where r is the tooling radius and A r is the clearance for compounding. Machine modifications are listed in Table 2, along with the maximum achievable shear rate. The newly designed mixer has a maximum shear rate 22 times that of the current mixer, which will provide enhanced mechanical exfoliation of graphite within a polymer matrix at shorter lengths of time. In other words, the crystal size, D, may be reduced to smaller dimensions in a more efficient length of time. 24 Substitute Specification_Marked-Up TABLE 2. Modifications of the Randcastle Extrusion System's Small Scale Extension Mi x er to provide enhanced mechanical exfoliation SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.24.4.276.465.2273.825.svg 1.20 6.657 Chemistry Black and white Modified Single Screw Extrusion: Randcastle has made modifications to the extruder screw that will better enable mechanical exfoliation of the graphite into multi-layer graphene or graphene in a polymer matrix to fabricate a G-PMC. MATERIALS Raw graphite was extracted from the ground, crushed to powder, and float separated to obtain Separated Mineral Graphite ("SMG"). PEEK has a specific gravity of 1.3, a melt flow of 3 g/10 min (400 °C, 2.16 kg), a glass transition temperature at 150 °C, and a melting point at 340 °C. The tensile modulus and strength are 3.5 GPa and 95 MPa, respectively. Prior to the creation of the xG-PMC in this example, SMG and PEEK were dried for approximately 12 hours at 100 °C and 150 °C, respectively. In this example, SMG was blended with PEEK using a Randcastle micro-batch mixer with a 10-gram capacity at 360 °C (680 °F) and 100 RPM under a nitrogen blanket, according to the following steps: PEEK₃ -- To create a control sample, 10 grams of PEEK was added to the mixer. After three minutes of mixing time, the port was opened to allow PEEK to flow out as extrudate and 2.6 grams were extruded out until no more material was able to flow. SMG-PEEK₃ -- To create a weight composition ratio of 2-98 % SMG-PEEK, 2.4 g of PEEK and 0.2 g of SMG were added to the mixer. After three minutes 25 Substitute Specification_Marked-Up of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 1.96 g were extruded out until no more material was able to flow. SMG-PEEK₃0 -- To maintain the 2-98 wt % composition ratio, 1.92 g of PEEK and 0.04 g of SMG were added to the mixer. After 30 minutes of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 0.94 g were extruded out until no more material was able to flow. SMG-PEEK₉0 -- To maintain the 2-98 wt % composition ratio, 0.92 g of PEEK and 0.02 g of SMG were added to the mixer. After 90 minutes of mixing time, the port was opened to allow G-PMC to flow out as extrudate, however, no more material was able to flow. The experiment was terminated and the mixer opened. Under visual observation, the G-PMC did not appear as a standard molten polymer, but rather was in a rubber-like, fibrous form. In this next example, SMG and PEEK were processed in a Randcastle micro-batch mixer with a 100-gram capacity at 360 ° C (680 ° F) and 30 RPM under a nitrogen blanket, according to the following steps: PEEK₉0 -- To create a control sample, 100 g of PEEK was added to the mixer. After 90 minutes of mixing time, the port was opened to allow PEEK to flow out as extrudate and 28.5 g were extruded out until no more material was able to flow. SMG-PEEK₂5 -- To create a weight composition ratio of 2-98 % SMG-PEEK, 98 g of PEEK and 2 g of SMG were added to the mixer. After 25 minutes, of mixing time, the port was opened to allow G-PMC to flow out as extrudate and 5.1 g were extruded out until no more material was able to flow. Characterization The samples used for characterization appear in Table 3, as follows: 26 Substitute Specification_Marked-Up Table 3: Samples Used for Characterization SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.26.3.276.415.2273.1004.svg 1.963 6.657 Chemistry Black and white Morphology The morphology of the xG-PMC was examined using a Zeiss Sigma Field Emission Scanning Electron Microscope ("FESEM") with Oxford EDS. An accelerating voltage of 3kV and working distance of approximately 8.5 mm was used during viewing. Prior to viewing, specimens were notched, cryogenically fractured to produce a flat fracture surface, placed under vacuum for at least 24 hours, gold coated, and stored under vacuum. As illustrated in Fig. 3, the morphology of SMG-PEEK₉0 is shown in (a) 10 pm scale and 1,000 magnification (b) 10 pm scale and 5,000 magnification, (c) 1p m scale and 10,000 magnification, and (d) 1 pm scale and 50,000 magnification. Thermal Analysis The thermal properties of the samples were characterized using a TA Instruments Q 1000 Differential Scanning Calorimeter (DSC). Each sample was subject to a heat/cool/heat cycle from 0-400 °C at 10 °C/min. The glass transition temperature (Tg) and melting temperature (Tm) for the initial heat scan are illustrated in Fig. 3. The Tg increases from 152 °C for PEEK₃ to 154 for SMG-PEEK₉0, however, this increase is not significant. The Tm is consistent for samples PEEK₃, SMG-PEEK₃, and SMG-PEEK₃0 at almost 338 °C but decreases significantly to 331.7 °C for SMG-PEEK₉0. The delta H is similar for samples PEEK₃, SMG-PEEK₃, and SMG-PEEK₃0, and varies between the initial, cool, and reheat scans, and ranges between 116-140 J/g. However, the delta H for SMG-PEEK₉0 is much lower and consistent at approximately 100 J/g for the initial, cool, and reheat scans. The observable difference in the heat of fusion of PEEK for the SMG-PEEK₉0 sample, as compared with the 27 Substitute Specification_Marked-Up other samples, indicates a major difference in the morphology. Furthermore, the constant heat of fusion between the initial, cool, and reheat scans of the SMG-PEEK₉0 sample supports the existence of cross links between the graphene and PEEK matrix. Parallel Plate Rheology A frequency sweep from 100-0.01 Hz at 1.0 % strain and at a temperature of 360 ° C was performed using a TA Instruments AR 2000 in parallel plate mode. Samples SMG-PEEK₃0, SMG-PEEK₃, and PEEK₃ were tested. The G' and G" and the tan delta for samples SMG- PEEK ₃0, SMG-PEEK₃, and PEEK₃ were recorded. Tan delta is equal to the G"/G'. This rheology data provides information regarding the morphology of the sample, according to Table 4, as shown below. The so l/gel transition point, or "gel point", of a thermoset resin occurs when tan delta = 1, or rather when G'=G". For samples SMG-PEEK₃ and PEEK ₃, the G" is greater than the G', indicating liquid-like behavior. Contrastingly for sample SMG-PEEK₃0, the G' is greater than G", indicating more elasti c -like or solid-like behavior. Furthermore, tan delta is less than 1 and remains nearly constant across the entire frequency range for SMG-PEEK₃0, indicating that SMG-PEEK₃0 has undergone some degree of cross-linking. Table 4. Rheology data and the so l/gel transition point SVG 14784974.10-16-2015.IFTQQB₈YPXXIFW3.REM.27.18.276.1808.2273.2309.svg 1.67 6.657 Chemistry Black and white Dissolution Lightly gelled thermosetting resins when placed in solvents swell through imbibition to a degree depending on the solvent and the structure of the polymer. The original shape is preserved, and the swollen gel exhibits elastic rather than plastic properties. Cross-linking in thermoplastic polymers is commonly accomplished by 1) peroxides, 2) a grafted silane process cross-linked by water, 3) electron beam radiation, and 4) UV light. 28 Substitute Specification_Marked-Up In this example, cross-linking was induced between SMG and PEEK during a mechanical exfoliation process due to the cleavage of graphene flakes that results in dangling free radicals. To confirm the presence of cross-linking in the SMG-PEEK XG-PMC, a dissolution method was used by placing neat PEEK, PEEK ₃, PEEK ₉0, SMG-PEEK₃, SMG-PEEK ₃0, and SMG- PEEK₉0 samples in sulfuric acid, according to the following steps. A 10 mg specimen from each sample was prepared; Each specimen was placed in a test tube with 20 mL of 95 -98% w/w sulfuric acid (A₃₀₀ S 500 Fisher Scientific); The solution was shaken for 5 minutes; Each test tube was capped with Teflon ® tape to form a seal; Photographs of each sample were taken at times 0, 24, 48, and 72 hours. Upon visual observation, the PEEK samples all dissolve within the sulfuric acid before 24 hours, and the SMG-PEEK₉0 sample is the only one that remains in the sulfuric acid after 72 hours. The SMG-PEEK₉0 sample was cross-linked and swelled when placed in the solvent similar to a thermoset resin. The SMG-PEEK₃0 sample remained in the sulfuric acid after 24 hours but dissolved before 48 hours. SMG-PEEK₃0 required further testing to determine if cross-linking was induced, since the other data suggests that SMG-PEEK₃0 was cross-linked. The foregoing examples and description of the preferred embodiments should be taken as illustrating, rather than as limiting the present invention as defined by the claims. As will be readily appreciated, numerous variations and combinations of the features set forth above can be utilized without departing from the present invention as set forth in the claims. Such variations are not regarded as a departure from the spirit and scope of the invention, and all such variations are intended to be included within the scope of the following claims. Claims What is claimed is:

A graphene-reinforced polymer matrix composite prepared according to the method of Claim

A thermoplastic polymer composite comprising thermoplastic polymer chains intermolecularly cross-linked by torn single- and/or multi-layer graphene sheets having carbon atoms with reactive bonding sites on the torn edges of said sheets. Withdrawn