Abstract
Geopolymers are emerging as sustainable alternatives to Ordinary Portland Cement (OPC), offering high strength, lightweight properties, and a lower environmental impact, making them promising materials for green concrete technologies. In this study, we synthesized graphene-based geopolymer nanocomposites using various functional graphene derivatives, such as graphene oxide (GO), sulfonated graphene oxide (G-SO3H) thiographene (G-SH), and phosphate graphene (G-PO3H), along with alumina- and silica-rich waste materials, such as fly ash and dolomite, to enhance mechanical properties, including setting time, flowability, compressive strength, and water absorption. The functional groups on graphene derivatives improve the particle dispersion and matrix density, enhancing compressive strength, while Raman spectroscopy reveals spectral shifts at interfaces of phosphate graphene with dolomite and fly ash, indicating interactions. The resultant FDGP exhibits a significantly higher compressive strength of 45.60 MPa at 7 days and 50.20 MPa at 28 days compared to GO, G-SH, and G-SO3H. The high concentration of phosphate functional groups promotes strong interactions with the geopolymer matrix, improving its workability. Furthermore, density functional theory (DFT) calculations elucidate the role of functional groups in graphene-based geopolymer concrete, enhancing molecular interactions and promoting robust interfacial adhesion with the geopolymer matrix for a superior performance. We studied the time-dependent interactions of functionalized graphene oxide phosphate using DFT and other characterization methods, revealing strong hydrogen bonding that enhances dispersion and reinforcement within the geopolymer matrix.
Keywords: functional graphene derivatives, geopolymers, fly ash (FA), interfacial chemistry, density functional theory (DFT), compressive strength, water absorption


1. Introduction
The civil construction industry encounters significant challenges especially the environmental impact of traditional cement production as it substantially contributes to carbon emissions and exacerbates climate change. − Geopolymers can reduce carbon emissions by up to 80% compared to Portland cement, reuse industrial byproducts, and provide an energy-efficient, sustainable solution. Geopolymers are inorganic polymers that form a robust three-dimensional network of silica–alumina (–Si–O–Al–O–) linkages, providing exceptional durability. − When aluminosilicate precursors dissolve, tetrahedral Si4+ and Al3+ units are released, which then polymerize into chains. A low silica-to-alumina ratio fosters the formation of strong 3D networks, while an excess of alkaline ions can destabilize the structure, weakening its integrity. −
Recently, numerous research groups have investigated the incorporation of fillers into the geopolymer matrix, demonstrating improvements in fracture toughness, reduced brittleness, and prevention of crack propagation, thereby enhancing the overall material performance. , More importantly, the incorporation of 2D graphene derivatives enhances the strength of geopolymers, improving their mechanical properties and competitiveness, thereby driving innovation across the construction industry. − Especially, graphene, a two-dimensional carbon allotrope, was first isolated through the mechanical exfoliation of graphite in 2004. It consists of a single layer of graphite made up of sp2-hybridized carbon atoms arranged in a flat honeycomb lattice. − This unique structure imparts exceptional physical and chemical properties to graphene, contributing to its remarkable mechanical characteristics, such as high stiffness, strength, and toughness. , However, pristine graphene lacks functional groups for proper dispersion and linking with the geopolymer. To address this, various methods have been developed to introduce chemical functionality on graphene surfaces or edges, with notable derivatives, including graphene oxide (GO) containing oxygen-functional groups, such as carboxyl, epoxy, and hydroxyl, which enable dispersion in water and facilitate hybrid formation. − Nevertheless, the counter Na+, K+, and Ca+ ions in the geopolymer interact with the oxygen functional groups on graphene oxide (GO), helping to maintain the system balance and accelerate the geopolymerization process. , Despite its exceptional strength and crack propagation resistance, the mechanical performance of the material is limited by weak interactions between the edge-functionalized graphene and the geopolymer matrix, hindering optimal dispersion and reinforcing effectiveness for concrete applications. ,− However, surface functionalization of graphene enhances interactions and dispersion, leading to improved mechanical properties in graphene-based geopolymers. − Herein, we engineered graphene-derived geopolymers as FDGO, FDGS, FDGSH, and FDGP using functional graphene derivatives graphene oxide (GO), sulfonated graphene oxide (G-SO3H), thiographene (G-SH), and phosphate graphene (G-PO3H)in combination with silica/alumina-rich fly ash and dolomite and incorporated them into geopolymer concrete to enhance its compressive strength as shown in Scheme .
1. (Top) Schematic Illustration Depicting a Graphene-Based Geopolymer Composed of Phosphate Graphene with Fly Ash (SiO2, Al2O3) and Dolomite [CaMg(CO3)2], Designed to Enhance Mechanical Properties .
a (bottom) Structure of graphene oxide derivatives: graphene oxide, thiographene, and sulfonated graphene.
The functional groups on these derivatives form strong chemical bonds with the aluminosilicate matrix, improving the particle dispersion and overall matrix density. More importantly, GO–PO3H improves matrix integrity, GO–SO3H enhances particle interaction, and GO–SH aids in crack resistance, collectively increasing the compressive strength and making geopolymer concrete more suitable for high-strength applications. To the best of our knowledge, this work is the first to tailor functionalized graphene specifically for geopolymer concrete applications. Moreover, density functional theory (DFT) calculations reveal that functional groups (phosphate, sulfate, thiol, carboxylate, and hydroxy) on graphene enhance molecular interactions and interfacial adhesion, significantly improving the performance of graphene-based geopolymer concrete.
2. Experimental Section
2.1. Materials
All chemicals were purchased from commercial suppliers and used without further purification, unless otherwise mentioned. Sodium hydroxide and sodium silicate were purchased from Sigma-Aldrich and used without any further purification. Fly ash of class F was obtained from Nabha Power Limited in Rajpura, Punjab, India, for this investigation. Fly ash (FA) is an industrial waste aluminosilicate-rich pozzolanic material. The reactivity test for the pozzolanic material is performed as per IS: 1727, 2013. The reported compressive strength for the mortar cube was 3.42 MPa. Dolomite used in this study was procured from a local supplier in Jammu, India. It is a carbonate-based mineral primarily composed of calcium magnesium carbonate [CaMg(CO3)2] and was utilized as a partial replacement for fly ash. Dolomite is known for its filler effect and its potential to enhance the packing density of the binder matrix.
2.2. Synthesis of Functionalized Graphene Oxides
2.2.1. Synthesis of Graphene Oxide
In a typical synthesis, 20 g of fine graphite powder, 1 g of sodium nitrate, and 46 mL of concentrated H2SO4 were added into a 250 mL RB flask, and the temperature was maintained at 0 °C with the help of an ice bath with continuous stirring. After 20 min, the temperature was maintained between 20° to 25 °C and then 6 g of KMnO4 were added slowly over the duration of 2 h and then the mixture was stirred for 4 h maintaining a temperature between 20° to 25 °C; after this, the temperature was increased to 35 °C and was stirred for another 30 min. Further, 92 mL of D.I. water was added slowly while keeping the mixture in an ice bath under continuous stirring then the temperature was further increased to 90 °C and was maintained for the next 15 min, the contents of RB were transferred to a 1 L beaker containing 500 mL of 3%H2O2 solution, this mixture was stirred for another 10 min, and then the mixture was kept to settle for the next 12 h. Further, the mixture was centrifuged at 5500 rpm and washed with 10% HCl solution and deionized water until the pH becomes neutral. Then, it was tried at 60 °C for 8 h.
2.2.2. Synthesis of Phosphate Functionalized Graphene Oxide (GO–PO3H)
150 mg of GO were suspended in 300 mL of D.I. water for 90 min sonication. The solution was further transferred to a Teflon bottle followed by the addition of 37.5 mL phosphoric acid, the contents were stirred for 30 min before transferring the Teflon bottle into a autoclave. The mixture was heated at 180 °C for 5 h. The product was washed with deionized water until the pH becomes neutral and dried using freeze-drying.
2.2.3. Synthesis of Sulfate-Functionalized Graphene Oxide (GO–SO3H)
100 mg of GO was suspended in 5 mL of CHCl3 and was sonicated for 60 min. The exfoliated solution was transferred to an RB followed by the addition of 50 mg ClSO3H, the mixture was heated for 4 h at 70 °C; afterward, it was cooled to room temperature and washed with methanol and deionized water until the pH becomes neutral and dried at 80 °C for 8 h.
2.2.4. Synthesis of Thiol-Functionalized Graphene Oxide (GO–SH)
Twenty milligrams of GO were suspended in 20 mL of DMF and sonicated for 30 min; the contents were then transferred to a three-necked RB and three cycles of nitrogen heating and cooling were given. Further, 22 mg AIBN, 100 μL of propanethiol were added, and again three nitrogen cycles were again given to the RB, and the mixture was stirred for 24 h at 70 °C. Afterward, it was cooled to room temperature and washed with deionized water until the pH becomes neutral and was dried at 80 °C for 8 h.
2.3. Synthesis of Geopolymer Mortar
The geopolymer mortar synthesis depends on the composition and type of binders, the type and composition of alkali activators, the curing method, and the time. The material selection was conducted diligently through a number of trials. A series of trial mixes were created, each with varying molarity levels (10 M, 8 M, 6 M) and Na2SiO3/NaOH ratios (1, 1.5, 2, and 2.5), to determine the ideal mix for achieving the targeted properties. Dolomite was added to the geopolymer mortar to improve compressive strength and durability while also allowing curing at room temperature (25 ± 2 °C) rather than 60 °C. This adjustment increases the concrete’s workability and adaptability across different environments. After extensive testing, the most effective mix (NaOH = 10 M and Na2SiO3/NaOH = 2.5) was selected as the base for further refinement. To enhance this optimized mix without repeating data, functionalized graphene oxides and graphene oxides were incorporated to improve their properties further. The optimization process was meticulously designed to focus on the key factors that influence the performance of geopolymer concrete. Crucial parameters such as the molarity of the alkaline activator, the sodium hydroxide to sodium silicate ratio, and the overall mix composition were systematically varied and analyzed. The aim was to achieve an optimal balance among compressive strength, water absorption, and durability. The goal of the optimization was to enhance the material’s mechanical properties while minimizing permeability to ensure long-term durability in advanced construction applications.
In this study, 24 geopolymer mortar cubes were cast, with three serving as control samples made from 80% fly ash (FA) and 20% dolomite with 10 M sodium hydroxide (NaOH). The alkali-to-binder ratio (A/B) was set at 0.4, and the binder concentration was kept consistent at 480 kg/m3 for all mixes. The alkali activators used were 10 M NaOH and sodium silicate (Na2SiO3) in a 2.5:1 ratio (shown in Table S1). The sodium hydroxide solution was prepared 24 h before mixing to ensure complete dissolution, and sodium silicate was added to the NaOH solution in the specified ratio. The objective was to replace traditional materials with industrial byproducts, such as FA and dolomite, without compromising strength and durability. Furthermore, 1% graphene oxide with different functional groups (by the binder weight) was incorporated to further enhance the mechanical and durability properties of the geopolymer concrete. Six groups of geopolymer mortar (GPM) mixes were prepared, with varying types of graphene oxide:
Group 1: FA-based GPM (FA: Dolomite = 100:00).
Group 2: FA and dolomite-based GPM (FA: Dolomite = 80:20).
Group 3: FA and dolomite-based GPM with GO (FA: Dolomite = 80:20 with 1% GO).
Group 4: FA and dolomite-based GPM with GO (FA: Dolomite = 80:20 with 1% GO–SH).
Group 5: FA and dolomite-based GPM with GO (FA: Dolomite = 80:20 with 1% GO–SO3H).
Group 6: FA and dolomite-based GPM with GO (FA: Dolomite = 80:20 with 1% GO–PO3H).
2.4. Mixing, Molding, and Curing Measurements
For the preparation of geopolymer mortar, raw materials such as fly ash and dolomite were added into a mortar mixer for mixing. The mixing process involved dry mixing the binder and aggregates for 3–5 min, followed by the gradual addition of the alkali activator solution (prepared 24 h before casting) and continuous mixing for 5–7 min to ensure uniformity. The mortar was poured into oiled molds, compacted to remove air bubbles, and left to set at room temperature for 24 h under plastic covers as shown in Scheme S1.
3. Results and Discussion
3.1. Synthesis and Characterization of Graphene-Derived Geopolymers
The functionalized graphene derivatives are synthesized using established methods. Graphene oxide (GO) is first prepared by oxidizing graphite using the modified Hummers’ method, which introduces oxygen-containing groups. To create functionalized derivatives, GO is then reacted with specific chemical agents. For GO-PO3H, GO is treated with phosphorus-based agents such as phosphoric acid, incorporating phosphate groups on the graphene plane and edges. − GO–SO3H is synthesized by sulfonating GO with sulfuric acid, introducing sulfonate groups that improve dispersion in water. Lastly, GO-SH is produced by reacting GO with thiol agents like thioglycolic acid and adding thiol groups to the graphene basal plane. − The structure, coordination environment, and phase purity of GO, GO–PO3H, GO–SO3H, and GO–SH were characterized using powder XRD, FT-IR spectroscopy, Raman spectroscopy, and X-ray photoelectron spectroscopy (XPS) analysis (Figures S1–S7). The XRD pattern of GO-PO3H shows typical graphite-related peaks between 20 and 25°, with a peak at around 43° indicating a disorder in the graphite 101 and 012 planes characteristic of GO (Figure a). The FT-IR spectra of GO–PO3H show typical peaks for hydroxyl (O–H), carboxyl (CO), and epoxy (C–O) groups from GO, along with a distinct PO stretching peak (1200–1300 cm–1) indicating the incorporation of phosphate groups. Additionally, a C–P stretching peak at around 900–1000 cm–1 confirms the successful functionalization of GO with phosphate groups (Figure b). The XPS survey spectrum of GO–PO3H shows peaks corresponding to carbon, oxygen, and phosphorus (Figure S7). The P 1s spectrum was deconvoluted into two peaks at 1335.5 and 134.9 representing different phosphorus environments as P–C and P–O, respectively. Besides, SEM analysis of GO-PO3H shows a bundle of uniform nanosheet length of ∼200 nm. Fly ash (class-F) from the thermal power plants was used in the geopolymer mortar. X-ray diffraction (XRD) analysis was used to determine the fly ash’s phase purity and crystal structures. The results showed that the fly ash sample contained prominent peaks that corresponded to crystalline phases like quartz (SiO2) (JCPDS 46-1045) and mullite (Al6Si2O13) (JCPDS card 06-0258) (Figure a). The pure fly ash (FA) Fourier transform infrared (FT-IR) spectra showed that the existence of quartz and mullite phases inside the samples was further supported by the appearance of a peak at 1161 cm–1 corresponding to Si–O–Si or Al–O–Si asymmetric stretching (Figure b). Additionally, a broad absorption band in the –OH region (about 3800–2700 cm–1) was mostly ascribed to surface –OH groups from silica and water molecules adsorbed on the surface. To lower the curing temperature from 60 °C to room temperature (27 °C ± 2 °C), dolomite was used in the geopolymer concrete as the binder. Powder XRD analysis shows the existence of calcium oxide and magnesium oxide. , To develop geopolymer concrete, we combined structurally rich silica- and mullite-based fly ash, calcium-rich dolomite, and graphene derivatives such as GO, GO-PO3H, GO–SO3H, and GO–SH. These were used to create innovative geopolymer concrete hybrids, FDGO, FDGP, FDGS, and FG-SH, under alkaline activation with sodium silicate (Na2SiO3) and sodium hydroxide (NaOH) solutions, as shown in Scheme . To enhance the mechanical properties of geopolymer concrete, 1% graphene oxide with different functional groups (by the binder weight) was incorporated. We have prepared six groups of geopolymer mortar (GPM) mixes were prepared, varying the type of graphene oxide. The first group was FA-based GPM (FA: Dolomite = 100:0), followed by a mixture of FA and dolomite-based GPM (FA: Dolomite = 80:20) denoted as FD. The third group involved FA and dolomite-based GPM with 1% GO (FDGO), while the fourth group included FA and dolomite-based GPM with 1% GO-SH (FDGSH). The fifth group contained FA and dolomite-based GPM with 1% GO–SO3H (FDGS), and the final group was FA and dolomite-based GPM with 1% GO-PO3H (FDGP).
1.
(a) Powder X-ray diffraction (XRD) pattern and (b) Fourier-transform infrared (FT-IR) spectra of fly ash (green line), dolomite (blue line), phosphate graphene (red line), and their hybrid FDGP (violet).
The powder X-ray diffraction (XRD) analysis (FDGP) provides important insights into the formation of key compounds crucial for the structural rigidity of the phosphate-based graphene geopolymer (Figure a). The XRD pattern shows prominent peaks, indicating the successful development of N–A–S–H and C–A–S–H phases, along with quartz and the 101-plane characteristic of GO-PO3H. The formation of the FDGP geopolymer concrete was confirmed by FT-IR spectroscopy (Figure b). The spectrum reveals a distinct PO stretching peak in the range of 1200–1300 cm–1 and a C–P stretching peak around 900–1000 cm–1, indicating the presence of phosphate groups. Additionally, the presence of Si–O–Al bonds is confirmed by the observed band between 700 and 1000 cm–1. A band at 970 cm–1 suggests the formation of C–A–S–H and N–A–S–H phases.
Furthermore, Raman spectroscopic measurements were conducted on all pristine materials, including fly ash (FA), dolomite (D), graphene derivatives, showing 495, 1099, and 1586 cm–1, corresponding to Si–O, Ca–O, and D band (sp3) vibrations, respectively (Figure a). FDGP exhibits combined peaks corresponding to fly ash, dolomite, and GO-PO3H. More importantly, a spectral shift is observed at the interface between dolomite and phosphate graphene in the hybrid (Figure c). Furthermore, an additional spectral shift is evident at the interface between fly ash and phosphate graphene (Figure d). The Raman intensity mapping of the composite demonstrates peaks corresponding to the 460 cm–1 band for fly ash (blue), the 1099 cm–1 band for dolomite (green), and the 1586 cm–1 band for graphene phosphate graphene (red). The combined mapping highlights the distribution of these components and clearly illustrates the interfaces among fly ash, dolomite, and phosphate graphene, with a distinct interface observed between dolomite and phosphate graphene in the hybrid (Figure b).
2.
(a) Raman spectra of fly ash (green), dolomite (blue), GO–PO3H (red), and FDGP (violet), showcasing their characteristic peaks. (b) Raman intensity mapping of the composite, highlighting the distribution of fly ash (blue), dolomite (green), GO–PO3H (red), and their combined presence in FDGP. (c) Spectral shift observed at the interface between dolomite and phosphate graphene in the hybrid. (d) Spectral shift observed at the interface between fly ash and phosphate graphene in the hybrid.
The XPS survey spectrum of FDGP confirms the presence of aluminum, silicon, calcium, magnesium, sodium, carbon, oxygen, and phosphorus elements (Figure S8a). As shown in Figure , high-resolution XPS analysis of Al 2p peaks at 74.3, 73.6, and 74.8 eV correspond to Al–O–Si, Al–O, and AlO(OH) bonds, respectively. The Ca 2p spectrum reveals Ca 2p1/2 and Ca 2p3/2 peaks at 350.6 and 346.9 eV, confirming the divalent nature of calcium. The P 2p peaks at 133.6 and 134.5 eV are attributed to P–O and P–C bonds, while the C 1s spectrum shows peaks at 285.4, 286.3, and 289.4 eV, corresponding to C–C(sp2), C–O–C, and C–C–O groups, respectively. The O 1s peaks at 531.7 and 532.8 eV are assigned to C–O and P–O bonds, respectively.
3.
High-resolution XPS spectra of FDGP: (a) Al 2p, (b) Ca 2p, (c) Si 2p, (d) C 1s, (e) O 1s, and (f) P 2p of FDGP materials.
Additionally, the Na 1s peak at 1071.9 eV indicates the presence of Na–O bonds (Figure S8b), and the Mg 1s peak at 1303 eV confirms Mg–O bonds (Figure S8c). Both X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy revealed collaborative bands originating from FDGP, providing insights into the hydrogen bonding between phosphate-functionalized graphene and the silicate chain. Scanning electron microscopy (SEM) analysis of FDGP at various magnifications reveals a structure composed of intercalated nanosheets and nanospheres (Figure a,b). High-resolution transmission electron microscopy (HRTEM) further confirms the presence of nanospheres, ranging from 10 to 50 nm, embedded within graphitic nanosheets (Figure c–f).
4.
Microscopy analysis of FDGP. (a,b) Scanning Electron Microscopy (SEM) images revealing the surface morphology of FDGP, where arrows showing phosphate graphene oxide nanosheets covered with spheres. (c,d) High-Resolution Transmission Electron Microscopy (HRTEM) images illustrating spherical nanostructures covered with phosphate graphene layers. High-angle annular dark field (HAADF) elemental mapping of FDGP, displaying the spatial distribution of key elements, including (e) carbon, (f) sodium, (g) magnesium, (h) oxygen, (i) alumium, (j) silicon, (k) phoshorous and (l) calcium.
High-angle annular dark field (HAADF) elemental mapping demonstrates a uniform distribution of aluminum, calcium, silicon, sodium, magnesium, carbon, oxygen, and phosphorus throughout the sample (Figure g–n). Furthermore, the complete characterization of five additional geopolymersFA, FD, FDGSH, FDGO, and FDGSwas carried out using FT-IR, PXRD, Raman spectroscopy, and Field-Emission Scanning Electron Microscopy (FE-SEM) analyses, and elemental mapping data are also provided in the Supporting Information (Figure S9–S14). The interactions between alkali-activated aluminosilicate geopolymers and graphene derivatives were investigated using first-principles calculations. This study elucidates the charge-balancing mechanisms that facilitate the formation of GO, GO–SO3H, G-SH, and GO–PO3H, and their composites with C–A–S–H and N–A–S–H gel phases. A model of highly ordered C–A–S–H was employed to analyze these interactions, with a focus on multicomponent calcium (alumino)silicate hydrates [C–A–S–H] as the primary binding phase in concrete. Furthermore, we have investigated the time-dependent (1, 7, and 28 days) interactions and reinforcement mechanism between functionalized graphene oxide phosphate (GO–PO3H) and the fly ash–dolomite (FD)-based geopolymer matrix using X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and Raman spectroscopy (Figures S15–S18). The results from these measurements collectively confirm that the interaction between GO–PO3H and the FD-based geopolymer matrix evolves progressively with curing time. Initially, weak or absent bonding transitions into strong chemical and structural integration in 28 days, culminating in a highly cohesive and reinforced system. These time-dependent interactions underscore the critical role of functional group chemistry and curing conditions in optimizing the performance of nanomaterial-reinforced geopolymer concretes.
3.2. Mechanical Properties of Graphene-Derived Geopolymers
The compressive strength of each mortar mix was determined based on the average of three cube specimens, as illustrated in Figure . For fly ash-based mortars activated with a 10 M NaOH solution, the compressive strength of pure fly ash mortar (FA) was 14.57 MPa at 7 days, increasing to 25.3 MPa at 28 days. When 20% of the fly ash was replaced with dolomite (FD: 80% FA + 20% D), the strength improved significantly to 23.5 MPa at 7 days and 35.8 MPa at 28 days (Figure a). Remarkably, the addition of graphene oxide (FDGO) further enhanced the compressive strength by approximately 32%. The improvement in strength can be attributed to the microreinforcement effect of graphene oxide, which bridges microcracks and prevents their propagation, thereby strengthening the geopolymer matrix. As a nanoparticle, graphene’s high surface area-to-volume ratio enables it to infiltrate and fill micropores and mesopores, densifying the material. This densification reduces weak points, increases homogeneity, and enhances the mechanical strength and durability. Furthermore, we have another graphene-derived geopolymers FDGS, FDGSH, and FDGP that had a strong hydrogen bonding between hydroxy functional groups with a silicate chain. Among the functionalized graphene materials, FD–GO–PO3H exhibited the highest compressive strength, achieving 45.60 MPa at 7 days and 50.20 MPa at 28 days. This superior performance is attributed to the high acidity of phosphonic acid groups, which enhance integration and bonding within the geopolymer network. FD–GO–SO3H also demonstrated significant improvements, reaching 43.04 MPa at 7 days and 46.48 MPa at 28 days (Figure b). Unmodified graphene oxide (FDGO) achieved strengths of 40.39 MPa at 7 days and 43.52 MPa at 28 days, highlighting its inherent reinforcing properties despite the absence of functional groups. FDGSH, incorporating thiol groups, exhibited the lowest improvement among the functionalized derivatives, with compressive strengths of 37.49 MPa at 7 days and 39.73 MPa at 28 days, a similar observation in the case of flowability at all hybrids (Figure ).
5.
(a) Compressive strength and (b) water absorption of fly ash (FA), fly ash-based dolomite (FD), FDGO, FDGS, FDGSH, and FDGP hybrids.
6.
Flowability of fly ash (FA), fly ash-based dolomite (FD), FDGO, FDGS, FDGSH, and FDGP hybrids.
This comparatively lower performance may be due to the lesser acidity of the thiol groups, resulting in weaker bonding interactions within the matrix. Overall, functionalized graphene derivatives enhance the mechanical properties of geopolymer concrete with phosphonic acid-functionalized graphene oxide showing the most pronounced effect. The mechanism of geopolymer concrete involves a series of interactions between silica (SiO2) particles, graphene, and the alkali-activated silicate (N–A–S–H) gel. Initially, SiO2 particles interact with the graphene surface, forming a SiO2/graphene derivative that increases the contact area between the materials. When protons (H+) are introduced, they protonate SiO2, leading to the formation of protonated SiO2 (SiO2H+) in the presence of graphene. This protonated SiO2 can stabilize on the graphene surface, enhancing the reaction efficiency and stability of the protonated product. The protonated SiO2 then interacts with the N–A–S–H gel, starting with an initial contact facilitated by the high surface area and reactive sites of both materials. During this interaction, SiO2H+ may undergo ion exchange with sodium ions (Na+) present in the N-A–S–H gel, leading to surface adsorption through electrostatic interactions and hydrogen bonding. Subsequently, the protonated SiO2 integrates into the N–A–S–H network, modifying its structure and potentially participating in the polymerization process. This integration contributes to the formation of a modified N–A–S–H framework, enhancing the overall mechanical properties and structural integrity of the geopolymer concrete.
The water absorption behavior of geopolymer mortar mixes was evaluated at 7 and 28 days, demonstrating significant improvements with the incorporation of functionalized graphene oxide materials. The fly ash- and dolomite-based geopolymer mortar (FD) showed a reduction in water absorption from 4.06% at 7 days to 3.50% at 28 days, reflecting improved water resistance over time. Notably, the FDGP mix exhibited the lowest water absorption, decreasing to 2.67% at 7 days and further to 2.36% at 28 days, signifying exceptional water resistance attributed to the presence of phosphonic acid functional groups. The FDGS mix also showed enhanced water resistance, with absorption values of 2.93% and 2.44% at 7 and 28 days, respectively. Comparatively, the FDGSH mix displayed moderate improvements, with absorption rates of 3.59% at 7 days and 3.17% at 28 days, higher than those of other functionalized variants. Similarly, the FDGO mix achieved moderate water resistance, with absorption rates of 3.57% on day 7 and 3.10% at 28 days. These findings underscore the role of functionalized graphene derivatives, particularly those with phosphonic acid groups, in significantly reducing water absorption and enhancing the durability and water resistance of geopolymer concrete.
3.3. Interfacial Interactions of Graphene-Derived Geopolymers
Further, we employed Density Functional Theory (DFT) to investigate the interactions between geopolymers and various surface-functionalized graphene derivatives: graphene oxide (GO), sulfonated graphene oxide (G–SO3H), thiographene (G–SH), and phosphate graphene (G–PO3H) (Figures a and S19,20). , We utilized a model of highly ordered calcium-alumino-silicate hydrates, the primary binding phase in concrete, to examine these interactions. To enhance the mechanical properties of graphene-geopolymer composites, it is crucial to achieve an atomic-level understanding of the electronic and bonding characteristics between functionalized graphene and the geopolymer. Through our DFT analysis, we demonstrated the important role of intermolecular hydrogen bonding between the functionalized graphene derivatives and the geopolymer. This interaction is significant in enhancing the mechanical properties of the geopolymer.
7.

Optimized structures of (a) GO–PO3H and (b) FDGP. [C: gray, O: red, H: white, P: orange, Si: blue, Al: violet, and Ca: golden].
The electronic structures of surface-functionalized graphene derivatives and their geopolymer composites were analyzed by using ab initio DFT methods. Figures and S20present the optimized geometries of surface-functionalized graphene derivatives and their respective geopolymer composites. In GO–PO3H, intramolecular hydrogen bonds are observed between the hydroxyl group of the phosphate moiety and either the oxygen atom of the epoxy group or the hydroxyl group of graphene, with a bond distance of 1.64 Å. Upon the interaction with the geopolymer, intermolecular hydrogen bonds form between the hydroxyl group of the phosphate moiety in GO–PO3H and the hydroxyl oxygen within the silicate chain of the geopolymer structure, exhibiting a bond distance of 2.04 Å. In addition to these hydrogen bonds, the alkali ions within the geopolymer can form bidentate interactions with the doubly bonded oxygen atoms of the phosphate group, further contributing to the stabilization of the composite. The alkali ion–oxygen distances are measured to be 2.66 and 2.77 Å. This type of interaction is not observed in GO or GO–SH. In the case of GO, the hydroxyl group interacts with alkali ions, with the alkali ion–oxygen distance measured at 2.53 Å. For systems with thiol-functionalized graphene, the interaction is primarily limited to intermolecular S–H···O hydrogen bonding with a distance of 2.63 Å. Only intermolecular hydrogen bonds form in GO–SO3H due to interactions between the hydroxyl group of its sulfonated moiety and the hydroxyl oxygen atoms within the geopolymer’s silicate chain, particularly when the distance between these composites is larger. Furthermore, the stability of geopolymer composites was evaluated through ab initio molecular dynamics simulations. The interactions between geopolymers and various surface-functionalized graphene derivatives are analyzed using the radial distribution function (RDF) analysis. Figure S21 presents the RDF curves, g(r), for the functionalized graphene derivatives in relation to the geopolymer matrix. In the g(r) plot of GO-PO3H and the geopolymer, three prominent peaks are observed below 3 Å, indicating the presence of strong intermolecular hydrogen bonding throughout the simulation period. RDF analysis of these hydrogen bonds reveals that one particular hydrogen bond contributes more significantly than the second (Figure S22).
4. Conclusion
In summary, we have successfully designed and synthesized four surface-functionalized graphene-derived geopolymersGO, G–SO3H, G–SH, and G–PO3Husing alumina- and silica-rich waste materials such as fly ash and dolomite. These geopolymers demonstrate significant enhancements in compressive strength, setting time, flowability, and water resistance, driven by robust interactions between graphene functional groups and the geopolymer matrix, alongside improved graphene dispersion. Among the derivatives, G–PO3H-based geopolymers exhibit an exceptional performance, with compressive strengths reaching 45.60 MPa at 7 days and 50.20 MPa at 28 days. This superior performance is attributed to the high concentration of phosphate functional groups, which fosters strong interactions with the geopolymer matrix. Additionally, density functional theory (DFT) calculations highlight the pivotal role of functional groups in reinforcing interfacial adhesion and molecular interactions, further enhancing the mechanical and durability properties of the geopolymer matrix.
Supplementary Material
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsmaterialsau.5c00028.
Characterization techniques employed include XRD, FT-IR, XPS, Raman spectroscopy, SEM, and HRTEM analyses of fly ash, dolomite, graphene derivatives, and their resultant hybrids, phosphate graphene data, and DFT calculations (PDF)
⊥.
M.R. and H.K.S. equally contributed this work. M.R- synthesis, conceptualization, H.Sanalysis, conceptualization. N. analysis, supervision, R.L- writing, analysis, conceptualization, A. M- supervision and KJ writing, conceptualization, supervision.
K. J. R. acknowledges support providing UGC-DAE CSR project CRS/2022-23/01/708, SERB CRG/2023/004685, CSIR-HRDG 01/3101/23/EMR-II and DST/INT/DAAD/P-06/2023.A.M. acknowledges IIT Jammu, the Center for Strategic and Sustainable Infrastructure (CSSI), and the Interdisciplinary Research Centre (SAPTARSHI), IIT Jammu.C.N. would like to thank the Department of Science and Technology, India, (DST/TDT/DDP-47/2021). KJR thanks IIT Jammu Director Prof. Manoj Singh Gaur and Mr. Rakesh Magotra (Deputy General Manager, J & Bank) for their constant support and encouragement.
The authors declare no competing financial interest.
References
- Scrivener K. L., John V. M., Gartner E. M.. Eco-efficient cements: Potential economically viable solutions for a low-CO2 cement-based materials industry. Cem. Concr. Res. 2018;114:2. doi: 10.1016/j.cemconres.2018.03.015. [DOI] [Google Scholar]
- Singh N. B., Middendorf B.. Geopolymers as an alternative to Portland cement: An overview. Constr. Build. Mater. 2020;237:117455. doi: 10.1016/j.conbuildmat.2019.117455. [DOI] [Google Scholar]
- Verma M., Upreti K., Vats P., Singh S., Singh P., Dev N., Kumar Mishra D., Tiwari B.. Experimental Analysis of Geopolymer Concrete: A Sustainable and Economic Concrete Using the Cost Estimation Model. Adv. Mater. Sci. Eng. 2022;2022(1):1–16. doi: 10.1155/2022/7488254. [DOI] [Google Scholar]
- Chandra S. S., Shakor P., Hasan S., Awuzie B. O., Singh A. K., Rauniyar A., Karakouzian M.. Evaluating the potential of geopolymer concrete as a sustainable alternative for thin white-topping pavement. Front. Mater. 2023;10:1181474. doi: 10.3389/fmats.2023.1181474. [DOI] [Google Scholar]
- Cong P., Cheng Y.. Advances in geopolymer materials: A comprehensive review. J. Traffic Transp. Eng., Engl. Ed. 2021;8(3):283. doi: 10.1016/j.jtte.2021.03.004. [DOI] [Google Scholar]
- Odeh A., Al-Fakih A., Alghannam M., Al-Ainya M., Khalid H., Al-Shugaa M. A., Thomas B. S., Aswin M.. Recent Progress in Geopolymer Concrete Technology: A Review. Iran. J. Sci. Technol., Trans. Civ. Eng. 2024;48(5):3285. doi: 10.1007/s40996-024-01391-z. [DOI] [Google Scholar]
- Almutairi A. L., Tayeh B. A., Adesina A., Isleem H. F., Zeyad A. M.. Potential applications of geopolymer concrete in construction: A review. Case Stud. Constr. Mater. 2021;15:e00733. doi: 10.1016/j.cscm.2021.e00733. [DOI] [Google Scholar]
- Alaneme G. U., Olonade K. A., Esenogho E., Lawan M. M.. Proposed simplified methodological approach for designing geopolymer concrete mixtures. Sci. Rep. 2024;14(1):15191. doi: 10.1038/s41598-024-66093-y. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Yang H., Li H., Jiang J.. Predictive modeling of compressive strength of geopolymer concrete before and after high temperature applying machine learning algorithms. Struct. Concr. 2025;26:1699. doi: 10.1002/suco.202400552. [DOI] [Google Scholar]
- Furtos G., Sarosi C., Moldovan M., Korniejenko K., Łach M., Ungureanu V., Miller L., Nováková I.. The Influence of Alkali-Resistant MiniBars on the Mechanical Properties of Geopolymer Composites. Materials. 2025;18:778. doi: 10.3390/ma18040778. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Furtos G., Prodan D., Sarosi C., Moldovan M., Korniejenko K., Miller L., Fiala L., Iveta N.. Mechanical Properties of MiniBars Basalt Fiber-Reinforced Geopolymer Composites. Materials. 2024;17:248. doi: 10.3390/ma17010248. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Solouki A., Fathollahi A., Viscomi G., Tataranni P., Valdrè G., Coupe S. J., Sangiorgi C.. Thermally Treated Waste Silt as Filler in Geopolymer Cement. Materials. 2021;14:5102. doi: 10.3390/ma14175102. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Nguyen V. V., Le V. S., Louda P., Szczypiński M. M., Ercoli R., Růžek V., Łoś P., Prałat K., Plaskota P., Pacyniak T.. et al. Low-Density Geopolymer Composites for the Construction Industry. Polymers. 2022;14:304. doi: 10.3390/polym14020304. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Shamsol A. l. S., Apandi N. M., Zailani W. W. A., Izwan K. N. K., Zakaria M., Zulkarnain N. N.. Graphene oxide as carbon-based materials: A review of geopolymer with addition of graphene oxide towards sustainable construction materials. Constr. Build. Mater. 2024;411:134410. doi: 10.1016/j.conbuildmat.2023.134410. [DOI] [Google Scholar]
- Tay C. H., Norkhairunnisa M.. Mechanical Strength of Graphene Reinforced Geopolymer Nanocomposites: A Review. Front. Mater. 2021;8:661013. doi: 10.3389/fmats.2021.661013. [DOI] [Google Scholar]
- Maglad A. M., Zaid O., Arbili M. M., Ascensão G., Serbănoiu A. A., Grădinaru C. M., García R. M., Qaidi S. M. A., Althoey F., de Prado-Gil J.. A Study on the Properties of Geopolymer Concrete Modified with Nano Graphene Oxide. Buildings. 2022;12(8):1066. doi: 10.3390/buildings12081066. [DOI] [Google Scholar]
- Geim A. K., Novoselov K. S.. The rise of graphene. Nat. Mater. 2007;6(3):183. doi: 10.1038/nmat1849. [DOI] [PubMed] [Google Scholar]
- Mbayachi V. B., Ndayiragije E., Sammani T., Taj S., Mbuta E. R., khan A. u.. Graphene synthesis, characterization and its applications: A review. Results Chem. 2021;3:100163. doi: 10.1016/j.rechem.2021.100163. [DOI] [Google Scholar]
- Allen M. J., Tung V. C., Kaner R. B.. Honeycomb Carbon: A Review of Graphene. Chem. Rev. 2010;110(1):132. doi: 10.1021/cr900070d. [DOI] [PubMed] [Google Scholar]
- Ji X., Xu Y., Zhang W., Cui L., Liu J.. Review of functionalization, structure and properties of graphene/polymer composite fibers. Composites, Part A. 2016;87:29. doi: 10.1016/j.compositesa.2016.04.011. [DOI] [Google Scholar]
- Poorna A. R., Saravanathamizhan R., Balasubramanian N.. Graphene and graphene-like structure from biomass for Electrochemical Energy Storage application- A Review. Electrochem. Sci. Adv. 2021;1(3):e2000028. doi: 10.1002/elsa.202000028. [DOI] [Google Scholar]
- Georgakilas V., Otyepka M., Bourlinos A. B., Chandra V., Kim N., Kemp K. C., Hobza P., Zboril R., Kim K. S.. Functionalization of Graphene: Covalent and Non-Covalent Approaches, Derivatives and Applications. Chem. Rev. 2012;112(11):6156. doi: 10.1021/cr3000412. [DOI] [PubMed] [Google Scholar]
- Jayaramulu K., Mukherjee S., Morales D. M., Dubal D. P., Nanjundan A. K., Schneemann A., Masa J., Kment S., Schuhmann W.. et al. Graphene-Based Metal–Organic Framework Hybrids for Applications in Catalysis, Environmental, and Energy Technologies. Chem. Rev. 2022;122(24):17241. doi: 10.1021/acs.chemrev.2c00270. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Brisebois P. P., Siaj M.. Harvesting graphene oxide – years 1859 to 2019: a review of its structure, synthesis, properties and exfoliation. J. Mater. Chem. C. 2020;8(5):1517. doi: 10.1039/C9TC03251G. [DOI] [Google Scholar]
- Chen D., Feng H., Li J.. Graphene Oxide: Preparation, Functionalization, and Electrochemical Applications. Chem. Rev. 2012;112(11):6027. doi: 10.1021/cr300115g. [DOI] [PubMed] [Google Scholar]
- Ajala O. J., Tijani J. O., Bankole M. T., Abdulkareem A. S.. A critical review on graphene oxide nanostructured material: Properties, Synthesis, characterization and application in water and wastewater treatment. Environ. Nanotechnol., Monit. Manage. 2022;18:100673. doi: 10.1016/j.enmm.2022.100673. [DOI] [Google Scholar]
- Mohammed S.. Graphene oxide: A mini-review on the versatility and challenges as a membrane material for solvent-based separation. Chem. Eng. J. Adv. 2022;12:100392. doi: 10.1016/j.ceja.2022.100392. [DOI] [Google Scholar]
- Guo S., Garaj S., Bianco A., Ménard-Moyon C.. Controlling covalent chemistry on graphene oxide. Nat. Rev. Phys. 2022;4(4):247. doi: 10.1038/s42254-022-00422-w. [DOI] [Google Scholar]
- Intarabut D., Sukontasukkul P., Phoo-Ngernkham T., Zhang H., Yoo D. Y., Limkatanyu S., Chindaprasirt P.. Influence of Graphene Oxide Nanoparticles on Bond-Slip Responses between Fiber and Geopolymer Mortar. Nanomaterials. 2022;12(6):943. doi: 10.3390/nano12060943. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Danial N. S., Che Halin D. S., Ramli M. M., Abdullah M. M. A., Mohd Salleh M. A. A., Mat Isa S. S., Talip L. F. A., Mazlan N. S.. Graphene geopolymer hybrid: A review on mechanical properties and piezoelectric effect. IOP Conf. Ser.:Mater. Sci. Eng. 2019;572(1):012038. doi: 10.1088/1757-899X/572/1/012038. [DOI] [Google Scholar]
- Liu C., Huang X., Wu Y.-Y., Deng X., Liu J., Zheng Z., Hui D.. Review on the research progress of cement-based and geopolymer materials modified by graphene and graphene oxide. Nanotechnol. Rev. 2020;9(1):155–169. doi: 10.1515/ntrev-2020-0014. [DOI] [Google Scholar]
- Kumar S., Bheel N., Zardari S., Alraeeini A. S., Almaliki A. H., Benjeddou O.. Effect of graphene oxide on mechanical, deformation and drying shrinkage properties of concrete reinforced with fly ash as cementitious material by using RSM modelling. Sci. Rep. 2024;14(1):18675. doi: 10.1038/s41598-024-69601-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Yan S., He P., Jia D., Duan X., Yang Z., Wang S., Zhou Y.. Effects of graphene oxide on the geopolymerization mechanism determined by quenching the reaction at intermediate states. RSC Adv. 2017;7(22):13498. doi: 10.1039/C6RA26340B. [DOI] [Google Scholar]
- Saafi M. A., Tang L., Fung J., Rahman M., Liggat J. J. J. C.. Enhanced properties of graphene/fly ash geopolymeric composite cement. Cem. Concr. Res. 2015;67:292–299. doi: 10.1016/j.cemconres.2014.08.011. [DOI] [Google Scholar]
- Qureshi, T. ; Vickery, C. . Proceedings of the 2nd International Conference on Advances in Civil Infrastructure and Construction Materials (CICM 2023), Volume 1; Springer: Cham, 2024, p 25. [Google Scholar]
- Izadifar M., Sekkal W., Dubyey L., Ukrainczyk N., Zaoui A., Koenders E.. Theoretical Studies of Adsorption Reactions of Aluminosilicate Aqueous Species on Graphene-Based Nanomaterials: Implications for Geopolymer Binders. ACS Appl. Nano Mater. 2023;6(18):16318. doi: 10.1021/acsanm.3c02438. [DOI] [Google Scholar]
- Yu H., Zhang B., Bulin C., Li R., Xing R.. High-efficient Synthesis of Graphene Oxide Based on Improved Hummers Method. Sci. Rep. 2016;6(1):36143. doi: 10.1038/srep36143. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Vasudevan S., Lakshmi J.. The adsorption of phosphate by graphene from aqueous solution. RSC Adv. 2012;2(12):5234. doi: 10.1039/c2ra20270k. [DOI] [Google Scholar]
- Daneshmandi L., Holt B. D., Arnold A. M., Laurencin C. T., Sydlik S. A.. Ultra-low binder content 3D printed calcium phosphate graphene scaffolds as resorbable, osteoinductive matrices that support bone formation in vivo. Sci. Rep. 2022;12(1):6960. doi: 10.1038/s41598-022-10603-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Showman M. S., Omara R. Y., El-Ashtoukhy E. S. Z., Farag H. A., El-Latif M. M. A.. Formulation of silver phosphate/graphene/silica nanocomposite for enhancing the photocatalytic degradation of trypan blue dye in aqueous solution. Sci. Rep. 2024;14(1):15885. doi: 10.1038/s41598-024-66054-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Tian J., Li H., Asiri A. M., Al-Youbi A. O., Sun X.. Photoassisted Preparation of Cobalt Phosphate/Graphene Oxide Composites: A Novel Oxygen-Evolving Catalyst with High Efficiency. Small. 2013;9(16):2709. doi: 10.1002/smll.201203202. [DOI] [PubMed] [Google Scholar]
- Gil-Gavilán D. G., Amaro-Gahete J., Rojas-Luna R., Benítez A., Estevez R., Esquivel D., Bautista F. M., Romero-Salguero F. J.. Sulfonated Graphene-Based Materials as Heterogeneous Acid Catalysts for Solketal Synthesis by Acetalization of Glycerol. ChemCatChem. 2024;16(20):e202400251. doi: 10.1002/cctc.202400251. [DOI] [Google Scholar]
- Luong N. D., Sinh L. H., Johansson L.-S., Campell J., Seppälä J.. Functional Graphene by Thiol-ene Click. Chemistry. 2015;21(8):3183. doi: 10.1002/chem.201405734. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Sturala J., Hermanová S., Artigues L., Sofer Z., Pumera M.. Thiographene synthesized from fluorographene via xanthogenate with immobilized enzymes for environmental remediation. Nanoscale. 2019;11(22):10695. doi: 10.1039/C9NR02376C. [DOI] [PubMed] [Google Scholar]
- Urbanová V., Holá K., Bourlinos A. B., Čépe K., Ambrosi A., Loo A. H., Pumera M., Karlický F., Otyepka M., Zbořil R.. Thiofluorographene–Hydrophilic Graphene Derivative with Semiconducting and Genosensing Properties. Adv. Mater. 2015;27(14):2305. doi: 10.1002/adma.201500094. [DOI] [PubMed] [Google Scholar]
- Gomes S., François M.. Characterization of mullite in silicoaluminous fly ash by XRD, TEM, and 29Si MAS NMR. Cem. Concr. Res. 2000;30(2):175. doi: 10.1016/S0008-8846(99)00226-4. [DOI] [Google Scholar]
- Rathee M., Surendran H. K., Narayana C., Lo R., Misra A., Jayaramulu K.. Interfacial Chemistry of Ti3C2Tx MXene in Aluminosilicate Geopolymers for Enhanced Mechanical Strength. ACS Appl. Eng. Mater. 2024;2(8):2027. doi: 10.1021/acsaenm.4c00184. [DOI] [Google Scholar]
- Samtani M., Skrzypczak-Janktun E., Dollimore D., Alexander K.. Thermal analysis of ground dolomite, confirmation of results using an X-ray powder diffraction methodology. Thermochim. Acta. 2001;367–368:297. doi: 10.1016/S0040-6031(00)00663-8. [DOI] [Google Scholar]
- Potgieter-Vermaak S. S., Potgieter J. H., Belleil M., DeWeerdt F., Van Grieken R.. The application of Raman spectrometry to the investigation of cement: Part II: A micro-Raman study of OPC, slag and fly ash. Cem. Concr. Res. 2006;36(4):663. doi: 10.1016/j.cemconres.2005.09.010. [DOI] [Google Scholar]
- Campbell J. A., Smith R. D., Davis L. E., Smith K. L.. Characterization of micron-size flyash particles by X-ray photoelection spectroscopy (ESCA) Sci. Total Environ. 1979;12(1):75. doi: 10.1016/0048-9697(79)90007-X. [DOI] [Google Scholar]
- Wang A., Zhang C., Sun W.. Fly ash effects: I. The morphological effect of fly ash. Cem. Concr. Res. 2003;33(12):2023. doi: 10.1016/S0008-8846(03)00217-5. [DOI] [Google Scholar]
- Kresse G., Furthmüller J.. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996;6(1):15. doi: 10.1016/0927-0256(96)00008-0. [DOI] [PubMed] [Google Scholar]
- Kresse G., Joubert D.. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B. 1999;59(3):1758. doi: 10.1103/PhysRevB.59.1758. [DOI] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.







