CARBON FIBER-REINFORCED METAKAOLIN-BASED GEOPOLYMER COMPOSITES

Abstract

Methods for making carbon-fiber reinforced geopolymer composites are provided. The methods produce metakaolin-based geopolymer composites in which multiwalled carbon nanotubes and/or carbon nanofibers are well dispersed in an metakaolin-based geopolymer matrix. The mixing protocols of the methods used to produce carbon-fiber reinforced geopolymer composites produce composites with reduced porosity, high elastic moduli, high strength, and/or high fracture toughness.

Claims

1. A carbon nanotube-reinforced geopolymer composite comprising: metakaolin-based geopolymer matrix; and multiwalled carbon nanotubes dispersed in the metakaolin-based geopolymer matrix, wherein the concentration of the multiwalled carbon nanotubes is in the range from 0.5 to 2 weight percent, per weight of metakaolin in the metakaolin-based geopolymer matrix; the carbon nanotube-reinforced geopolymer composite having a porosity of less than 7.5%, an indentation modulus of at least 7.0 GPa, and a fracture toughness of at least 0.57 MPa.Math.sqrt (m).

2. The composite of claim 1 having a plastic viscosity of at least 10 Pa s.

3. The composite of claim 1 having a yield shear stress of at least 50 Pa.

4. The composite of claim 1, wherein the composite is free of organic surfactants and organic dispersing agents.

5. The composite of claim 1, wherein the multiwalled carbon nanotubes are not functionalized with surface carboxy groups.

6. The composite of claim 1, wherein the metakaolin is potassium metakaolin.

7. The composite of claim 6 having a multiwalled carbon nanotube concentration in the range from 0.55 to 1.5 weight percent, per weight of metakaolin in the metakaolin-based geopolymer matrix.

8. The composite of claim 7, wherein the composite is free of organic surfactants and organic dispersing agents and the multiwalled carbon nanotubes are not functionalized with surface carboxy groups.

9. The composite of claim 8 having a porosity in the ranges from 5.5% to 7.5%, an indentation modulus in the range from 7.5 to 8.5 GPa, and a fracture toughness in the range from 0.58 MPa sqrt (m) to 0.65 MPa.Math.sqrt (m).

10. A carbon nanofiber-reinforced geopolymer composite comprising: metakaolin-based geopolymer matrix; and carbon nanofibers having diameters in the range from 50 nm to 250 nm and lengths in the range from 50 μm to 500 μm dispersed in the metakaolin-based geopolymer matrix, wherein the concentration of the carbon nanofibers is in the range from 0.3 to 2 weight percent, per weight of metakaolin in the metakaolin-based geopolymer matrix; the carbon nanofiber-reinforced geopolymer composite having a porosity of less than 7.5%, an indentation modulus of at least 9.0 GPa and a fracture toughness of at least 0.8 MPa.Math.sqrt (m).

11. The composite of claim 10, wherein the composite is free of organic surfactants and organic dispersing agents.

12. The composite of claim 10, wherein the carbon nanofibers are not functionalized with surface carboxy groups.

13. The composite of claim 10, wherein the metakaolin is potassium metakaolin.

14. The composite of claim 13 having a carbon nanofiber concentration in the range from 0.6 to 1.5 weight percent, per weight of metakaolin in the metakaolin-based geopolymer matrix.

15. The composite of claim 14, wherein the composite is free of organic surfactants and organic dispersing agents and the carbon nanofibers are not functionalized with surface carboxy groups.

16. The composite of claim 15 having an indentation modulus in the range from 9.0 to 10.5 GPa, and a fracture toughness in the range from 0.80 MPa sqrt (m) to 0.90 MPa.Math.sqrt (m).

17. A method of making a carbon fiber-reinforced geopolymer composite, the method comprising: forming an aqueous dispersion of multiwalled carbon nanotubes, carbon nanofibers, or a combination thereof, ultrasonicating the aqueous dispersion; subsequently dissolving potassium hydroxide and silica in the aqueous dispersion to form a waterglass solution; adding metakaolin to the waterglass solution to form a geopolymer solution; mixing and degassing the geopolymer solution in a centrifugal mixer; and curing the geopolymer solution with continuous mixing to form the carbon fiber-reinforced geopolymer composite.

18. The method of claim 17 comprising the multiwalled carbon nanotubes, wherein the concentration of the multiwalled carbon nanotubes in the carbon fiber-reinforced geopolymer composite is in the range from 0.5 weight percent to 2.0 weight percent, per weight of metakaolin.

19. The method of claim 17 comprising the carbon nanofibers, wherein the concentration of carbon nanofibers in the carbon fiber-reinforced geopolymer composite is in the range from 0.15 weight percent to 0.6 weight percent, per weight of metakaolin.

20. The method of claim 17, wherein the aqueous dispersion and the waterglass solution are free of organic surfactants and organic dispersing agents.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Illustrative embodiments of the invention will hereafter be described with reference to the accompanying drawings.

[0010] FIG. 1 shows a schematic of a scratch testing set-up.

[0011] FIG. 2 shows representative indentation curves for the geopolymer nanocomposites of Example 1.

[0012] FIG. 3 shows representative scratch curves for the geopolymer nanocomposites of Example 1.

[0013] FIG. 4 shows representative scratch toughness curves for the pure geopolymer and geopolymer nanocomposites of Example 1.

[0014] FIGS. 5A-5B show optical micrograph images of the microstructure of the pure geopolymer and the nanocomposite geopolymer of Example 1. FIG. 5A shows KGP. FIG. 5B shows KGP-0.5 wt. % CNF.

[0015] FIGS. 6A-6D show optical micrograph images of the fracture micromechanisms of the geopolymer nanocomposites of Example 1. FIGS. 6A-6B show KGP. FIG. 6C shows KGP-0.1 wt. % CNF. FIG. 6D shows KGP-0.5 wt. % CNF.

[0016] FIGS. 7A-7D show digital photos of geopolymer nanocomposites after the cold-mounting step: FIG. 7A shows KCT0.0; FIG. 7B shows KCT0.3; FIG. 7C shows KCT0.6; FIG. 7D shows KCT1.5.

[0017] FIGS. 8A-8B show fracture analysis of scratch tests: FT is the horizontal force and FV is the vertical force. FIG. 8A shows FT/√{square root over (2pA)} versus X for a scratch test on plain geopolymer KCT0.0. 2pA is the scratch probe shape function and X is the scratch path. The dashed horizontal line defines the fracture toughness Kc. FIG. 8B shows the scratch panorama of plain geopolymer KCT0.0.

[0018] FIG. 9A shows viscosity η—shear stress τ.sub.0 relationships; FIG. 9B shows the relationship between shear rate and shear stress of KCT0.0; KCT0.3; KCT0.6; KCT1.5.

[0019] FIG. 10 shows a bar plot of plastic viscosity r/p and yield shear stress τ.sub.0.

[0020] FIG. 11 shows X-Ray powder diffraction (XRPD) results of KCT0.0, KCT0.3, KCT0.6, KCT1.5, metakaolin. (Background subtraction) (Stacked).

[0021] FIGS. 12A-12D show statistical analysis of Fourier-Transform Infrared Spectroscopy (FTIR) results of KCT0.0, KCT0.3, KCT0.6, KCT1.5 from 820-1250 cm.sup.−1.

[0022] FIG. 13 shows scratch results of KCT0.0; KCT0.3; KCT0.6; and KCT1.5.

[0023] FIGS. 14A-14D show microscopic images of (FIG. 14A) KCT0.0; (FIG. 14B) KCT0.3; (FIG. 14C) KCT0.6; (FIG. 14D) KCT1.5.

[0024] FIGS. 15A-15D show an indentation modulus M histogram: (FIG. 15A) KCT0.0; (FIG. 15B) KCT0.3; (FIG. 15C) KCT0.6; (FIG. 15D) KCT1.5.

[0025] FIGS. 16A-16D show a cluster analysis of the indentation hardness H (GPa) and indentation modulus M (GPa): (FIG. 16A) KCT0.0; (FIG. 16B) KCT0.3; (FIG. 16C) KCT0.6; (FIG. 16D) KCT1.5. Diamonds represent geopolymer with porous phase; circles represent main geopolymer phase; pentagons represent stronger phase; squares represent geopolymer with porous phase.

[0026] FIGS. 17A-17D show fracture toughness plots of all scratch results: (FIG. 17A) KCT0.0; (FIG. 17B) KCT0.3; (FIG. 17C) KCT0.6; (FIG. 17D) KCT1.5. Plot displays the average number of fracture toughness K.sub.c.

[0027] FIGS. 18A-18D show indentation hardness histograms: (FIG. 18A) KCT0.0; (FIG. 18B) KCT0.3; (FIG. 18C) KCT0.6; (FIG. 18D) KCT1.5.

[0028] FIG. 19 shows an image analysis illustration for plain geopolymer KCT0.0.

[0029] FIG. 20 shows an image analysis greyscale illustration for plain geopolymer KCT0.0.

[0030] FIGS. 21A-21B show FTIR results of KCT0.0, KCT0.3, KCT0.6, KCT1.5.

DETAILED DESCRIPTION

[0031] Methods for making carbon-fiber reinforced geopolymer composites are provided. The methods produce metakaolin-based geopolymer composites in which carbon fibers, such as multiwalled carbon nanotubes and/or carbon nanofibers, are well dispersed in an metakaolin-based geopolymer matrix. As a result, various embodiments of the carbon-fiber reinforced geopolymer composites are characterized by high elastic moduli, high strength, and/or high fracture toughness.

[0032] The composites have uses in such applications as: the passive cooling of buildings in hot weather; affordable housing construction materials; fire-resistant structural elements; low-level nuclear waste encapsulation; and electrodes for clean energy generation. Concrete can be made by mixing the carbon-fiber reinforced geopolymer composite with aggregate. In the concrete, the carbon-fiber reinforced geopolymer composites acts as a paste coating on aggregate particles.

[0033] Without binding the inventions described herein to any particular theory of operation, the improved properties may be attributed, at least in part, to that ability of the highly dispersed carbon nanofibers and MWCNTs to promote the geopolymerization reaction, strengthen the geopolymer skeleton by promoting hydroxylation of silicon atoms, and/or reducing the mircoporosity of the composites.

[0034] One embodiment of a method for making a carbon-fiber reinforced geopolymer composite includes the steps of: (a) forming an aqueous dispersion of multiwalled carbon nanotubes (MWCNTs), carbon nanofibers (CNFs), or a mixture thereof, (b) dissolving sodium hydroxide, potassium hydroxide, or a mixture thereof, and fumed silica in the aqueous dispersion to form a waterglass solution; (c) adding metakaolin to the waterglass solution to form a geopolymer solution; (d) degassing the geopolymer solution under vacuum; and (e) curing the geopolymer solution to form carbon-fiber reinforced geopolymer composite comprising the MWCNTs and/or CNFs dispersed in a metakaolin-based geopolymer matrix.

[0035] A high degree of dispersion of the carbon fibers in the matrix material can be achieved by ultrasonicating the aqueous dispersion of carbon fibers prior to the addition of the sodium or potassium hydroxide, centrifugal mixing of the geopolymer solution, and continuously mixing the geopolymer solution using an orbital shaker during the cure. Geopolymer composites made using these mixing protocols can have high carbon fiber loadings and exception mechanical properties. The carbon fiber loadings can be measured per mass of the metakaolin in the geopolymer matrix. Various embodiments of the metakaolin-based geopolymer composites have carbon fiber (i.e., CNF and/or MWCNT) loadings in the range from 0.3 wt. % to 2.0 wt. %, per mass of metakaolin. This includes embodiments of the metakaolin-based geopolymer composites have CNF and/or MWCNT loadings in the range from 0.5 wt. % to 1.5 wt. %, per mass of metakaolin.

[0036] The carbon fibers used in the composites are referred to as nanomaterials because they have at least one nano-scale dimension, where a nano-scale dimension is a dimension (e.g., diameter and/or length) that is no greater than 1000 nm. Carbon fibers that can be used in the geopolymer composites include MWCNTs and CNFs. Carbon nanotubes (CNTs) are cylindrical tubes of sp.sup.2 carbon having nano-scale diameters and relatively long length dimensions. For example, MWCNT having lengths of 100 nm or smaller and aspect ratios or at least 5, at least 10, or even higher can be used. MWCNTs are composed of two or more nested, concentric single-walled CNTs. Typically, MWCNTs have diameters that are no greater than 50 nm and, more commonly, no greater than 20 nm or no greater than 10 nm. By way of illustration, the MWCNTs can have diameters in the range from about 2 nm to about 10 nm. MWCNTs typically have lengths of 1 μm or greater, including lengths of at least 2 μm and at least 5 μm. By way of illustration, the MWCNTs can have lengths in the range from about 1 μm to about 10 μm. In a MWCNT sample, all or nearly all (e.g., >90%) of the MWCNTs may have dimensions falling into the above-recited ranges, and/or the average dimensions for the MWCNTs making up the sample may fall into the above-recited ranges.

[0037] CNFs are long filaments composed of stacked layers of graphene. The graphene in the CNFs may be in the form of, for example, stacked plates, cones, or cups. Typically, CNFs have diameters in the range from about 50 nm to about 250 nm, or greater, and lengths in the range from about 50 μm to about 500 μm, or longer. In a CNF sample, all or nearly all (e.g., >90%) of the CNFs may have dimensions falling into the above-recited ranges, and/or the average dimensions for the CNFs making up the sample may fall into the above-recited ranges.

[0038] To prepare the carbon fibers for incorporation into a geopolymer composite, they are dispersed in water to form an aqueous dispersion. The concentration of the carbon fibers in the dispersion should be selected to provide a carbon fiber-reinforced geopolymer composite having the intended carbon fiber loading, as illustrated in the Examples below.

[0039] The dispersion of the carbon fibers can be aided by the use of ultrasonic energy, which may be provided by a sonic horn, wherein higher sonication energies are generally used with higher carbon fiber concentrations. By way of illustration only, sonic energies in the range from about 5 kJ to about 100 kJ, including energies in the range from 8 kJ to 80 kJ, may be used. In order to avoid water evaporation during sonication, the dispersion can be cooled using, for example, an ice bath.

[0040] Once the carbon fibers are adequately dispersed, potassium hydroxide and/or sodium hydroxide and silica are dissolved in the aqueous dispersion of the carbon fibers. Fumed silica may be used. The alkali hydroxide (potassium and/or sodium) and the silica can be added sequentially or simultaneously. The resulting aqueous solution of potassium silicates, sodium silicates, or potassium and sodium silicates is referred to as a waterglass solution. The dissolution of the alkali hydroxides and the silica can be aided by agitating the solution. This can be accomplished by stirring, shaking, sonication, or a combination thereof. For example, an orbital shaker can be used to provide a continuous centrifugal motion, or a magnetic stir bar can be used to provide vigorous mixing. The solution is desirably agitated until full dissolution of the alkali hydroxide and silica has been achieved. The duration required for full dissolution will depend on the effectiveness of the mixing. By way of illustration, agitating the solution using an orbital shaker with an angular speed of about 100 rpm will generally achieve full dissolution in a period of about 24 hours, while the use of a magnetic stir bar with a rotation speed in the range from about 150 to 200 rpm may achieve full dissolution in a period of less than 24 hours. Because the dissolution process is exothermic, it is advantageous to add the alkali hydroxide and silica in small amounts and to cool the solution during dissolution.

[0041] Metakaolin is then added to the waterglass solution containing the dispersed carbon fibers where it undergoes polymerization reactions with the silica and alkali oxides to form the metakaolin-based geopolymer. Metakaolin is an aluminosilicate that can be formed by the calcination of kaolin at high temperatures (e.g., 650° C. to 800° C.). It is available as a high-purity, homogeneous synthetic material. Metakaolin is composed primarily of silica (SiO.sub.2) and aluminum oxide (Al.sub.2O.sub.3), with variable contents of other oxides that are present in small amounts (e.g., less than about 10 wt. % and, more commonly, less than about 5 wt. %). These other oxides may include, for example, Fe.sub.2O.sub.3, TiO.sub.2, MgO, CaO, Na.sub.2O, and K.sub.2O. Typically, metakaolin has a silica content in the range from about 40 wt. % to about 80 wt. % (including from about 45 wt. % to about 75 wt. %) and an aluminum oxide content in the range from about 10 wt. % to about 50 wt. % (including from about 15 wt. % to about 45 wt. %), with any balance being composed of other oxides and/or other impurities. The appropriate mass ratio of the metakaolin to the silica and alkali hydroxides will be determined by the stoichiometry of the geopolymer. Typically, then, the amount of metakaolin added will provide a silicon to aluminum ratio of about 2.

[0042] A slurry solution of the metakaolin-based geopolymer is formed during continuous mixing of the metakaolin with the waterglass solution via centrifugal mixing, followed by degassing under vacuum to defoam the resulting mixture to remove air. Generally, higher rotational mixing speeds and longer degassing periods will be used for higher carbon fiber concentration in the mixture, due to the increased viscosity of the mixture. By way of illustration only, in some embodiments of the methods, a mixing time of about 1 to about 5 minutes at a rotational mixing speed of about 1000 to about 1500 rpm, followed by a degassing time of about 1 to about 15 minutes at a rotational mixing speed of about 1200 to about 2000 rpm is used.

[0043] The geopolymer solution can then be cast as a film or as a layer or three-dimensional object with the use of a mold and then cured to form the carbon fiber-reinforced geopolymer composite. During the initial stage of molding, the mold should be covered with plastic to prevent moisture from escaping. During curing, the metakaolin reacts with the polysilicates of the waterglass to form polymers with Si—O—Al bonds, which are referred to as metakaolin-based geopolymers. Depending on the particular make-up of the waterglass and the metakaolin, the stoichiometry of the geopolymer may vary. Curing can be aided by heating and continuous agitation of the geopolymer slurry solution in an orbital shaker to remove air bubbles. Typical curing temperatures are in the range from about 30° C. to about 100° C., and typical curing times are in the range from about 24 hours to 5 days. However, temperatures and durations outside of these ranges can be used.

[0044] Notably, the geopolymer composites can be made without the use of organic surfactants and organic dispersing agents that promote the dispersion of the carbon fibers in water, such as polycarboxylates, carboxymethyl cellulose, and sodium dodecylsulfate, and the carbon fibers need not be treated to provide surface-functionalized with groups that promote dispersion in water, such as carboxyl functionalities. Some embodiments of the geopolymer composites consist of only the metakaolin-based geopolymer matrix and the carbon fibers dispersed therein.

[0045] The examples that follow illustrate methods of forming CNF-reinforced and MWCNT-reinforced geopolymer composites having reduced porosities and mechanical properties that are enhanced relative to their non-reinforced geopolymer counterparts. Mechanical properties that can be enhanced by the presence of well dispersed CNFs and MWCNTs include fracture toughness, indentation modulus, yield shear stress, and plastic modulus. By way of illustration, carbon-fiber reinforced geopolymer composites having CNF, MWCNT, or combined CNF and MWCNT loadings of at least 0.3 wt. % per mass of the metakaolin in the matrix and one or more of the following characteristics can be produced: porosities of less than 8%, including less than 7.5%, and further including porosities in the range from 5.5% to 7.3%; indentation moduli of at least 7.0 GPa or even at least 9.0 GPa, including indentation modulus in the range from 7.5 to 8.5 GPa and in the range from 9.0 to 10.5 GPa; fracture toughness of at least 0.57 MPa.Math.sqrt (m) or even at least 0.80 MPa.Math.sqrt (m), including fracture toughness in the range from 0.58 MPa.Math.sqrt (m) to 0.65 MPa.Math.sqrt (m) or in the range from 0.80 MPa.Math.sqrt (m) to 0.90 MPa.Math.sqrt (m); a plastic viscosity of at least 10 Pa s; and a yield shear stress of at least 50 Pa.

[0046] Methods for measuring these and other properties of geopolymer composites are described in the examples. Unless otherwise indicated, for any measured values that are dependent upon temperature and/or pressure, the values recited for a given property refer to values at room temperature (23° C.) and standard atmospheric pressure.

EXAMPLES

Example 1: This Example Describes the Synthesis of a Metakaolin-Based Geopolymer Reinforced with Carbon Nanofibers

Experimental Procedures

Materials

[0047] Metakaolin-based potassium geopolymer (KGP) nanocomposites were manufactured of KGP-xCNF. Here, x represents the weight of the CNFs, based on the weight of the metakaolin. In the experiments reported below, CNF concentrations of 0; 0.3; 0.6; and 1.5 weight percent, per weight of metakaolin were studied. These weight fractions correspond to 0; 0.1; 0.2; and 0.5 weight percent, based on the total weight fraction of carbon nanofibers in the geopolymer composite. The reference geopolymer matrix, KGP, is the metakaolin-based potassium polysialate disoloxo of chemical formula K.sub.2O—Al.sub.2O.sub.3.4SiO.sub.2.11H.sub.2O. Highly graphitic, vapor-grown and tubular carbon nanofibers were used that were characterized by an average fiber diameter of 150 nm, a surface area of 20-30 m.sup.2/g, and an average fiber length of 50-300 μm. Table 1 provides the manufacturer specifications for the carbon nanofibers used.

[0048] The manufacturing process occurred in three steps. First, the carbon nanofibers were dispersed in a surfactant using ultra-sonic energy. Second, the waterglass was synthesized by mixing deionized water, amorphous fumed silica, potassium hydroxide pellets, and dispersed carbon nanofibers. The waterglass solution was left to age for 24 hours under continuous stirring. Afterwards, synthetic metakaolin was added to the waterglass using centrifugal mixing followed by vacuum degassing. Metakaolin calcined at a temperature of 750° C., with an average particle sized of 1.2 μm and a specific surface area of 1.3 m.sup.2/g was used. After centrifugal mixing, the resulting geopolymer precursor slurry was cast into plastic molds and cured in an incubator at 50° C. for 24 hours under continuous stirring.

Grinding and Polishing

[0049] After synthesis, the geopolymer nanocomposite specimens were further processed for microscale mechanical characterization. The grinding and polishing included three steps. First, the specimens were embedded in a low-viscosity epoxy resin and machined in 5-mm thick slices using a low-speed diamond saw; the rigorously flat 5-mm thick slices were then glued onto circular aluminum discs using cyanoacrylate adhesive. Second, the specimens were ground in several steps using a semi-automated grinder and polisher along with silicon carbide pads of particle size 58.5 μm down to 8.4 μm. Third, the specimens were polished using polishing pads with a napped cloth along with polycrystalline diamond slurries of particle sizes 1 μm and 0.25 μm. The specimens were regularly cleansed using an inert oil-based solvent in an ultrasonic bath to prevent cross-contamination. The grinding and polishing procedure resulted in polished surfaces with a surface roughness of 56-122 nm, as assessed via surface profilometry. After grinding and polishing, the specimens were stored under vacuum.

TABLE-US-00001 TABLE 1 Characteristics of carbon nanofibers used as reinforcement in this study. Fiber Surface Length, Modulus, Strength, diameter, nm area, m.sup.2/g μm Gpa GPa 150 20-30 50-200 600 8.7

Optical Microscopy and Scanning Electron Microscopy Analyses

[0050] The microstructure was observed using a Nikon high-resolution transmitted light optical microscope with a magnification of 200. Environmental scanning electron microscopy (ESEM) was employed to observe the failure mechanisms. ESEM was conducted on uncoated geopolymer nanocomposite specimens using an FEI Quanta 650 ESEM under low vacuum mode. In the tests, the accelerating voltage was 10.0 kV, the walking distance was 10.8 mm, and the magnification ranged from ×1,000 to ×20,000.

Microindentation Tests

[0051] In order to assess the mechanical behavior, microindentation tests were conducted using an Anton Paar Nanohardness Tester with a Berkovich diamond probe of tip radius 2 nm. Each indentation test was characterized by a maximum vertical force of 500 mN, a loading/unloading phase of 30 s and a holding phase of 10 s. A 11×11 grid of indent was carried out per specimen, spanning an area of 1 mm.sup.2. During each test, the vertical load P and the penetration depth h were continuously recorded at a frequency of 45 kHz using force and depth sensors with a resolution of 0.3 nN for the load and 0.06 nm for the penetration depth. The indentation modulus M and the indentation hardness H were computed from the force and depth measurements by application of the Oliver & Pharr's model: (Oliver, W. C. et al., 1992. Journal of materials research, 7(6), pp. 1564-1583.)

[00001]$\begin{array}{cc}M=\frac{\sqrt{\pi }}{2}\frac{S}{\sqrt{A}};H=\frac{P_{\max }}{A}& \left(1\right)\end{array}$

where S is the stiffness of the vertical force-penetration depth curve upon unloading, P.sub.max is the maximum vertical force, and A is the contact area at maximum depth. Prior to indentation testing, the contact area function was calibrated using fused silica as a reference material.

Microscopic Scratch Tests

[0052] The fracture response was assessed using microscopic scratch tests. As illustrated in FIG. 1, the scratch test consisted of pushing a hard probe across the surface of the material under a linearly increasing load. In the tests, a Rockwell probe was used, characterized by a half-apex angle of 60° and a tip radius of R=200 μm. Each scratch test was characterized by a prescribed maximum vertical force of 5.5 N, a scratch length of 3 mm, and a scratch speed of 6 mm/min. The vertical force was prescribed using a closed-feedback loop, whereas the forces and penetration depth were recorded using high-accuracy transducers with a resolution of 1 mN for the forces and 3 nm for the penetration depth.

[0053] A nonlinear fracture mechanics model was applied to compute the fracture toughness K, from the measurements of the horizontal force F.sub.T and the penetration depth d: (Ange-Therese Akono et al., Physical Review Letters, Vol. 106, pp. 204302, (2011); and Ange-Therese Akono et al., Journal of the Mechanics and Physics of Solids, Vol. 60, pages 379-390, (2012).)

[00002]$\begin{array}{cc}{K}_c=\frac{F_T}{\sqrt{2p{A}_{LB}}}& \left(2\right)\end{array}$

where p is the perimeter and A.sub.LB is the horizontally projected load-bearing contact area. 2pA.sub.LB is the shape function of the material that varies with the probe geometry and the penetration depth d. For instance, in the case of a spherical probe of radius R, the shape probe function is a quadratic function of the depth according to: 2pA.sub.LB=a(d/R).sup.2, where a is calibrated using a reference material. (Ange-Therese Akono et al., Journal of Materials Research, Vol. 27, pp. 485-493, (2012); and Ange-Therese Akono et al., Wear, Vol. 313, pp. 117-124, (2014).)

Results

Elasto-Plastic Behavior

[0054] FIG. 2 displays representative indentation curves for the materials studied. The microindentation test in pure geopolymer, KGP, resulted in a maximum penetration depth of 7989 nm, whereas the tests in geopolymer nanocomposites resulted in maximum penetration depths of 7493 nm, 7485 nm, and 7056 nm, corresponding respectively to weight fractions of carbon nanofibers 0.1%, 0.2%, and 0.5%. Thus, the maximum penetration depth decreased as the weight fraction of carbon nanofiber reinforcement increased, pointing to a beneficial effect of carbon nanofibers on the mechanical performance. Moreover, for all materials, the maximum penetration depth was more than an order of magnitude higher than the surface roughness, supporting the accuracy of the mechanical assessment approach.

[0055] Table 2 gives the average values of the indentation modulus M and of the indentation hardness H; for each material, 121 tests were conducted. Pure geopolymer exhibited an indentation modulus of 8.30±0.25 GPa, and an indentation hardness of 430.43±23.34 MPa. Assuming a Poisson's ratio of v=0.2 for pure geopolymer, the tests yielded an elastic modulus of 7.96±0.24 GPa for pure geopolymer.

TABLE-US-00002 TABLE 2 Influence of carbon nanofiber content on the indentation modulus (M) and of the indentation hardness (H) of metakaolin-based potassium geopolymer nanocomposites. 121 indentation tests were conducted for each material. M, GPa H, MPa KGP 8.30 ± 0.25 430.43 ± 23.34 KGP-0.1 wt. % 8.69 ± 0.35 470.87 ± 20.44 CNF KGP-0.2 wt. % 9.41 ± 0.36 506.86 ± 32.92 CNF KGP-0.5 wt. % 10.04 ± 0.32  538.05 ± 31.33 CNF

[0056] The addition of carbon nanofibers led to an enhancement of the elasto-plastic properties. The indentation modulus (M) and indentation hardness (H) of KGP-0.1 wt. % CNF was respectively 5% and 9% greater than those of pure geopolymer. Moreover, adding 0.2 wt. % of carbon nanofibers resulted in an increase of 13% in Ma nd 18% in H. Finally, adding 0.5 wt. % of carbon nanofibers resulted in an increase of 21% in M and 25% in H. Overall, greater gains were observed in the indentation hardness due to the presence of carbon nanofibers. Nonetheless, carbon nanofibers resulted in an overall increase in both the modulus and the strength.

Fracture Response

[0057] FIG. 3 investigates the influence of carbon nanofibers on the scratch response. For pure geopolymer, the maximum penetration depth was 60.90 μm. Meanwhile, for geopolymer nanocomposites, the maximum penetration depths were 53.34 μm, 45.75 μm, and 45.07 μm, corresponding respectively to KGP-0.1 wt. % CNF, KGP-0.2 wt. % CNF, and KGP-0.5 wt. % CNF. Thus, the addition of carbon nanofibers led to significant reduction in the maximum penetration depth during scratch testing.

[0058] FIG. 4 displays the quantity F.sub.T/√{square root over (2pA)} as a function of the scratch path, X, for the geopolymer nanocomposites studied. F.sub.T is the horizontal force and 2pA is the probe shape function. In order to apply the scratch fracture model for a spherical probe, penetration depths less than 27 μm were selected, to remain within the spherical range of the Rockwell C scratch probe. For all materials, the quantity F.sub.T/√{square root over (2pA)} converged for large values of X (and large values of the penetration depth d) towards a constant. This convergence reflects a transition from ductile processes to brittle energy dissipation processes at large penetration depths. In the brittle regime, the fracture toughness is given by the asymptotic value of the function F.sub.T/√{square root over (2pA)}.

[0059] Table 3 displays the values of the fracture toughness K.sub.c and of the fracture energy G.sub.f for pure geopolymer and for KGP×CNF hybrids. The fracture energy was computed using the Griffith-Irwin equation G.sub.f=K.sub.c.sup.2/M. The fracture toughness K.sub.c of pure geopolymer was 0.60±0.02 MPa √{square root over (m)} and the corresponding fracture energy G.sub.f was 43.4 J/m.sup.2.

TABLE-US-00003 TABLE 3 Influence of carbon nanofiber content on fracture toughness (Kc) of metakaolin-based potassium geopolymer nanocomposites, 7-8 scratch tests were conducted for each material. K.sub.C, MPa, {square root over (m)} Fracture Energy J/m.sup.2 KGP 0.60 ± 0.02 43.4 KGP-0.1 wt.% 0.83 ± 0.02 79.3 CNF 0.84 ± 0.02 74.5 KGP-0.2 wt.% CNF KGP-0.5 wt.% 0.87 ± 0.02 75.4 CNF

[0060] Carbon nanofibers contributed to a toughening of the geopolymer matrix. The fracture toughness Kc increased by 38%, 40%, and 25%, for KGP-0.1 wt. % CNF, KGP-0.2 wt. % CNF, and KGP-0.5 wt. % CNF, respectively. The fracture energy was enhanced by 83%, 72%, and 74%, respectively, for KGP-0.1 wt. % CNF, KGP-0.2 wt. % CNF, and KGP-0.5 wt. % CNF. This gain in toughness and fracture energy is significant and much larger than the observed gains in elastic modulus and indentation hardness.

Densification of Geopolymer Matrix Due to Carbon Nanofibers

[0061] An important mechanism for both strengthening and toughening is carbon nanofiber-induced densification. FIGS. 5A-5B display optical microscopy images for pure geopolymer, KGP, and KGP-0.5 wt. % CNF. Pure geopolymer exhibited a homogeneous and three-dimensional porous microstructure with the pore diameter ranging from ˜7 μm to ˜47 μm. In contrast, KGP-0.5 wt. % CNF showed an absence of micropores with a diameter less than 30 μm and a sharp reduction in the total fraction of air voids. Yet, a couple of spare air voids could be seen, with the pore diameter ranging from 37 μm to 77 μm. Thus, two competing trends were observed: (i) a reduction in the fraction of micropores, and (ii) an increase in the macropore size. The former trend can be explained by the seeded nucleation effect: nanofibers act as heterointerfaces that promote geopolymerization along carbon nanofiber surfaces. The latter trend, increase in the size of macropores, is due to the increase in viscosity for geopolymer nanocomposite precursor paste. This increase in viscosity increases the presence of macropores even after employing advanced mixing methods such as centrifuge mixing and vacuum degassing. Thus, the presence of carbon nanofibers resulted in a reduction of the overall porosity. Classical models for ceramics have linked the elasticity and strength to the total porosity.

Fracture Micromechanisms

[0062] Another important toughening mechanism is carbon nanofiber bridging. FIGS. 6A-6D display the fracture micromechanisms during scratch testing of pure geopolymer and of geopolymer nanocomposites. FIG. 6A displays the presence of curved cracks visible in the residual scratch groove: these cracks point to the predominance of brittle fracture processes at large penetration depths. FIGS. 6B-6D compare representative fractures for pure geopolymer, KGP-0.1 wt. % CNF, and KGP-0.5 wt. % CNF. For pure geopolymer, the fracture was unobstructed with an average crack width of 1.0 μm. In contrast, for carbon nanofiber-reinforced geopolymers, see FIGS. 6C-6D, ligament bridging was observed, leading to reduced fracture widths, with an average crack width of 0.8 μm for KGP-0.1 wt. % CNF and of 0.6 μm for KGP-0.5 wt. % CNF.

Water Absorption and Porosity Measurements

[0063] The water absorption and the porosity were measured after 24 hours of curing following the standard ASTM C20-00 with minor modifications, as described below. (ASTM C20-00(2015), Standard Test Methods for Apparent Porosity, Water Absorption, Apparent Specific Gravity, and Bulk Density of Burned Refractory Brick and Shapes by Boiling Water, ASTM International, West Conshohocken, Pa., 2015, www.astm.org) First, the specimens were dried, and the dry mass M.sub.dry and dry specific gravity P.sub.dry were measured. Then, the specimens were saturated by submersion in deionized water at 23° C. for 48 hours, and the saturated mass was measured M.sub.saturated. The water absorption, W, was calculated as the relative difference between the dry and the saturated mass:

[00003]$\begin{array}{cc}W=\frac{M_{saturated}-M_{\mathrm{dry}}}{M_{\mathrm{dry}}}\times 100& \left(1\right)\end{array}$

[0064] The porosity, P, was computed as the product of the water absorption and the dry specific gravity:

P=W×ρ.sub.dry  (2)

(Théréné F, Keita E, Nael-Redolfi J, Boustingorry P, Bonafous L, Roussel N. 2020. Water absorption of recycled aggregates: Measurements, influence of temperature and practical consequences. Cem. Concr. Res. 137.106196-106204.)

[0065] A porosity of 7% for KGP+0.6 wt % CNF and 4% for KGP+1.5 wt % CNF, see Table 1 below.

TABLE-US-00004 Porosity Table: Porosity measurements for carbon nanofiber-reinforced geopolymers. Dry density Water absorption Porosity Specimen (g/cc) (%) (%) KGP + 0.6 wt % CNF 1.37 5.12 7.04 KGP + 1.5 wt % CNF 1.46 2.95 4.30

Conclusions

[0066] The mechanical performance of metakaolin-based polysialate disiloxo nanocomposites with 0.1 wt. %, 0.2 wt. %, and 0.5 wt. % of carbon nanofibers was investigated. The elasto-plastic behavior and fracture behavior were characterized via microindentation and microscopic scratch tests. These are the major findings:

[0067] Carbon nanofibers result in an increase in indentation modulus and indentation hardness. The indentation modulus (M) and indentation hardness (H) of KGP-0.1 wt. % CNF was respectively 5% and 9% greater than those of pure geopolymer. Moreover, adding 0.2 wt. % of carbon nanofibers resulted in an increase of 13% in M and 18% in H. Finally, adding 0.5 wt. % of carbon nanofibers resulted in an increase of 21% in M and 25% in H.

[0068] Carbon nanofibers lead to an increase in fracture toughness and fracture energy. The fracture toughness K.sub.c increased by 38%, 40%, and 25%, respectively, for 0.1 wt. % CNF, 0.2 wt. % CNF, and 0.5 wt. % CNF. The fracture energy was enhanced by 83%, 72%, and 74%, respectively, for 0.1 wt. % CNF, 0.2 wt. % CNF, and 0.5 wt. % CNF.

[0069] Carbon nanofibers lead to a densification of the geopolymer matrix and a reduction of micropores less than 30 μm.

[0070] Carbon nanofibers give rise to crack bridging mechanisms.

Example 2: This Example Describes the Synthesis of a Metakaolin-Based Geopolymer Reinforced with Multiwalled Carbon Nanotubes

Materials and Methods

Materials

[0071] The chemical composition of the reference geopolymer was K.sub.2O.Al.sub.2O.sub.3.4SiO.sub.2. 11H.sub.2O. To synthesize metakaolin-based potassium geopolymer nanocomposites, potassium hydroxide, silica fume, deionized water, and metakaolin were used, along with MWCNTs. The fume silica had a particle size of 70 nm and a surface area of 300 m.sup.2/g. The MWCNTs had an outer diameter <8 nm and an inner diameter of 2-5 nm, a length of 10-30 μm, and a specific surface area of 500 m.sup.2/g. Four types of geopolymer nanocomposites were manufactured as shown in Table 4. The plain geopolymer without MWCNTs is named KCT0.0. The geopolymer nanocomposites reinforced with 0.3 wt. %, 0.6 wt. %, and 1.5 wt. % MWCNTs per mass of metakaolin are named KCT0.3, KCT0.6, and KCT1.5, respectively.

[0072] The nomenclature list below introduces the mathematical notations used in this example.

TABLE-US-00005 Nomenclature Symbol Physical Meaning Ac Contact Area F.sub.T Horizontal Force Y Shear Rate H Indentation Hardness h Indentation Depth Kc Fracture Toughness M Indentation Modulus MWCNTs Multi-walled Carbon Nanotubes μ Mean η.sub.p Plastic Viscosity P Vertical Force φ Porosity R.sup.2 Coefficient of Determination s Standard Derivation S Indentation Stiffness τ.sub.0 Yield Shear Stress τ Shear Stress

[0073] Table 4. Mix design of MWCNT-reinforced geopolymer per 100 g of specimen. KCT0.0 represents plain geopolymer; KCT0.3, KCT0.6, KCT1.5 represent geopolymer reinforced with 0.3 wt. % MWCNTs, 0.6 wt. % MWCNTs, 1.5 wt. % MWCNTs, respectively, per weight of metakaolin. For all mix designs, 18.43 g of fume silica, 19.87 g of potassium hydroxide, 27.61 g of water, and 34.08 g of metakaolin were used per 100 g of specimen.

TABLE-US-00006 Sample Name Concentration (wt %) MWCNT (g) KCT0.0 0.00 0.00 KCT0.3 0.29 0.10 KCT0.6 0.58 0.20 KCT1.5 1.47 0.50

[0074] To synthesize geopolymer nanocomposites, three main steps were used. The first step was to pre-disperse MWCNTs in 27.61 g of deionized water using the ultrasonic energy provided by a VCX 750 ultrasonic horn. The dispersion energy was 2.8975 kJ per grams of MWCNTs, and per mL of deionized water. The dispersion energy was proportional to the amount of MWCNTs. 8 kJ, 16 kJ, 40 kJ were used for KCT0.3, KCT0.6, and KCT1.5, respectively. To reduce the heat generated by the concentrated dispersion energy, an ice bath was implemented. The MWCNTs were further dispersed in the following two steps. The next step was to produce potassium silicate solution. The well-dispersed MWCNTs suspension was mixed with 19.87 g of potassium hydroxide and 18.43 g of fumed silica until a uniform viscous solution was produced. The final solution continued to be mixed on a 3-mm orbital shaker at a rotational speed of 100 rpm, at room temperature for 24 hours. The continuous stirring under the orbital shaker was used to prevent MWCNT agglomeration and sedimentation within the potassium silicate solution. The final step was to manufacture geopolymer nanocomposites by mixing the potassium silicate solution with metakaolin using a planetary centrifugal mixer, THINKY ARE 310. The mixing occurred in two stages. The first stage was centrifugal mixing at 1200 rpm for 3 minutes. The second stage was vacuum degassing. Proportional parameters for different concentration levels were used to account for the MWCNT-induced increase in viscosity of the MWCNT-reinforced geopolymer slurry. The selected vacuum degassing speed and time were 1400 rpm for 3 minutes for KCT0.0 and KCT0.3, 1600 rpm for 5 minutes for KCT0.6, and 1800 rpm for 10 minutes for KCT1.5. The geopolymer slurries were then poured into 30-mm diameter cylindrical molds and sealed with plastic wraps. The specimens were cured in a 19-mm orbital shaker at a rotational speed of 150 rpm and under a temperature of 50° C. for 24 hours. Digital photographs of the specimens are shown in FIGS. 7A-7D.

Rheology Characterization

[0075] In order to characterize the rheology of the fresh geopolymer slurries, an Anton Paar Modular Compact Rheometer was used, equipped a plate-plate system with a plate diameter of 24.98 mm. The measured distance was 0.25 mm and the measuring temperature was 25±0.05° C. Flow curves in a shear rate ranging from 1 to 100 1/s were measured in 17 constant logarithmically-spaced steps with a time delay of 5 seconds between successive measurements. The modified Bingham Model (MBM) was implemented to fit the shear stress and shear rate curves as shown in Eq. 1 due to the non-Newtonian nature of fresh geopolymer nanocomposites: τ is the shear stress, γ is the shear rate, and c is a constant. Meanwhile, yield shear stress τ.sub.0 and plastic viscosity η.sub.P are the rheology characteristics.

τ=τ.sub.0+η.sub.P.Math.γ+cγ.sup.2  (3)

[0076] The rheology parameters yield shear stress τ.sub.0 and plastic viscosity η.sub.P, were determined through nonlinear fitting of Eq. (2) using the Python computer programming language. (Chougan M et al., (2020) Constr Build Mater 250:118928. https://doi.org/10.1016/j.conbuildmat.2020.118928.)

X-Ray Diffraction and Fourier-Transform Infrared Spectroscopy

[0077] XRPD was used to characterize the influence of MWCNTs on the chemistry of geopolymer nanocomposites. Prior to testing, the samples were milled with ethanol using a McCrone mill to generate a powder of uniform fineness, less than 44 μm. XRPD tests were conducted using a Smartlab Gen2 3 kW X-ray diffractometer of 40 keV accessible energy and a 30 mA current, with a Bragg angle 2θ in the range 10° to 90°. The step size was 0.05°. FTIR was performed using a Nicolet iS50 spectrometer (Thermo Nicolet) at the NUANCE Keck-II facility. The powder specimens were prepared using the same method as for XRPD analysis. In addition, KBr pellets were prepared by pressing the mixture of specimen powder and KBr with a powder:KBr weight ratio of 1:100. Regular adsorption-transmission mode was used with a frequency range from 4000 to 400 cm.sup.−1, at a resolution of 4 cm.sup.−1, and using an average of 64 scans. Statistical deconvolution was applied on the FTIR results using the Python computer programming language. (Chen X, et al. (2020) J Sol-Gel Sci Technol. https://doi.org/10.1007/s10971-020-05360-6.)

Grinding and Polishing

[0078] In order to perform microscopic testing such as scratch tests and indentation tests, a rigorous specimen preparation procedure was implemented to yield a low surface roughness. The cured geopolymers were cold mounted using a low-viscosity epoxy resin in 35-mm diameter cylindrical molds. A high precision low-speed saw with a diamond blade was utilized to generate 5-mm thick cylindrical slices. The slices were mounted onto 35-mm diameter aluminum disks. Digital photography images of the four types of geopolymer nanocomposites are shown in FIGS. 7A-7D. The mounted specimens were then ground and polished using a semi-automated grinder/polisher. Grinding was accomplished using silicon carbide abrasives of different grit sizes, consecutively 400, 600, and 1200 grit. Afterward, specimens were polished using synthetic long-napped rayon cloths with diamond suspensions of particle size 3 μm, 1 μm, and 0.05 μm. In between each step, the specimens were rinsed in an oil-based solution using an ultrasonic bath for 2 minutes to avoid contamination. The polished specimens were stored in a vacuum desiccator at room temperature.

Microscopic Image Analysis

[0079] Optical microscopy imaging was conducted using a Nikon high-resolution microscope. Afterward, the optical microscopy images were processed through digital image analysis to yield the meso-porosity. The image size was 1026 μm in width and 821 μm in height. Four images at different locations were used to get the average porosity.

Scratch Testing

[0080] Scratch testing was utilized to evaluate the fracture behavior of geopolymer nanocomposites at the microscopic length-scale. Scratch testing entails pulling a hard probe across the surface of the material under a prescribed linear vertical force. An Anton Paar microscopic scratch tester (Ashland, Va.) was used, equipped with a 200-μm Rockwell C diamond probe. For each type of geopolymer nanocomposites, 11 scratch tests were performed, each test being characterized by a length of 3 mm, a scratch speed of 6 mm/min, and a maximum vertical force of 5.5 N. The microscopic scratch was integrated with an optical microscope to test regions void of pre-existing cracks.

Micro-Indentation Testing

[0081] The grid indentation method was implemented to evaluate the mechanical behavior of geopolymer nanocomposites. For each series of tests, an 11 by 11 array of indentation tests was conducted using a Berkovich indenter. The indenter contact area function was calibrated using fused silica before testing. Each indentation test was characterized by a maximum vertical force of 500 mN, a loading/unloading rate of 1000 mN/min, and a 10-second pause. The interindent spacing was 100 μm. For each indent, the vertical force P and penetration depth h were recorded using high-resolution force and displacement sensors with a precision of respectively 20 nN and 0.01 nm. For each indent, the indentation hardness H and indentation modulus M were calculated using the Oliver and Pharr's method as shown in Eqs. (1) and (4). (Oliver, 1992; Sorelli L et al., Cem Concr Res 38:1447-1456. https://doi.org/10.1016/j.cemconres.2008.09.002.)

[00004]$\begin{array}{cc}S=\frac{dP}{dh}{|}_{h=h_{\max }}& \left(4\right)\end{array}$

S is the unloading slope as defined in Eq. (3). The contact area Ac is calculated from the maximum depth hmax using the calibrated contact area function for the indenter.

Theoretical Approach

[0082] Fracture Toughness Determination using Scratch Testing

[0083] The nonlinear elastic fracture model described in Akono et al., 2012 and Akono et al., 2014 was used to analyze the scratch test results. The geopolymer nanocomposites at the microscopic length-scale were assumed to be linear elastic isotropic with a crack developing from the tip of the probe. Therefore, nonlinear fracture mechanics and the J-integral were implemented to calculate the critical energy release rate along with the fracture toughness Kc. The fracture toughness Kc was related to the horizontal force FTand the probe shape function 2pA as shown in Eq. 5.

[00005]$\begin{array}{cc}{K}_c=\frac{F_T}{\sqrt{2pA}}\left(\frac{d}{R}\right)& \left(5\right)\end{array}$

d is the penetration depth and R=200 μm is the probe tip radius. The inventors focused on the spherical region of the scratch probe characterized by d<27 μm and calibrated the scratch probe prior to scratch testing using a reference material. F is a function equal to unity at infinity. FIG. 8A displays the quantity FT/√{square root over (2pA)} as a function of the scratch length X. An optical microscopic image of the residual groove after scratch testing is also shown in FIG. 8B: a groove of increasing width was observed, pointing to material removal processes at work during scratch testing. For scratch lengths less than 400 μm, FT/√{square root over (2pA)} decreased sharply, pointing to a ductile failure process. For scratch lengths greater than 400 μm, the quantity FT/√{square root over (2pA)} converged toward a horizontal asymptote that is the size-independent fracture toughness value. Additional details regarding fracture toughness measurements are provided in the Supplementary Information below.

Cluster Analysis of Micro-Indentation Data

Micro-Mechanics Model

[0084] The aim was to employ micromechanical modeling to connect the elastic modulus to the micro-porosity. (Kendall A K, et al. (1983) The Relation between Porosity, Microstructure and Strength, and the Approach to Advanced Cement-Based Materials and Discussion, Source: Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.) A classic model proposed by Rice postulates an exponential relationship between the elastic modulus and the microporosity: M.sub.i=M.sub.0 exp(−tφi). (Rice R W (1999) J Mater Sci 34:2769-2772. For a given indentation test i, M.sub.i is the indentation modulus and φ.sub.i is the local porosity of the probed volume. t is a fitting constant and M.sub.0 is the ideal solid skeleton indentation modulus with zero micro-porosity. (Akono A T et al. (2019) Cem Concr Compos 104:103361. https://doi.org/10.1016/j.cemconcomp.2019.103361.) A nonlinear regression and minimization algorithm were utilized in Python to obtain the optimal relationships for the microindentation tests on geopolymer nanocomposites. The nonlinear regression and minimization algorithm relied on the Truncated Newton's method (or Hessian-free optimization). (Nash S G (2000) J Comput Appl Math 124:45-59. The initial value of the microporosity was obtained from the average porosity calculated from digital image analysis.

Bayesian Gaussian Mixture Model

[0085] The cluster analysis method was applied to the distribution of the indentation data and local porosity: (M.sub.i, H.sub.i, φ.sub.i), 1≤i≤121. (Michie D (1968) Nature 218:19-22. Akono A et al. (2016) New Front Oil Gas Explor 40124 and Constantinopoulos C, et al. (2006) IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 6, pp. 1013-1018, June, doi:10.1109/TPAMI.2006.111.) The mechanical phases were identified via the Bayesian Gaussian Mixture programmed in Python. (Rasmussen C E (2000) Adv Neural Inf Process Syst 554-559; and Chellappa R, et al. (2009) Gaussian Encycl Biometrics 659-663. https://doi.org/10.1007/978-0-387-73003-5 196.) A Gaussian mixture Expectation-Maximization algorithm P(X|θ)=Σ.sub.i=0.sup.Kπ.sub.iN(X|μ.sub.i, Σ.sub.i) was used. (Vila J P, et al. (2013) IEEE Transactions on Signal Processing, vol. 61, no. 19, pp. 4658-4672, Oct. 1, doi: 10.1109/TSP.2013.2272287.) P(XI) is a Gaussian distribution with mean μ.sub.i and covariance matrix Σ.sub.i. π.sub.i is the weight of each phase. K=5 is the number of phases assumed initially. In addition, with the Bayesian Gaussian Mixture method, there is a prior distribution for parameters θ=(π, μ, μ). Here X=(M, H, φ) with M being the indentation modulus, H being the indentation hardness, and φ being the local porosity. P refers to the probability distribution function. The Bayesian Gaussian mixture model postulates a prior distribution of the vector of estimates following Eq. 6:

[00006]$\begin{array}{cc}p\left(\theta .Math.X\right)=\frac{P\left(\theta \right)P\left(X.Math.\theta \right)}{\int P\left(\theta \right)P\left(X.Math.\theta \right)d\theta }& \left(6\right)\end{array}$

A diagonal covariance type was used. A Dirichlet distribution vector was used for weight concentration type.

Results

Rheology Test Results

[0086] Rheology tests were employed to investigate the behavior of geopolymer nanocomposites under fresh state. The evolution of the viscosity is shown for different shear rates in FIG. 9A. In addition, the shear stress-shear rates curves are presented in FIG. 9B along with the Modified Bingham Model fitting curves. Shear-thickening non-Newtonian behavior was observed. The results showed that the addition of 0.3 wt % MWCNTs decreased the plastic viscosity compared to the plain geopolymer. However, for KCT0.6 and KCT1.5, a higher plastic viscosity and shear stress were observed compared to plain geopolymer. When the shear rate was less than 40 1/s, KCT0.6 had the highest plastic viscosity. Moreover, when the shear rate increased, KCT1.5 had the highest plastic viscosity. The plastic viscosity and yield shear stress values obtained from the Modified Bingham Model are shown in Table 5. There was an increasing trend of yield shear stress with the addition of MWCNTs as shown in FIG. 10. Except for KCT0.3, KCT0.6, and KCT1.5, an increase in plastic viscosity by 79.79% and 56.37%, respectively, were noted. Similarly, the yield shear stress increased by 28.29%, 560.32%, and 280.96% for KCT0.3, KCT0.6, and KCT1.5.

TABLE-US-00007 TABLE 5 Rheology results of KCT0.0; KCT0.3; KCT0.6; KCT1.5. ηp represents plastic viscosity, while τ.sub.0 represents yield shear stress. R.sup.2 represents coefficient of determination. Specimen η.sub.p (Pa .Math. s) τ.sub.0, Pa c R.sup.2 KCT0.0 6.83 13.61 0.015 0.999956 KCT0.3 4.32 17.46 0.016 0.999957 KCT0.6 12.28 89.87 −0.021 0.999975 KCT1.5 10.68 51.85 0.037 0.999987

X-Ray Powder Diffraction and Fourier-Transform Infrared Spectroscopy

[0087] To understand the chemical influence of MWCNTs on the chemistry of geopolymer nanocomposites in the hardened state, XRPD and FTIR were applied. FIG. 11 displays the X-ray diffractograms for the geopolymer nanocomposites. For KCT0.0, the XRD is amorphous with a broad peak located around 20=28°. The sharp peak located around 2θ=25° refers to the titanium dioxide present in the raw metakaolin material. The results show that MWCNTs preserve the amorphous structure of geopolymer nanocomposites.

[0088] The FTIR spectra are shown in FIGS. 12A-12D. The wavenumber range 800-1250 cm.sup.−1 was the focus. A statistical deconvolution of the FTIR spectrum was performed: the computed peaks are given in Table 6. Three main peaks were observed. The first peak around 840 cm.sup.−1 represents the Si—OH bending vibration. The second peak around 1008 cm.sup.−1 represents the asymmetrical vibration of Si(Al)—O. Finally, the third peak around 1080-1100 cm.sup.−1 represents the symmetrical vibration of Si—O. A decrease in the wave number characteristic of the bending vibration of Si—OH was observed: this decrease points to an increase in mass of Si—OH bonds. Thus, MWCNTs promote the formation of Si—OH bonds. In return, there was a decrease in the wave number characteristic of symmetrical vibration in Si—O bonds, pointing to a reduction of Si—O bonds. Thus, MWCNTs prohibit Si—O bonding. Finally, the wave number for the asymmetrical vibration for Si(Al)—O remained the same for KCT0.3 and KCT0.6 and decreased for KCT1.5. Prior studies have related the frequency of the Si(Al)—O asymmetrical vibration band to the Si/Al ratio. (Davidovits, J. (2015) Geopolymer Chemistry and Applications. 5th edition. Saint-Quentin, France.) Thus, the findings indicate that the Si/Al ratio remains unchanged for low fraction of MWCNTs.

TABLE-US-00008 TABLE 6 Statistical analysis results of FTIR, where Vol. represents volume fraction, and s.sup.i presents standard deviation of each peak. Peak 1 s.sup.1 Peak 2 s.sup.2 Peak 3 s.sup.3 Name cm.sup.−1 Vol. cm.sup.−1 cm.sup.−1 Vol. cm.sup.−1 cm.sup.−1 Vol. cm.sup.−1 KCT0.0 851.0 22.6% 49.2 1011.7 45.8% 64.9  1176.7 31.5% 77.9  KCT0.3 847.7 23.2% 51.7 1011.0 45.5% 68.0  1180.5 31.3% 82.1  KCT0.6 836.6 16.1% 34.7 1012.4 54.5% 113.8  1250.0 29.3% 123.8  KCT1.5 836.8 21.9% 43.5 1003.6 45.7% 91.2  1213.4 32.4% 118.6 

Fracture Toughness of Geopolymer Nanocomposites

[0089] Scratch testing was used to understand the influence of MWCNTs reinforcement on the fracture performance. The results of scratch testing were shown in FIG. 13. The quantity FT/√{square root over (2pA)} was plotted along scratch length X. FT was defined as the horizontal force while 2pA was the scratch probe shape function. At the beginning of the scratch, penetration depths were relatively low, which resulted in the extreme variation of the FT/√{square root over (2pA)}. At this stage, the fracture mechanism combines plasticity and elasticity. With the development of scratch, FT/√{square root over (2pA)} reached a convergence regime. The convergence of FT/√{square root over (2pA)} indicates that the fracture mechanism developed from ductile to brittle, where linear elastic fracture mechanics domains. The fracture toughness value of plain geopolymer is 0.57±0.03 MPa√{square root over (m)}, which agrees with the fracture toughness of plain metakaolin geopolymer measured at the macroscopic scale using three-point bending tests. (Zhang P et al. (2020) 46:20027-20037.) Therefore, the model to assess the fracture toughness at the microscopic scale is valid. High fractions of MWCNTs improved the fracture toughness of metakaolin-based potassium geopolymer. The fracture toughness values were 0.53±0.02, 0.58±0.01, 0.63±0.03 MPa√{square root over (m)}, respectively, for KCT0.3, KCT0.6, and KCT1.5. A drop in fracture toughness was observed with the addition of 0.3 wt. % MWCNTs. There was a slight increase of 1.75% with the addition of 0.6 wt. % MWCNTs. There was a huge increase of 10.52% with the addition of 1.5 wt. % MWCNTs compared to the plain geopolymer.

Optical Microscopy Imaging Results

[0090] The optical microscopy images shown in FIGS. 14A-14D show the presence in plain geopolymer of large microscopic pores, 100 μm in size. With the addition of MWCNTs, the size of pores decreased. To quantify the change in microporosity, digital image analysis was applied. The computed average microporosity values were 8.698%, 4.576%, 5.664%, and 7.072%, respectively, for KCT0.0, KCT0.3, KCT0.6, and KCT1.5. Overall, a decrease in microporosity was noted in MWCNT-reinforced geopolymers compared to the plain geopolymer. Yet, by comparing MWCNT-reinforced geopolymers, an increase in microporosity was noted as the fraction of MWCNT reinforcement increased. Recalling the rheology test results, see FIGS. 9A-9B and FIG. 10, the plastic viscosity increased as the fraction of MWCNT increased, which may explain the observed increase in microporosity for MWCNT-reinforced geopolymers. Thus, two competitive trends were observed: (i) on the one hand, MWCNTs lead to a reduction in pore size and pore fraction; (ii) on the other hand, the increase in plastic viscosity of the MWCNT-reinforced geopolymer slurries promotes the development of microscopic air voids. Additional details regarding optical microscopy image analysis are provided in the Supplementary Information below Grid Indentation and Statistical Deconvolution Results

Grid Indentation was Implemented to Characterize the Underlying Mechanical

[0091] phases at the microscopic length-scale, based on the distribution of the indentation modulus M, indentation hardness H, and local microporosity p. FIGS. 15A-15D display the histograms of the indentation modulus. The presence of MWCNTs affects the frequency of the indentation modulus. A broadening of the peak of the indentation modulus was also observed. This broadening of the peak points to an increase in the heterogeneity leveled as the fraction of MWCNTs increased. The measured average indentation modulus was 7.76±0.23, 7.83±0.31, 8.01±0.44, and 7.48±0.49 GPa, respectively, for plain geopolymer, KCT0.3, KCT0.6, and KCT1.5. Thus, the average indentation modulus increased by 0.9% and 3.2% with the addition of 0.3 wt. % and 0.6 wt. % MWCNTs. However, incorporating 1.5 wt. % MWCNTs decreased the indentation modulus by 3.6%. Similarly, the measured average value of the indentation hardness is 388.27±16.93, 414.41±23.60, 431.33±37.67, and 392.31±41.20 MPa, respectively, for plain geopolymer, KCT0.3, KCT0.6, and KCT1.5. Thus, the addition of MWCNTs increased the indentation hardness by 6.7%, 11.1%, and 1.04%, respectively, for 0.3 wt. %, 0.6 wt. %, and 1.5 wt. % MWCNTs.

[0092] To quantify the phase transformation or the shift, cluster analysis was implemented. FIGS. 16A-16D display the results of the cluster analysis. The detailed characteristics for all phases in all specimens are given in Table 7. The main phase had a 7.834 GPa indentation modulus, a 0.388 GPa indentation hardness, and an 8.7% porosity. For KCT0.3, the main phase characteristics increased to 7.821 GPa for the indentation modulus and 0.414 GPa for the indentation hardness; meanwhile, the porosity decreased to 5.6%. For KCT0.6, the reinforcement effects prevailed, where the main phase was strengthened with an 8.012 GPa modulus, a 0.431 GPa hardness, and a 3.3% porosity. However, for KCT1.5, a bimodal distribution was observed with two dominating phases. One is a weaker phase with a 7.418 GPa modulus, a 0.389 GPa indentation hardness, and a 7.5% porosity. The other one is a stronger phase with an 8.0803 GPa modulus, a 0.434 GPa hardness, and a 0.4% porosity. Here, the FTIR results were recalled. see FIGS. 12A-12D and statistical results in Table 6, where KCT0.6 showed an increase in structural changes, which refers to the geopolymerization. The indentation results agree with the FTIR result and show that KCT0.6 exhibits the highest values of the indentation modulus and hardness. Overall, the indentation results show that the addition of MWCNTs promotes the growth of a stronger geopolymer phase.

TABLE-US-00009 TABLE 7 Cluster analysis volume fraction results of KCT0.0, KCT0.3, KCT0.6, KCT1.5, where μ.sup.M, μ.sup.H, μ.sup.φ represents the average indentation modulus, hardness, and porosity while s.sup.M, s.sup.H, s.sup.φ represents the standard derivation of indentation modulus, hardness, and porosity. Sample Volume μ.sup.M s.sup.M μ.sup.H s.sup.M Name Phase Fraction GPa GPa GPa GPa μ.sup.φ s.sup.φ KCT0.0 Porous Phase 0.991 7.752 0.047 0.388 0.001 0.088 0.000 Geopolymer 0.004 7.763 0.167 0.388 0.033 0.087 0.007 Geopolymer 0.000 7.763 0.167 0.388 0.033 0.087 0.007 Geopolymer 0.000 7.763 0.167 0.388 0.033 0.087 0.007 Stronger 0.004 8.999 0.129 0.498 0.025 0.038 0.005 KCT0.3 Porous Phase 0.005 6.700 0.128 0.336 0.025 0.107 0.005 Geopolymer 0.967 7.821 0.061 0.414 0.001 0.056 0.000 Geopolymer 0.008 7.834 0.167 0.415 0.033 0.055 0.007 Geopolymer 0.006 7.834 0.167 0.479 0.033 0.055 0.007 Stronger 0.014 9.156 0.106 0.498 0.020 0.003 0.004 KCT0.6 Porous Phase 0.016 6.087 0.110 0.256 0.020 0.149 0.004 Geopolymer 0.008 8.012 0.167 0.431 0.033 0.058 0.007 Geopolymer 0.000 8.012 0.167 0.431 0.033 0.058 0.007 Geopolymer 0.000 8.012 0.167 0.431 0.033 0.058 0.007 Stronger 0.975 8.044 0.128 0.434 0.002 0.056 0.000 KCT1.5 Porous Phase 0.016 4.901 0.142 0.191 0.025 0.213 0.005 Geopolymer 0.062 6.493 0.080 0.311 0.011 0.119 0.002 Geopolymer 0.699 7.418 0.068 0.389 0.002 0.075 0.000 Geopolymer 0.008 7.487 0.167 0.393 0.033 0.073 0.007 Stronger 0.215 8.083 0.049 0.434 0.004 0.046 0.001
Additional details regarding indentation hardness measurements are provided in the Supplementary Information below

Discussion

Potential Applications of MWCNT-Geopolymer for 3-D Printing

[0093] In terms of rheology, two of the most important factors in 3-D printing geopolymers are the plastic viscosity and the yield shear stress. The plain geopolymer KCT0.0 had a yield stress of 13.61 Pa. For higher fractions of MWCNTs, >0.3 wt. %, it was found that MWCNTs had a significant effect on the rheological properties. For KCT0.6 and KCT1.5, the plastic viscosity increased by 79.8% and by 56.37%. Finally, the yield shear stress increased by 28.29%, 560.32%, and 280.96% for KCT0.3, KCT0.6, and KCT1.5.

[0094] The plastic viscosity for geopolymer nanocomposites is in the range of the viscosity of geopolymer mortars used for 3-D printing. The increase in both the yield shear stress and plastic viscosity makes MWCNT-reinforced geopolymer inks attractive for 3-D printing applications. In addition, the MWCNT fraction influenced the rheological properties. As a result, for future applications, the yield stress and plastic viscosity can be tailored by adjusting the fraction of reinforcing nanomaterials like MWCNTs so as to optimize simultaneously the rheological behavior in the fresh state and the mechanical properties in the hardened state.

Effect of MWCNTs on Microstructure and Mechanical Response

[0095] X-ray diffraction (XRD) shows that MWCNTs preserve the amorphous structure of metakaolin-based potassium geopolymer. FTTR results show that MWCNTs affect chemical bonds: specifically, an increase in Si—OH bonds and a reduction in Si—O bonds were observed. Thus, MWCNTs promote the hydroxylation of Si atoms in geopolymer. The inner strengthening is corroborated by the reduction in porosity, see FIGS. 14A-14D. Moreover, this inner strengthening effect was also observed in the statistical deconvolution results, see Table 7, as the mechanical properties of the dominant phase increased.

[0096] MWCNTs stiffen metakaolin-based geopolymer matrices. For low mass fractions of MWCNTs, less than 0.6 wt. %, the average indentation modulus increased as the mass fraction of MWCNTs increased. The sharp decline in indentation modulus for 1.5 wt. % can be explained by the increase in microporosity. Furthermore, the microscopic fracture tests indicate a positive correlation between the fracture toughness and the mass fraction of MWC-NTs.

Conclusions

[0097] Four types of metakaolin-based potassium geopolymer nanocomposites were studied, including plain geopolymers and geopolymers reinforced with 0.3 wt %, 0.6 wt %, and 1.5 wt % MWCNTs. Scratch testing was implemented to evaluate the fracture behavior at the micro-scale level. The mechanical behavior was investigated, including indentation hardness and indentation modulus, using statistical analysis. XRPD and FTIR were implemented to study the chemical influence by MWCNTs. Coupling the indentation results for mechanical testing, scratch results for fracture behavior, chemical characterization, and fresh state rheology characterization, the following conclusions were derived:

[0098] A mixing method is presented to yield high-performance metakaolin-based geopolymer nanocomposites reinforced with 0.6-1.5 wt % MWCNTs.

[0099] FTIR analysis showed that the structural changes were most pronounced for 0.6 wt. %, suggesting that MWCNTs accelerated the geopolymerization reaction. This result agrees with the XRD analysis.

[0100] The indentation modulus of plain geopolymer is 7.7 GPa: a 5% increase was observed with the addition of 0.6 wt. % MWCNTs. Statistical deconvolution analysis shows that MWCNTs strengthen the geopolymer matrix.

[0101] The fracture toughness of plain geopolymer is 0.57 MPa. √{square root over (m)}: a 10% increase was observed with the addition of 0.6 wt. % MWCNTs and a 15% increase was observed with addition of 1.5 wt. % MWCNTs.

[0102] The micro-porosity initially decreased by 50% with the addition of 0.3 wt. % MWCNTs. Afterward, a steady increase in micro-porosity was observed as the fraction of MWCNTs increased.

[0103] An increase in the plastic viscosity and the shear yield stress was observed with the addition of MWCNTs, with the highest increase being for 0.6 wt. %. These results suggest that the plastic viscosity and the shear yield stress can be tailored with the addition of MWCNTs, with important implications for 3-D printing applications.

Supplementary Information

Fracture Toughness

[0104] Surface roughness less than 0.2 was selected for calculating the fracture toughness. Y-axis represents F.sub.T/√{square root over (2pA)} while X-axis represents scratch length X as shown in FIGS. 17A-17D. K.sub.c was calculated by taking average of the F.sub.T/√{square root over (2pA)} values in the linear fracture region, where X was larger than 600 μm. The mean value of fracture toughness K, on each type of sample was calculated by using 11 scratch tests. The average fracture toughness was 0.57, 0.53, 0.58, 0.63 MPa√{square root over (m)} for KCT0.0, KCT0.3, KCT0.6, and KCT1.5.

Indentation Hardness

[0105] Indentation hardness H histograms were shown in FIGS. 18A-18D. From plain geopolymer to geopolymer reinforced with MWCNTs, a shift from lower hardness value to higher hardness values was observed. In addition, there was an increase in terms of the average hardness value. From indentation, it was observed that the MWCNTs optimum amount was 0.6 wt. %, which agrees with the results for indentation modulus.

Image Analysis

[0106] Image analysis was implemented using computer programming to characterize the pore phase. A greyscale histogram was used to determine porosity phase (dark). FIG. 19 shows images, with markers, and after analysis. The four images of plain geopolymer KCT0.0 in FIG. 19 show the image analysis porosity. The black areas represent the porous areas. FIG. 20 shows one greyscale histogram of a plain geopolymer image. The greyscale less than 0.35 as porosity was selected. Using a calculation from the microscope images, the average porosity was 8.70%, 4.58%, 5.67%, and 7.07% for KCT0.0, KCT0.3, KCT0.6, and KCT1.5. Thus, a decrease in porosity with the addition of 0.3 wt. %, 0.6 wt. % and 1.5 wt. % MWCNTs was observed.

Fourier-Transform Infrared Spectra

[0107] FTIR spectra data is shown in FIGS. 21A-21B. FIG. 21A represents the raw data from 400-4000 cm.sup.−1 while FIG. 21B represents a smaller region for the chemical group in a clear way with marked peaks from 400-1200 cm.sup.−1.

[0108] The word “illustrative” is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “illustrative” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Further, for the purposes of this disclosure and unless otherwise specified, “a” or “an” means “one or more.”

[0109] The foregoing description of illustrative embodiments of the invention has been presented for purposes of illustration and of description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the invention. The embodiments were chosen and described in order to explain the principles of the invention and as practical applications of the invention to enable one skilled in the art to utilize the invention in various embodiments and with various modifications as suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents.