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Chem Synth 2023;3:46. 10.20517/cs.2023.34 © The Author(s) 2023.

Strain engineering of two-dimensional materials for energy storage and conversion applications

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Key Laboratory for Soft Chemistry and Functional Materials of Ministry Education, School of Chemistry and Chemical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China.

#Authors contributed equally.

*Correspondence to: Profs. Pan Xiong, Junwu Zhu, Key Laboratory for Soft Chemistry and Functional Materials of Ministry Education, School of Chemistry and Chemical Engineering, Nanjing University of Science and Technology, 200 Xiaolingwei Street, Xuanwu District, Nanjing 210094, Jiangsu, China. E-mail:;

© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License (, which permits unrestricted use, sharing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.


Two-dimensional (2D) materials have garnered much interest due to their exceptional optical, electrical, and mechanical properties. Strain engineering, as a crucial approach to modulate the physicochemical characteristics of 2D materials, has been widely used in various fields, especially for energy storage and conversion. Herein, the recent progress in strain engineering of 2D materials is summarized for energy storage and conversion applications. The fundamental understanding of strain in 2D materials is first described. Then, some synthetic methods for modulating the properties of 2D materials via strain engineering are introduced. Further, the applications of strain engineering of 2D materials in energy storage, photocatalysis, and electrocatalysis are discussed. Finally, the challenges and perspectives on strain engineering of 2D materials are also outlined.


Two-dimensional materials, strain engineering, energy storage and conversion, electrocatalysis, photocatalysis


The awareness of two-dimensional (2D) materials has been steadily growing among the public since the discovery of graphene through mechanical exfoliation in 2004[1]. Thanks to the ultrathin characteristics of 2D materials, they exhibit favorable morphological, electrical, optical, magnetic, and chemical properties[2-6]. Compared with the bulk structure of three-dimensional (3D) materials, 2D materials exhibit remarkable properties in energy storage and catalysis due to their large specific surface and fully exposed atoms[7-11]. To broaden the utilization of 2D materials, diverse approaches have been developed to adjust their properties, such as doping[12,13], defects engineering[14,15], alloying[16], substrate engineering[17], and heterostructures[18], etc.

Among these methods, strain engineering is widely employed to modify the properties of 2D materials due to its simplicity and large adjustable range. The application of strain on the surface of 2D materials is intricately related to the electronic structure of the material’s surface, which plays a pivotal role in determining the absorbate-surface bond strength and the occurrence of numerous catalytic and electrochemical reactions[19,20]. Positive strain applied to 2D material usually confers suitable adsorption energy upon the material, thus facilitating its desired development in electrochemical reactions, while unfavorable strain frequently results in subpar material performance. The primary objective of strain engineering of 2D materials lies in regulating the properties of 2D materials and optimizing the properties towards related devices through the application of tensile or compressive strain.

To date, various strategies have been implemented for generating strain to explore new physicochemical properties of 2D materials. The strain in 2D materials can be categorized into two types: internally generated and externally applied[21]. Internal strain is mainly generated by manufacturing local lattice distortion or interface interaction[22], including heteroatom doping, lattice vacancies, local lattice mismatch, heterostructure, etc. While external strain mainly involves external force or stimulation, such as substrate bending[23] and rigid substrates[24]. In comparison, internal strain exhibits greater stability and durability. However, it poses challenges in terms of control. On the contrary, external strain offers more precise controllability but relies on external force support. Once the external force is removed, the strain dissipates as well.

Compared with 3D bulk materials, 2D materials with ultrathin morphology have unique advantages in strain engineering. On the one hand, the high Young’s modulus and excellent deformability of 2D materials ensure significant uniaxial or biaxial strain without fracturing. On the other hand, the electron cloud of 2D materials is confined to a 2D plane, rendering it more susceptible to external influences[25-27]. The local strain introduced into 2D materials stretches or compresses the nearby lattice, alters the microenvironment of atoms, and imparts completely different properties to the material. According to the d-band theory raised in 1998[28], the strain-induced variation of atomic distance can significantly influence the density of the d-state, which affects the adsorption performance of the material surface. For 2D materials, strain changes the atomic bond configuration (length and angle) and the interactions between the electron orbitals of adjacent atoms, thus adjusting the properties of 2D materials and providing a rich library for advanced applications[29-31].

So far, numerous methods have been developed for applying strain to 2D materials [Figure 1][32-43]. According to the source of strain, the methods for introducing strain can be roughly divided into three types: defect-induced, lattice-induced, and substrate-induced. There are different advantages and disadvantages among diverse strain introduction methods, which are suitable for diverse applications. For instance, defects can always trigger nonuniform microstrain, which is closely associated with the active site located on the material’s surface, thereby potentially endowing the material with enhanced catalytic properties[19,21]. In contrast, substrate-induced strain provides uniform and continuously adjustable strain in the material. However, the removal of the substrate leads to an immediate change in internal strain. For lattice mismatch-induced strain, the compression of crystals possessing larger lattice parameters is concomitant with the stretching of crystals with smaller lattice parameters at the contacted interface, resulting in a controllable interfacial strain type. However, determining the specific strain magnitude and location of the strain can be challenging[19].

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 1. Development timeline of strategies for strain engineering of 2D materials. (2009): quoted with permission from Mohiuddin et al.[32]; (2014): quoted with permission from Lu et al.[33]; (2015): quoted with permission from Li et al.[34]; (2016): quoted with permission from Azcatl et al.[35]; (2017): the figure on the left is quoted with permission from Pierucci et al.; the figure on the right is quoted with permission from Hsu et al.[36,37]; (2019): quoted with permission from Yang et al.[38]; (2020): the figure on the left is quoted with permission from Lee et al.; the figure on the right is quoted with permission from Li et al.[39,40]; (2021): quoted with permission from Li et al.[41]; (2022): quoted with permission from Wu et al.[42]; (2023): quoted with permission from Cao et al.[43]. 2D: Two-dimensional.

Strain engineering is essential for tailoring the properties of 2D materials to meet specific requirements in various applications. In terms of energy storage, strain engineering of 2D materials shows a prospect of effectively reducing the diffusion barrier for mental ions, optimizing the adsorption model, and enhancing the material’s diffusion kinetics. Simultaneously, strain engineering of 2D materials can mitigate volume expansion resulting from ion intercalation, which imparts enhanced stability and superior energy storage performance to the material[44,45]. For electrocatalysis, strain engineering of 2D materials shows the potential to modify the internal electronic states of surface atoms and optimize intermediate adsorption models, thereby significantly influencing the electrochemical reactivity in electrocatalysis[46-48]. While the perspective moves to photocatalysis, strain engineering of 2D materials presents a promising avenue for narrowing the bandgap, enhancing the separation of photogenerated carriers, and tuning the absorption, comprehensively improving the photocatalytic performance of materials[49].

Herein, this review provides a comprehensive overview of the latest advancements in strain engineering of 2D materials for energy storage and conversion applications. First, a brief introduction concerning the basic concept, characterization, and quantization of strain is delivered. Subsequently, different strategies for strain engineering of 2D materials are systematically summarized and compared, such as defect-induced, substrate-induced, and lattice mismatch-induced. Further, the recent applications of strain engineering of 2D materials in energy storage and conversion are discussed. Finally, we propose potential avenues and challenges for optimizing 2D materials by strain engineering.


Definition and characterization of strain in 2D materials

Among various material properties, strain holds significant importance in numerous fields, including materials science[50], chemistry[51], and molecular catalysis[19]. Correspondingly, different definitions and quantification methods for observed strain have been proposed for different fields and applications. For materials science, the local strain of 2D materials is usually defined as:

$$ \varepsilon=\left(I_{b}-I_{a}\right) / I_{a} $$

where Ɛ represents the strain magnitude, and Ia and Ib represent the length of the atomic bond before and after the straining process, respectively. However, in practical applications, the strain within the material may not be uniform; it is not easy to evaluate atomic bond lengths and internal strain accurately and statistically (i.e., using large samples). Local strain measurement and global strain measurement are the two most frequently employed methods for measuring strain to simplify the strain model. Correspondingly, spectral measurement and microscopic visual measurement are two classical methods employed for the global and local identification of surface strain in 2D materials, respectively. Additionally, theoretical calculations also serve as a crucial supplement in verifying the strain in 2D materials.

For spectroscopy measurements, as phonon modes and band gaps of 2D materials exhibit sensitivity to strain, their change can be measured by Raman and photoluminescence (PL) spectra in practical applications[25,52]. Strain changes the crystal vibration and usually results in a change in phonon modes. Therefore, the strain inside the material can be easily characterized by monitoring the crystal vibration through Raman spectroscopy. For instance, Liu et al. conducted various spectroscopic analyses at different regions of MoS2/ZnO heterostructure arrays, and the maximum strain of approximately 0.6% was detected near the edge of ZnO nanorod[53]. Meanwhile, the band gap of the material is closely related to the internal strain, which can be reflected in the PL spectrum[39]. Conley et al. used PL spectroscopy to measure the optical band gap of MoS2 and found that the PL shift exhibited an approximately linear relationship with strain[54]. In addition, X-ray absorption spectroscopy is also an effective way to characterize the strain. Di et al. used this technology to measure the Bi-Bi and Bi-O bond length inside the Bi12O17Br2 nanoplates and nanotubes, and the variation in bond length indicated the tensile lattice strain in Bi12O17Br2 nanotubes[55].

For microscopic visual measurements, the determination of materials’ lattice spacing is typically achievable through high-resolution transmission electron microscope (HRTEM) lattice images[56], Through geometric phase analysis (GPA)[57], etc. By comparing the image features with the reference lattice, the local lattice spacing is explained as the component variation and strain. The GPA allows the evaluation of the degree of local lattice distortion in 2D materials, making the strain distribution visible in the form of strain mapping. Other characterization techniques that can be employed include spherical aberration corrected transmission electron microscope (ACTEM), scanning transmission electron microscopy (STEM), etc.

Theoretical calculations are another important method to simulate the strain effect and further verify the strain in materials. Zhang et al. calculated the bandgap of Nb-substituted WS2 and found that this variant with lattice strain showed a bandgap consistent with the experimental results, suggesting the presence of lattice strain within the material[58].

Quantization of strain in 2D materials

As mentioned above, the measurements of strain encompass both local and global aspects, and different characterization methods correspond to distinct means of quantization. For local strain measurement, microscopic visual measurement has been widely used to determine the lattice spacing of materials. Image features are compared to the reference lattice using techniques such as cross-correlation, peak finding, or GPA, which enables precise atomic localization[19]. The local strain is quantified by comparing the lattice constants of the local atoms with the reference lattice. For instance, Yang et al. compared the bond length of the Mo-Mo bond near the Mo vacancy with the standard MoS2 lattice and found that local strain of ~3% occurred in the surrounding atoms[38]. For global strain measurement, for instance, the Raman spectroscopy technique has proven to be an effective approach for characterizing and quantifying strain. There exist two formulas for computing strain in the material through Raman change:

$$ \varepsilon=\left(\omega-\omega_{0}\right) / \chi \text { or } \varepsilon=\left(\omega-\omega_{0}\right) / 2 \gamma \omega_{0} $$

where the ω and ω0 represent the Raman frequencies under detected strain and zero strain, respectively. The transfer rate of the χ is the Raman mode of vibration, and γ is the Grayson parameter[19,53]. Castellanos-Gomez et al. measured the Raman spectra on both the flat and top regions of the MoS2 flake, both in-plane mode ($$ E_{2 g}^{1} $$) and out-of-plane mode (A1g) on the top of the wrinkle, showing a redshift[59]. Based on the redshifted Raman spectrum, the maximum strain (tensile) is estimated to be 2.5%. For the strain in 2D materials on the elastic substrate, the strain exerted on the flexible substrate can be expressed by a simple equation:

$$ \varepsilon=\tau / R $$

where τ and R represent the thickness and radius of curvature of the substrate, respectively. The radius of curvature can be calculated ideally as the substrate bends or shapes change[39].


Atomically thin 2D materials have raised much attention for strain engineering due to their ultrathin characteristic and stronger deformation capacity than bulk materials[27,29]. With regard to strain, it can be generally divided into macrostrain and microstrain[60]. Macrostrain (also referred to as global strain in material science)[61] always refers to the distortion of the global crystal structure, accompanied by the global deviation of the lattice parameters from the perfect crystal. It induces a modification in the orbital overlap between adjacent atoms, leading to a shift of the d-band center and alterations in bonding energies with adsorbates. Microstrain, on the other hand, refers to the nonuniform strain effect caused by local deviations of atoms from their ideal positions. Since microstrain involves the local distortion of atoms, the introduction of microstrain brings more active sites to the material, which endows the material with better catalytic activity[60]. So far, the application of strain to 2D materials has been widely employed by various experimental methods and strategies (defect, lattice mismatch, substrate, etc.). This section provides a summary of various methods for introducing strain to 2D materials.

Defect-induced strain

On account of the ultra-thin characteristic of 2D materials, it provides an ideal platform for studying the strain effect caused by local defects[62]. In general, defect consists of point defects, line defects, planar defects, and body defects[63,64]. Local defects or lattice disorders in the material are always entangled with microstrain. In other words, microstrain represents the local deviation of an atom from its ideal position[60]. Meanwhile, the change of the relative position of atoms in 2D materials can induce compression or expansion among local lattice and manifests as the change of lattice constant. By comparing the deviation of the lattice constant between the lattice near the defect and the ideal lattice, the magnitude of the strain near the defect can be quantized. Since point defects (vacancies and dopants) are the predominant and most effortless type, we discuss them in detail in this section.

Doping-induced Strain

Doping, as a crucial type of point defects, can be classified into substitutional doping and interstitial doping. Regardless of the type of doping, it can cause the local deviation of nearby atoms from their ideal position, affect the bond length of the chemical bond, and bring microstrain to the local material[46,60]. Depending on the doping type and the size of each atom, local tensile and compressive strain can be generated near the doping site.

Plasma exposure is a widely used practical technique for incorporating heterogeneous atoms into 2D materials. Azcatl et al. utilized N2 plasma to expose nitrogen (N) to MoS2 for stable covalent doping [Figure 2A][35]. Due to the substitution of smaller N atoms with sulfur (S) atoms, the compressive strain was generated in the MoS2 lattice. The Raman spectra for exfoliated N-doped MoS2 flake displayed a blue shift of the ($$ E_{2 g}^{1} $$) mode, indicating compressive strain was generated due to the introduction of N atoms [Figure 2B]. In another work, Pierucci et al. reported the doping of atomic hydrogen (H) to a single layer of MoS2 by exposing single-layer MoS2 to a H2 atmosphere[36]. The blue shift of ($$ E_{2 g}^{1} $$) mode in Raman spectra indicated the intercalation of H atoms and the occurrence of tensile strain.

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 2. Doping-induced strain for 2D materials. (A) Schematic diagram of covalent nitrogen doping in MoS2 via N2 plasma treatment; (B) Raman shift after sequential N2 plasma exposure for different times; (A-B): quoted with permission from Azcatl et al.[35]; (C) Schematic of the synthesis of NbS2 and NbxW1-xS2 monolayers via a CVD method; (D) Atomic models of three doping configurations; (C-D): quoted with permission from Zhang et al.[58]; (E) Schematic of Se replacing S from the edge to the center in MoS2; (F) Lattice constant at different positions as most of the outer S atoms are substituted by Se; (G) Calculation results illustrating the relationship among Se occupation, lattice constant, and substitution barrier; (E-G): quoted with permission from Li et al.[22]. CVD: Chemical vapor deposition; 2D: two-dimensional.

Compared with plasma post-processing, introducing doping-induced strain during the synthesis is a simpler method. Zhang et al. synthesized Nb-doped WS2 with various Nb concentrations via a chemical vapor deposition (CVD) method [Figure 2C][58]. The deviation of Nb atoms led to a deformation of the lattice and brought local tensile and compressive strain. A simple schematic diagram was shown to further reveal the internal structure of the material [Figure 2D]. Further, Li et al. reported the strain-driven mechanism of 2D atomic layered MoS2 nanosheets [Figure 2E][22]. During the process of substitution of selenium (Se) with S in MoS2, an increased lattice constant was observed at the edge, suggesting that the substitution occurred at the edge firstly. Theoretical calculation suggested a strong correlation between the substitution barrier and the local strain surrounding the substituted atom. The relaxation of strain at the periphery was easier than that in the inner region, resulting in a long-range strain field extending from the edge to the center [Figure 2F and G]. Moreover, doping-induced strain can also be observed in PdIr bimetallene[65], ZnO nanosheets[66], and nickel hydroxide nanosheets[67].

Vacancies-induced strain

Vacancies, another category of point defects in 2D materials, can be classified as cation and anion vacancies. In previous studies, it has been a challenge to differentiate vacancy and strain due to their entanglement[19]. The relationship between vacancies and strain can be summarized into three facets. First, vacancies can induce strain individually[40,68]. Regardless of the generation of cation and anion vacancies, they will induce local lattice compression and impose localized strain on the material[19,43]. As an illustration, Ni et al. demonstrated a linear correlation between oxygen vacancy (VO) concentration and lattice strain at the Co-CoO interfaces[60]. Second, the interfacial strain can promote the generation of vacancies[69,70]. Third, strain and vacancy can coexist and act simultaneously. For instance, S vacancies and strain were introduced separately into MoS2 nanosheets through argon plasma and capillary force[71]. As a result, under the synergistic effect of vacancy and strain, the material exhibited a promising property toward hydrogen evolution. In this part, our primary focus is on the strain induced by the introduction of vacancies.

Plasma treatment is a prevalent method for introducing vacancies and strains into 2D materials. For instance, atomic-scale vacancies were created into MoS2 nanosheets through helium ion irradiation [Figure 3A][38]. As a result, multiple types of vacancies were observed (single and double S vacancies and Mo vacancies) [Figure 3B]. An enlarged image of high-angle annular dark field STEM (HAADF-STEM) near the Mo vacancy showed a deviation of ± 10 pm of Mo-Mo distance around the vacancy site, indicating that local strain of ~3% exists near the vacancy [Figure 3C]. In addition, vacancy-induced strain can also be introduced in numerous ways during the synthesis. Recently, Zhao et al. demonstrated a layered double hydroxide (LDH) with severely distorted structures and compressive strain [Figure 3D][68]. The K-edge EXAFS spectrum of Cr showed a decreased coordination number in CuCr nanosheets compared with CuCr-bulk, indicating that severe structure deformation and abundant VO were formed [Figure 3E]. Similarly, Zhao et al. reported ultra-thin TiO2 nanosheets with abundant VO and compressive strain through Cu-doping strategies[72]. The substitution of copper for titanium caused a local charge imbalance and introduced additional VO, while abundant VO brought impressive compressive strain to the nanosheets. CVD is a crucial synthetic technique for inducing strain in 2D materials. For instance, a hexagonal monolayer WS2 single crystal composed of alternating W vacancies (WVs) (β region) and S vacancies (SVs) (α region) was synthesized through CVD methods [Figure 3F][73]. The strain-related ($$ E_{2 g}^{1} $$) mode showed a blue shift around 0.1 cm-1 in the β region, indicating that the generation of WVs brought compressive strain to this region [Figure 3G].

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 3. Vacancy-induced strain for 2D materials. (A) Schematic of MoS2 basal plane irradiated with helium ions; (B) HAADF-STEM image of MoS2 showing different types of vacancies; (C) Enlarged image of HADDF-STEM revealing the atomic structure in single layer MoS2 near the vacancy site; (A-C): quoted with permission from Yang et al.[38]; (D) 2D structure model for LDH monolayer with VO; (E) Schematic diagram illustrating the in-plane compressive strain induced by VO in LDH nanosheets; (D-E): quoted with permission from Zhao et al.[68]; (F) Schematic illustrating the alternant domain of WVs and SVs in WS2; (G) Raman spectrum for WV domains. Inset shows the frequency shifts for $$ E_{2 g}^{1} $$ and A1g modes; (F-G): quoted with permission from Jeong et al.[73]. HAADF-STEM: high-angle annular dark field scanning transmission electron microscopy; LDH: layered double hydroxide; SVs: S vacancies; WVs: W vacancies; 2D: two-dimensional.

Lattice mismatch-induced strain

In general, when two materials with different lattice parameters come into direct contact, lattice mismatch will occur at the interface, resulting in lattice strain in each component. The compressive strain occurs in the material with a larger lattice parameter, while the crystal with a smaller lattice parameter experiences tensile strain[74]. In the following, the lattice mismatch is divided into planar and vertical lattice mismatch, and the principle of strain introduction is discussed.

Planar lattice mismatch-induced strain

The planar lattice mismatch of 2D materials is invariably accompanied by the epitaxial growth of different materials. Researching the heterogeneous epitaxy and interfacial strain in various 2D materials has been a thriving research area for decades, owing to its technical relevance to solid-state devices and circuits[75]. Lattice-misfit strain in atomically abrupt lateral heterojunctions presents a novel approach for customizing their electronic properties.

The epitaxial growth of 2D materials with diverse lattice parameters will induce strain at the interface, which can be alleviated in the form of local lattice distortion. For instance, Lu et al. studied the strain propagation and relaxation mechanism at the interface of graphene/hexagonal boron nitride (h-BN) and found that an obvious sharp graphene/h-BN interface could be induced by forming a mismatch dislocation at the interface to relieve the accumulated strain[33]. Li et al. presented a two-step epitaxial growth method for the formation of lateral WSe2-MoS2 heterojunction [Figure 4A][76]. The strain originating from the lattice mismatch is detected by Raman and PL variations. The adjacent MoS2 exhibited a tensile state (cyan color) that gradually transitioned to a strain-free state (blue color). Some MoS2 regions even exhibited compressive strain (red color) to relax the strain built upon the MoS2 [Figure 4B]. Such a large strain difference caused by the planar heterostructure indicated the possibility of using strain to adjust the photoelectric properties of the material. Similarly, Hsu et al. studied the planar heterojunction of WSe2-MoS2 and found that it generated uneven strain in external MoS2 through the PL peak surface scan map[37]. Further, Xie et al. reported an alternate transition metal dichalcogenide (TMD) monolayer composed of different compositions (e.g., WS2 and WSe2), which was achieved by carefully controlling the release and time of precursors during the growth [Figure 4C][77]. With the change of the thickness ratio of WS2 and WSe2 in planar superlattice, it was found that the lattice constant was determined by thicker layers. The different thickness ratios of WS2 and WSe2 layers brought different tensile and compressive strains on WS2 and WSe2 [Figure 4D and E] and further adjusted the magnitude of the direct band gap. As the thickness ratio of WS2 to WSe2 varied from 2.4 to 0.1 (I to V), the bandgap exciton resonance of WS2 redshifted to a greater extent, which indicated the tensile (compressive) strain in WS2 (WSe2) [Figure 4F].

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 4. Planar lattice mismatch-induced strain for 2D materials. (A) Schematic illustrating the growth process of monolayer WSe2-MoS2 heterostructures; (B) PL spectra and its spatial mapping of MoS2 at different locations; (A-B): quoted with permission from Li et al.[76]; (C) Schematic of 2D superlattices growth process composed of different TMDs; (D) False-color SEM images of a superlattice with different thickness configurations from I to V, Scale bars, 200 nm; (E) The plot of WS2/WSe2 superlattices with thickness configurations from I to V; (F) Normalized PL spectra of intrinsic WS2 and WS2 in the superlattices I to V; (C-F): quoted with permission from Xie et al.[77]. PL: Photoluminescence; TMDs: transition metal dichalcogenides; 2D: two-dimensional.

Vertical lattice mismatch-induced strain

Similar to the epitaxial growth of two different materials, the interaction of materials in the vertical direction can also cause a lattice mismatch, resulting in local strain[78]. Li et al. reported a vertical integration of borophene and tetraphenyldibenzoperiflflanthene (DBP) and revealed that compressive strain was induced to borophene underneath the molecular layer with tip-enhanced Raman spectroscopy [Figure 5A][41]. As the tip moved through the complete borophene (green spot), island edge (red spot), and absorbed borophene, different Raman shifts indicated distinct structure properties among different positions. The position far away from DBP exhibited a strong peak at 190 cm-1, which corresponded to the characteristic of pristine borophene. The redshift at the island edge and the blue shift at absorbed borophene indicated compressive strain occurred at borophene underneath the molecular layer, while tensile strain occurred near the island edge [Figure 5B and C]. Further, Zhang et al. performed scanning tunneling microscopy (STM) imaging on the WSe2-MoS2 transverse heterojunction to map the full 2D strain tensor with a high spatial resolution. The moiré pattern resulting from the lattice mismatch between the underlying WSe2 and MoS2 was observed clearly [Figure 5D][79]. As a result, it produced tensile strain εaa = 1.17% in direction a and compressive strain εbb = 0.26% in direction b [Figure 5E]. For strain-free WSe2-MoS2, the moiré pattern appeared as a regularly arranged hexagonal superlattice with a fixed lattice constant that exhibited rotationally alignment [Figure 5F]. Our group synthesized a 2D multilayered VOPO4-graphene heterostructure through interface strain engineering, which exhibited promising potential for energy storage beyond Li+ ions (Na+, K+, Zn2+, Al3+) [Figure 5G][80]. Due to the mismatch of in-plane lattice distance between VOPO4 and graphene, significant interfacial strain propagates from the interface of VOPO4-graphene to the VOPO4 nanosheets. The Raman spectra over 100 times performed on the O-P-O and V=O mode showed a blue shift of ~15 cm-1 for O-P-O and ~3 cm-1 for V=O [Figure 5H and I], which indicated the interface strain between VOPO4 and graphene.

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 5. Vertical lattice mismatch-induced strain for 2D materials. (A) Experimental schematic diagram of TERS for Raman shift detection; (B) Spectral of 1D TERS measurements; (C) Tip-enhanced Raman spectroscopy was performed at the colored spots marked in the inset STM image; (A-C): quoted with permission from Li et al.[41]; (D) STM image of a transverse heterojunction of WSe2-MoS2; (E) An instance of the moiré pattern observed in a strain-free MoS2/WSe2 bilayer stack; (F) A close-up image of the moiré pattern in (D) shows spatially varying strains; (D-F): quoted with permission from Zhang et al.[79]; (G) Schematic diagram of the 2D multilayered VOPO4-graphene heterostructure; (H-I) Distribution from 100 individual scans of VOPO4-graphene heterostructures, showing the Raman shift of O-P-O and V=O (color orange indicates VOPO4 nanoflakes, color green indicates VOPO4-graphene, color blue indicates VOPO4·2H2O); (G-I): quoted with permission from Xiong et al.[80]. STM: Scanning tunneling microscopy; TERS: tip-enhanced Raman spectroscopy; 2D: two-dimensional.

Substrate-induced strain

Since ultra-thin 2D materials act as a thin plastic film, they can readily adhere to the substrate supporting them, and strain can be introduced through substrate modulation[25]. Compared with microscopic modulation methods (such as defect[13] and lattice mismatch[81]), macroscopic methods can be used to precisely adjust the properties of 2D materials by modifying the electron cloud and lattice structure via substrate engineering[25]. Flexible and rigid substrates have been utilized to modify the properties of 2D materials with more precision and controllability.

Flexible substrate-induced strain

Bending or stretching the substrate is a commonly utilized approach to induce surface strain in experimental settings, especially for flexible 2D materials. Due to the strong van der Walls interaction between the 2D material and substrate, the 2D material undergoes strain that is commensurate with the substrate, assuming that no interface slip occurs[82].

In early studies, a general approach to introduce strain is to place exfoliated 2D nanosheets onto a deformable substrate such as poly (ethylene terephthalate) (PET)[83], polydimethylsiloxane (PDMS)[84], poly(methyl methacrylate) (PMMA)[23], etc. For instance, Mohiuddin et al. used PET and acrylic films as a substrate for two-point and dour-point bending [Figure 6A and B][32]. The substrate was coated with photoresist to facilitate the identification of monolayer graphene on the substrate, followed by deposition of graphene layers prepared through micromechanical cleavage onto the substrates. The strong van der Walls interaction between graphene and the substrate ensured a synchronous deformation of the graphene layers with the substrate. This simple and effective approach facilitated the observation of a corresponding alteration in Raman spectra. Nevertheless, the interaction between 2D materials and the substrate was typically characterized by weak adhesion, which may leads to significant slippage during bending or stretching process and results in inefficient strain transfer[39]. In order to solve this problem, Huang et al. evaporated titanium to clamp the graphene onto the PDMS film[85], which prevented the slippage under mechanical force. In addition, Li et al. proposed a new approach involving polymer encapsulation to achieve effective strain transfer of 2D materials [Figure 6C and D][39]. First, monolayers of MoS2 were transferred onto Si/SiO2 substrates. Subsequently, a layer of polyvinyl alcohol (PVA) was applied via spin-coating to achieve complete encapsulation of MoS2. The robust interaction force between the spin-coated PVA and 2D material ensured efficient transfer of mechanical strain, thereby minimizing the slippage or decoupling. Moreover, the variation of Raman and PL also confirmed that strain can be introduced to a greater extent compared with the traditional exfoliating method.

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 6. Flexible substrate-induced strain. (A-B) Scheme for bending tests with two and four points; a graphene monolayer is positioned on a SU8-coated substrate in the center; (A-B): quoted with permission from Mohiuddin et al.[32]; (C-D) Schematic diagram of fabrication methods of using PVA spin coating encapsulation and conventional direct exfoliation; (C-D): quoted with permission from Li et al.[39]; (E) AFM topography image of wrinkled MoS2 flake created by buckling-induced delamination; quoted with permission from Castellanos-Gomez et al.[59]; (F) Schematic diagram of MoS2 layers sandwiched between the piezoelectric substrate and graphene top electrode; quoted with permission from Hui et al.[86]; (G) Schematic illustration of the lattice deformation in MoS2 on glass spheres with varying diameters; quoted with permission from Zeng et al.[87]. AFM: Atomic force microscopy.

Besides, using the elasticity and piezoelectricity of the substrate is a commonly utilized technique for inducing strain to 2D materials. Castellanos-Gomez et al. created local strain in MoS2 using prestretched elastomer substrates [Figure 6E][59]. At first, the elastomer base was prestrained. Then, the 2D material was deposited on the prestrained substrate. Wrinkles were formed in the MoS2 layers when the substrate tension was released, and the buckling-induced delamination and uniaxial tensile strain were introduced in MoS2. Hui et al. applied a bias voltage to a piezoelectric substrate to induce biaxial compressive strain in trilayer MoS2. The shrink uniformly of the piezoelectric substrate subjected the trilayer MoS2 to uniform compressive biaxial strain [Figure 6F][86]. In addition to these retractable substrates, heat-deformed liquid glass could also serve as an alternative method for inducing strain into 2D materials. Zeng et al. developed a method to introduce strain in-situ for growing MoS2 on spherical glass surfaces [Figure 6G][87]. MoS2 was first synthesized via CVD on a liquid glass substrate at low temperatures. As the temperature rose gradually, the flat liquid glass turned into a ball of a certain diameter, and then the strain was determined by the linear correlation with the curvature of the sphere. The smaller the radius, the greater the degree of lattice distortion. Interestingly, the positive (negative) curvature achieved a corresponding decrease (increase) in the bandgap through the PL spectrum.

Rigid substrate-induced strain

Due to their ultra-thin characteristics, 2D materials exhibit remarkable flexibility in conforming to the surface morphology of various substrates. The strong interfacial adhesion between 2D materials and substrate can result in strain accumulation near the prominent region of the substrate surface[34,88]. The rigid patterned substrate is an effective way to periodically introduce strain into 2D materials. Compared to flexible substrates, rigid substrates allow for a controlled introduction of strain through modulation of array element size (height, width, etc.), providing a foundation for establishing the correlation between substrate morphology and material properties[25].

When a 2D material is deposited on a nanostructured substrate, local strain can be introduced into the deformation region caused by the interaction between the substrate and the 2D materials[89]. Zhang et al. investigated the deformation and strain of graphene on densely packed SiO2 nanosphere arrays and revealed that the strain was amplified as the size of nanospheres reduced from 200 to 50 nm [Figure 7A][90]. Molecular dynamics simulations validated the identical microscopic structure and size-dependent strain behavior and unveiled that a stronger and nonuniform interaction force between smaller nanospheres and graphene led to larger strain [Figure 7B]. Similarly, Resebat-Plantey et al. investigated the strain domain of configuration with different configurations caused by state variation on a pillar array substrate[91]. As a result, a transition from the collapsed state to a suspended one occurred as the pillar pitch decreased and finally showed a low strain profile in the contact regions. Lee et al. discovered that the bandgap of graphene could be periodically modulated, which was realized by placing graphene on a nanostructured substrate[89].

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 7. Rigid substrate-induced strain. (A) The average areal strain of graphene on top of the different central spheres; (B) Strain profiles of graphene on the top of 20 nm nanospheres; (A-B): quoted with permission from Zhang et al.[90]; (C) Microscope image of a MoS2/SiO2 substrate delaminated device (scale bar is 5 μm); (D) AFM image of MoS2 in figure C; (C-D): quoted with permission from Lloyd et al.[92]; (E) Schematic diagram of the 1L-MoS2/ZnO heterostructure arrays; (F) Strain distribution analysis of 1L-MoS2 heterostructure on patterned ZnO substrate across various regions; (E-F): quoted with permission from Liu et al.[53].

In addition, making use of gas pressure difference is a common technique to introduce strain in 2D materials through patterned substrates. Lloyd et al. deposited a MoS2 monolayer on a SiO2 substrate with microcavities using CVD methods[92]. The microcavities were circular apertures with diameters of 5 µm and depths ranging from sub-micrometer to a few micrometers [Figure 7C]. The sample was subjected to high-pressure conditions in a chamber (P0) for an adequate duration, allowing the gas to permeate into the cavity that initially contained air at a pressure of 1 atm [Figure 7D]. When the internal pressure within the cavity reached P0, the sample was taken out of the chamber. The pressure differential between the ambient air and internal pressure caused inflation of the MoS2 layer and resulted in strain on MoS2.

Further, Tomori et al. devised a method for introducing strain in graphene by constructing a patterned substrate with dielectric nanopillars[93]. First, graphene was placed on a Si substrate coated with lift-off resist (LOR). Then, an excess dose of e-beam was irradiated on the partial region; the exposed LOR was insoluble, while the unexposed LOR was removed by soaking it with N-methyl-2-pyrrolidone (NMP), nonuniform strain in graphene was introduced in this process. This approach is applicable to various 2D materials, and the strain distribution can be tailored by controlling the morphology of the supporting nanopatterns. Based on the previous work, Liu et al. employed a PMMA-assisted wet transfer approach to optimize the strain transfer from the substrate to 2D materials [Figure 7E][53]. The procedures were as follows: The ZnO substrates were patterned using electron beam lithography techniques. After, the MoS2 nanosheets grown in-situ were precisely transferred onto ZnO nanorod arrays via a PMMA-assisted wet transfer method. Finally, the hybrid structures were immersed in acetone for PMMA removal and subsequently dried with a critical point dryer to eliminate residual acetone. The PMMA-assisted MoS2 was drawn down by capillary force generated by water evaporation within the spacing of ZnO nanorods, followed by removal of PMMA with acetone. As a result, the biaxial strain was localized near the ZnO nanorods at the van der Waals interfaces [Figure 7F].

Comparison of different strategies for strain engineering of 2D materials

In the above content, we have provided a systematic description and classification of experimental strategies for creation of strain in 2D materials, along with an analysis of the characteristics associated with each method. To facilitate a more intuitive comparison between different strain induction techniques, Table 1 presents the range and types of strains achievable in various 2D material systems. This comprehensive summary enables researchers to identify the most suitable approach based on their specific research needs.

Table 1

Summary of the technique, type, and range of the strain for different 2D materials

Strain technique Materials Type of strain Range Ref.
Flexible substrate Graphene Uniaxial homogeneous 0%-1.3% [32]
Planar lattice mismatch Graphene/h-BN Uniaxial inhomogeneous 1.9%-5.9% [33]
Rigid substrate MoS2 Local inhomogeneous 0%-3% [34]
Doping MoS2 Local inhomogeneous 0%-1.7% [35]
Doping MoS2 Local inhomogeneous - [36]
Planar lattice mismatch WSe2/MoS2 Uniaxial inhomogeneous 0%-2% [37]
Vacancy MoS2 Local inhomogeneous ~3% [38]
Flexible substrate MoS2 Uniaxial homogeneous 0%-1.49% [39]
Vacancy WSe2 Local inhomogeneous 4.8%-8% [40]
Vertical lattice mismatch DBP/Borophene Biaxial inhomogeneous ~0.6% [41]
Vertical lattice mismatch AC-Ir NSs Biaxial inhomogeneous ~4% [42]
Vacancy BiOBr Local inhomogeneous 5%-10% [43]


The utilization of 2D materials presents both technological opportunities and novel fundamental insights for energy storage and conversion. The engineering of strain in 2D materials presents boundless opportunities for the design and regulation of their properties across various fields[94-96]. In the following, the basic applications of strain engineering in energy storage and conversion of 2D materials are summarized.

Strain engineering of 2D materials for energy storage

Two-dimensional materials stripped from their layered precursors have attracted great attention due to their huge surface area and easy modification properties[97-100]. As a widely reported method in electronics, strain engineering represents an efficient and straightforward method to manipulate the 2D materials[101-104]. In terms of energy storage, strain acts on material, engineering absorption, diffusion[105], and electrochemical reactivity[106], resulting in a reduced barrier for the diffusion and reaction of metal ions, minimizing energy loss and enhancing the material’s performance in energy storage. Furthermore, during the intercalation process of metal ions for energy storage, the material always undergoes detrimental irreversible expansion, leading to poor cycling performance[107]. The introduction of appropriate interfacial strain can confer robust structural stability to the material during both the insertion and stripping of metal[80,108,109], thereby improving its overall energy storage capabilities. The application of strain engineering in energy storage is summarized below.

Regulating the electrochemical reactivity

The strain within the material can cause structural changes in the electron cloud, leading to alterations in both diffusion barrier and metal ion adsorption and imparting diverse energy storage properties to the material. For instance, Hao et al. demonstrated the tunability of Li/Na adsorption and storage in 2D MoS2 through strain engineering via first-principles calculations[105]. The result suggested that proper tensile strain could increase the absorption of energy for Li/Na ions, influence the diffusion batteries, and narrow the semiconducting gap of MoS2, thus leading to enhanced stability and improved electrical conductivity. In another work, Chen et al. suggested that the diffusion path of lithium atoms could be efficiently modified by uniaxial strain due to the variation in asymmetric surface geometry and electron polarization[110]. Further, Oakes et al. demonstrated that strain engineering at the interface of carbon-MoS2 (C-MoS2) heterostructure could guide the chemical storage pathway during lithium metal insertion into MoS2 [Figure 8A][106]. Raman spectroscopy was conducted on both pristine MoS2 nanosheets and interface-strained MoS2 nanosheets at various cathodic potentials to elucidate the mechanism of lithium insertion. As cathodic potential scanned from open-circuit voltage to 0.01V, a distinct Raman peak emerged from the stacked C-MoS2 nanosheets at a potential of 1.75V, while no change was observed in the Raman spectroscopy of pristine MoS2 nanosheets under the same conditions, indicating the generation of lithium polysulfides [Figure 8B and C]. As the open circuit voltage continued to decrease, the signature of lithium polysulfides appeared at cathodic potentials as low as 0.01 V [Figure 8D], indicating a distinct reaction pathway and the same final product. Moreover, the normalized differential capacity curves of vertically stacked C-MoS2 nanosheets and MoS2 exhibited distinct chemical pathways during lithium insertion, which can be attributed to interface strain [Figure 8E and F]. This study demonstrated the potential of strain engineering in regulating energy storage pathways and underscored the significance of mechanical strain in material-based energy storage processes.

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 8. Strain engineering on energy storage and its mechanism analysis. (A) Schematic showing the different chemical reaction pathways of the nanosheets. Ex-situ Raman spectroscopy reveals different electrochemical signatures based on the Raman of polysulfides for pristine MoS2 and interface-strained MoS2 at (B) OCV, (C) 1.75V and (D) 0.01 V. Normalized differential capacity measurement for MoS2 (E) and vertically stacked C-MoS2 nanosheets (F), with two arrows indicate the potential of direct chemical conversation and intercalation reactions; (A-F): quoted with permission from Oakes et al.[106]; (G) Schematic illustration of the reversible intercalation mechanism of K+ ions in 2D VOPO4-graphene multilayer heterostructures; (H) Charge and discharge profiles of VOPO4-graphene cathodes for K+ ion batteries and corresponding in-situ XRD patterns; (I) The interlayer spacing of VOPO4-graphene calculated from the XRD pattern during the process of charge and discharge; (J) Comparison of cycle performance of VOPO4-graphene heterostructure, restacked VOPO4 nanoflakes, and bulk VOPO4·2H2O at 0.1 C; (K) Rate capability comparison of VOPO4-graphene heterostructure, restacked VOPO4 nanoflakes, and bulk VOPO4·2H2O at various current densities from 0.1 to 20 C; (G-M): quoted with permission from Xiong et al.[80]. OCV: Open-circuit voltage; XRD: X-ray diffraction; 2D: two-dimensional.

Relieving the volume change

Relieving the volume change caused by metal ion intercalation through strain engineering can enhance cycling stability and reversibility of the material during energy storage. Guided by this, an xDA-Ti3C2 with special pillar and strain structures was prepared through the reaction between xDA molecules and -NH2 functionalized Ti3C2 through Liu et al. The unique strain structure of xDA-Ti3C2 relieved the volume change and maintained structural stability during ion insertion/extraction[109]. In addition, our group proposed a reversible intercalation mechanism for K+ ions in the zero-strain 2D multilayered heterostructure cathode [Figure 8G]. Due to the disparity in lattice spacing between VOPO4 and graphene, the interface-induced compressive strain was generated on VOPO4 nanosheets, which relieved the expansion brought by the insertion of K+ ions[80]. A reversible change in interlayer distance of VOPO4-graphene layered cathodes during the charge/discharge process was demonstrated through in-situ X-ray diffraction (XRD) measurements, indicating a promising potential for energy storage applications [Figure 8H and I]. Benefiting from its alternating stack structure and interface strain between VOPO4 and graphene nanosheets, the VOPO4-graphene multilayered heterostructures exhibited a superior cycling and rate capability performance compared to bulk VOPO4·2H2O and restacked VOPO4 [Figure 8J and K].

Strain engineering of 2D materials for photocatalysis

In recent years, 2D ultra-thin nanosheets have shown great potential in the development of novel semiconductor photocatalysts. Benefiting from their ultra-thin morphological characteristics and abundant surface defects, a large amount of unsaturated metal sites are exposed, providing abundant adsorption for the reactants[111,112]. Photocatalysis can be defined as the process in which light interacts with a semiconductor, and the generated electrons and holes induce a targeted redox reaction on the surface of the catalysts[49,113,114]. Photocatalysis involves four steps: (1) light absorption; (2) generation of electron-hole pairs; (3) transport of the photogenerated charge carriers from bulk to surface; and (4) catalysis on the surface of materials[115]. Strain engineering of 2D materials shows the potential to manipulate the band structure, enhance the separation efficiency of photogenerated electron-hole pairs, regulate intermediate absorption, and synergistically improve photocatalytic activity.

Regulating the band structure

Strain engineering is considered a highly effective way of regulating the bandgap and band position of materials, promoting efficient solar energy capture and enhancing the redox reactivity of photogenerated carriers[116]. As early as 2012, Feng et al. demonstrated a continuous band regulation of monolayer MoS2 nanosheets under biaxial tensile strain[117]. Furthermore, Pak et al. observed that the direct-to-indirect bandgap in WS2 can be induced by compressive strain[118]. Furthermore, Feng et al. manipulated the photocatalytic performance of BiOBr nanosheets in dye degradation and found that strain can modify the band structure of BiOBr[56]. Both tensile and compressive strain could lead to a narrowed bandgap of BiOBr nanosheets. In another work, a lepidocrocite-phase 2D TiO2 sheet with crumpled morphology and nonuniform strain was synthesized via a one-step solvothermal methodology[119]. STEM images revealed the significant nonuniform strain, and lattice distortion was observed in different parts of the crumpled sheet, with compressive strains of 4% and 20% along the a and b axes, respectively. The valence band (VB) analysis calculated for strained/ unstrained 2D lepidocrocite TiO2 showed that the theoretical band gap of strained titanium dioxide (1.80 eV) was in good agreement with the experimental value (1.84 eV), which was significantly smaller than the unstrained band gap (4.7 eV). The result indicated that the surface strain of lepidocrocite TiO2 significantly enhanced the light absorption of both visible and near-infrared light.

Enhancing the carrier separation

Apart from the material's light absorption property, its excellent carrier separation capability also plays a crucial role in achieving high photocatalytic performance. Di et al. successfully synthesized Bi12O17Br2 nanotubes as a photocatalyst for CO2 reduction[55]. The tensile strain of the curved Bi12O17Br2 nanotubes was approximately 5.5%. The surface tensile strain led to an increase in carrier separation and a better absorption model for CO2. As a result, the CO2 reduction performance of the nanotubes was enhanced by tensile strain tuning, surpassing that of Bi12O17Br2 nanoplates (14.4 times). Further, Liang et al. reported lattice-strained nickel hydroxide nanosheets via a V-doped strategy for CO2 reduction [Figure 9A][67]. The chemisorption profile of 10% V-doped Ni(OH)2 nanosheets showed a higher temperature shift, indicating an increased number of exposed sites available for CO2 adsorption and activation [Figure 9B]. The reduction in PL intensity after the introduction of vanadium (V) implied that surface strain on Ni(OH)2 was conducive to the separation of photogenerated electron-hole pairs [Figure 9C]. Benefiting from the lattice strain and enhanced carriers’ separation, the optimized Ni(OH)2 nanosheets demonstrated the highest CO yield and the best selectivity [Figure 9D]. Even in a diluted CO2 (0.1 atm) concentration, the lattice-optimized Ni(OH)2 exhibited a remarkable CO generation of 3.5 μmol·h-1, which was superior to that of pure Ni(OH)2 [Figure 9E]. The nearly identical Ni K-edge position before and after the reaction indicated that the original lattice strain structure was retained. [Figure 9F]. In another case, Hsu et al. reported a reversible photochromic BiOBr nanosheet, which exhibited excellent photocatalytic activity toward the coupling and oxidation of ethylbenzene. The presence of defects on the material surface induced lattice distortion in the nanosheets, leading to overall lattice strain in the structure. Theoretical calculation suggested that the lattice strain enhanced the probability of photocarrier transition and separation, thus facilitating hydroxyl radical generation and significantly improving the photocatalytic efficiency of C-H bond activation[37].

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 9. Strain engineering on photocatalysis and its mechanism analysis. (A) Proposed mechanism for photocatalytic CO2 reduction using lattice-strain optimized Ni(OH)2 nanosheets; (B) and (C) CO2-TPD and PL spectra plots of Ni(OH)2 nanosheets and 10% V-doped Ni(OH)2 nanosheets; (D) The gas production yield and CO selectivity of x% V-Ni(OH)2 nanosheets were evaluated under a pure CO2 atmosphere; (E) CO2 photo reduction performances of 10% V-Ni(OH)2 nanosheets and Ni(OH)2 were evaluated under varying CO2 concentrations within the first hour; (F) Comparison of Ni K-edgeXANES spectra of 10% V-Ni(OH)2 nanosheets before and after the reaction; (A-F): quoted with permission from Liang et al.[67]; (G) Schematic photocatalytic process of N2 fixation on the surface of ultrathin TiO2 nanosheets with VO and engineered strain; (H) UV-vis diffuse reflectance spectra for Bulk-TiO2 and the x%-TiO2 nanosheets (contain x% mol Cu); (I) Yield of NH3 of different samples after UV-vis illumination for 1h with water as the proton source; (J) The calculated adsorption energies of N2 on TiO2-Pure, TiO2-VO, and TiO2-VO-Strain; (K) N-N distance of N2 on TiO2-Pure, TiO2-VO, TiO2-VO-Strain, N2H2, and N2H4; (L) The free energy diagram depicting the N2 fixation process on the surface of TiO2-Pure, TiO2-VO, and TiO2-VO-strain; (G-L): quoted with permission from Zhao et al.[72]. PL: Photoluminescence; TPD: temperature programmed desorption; XANES: X-ray absorption near edge structure; UV-vis: ultraviolet-visible.

Tuning the absorption and optimizing the reaction path

The photocatalytic performance of the material is closely correlated with the absorption and desorption of intermediate products during the reaction. Strain engineering of 2D materials exhibits potential in optimizing intermediate product absorption through a low-energy pathway for the final reaction. Zhao et al. reported a co-precipitation method to enhance the chemisorption and activation of N2 through strain engineering[68]. Density function theory (DFT) calculations indicated that vacancy-introduced strain modified the gap state and enhanced the absorption and activation of H2O and N2. As a result, it endowed an excellent photocatalytic activity for converting N2 to NH3. Zhao et al. reported a facile copper-doping strategy for synthesizing ultrathin TiO2 nanosheets with VO-induced compressive strain for photocatalytic nitrogen fixation [Figure 9G][72]. A large amount of VO could be induced to TiO2 nanosheets with the doping of Cu to achieve local charge balance, thus introducing compression strain. As a result, the compressive strain-optimized TiO2 nanosheets showed superior light absorption [Figure 9H], and 6%-TiO2 exhibited an optimum performance for N2 fixation in water [Figure 9I]. Further DFT calculations suggested that the adsorption of N2 was most favorable on the surface of TiO2 nanosheets with VO and compressive strain [Figure 9J]. The increased absorption to N2 facilitated the charge transfer between TiO2 and N2 and weakened the N-N bond [Figure 9K]. Various Gibbs free energy diagrams for nitrogen fixation indicated that the sluggish Volmer step on TiO2 could be significantly accelerated after the introduction of strain [Figure 9L], leading to an enhanced N2 activation and fixation performance.

Strain engineering of 2D materials for electrocatalysis

Noble metals exhibit superior electrocatalytic performance. However, their limited reserves and high costs have prompted the exploration of alternative options[46,120,121]. Two-dimensional materials have garnered significant attention in the realm of electrocatalysis due to their unique characteristics, such as ultrathin morphology, fully exposed surface atoms, and exceptional mechanical properties[122]. Their application in electrocatalysis has been further expanded through strain engineering to achieve various properties. Electrocatalysis refers to the process in which the intermediate adsorbed on the catalyst surface undergoes oxidation-reduction reactions and desorption to produce the target product under the influence of electricity[123]. A proper adsorption ability between the intermediate and the catalyst surface plays an essential role in the electrocatalytic reaction. According to the d-band theory raised in 1998[25], the d-band center typically undergoes variations in response to the change in the local coordination environment surrounding metal atoms. As a result, compressive lattice strain will cause an increased overlapping of the d-orbitals of metal atoms. This overlap will increase the bandwidth and lower the d-band center energy, pushing more antibonding states below the Fermi level and allowing adsorbates to interact with them, which weakens the binding energy of adsorbates. On the contrary, tensile lattice strain shows the opposite effect. The change in atomic distance induced by strain can significantly impact the electron density of the d-state and enhance electrochemical activity on material surfaces[124-126]. The application of strain on 2D materials induces additional lattice irregularities, thereby optimizing the adsorption energy for intermediate products and boosting the catalytic performance[127-129].

Voiry et al. reported a highly strained WS2 nanosheet with abundant metallic 1T phase as an efficient catalyst for hydrogen evolution [Figure 10A][130]. Compressive and tensile strain was both produced in the highlighted zigzag chain superlattice region. Considering the transition from highly strained and distorted 1T phase to stable 2H phase at high temperatures, the monolayered WS2 nanosheets were incrementally annealed to obtain samples with varying 1T phase content. As a consequence, higher temperatures led to a decreased concentration of 1T phase, resulting in a suppressed electrocatalytic activity [Figure 10B]. DFT calculations revealed that the adsorption of atomic hydrogen on the surface of distorted 1T phase was significantly influenced by strain, and proper tensile strain (2.7%) could lead to a near thermoneutral free energy for a maximized electrocatalytic activity [Figure 10C]. Similarly, Hwang et al. reported the combinations of 2H/1T phase transition and bending strain by rolling up MoS2 nanosheets; the self-induced uniaxial strain caused by rolling-up allowed the lamellar sliding and high catalytic activity for hydrogen evolution reactions (HER)[131].

Strain engineering of two-dimensional materials for energy storage and conversion applications

Figure 10. Strain engineering on electrocatalysis and its mechanism analysis. (A) High-resolution STEM image of a WS2 monolayer exhibiting the highly distorted and strained 1T phase; (B) Relationship between 1T phase concentration and catalytic activity at different temperatures; (C) The absorption free energy of atomic hydrogen on the surface of distorted 1T phase under different strains; (A-C): quoted with permission from Voiry et al.[130]; (D) Schematic illustration of HER catalyzed by a monolayer MoS2 on nanoporous gold; (E) Annular bright-field STEM image illustrating the variation in S-Mo-S bonding angles (α); (D-E): quoted with permission from Tan et al.[132]; (F) Schematic diagram of a core/shell nanostructure consisting of Co9S8 and single-layer MoS2; (G) Comparison of overpotentials for HER at 10 mA·cm-2 among various Co9S8/nL MoS2 (n = 1-5) and Pt/C catalysts; (H) Absorption energy of H in strained MoS2 with ε% strain; (I) Reactive pathways for the transformation of hydrogen atoms into hydrogen molecules on Co9S8/1L MoS2 for HER; (J) Schematic of hydrogen atom transforms to hydrogen molecule on the surface of Co9S8/1L MoS2; (F-J): quoted with permission from Zhu et al.[134]. HER: Hydrogen evolution reactions; STEM: scanning transmission electron microscopy.

In addition to the strain introduced via phase transition, strain can also be introduced by the external substrate to optimize the electrocatalytic properties of materials. Tan et al. fabricated a strained monolayer MoS2 with controllable out-of-plane strain for higher HER catalytic activity[132]. A 3D nanoporous gold (NPG) substrate with a curved internal surface was employed for the growth of a continuous monolayer of MoS2 [Figure 10D], which provided a source of strain and served as a conductive channel for fast charge transfer and transport. The annular bright-field STEM image revealed a significant distortion of the S-Mo-S lattice, which was attributed to the strong coupling between the MoS2 layer and the curved gold surface [Figure 10E]. As a result, the as-fabricated monolayer MoS2 showed the best HER performance due to the out-of-plane strain introduced by lattice bending. Subsequently, Lee et al. employed contact printing to transfer vacuum-filtered MoS2 nanosheets onto an Ag/PET substrate, which functioned as the working electrode for HER[133]. By mechanical bending of the PET substrate, up to 0.02% tensile strain could be introduced into the MoS2 thin film. With the increase of tensile strain, the strained MoS2 nanosheets showed a lower Tafel slope and a steeper polarization curve than strain-free MoS2 nanosheets, demonstrating the correlation between mechanically bending strain and electrochemical activities.

In another work, a precise surface strain tuning strategy was proposed for Co9S8/MoS2 core/shell nanocrystals via lattice mismatch[134]. With the MoS2 layers changing from 1 to 5, a continuous adjustment of the bond lengths of Co-S and Mo-S occurred at the interface of Co9S8 and MoS2, resulting in tensile strain on the MoS2 shell and compressive strain on the Co9S8 core [Figure 10F]. As a result, the strained Co9S8/1L MoS2 (3.5%) manifested the best HER performance [Figure 10G]. Reaction pathways and absorption energy of hydrogen atoms for the strained MoS2 were investigated to elucidate the correlation between lattice strain and HER performance [Figure 10H]. The hydrogen absorption (stage 1 to stage 2) is the rate-determining step of the reaction. As a result, the larger strain in MoS2 made a more negative ΔEH (from -0.85 to -0.98 eV) [Figure 10I], indicating an enhanced combination of hydrogen atoms on a strained MoS2 surface and a better HER performance. Further, electron density maps revealed that the strain at the Co-S-Mo interface led to a redistribution of electron density, resulting in a low energy barrier for the reaction [Figure 10J].


Strain engineering is a crucial approach for modulating the electronic structure and properties, which have garnered significant attention in 2D materials. This article first provides an overview of the fundamental understanding of the strain. Then, several methods for introducing strain into 2D materials are proposed. Lastly, the application of strain engineering in energy storage, electrocatalysis, and photocatalysis are reviewed. Due to the unique morphology of 2D materials (high Young’s modulus and large surface area), they exhibit exceptional resistance to surface strain without fracturing. Additionally, the confinement of electrons within a 2D plane renders them highly susceptible to strain. As predicted, even minor strain can induce change in the lattice structure, thereby dramatically tuning its physical properties. Such a unique advantage endows 2D materials with more possibilities in the fields of energy storage and conversion. Despite the rapid development and advances of strain engineering for 2D materials, there are still some problems to be solved.

Decoupling strain effect

In 2D materials, the relationship between defects and strain is always entangled and indistinguishable. In other words, defects will be generated to relax the strain near the distorted region, while inherent defects of the material introduce strain. It still needs more rational experimental design and theoretical models for decoupling the effects of strain. Such complex synergy of strain and other factors requires complementary experimental and theoretical studies to deeply understand their interactions. These synergistic effects present novel opportunities for expanding the properties and applications of 2D materials.

Effective characterization techniques

A comprehensive comprehension of surface strain effects necessitates advanced characterization methods for both in-situ and ex-situ, which requires more advanced characterization techniques. There are numerous physiochemical characterizations of strain for 2D materials, such as Raman and PL spectroscopy, X-ray absorption spectroscopy, atomic-resolution electron microscopy, etc. However, these methods are mainly limited to low spatial resolution. It is still urgent for advanced strain characterization techniques to have a definite description.

Theoretical framework

Although DFT calculations, molecular dynamics, and continuum mechanics simulations have been widely used to explain the role of strain in energy storage and conversion, there is still a lack of sufficient theoretical guidance to rationally design a material with better performance. The d-band theory revealed the relationship between strain and catalytic properties for the first time, but it seems that it cannot fully explain the relationship between the strain-induced change in adsorption and reactions. Meanwhile, the relationship between strain and energy storage is mostly confined to theoretical calculations, with few proposed theories regarding strain-directed energy storage. The establishment of more rational theoretical frameworks is necessary to elucidate the fundamental intrinsic relationship between strain engineering and material properties.

In general, strain engineering of 2D materials provides an effective approach to modulating their physicochemical properties and expanding their applications in the realm of energy storage and conversion. It is believed that through continuous exploration, the realm of strain engineering in 2D materials will gain a deeper understanding and broader prospects.


Authors’ contributions

Prepared the manuscript: Peng X, Chen L, Liu Y, Liu C, Huang H, Fan J

Performed manuscript editing: Xiong P, Zhu J

Availability of data and materials

Not applicable.

Financial support and sponsorship

This work was supported by the Natural Science Foundation of China (No. 22179062, 52125202, and U2004209), the Natural Science Foundation of Jiangsu Province (BK20230035), the Fundamental Research Funds for the Central Universities (No. 30922010303), and the Intergovernmental Cooperation Projects in the National Key Research and Development Plan of the Ministry of Science and Technology of PRC (No. 2022YFE0196800).

Conflicts of interest

All authors declared that there are no conflicts of interest.

Ethical approval and consent to participate

Not applicable.

Consent for publication

Not applicable.


© The Author(s) 2023.


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Cite This Article

OAE Style

Peng X, Chen L, Liu Y, Liu C, Huang H, Fan J, Xiong P, Zhu J. Strain engineering of two-dimensional materials for energy storage and conversion applications. Chem Synth 2023;3:46.

AMA Style

Peng X, Chen L, Liu Y, Liu C, Huang H, Fan J, Xiong P, Zhu J. Strain engineering of two-dimensional materials for energy storage and conversion applications. Chemical Synthesis. 2023; 3(4): 46.

Chicago/Turabian Style

Peng, Xing, Long Chen, Yifan Liu, Chao Liu, Honglan Huang, Jinbo Fan, Pan Xiong, Junwu Zhu. 2023. "Strain engineering of two-dimensional materials for energy storage and conversion applications" Chemical Synthesis. 3, no.4: 46.

ACS Style

Peng, X.; Chen L.; Liu Y.; Liu C.; Huang H.; Fan J.; Xiong P.; Zhu J. Strain engineering of two-dimensional materials for energy storage and conversion applications. Chem. Synth. 2023, 3, 46.



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