Shear properties and stable wrinkle resistance in 2D Ti_3C_2T_x MXene monolayers

Domain: chemistry
Published: 2026-03-13
Editorial outcome: major_revision

Abstract
Two-dimensional (2D) transition metal carbides or nitrides (MXenes), represented by Ti3C2Tx, exhibit exceptional mechanical and electrical properties, making them ideal candidates in aerospace, structural membranes, and flexible electronics. Understanding the mechanical properties of 2D Ti3C2Tx under various load conditions is crucial for ensuring structural integrity and performance reliability. Here, we conduct direct in-situ shear test of monolayer Ti3C2Tx nanosheets using a push-to-shear strategy under the scanning electron microscope. Contrary to the expected ultra-low shear performance and wrinkle instability of 2D materials, we report a high in-plane shear modulus of 0.279±0.007 TPa for single-crystal monolayer Ti3C2Tx, along with stable wrinkle resistance. Additionally, the monolayer Ti3C2Tx exhibits a shear strength as high as ~18.6 GPa and an average shear strain of ~8.6%. This work provides direct measurement of the intrinsic shear properties of monolayer Ti3C2Tx and highlights the promising potential of Ti3C2Tx in maintaining device performance and reliability.

Introduction
Two-dimensional (2D) titanium carbide (Ti3C2Tx MXene) nanosheets have promising applications in aerospace, intelligent sensors, flexible electronics, and micro- and nanoelectromechanical devices (MEMSs and NEMSs), owing to their excellent mechanical properties, metallic conductivity, and solution-processability. In practical applications, the mechanical stress experienced by component units can significantly influence the performance and stability of functional nanodevices. Consequently, a comprehensive understanding of the mechanical properties of 2D Ti3C2Tx under various loading conditions is essential. While the mechanical properties of monolayer Ti3C2Tx under uniaxial tension have been extensively investigated through experiments and atomic simulation methods, the in-plane mechanical properties of monolayer Ti3C2Tx under shear loading remain unexplored. This gap is largely due to the limitations of micro- and nanomechanical testing techniques, as well as the absence of standardized testing protocols. Notably, the shear modulus quantifies the material’s resistance to shear deformation under stress. A detailed investigation of the shear modulus and mechanical behavior of 2D Ti3C2Tx under shear loading will provide valuable insights for the structural design of 2D flexible electronics devices.

Currently, the related work primarily focuses on investigating the interfacial shear modulus and interlayer shear stress of monolayer 2D materials, including tip-based adhesion measurement, pressurized bubbling method, and atomic force microscopy (AFM) nanoindentation strategy. However, these methods make it difficult to reveal the in-plane shear behavior of 2D materials and obscure their intrinsic shear properties. Specifically, the tip-based adhesion measurement relies on the interaction between the probe with the sample surface. Guo’s team systematically studied the shear mechanical properties of the surface and interface of 2D materials using graphite-wrapped AFM probes, but could not directly measure the shear mechanical properties of the 2D materials themselves. The pressurized bubbling method employs uniform bubbles on the surface of 2D materials to assess the shear mechanical properties. For instance, an interfacial shear stress of 1.64 MPa was determined by bubble loading monolayer graphene on a silicon oxide substrate. This technique, however, is affected by the unstable interfacial force between the 2D material and the substrate, necessitating an accurate assessment of the airtightness of the 2D material. Additionally, the inhomogeneity of bubble expansion and stress concentration impacts the measurement accuracy. The AFM nanoindentation strategy involves loading different layers of 2D materials suspended on a porous substrate, with the interlayer shear force determined by comparing and analyzing the load-displacement curves. However, nanoindentation method induces both uneven shear stress and tensile stress in the transverse test area of the 2D material, and different indenter sizes and indentation locations contribute to significant uncertainty in the results. In general, due to the limitations of current testing techniques, the intrinsic shear properties and mechanical behavior of 2D materials under in-plane shear loading are often overlooked. As highlighted in recent in-plane shear studies, internal shear deformation plays a crucial role in dictating both the mechanical stability and functional properties of atomically thin materials. Nevertheless, quantitative investigations of solution-processed Ti3C2Tx remain scarce. Therefore, there is an urgent need for a direct, quantitative, and reliable approach to study the in-plane shear properties of monolayer Ti3C2Tx nanosheets.

In this work, we synthesized high-quality, large-sized monolayer Ti3C2Tx nanosheets, which were fixed onto the nanomechanical testing device using improved dry transfer method and precisely controlled focused ion beam (FIB) technique, as previously reported by us. The “Push-to-Shear” (PTS) strategy was employed to apply in-plane shear loading. The shear modulus and shear strength of monolayer Ti3C2Tx nanosheets were directly measured, and the stable wrinkle resistance was observed, which differs from the behavior of monolayer graphene. Additionally, the experimental observations of in situ shear in monolayer Ti3C2Tx were validated through simulations. Our findings show that MXene can break the conventional understanding of ultra-low shear properties and wrinkle instability typically expected in 2D atomically thin materials. This work demonstrates that 2D Ti3C2Tx MXene holds significant potential for applications in structural composite films and flexible electronics devices that require specific mechanical properties and robust performance.

Results
Transfer of monolayer Ti3C2Tx samples
To successfully conduct in situ shear testing, a crucial prerequisite is the transfer of high-quality monolayer Ti3C2Tx nanosheets to the nanomechanical testing device without causing damage. Unlike the transfer process for large-area 2D materials synthesized via chemical vapor deposition (CVD), such as graphene and MoS2, which can be quickly and easily transferred by simply removing the polymer protective layer, 2D monolayer Ti3C2Tx nanosheets are obtained by mechanical exfoliation in solution (the synthesis steps are detailed in Supplementary Fig. 1), which significantly increases the difficulty of sample transfer. Therefore, we developed an improved dry transfer method. In detail, the monolayer Ti3C2Tx supernatant was dripped onto the bare copper mesh and dried under vacuum. Monolayer nanosheets will be suspended on the edge of bare copper mesh (Fig. 1a), thus avoiding the difficult transfer problem caused by the van der Waals force between the sample and the substrate, significantly facilitating the subsequent transfer process. Then, a rectangular sample was obtained by attaching the manipulator to one side of the sample via electron-beam (e-beam) platinum (Pt) deposition, while the other three sides were cut using FIB technique. The resulting sample was carefully transferred to the test area at the center of the nanomechanical device using the manipulator (Fig. 1b). The 2D monolayer Ti3C2Tx nanosheet was then subjected to in-plane shear testing using the “push-to-shear” strategy (Fig. 1c). Notably, in order to avoid curling of the samples during the transfer process, we reinforced the sample with e-beam Pt deposition around its edges (Fig. 1d). Ti3C2Tx nanosheets suspended on the PTS nanomechanical device are nearly transparent due to their monolayer nature. We used FIB to cut and shape the monolayer Ti3C2Tx nanosheets in the test area, and deposited e-beam Pt on both ends of the sample, which can avoid the slippage between the sample and the PTS device during the shear test (Fig. 1e).

It is worth noting that the PTS device was originally designed for uniaxial tensile loading (commonly referred to as push-to-pull loading). Here, it is employed to perform shear loading on monolayer Ti3C2Tx for shear strength measurement, with a discussion on the validity of the shear testing to demonstrate that the specimen experienced pure shear deformation. As shown in Supplementary Fig. 2a, b, the PTS device consists of a movable plate (purple region) and a fixed plate (gray region). When the hemispherical indenter is loaded, the purple movable plate translates downward to apply force on the specimen. Under loading, the entire region beneath the hemispherical indenter constitutes the effective testing area of the specimen (the boxed orange region), while the surrounding springs ensure the stability of the device. During the loading process, the gap width remains unchanged (Supplementary Fig. 2c), enabling one side of the specimen to be fixed while a tangential displacement is applied to the opposite side. Consequently, the specimen at the device side gap undergoes pure shear deformation. SEM images taken during the test further show that the gap width does not change (Supplementary Fig. 2d), confirming that the specimen experiences pure shear deformation, consistent with the testing requirement of fixing one side while applying a parallel tangential displacement to the otherside.

Characterization of monolayer Ti3C2Tx samples
As shown in the SEM image (Fig. 2a), the ends of the monolayer Ti3C2Tx were immobilized onto the test area of the PTS nanomechanical device by e-beam Pt deposition. The nanosheet suspended above the gap was milled using FIB to achieve the required shape and size for shear testing. A pushing force is applied to the hemispherical indenter on the PTS device via the probe (indicated by red arrows), and four springs (indicated by purple arrows) convert the pushing into shearing on the sample. The in-plane shear test of monolayer Ti3C2Tx nanosheets is achieved through the “push-to-shear” mechanism. The loading rate of the probe is 10 nm/s, and the load-displacement data can be recorded during the loading process using a mechanical sensor in the planar probe. Figure 2b shows the SEM image of monolayer Ti3C2Tx after FIB cutting; the length and width of the Ti3C2Tx nanosheet are 4.5 and 5.5 μm, respectively. The cyan arrow indicates the in-plane shear direction of the sample.

To ensure the accuracy of test results, it is essential to maintain the high quality of the samples during the transfer process. Therefore, we thoroughly characterized the monolayer Ti3C2Tx nanosheets both before and after the transfer. The properties of Ti3C2Tx were confirmed during the preparation process through X-ray diffraction (XRD, Supplementary Fig. 3), X-ray photoelectron spectroscopy (XPS, Supplementary Figs. 4 and 5), and energy dispersive X-ray spectroscopy (EDS, Supplementary Fig. 6). Prior to sample transfer, the high quality of the suspended Ti3C2Tx was verified using transmission electron microscopy (TEM) and EDS mapping (Supplementary Figs. 7 and 8). The corresponding selected area electron diffraction (SAED) pattern confirming the single-crystal nature of Ti3C2Tx (Fig. 2d, Supplementary Fig. 9). To minimize potential damage to the sample during FIB milling, we employed an ultra-low accelerating voltage of 2 kV for cutting. As shown in Fig. 2c, the corresponding SAED from the edge area of the Ti3C2Tx nanosheet confirms that the crystal structure remains intact after FIB cutting, and the sample retains its high-quality morphology. In addition, the TEM image of the central area of the tested Ti3C2Tx on the PTS device, along with the corresponding SAED pattern, also confirms the high quality and single-crystal properties of the Ti3C2Tx nanosheets after transfer (Fig. 2e). It is worth noting that during the transfer process of Ti3C2Tx nanosheets, the lateral size of the sample is typically larger than 10 μm due to the reduction in size caused by the Pt deposition and FIB cutting. Supplementary Fig. 10 shows that the average lateral size of the Ti3C2Tx nanosheets is about 11.9 μm, which provides sample size for the sample transfer process.

The thickness of a monolayer Ti3C2Tx is a key factor for the subsequent calculation of its in-plane shear properties, and therefore, accurate determination of its thickness is essential. Although AFM is commonly used to measure the thickness of 2D materials, the presence of water molecules and adsorbates on the surface of the Ti3C2Tx nanosheets, as well as the tapping and contact mode of the AFM and the interaction between the AFM tip and the Ti3C2Tx surface, can often lead to an overestimation of the monolayer thickness. Similarly, XRD measurements of the thickness of monolayer samples can be influenced by the amount and chemical properties of embedded substances, resulting in inaccurate measurements. Therefore, STEM characterization of the cross-section of a monolayer Ti3C2Tx nanosheet after fracture, combined with theoretical models, provides the most accurate method for determining the thickness (Fig. 2f). Furthermore, we used AFM to confirm the monolayer nature of Ti3C2Tx nanosheets. As shown in Fig. 2g, the thickness of the Ti3C2Tx nanosheet was found to be 1.5 nm. It is noteworthy that in other studies, the “nominal” thickness of the monolayer 2D material has been used as a calculation parameter rather than the thickness measured by AFM. For instance, the AFM-measured thickness of monolayer graphene typically ranges from 0.4 to 1.7 nm, which significantly overestimates the actual thickness of monolayer graphene. In studies evaluating the mechanical properties of monolayer graphene, the nominal thickness of 0.335 nm is typically used as the calculation parameter. Similarly, in this study, we used the nominal thickness of 0.98 nm for monolayer Ti3C2Tx nanosheet as the parameter for subsequent calculations of shear modulus. Specifically, we employed STEM to obtain high-resolution images of the cross-section of monolayer Ti3C2Tx. By analyzing the distinct boundary of the monolayer Ti3C2Tx in the STEM images, we were able to precisely measure its thickness, confirming that the material’s thickness is approximately 0.98 nm. To further validate the result obtained from the STEM images, we combined a theoretical model to derive the thickness of the monolayer Ti3C2Tx. The model predictions were consistent with the experimental results, further supporting the thickness value of 0.98 nm. Notably, this value has been widely used in the literature. Therefore, this value is supported by both STEM measurements and theoretical models (Fig. 2f).

In situ shear test of monolayer Ti3C2Tx nanosheets
To study the in-plane shear performance and mechanical behavior of monolayer Ti3C2Tx nanosheets, displacement-controlled in situ shear tests were conducted using a PTS device within the SEM chamber. During the shear test, it is necessary to avoid slippage between the sample and the device, as this could affect the experimental results. Therefore, we deposited a Pt strip on both ends of the sample for reinforcement, ensuring that both ends of the sample remained securely adhered to the device. As a result, no slippage was observed throughout the experiment. The entire experimental process was observed and recorded in real time (Supplementary Movie 1).

Before the shear test, the probe was positioned near the top of the hemispherical indenter on the PTS device and aligned on the same horizontal plane. The load-displacement curve began to be recorded as soon as the probe made contact with the PTS device (Fig. 3a). In the initial stage (as indicated by the red arrow), the monolayer Ti3C2Tx nanosheets were subjected to in-plane shear force and began to shear in situ. In mechanical testing of 2D materials, enlarging the lateral dimensions of the specimen (while keeping the thickness constant) generally mitigates size-dependent effects and yields measurements that better reflect the intrinsic mechanical properties. To validate this, we performed preliminary experiments and simulations on samples with varying widths, and found that the measured shear response approached the intrinsic behavior when the sample width exceeded 5 μm (Supplementary Figs. 11 and 12, Supplementary Tables 1 and 2). Considering the reliability of the measurements, the initial dimensions of monolayer Ti3C2Tx, the inevitable size loss during the experimental process, and the challenges associated with transfer. The actual dimensions of the sample in the test area were 4.5 μm in length and 5.5 μm in width, with a monolayer thickness of 0.98 nm. By subtracting the inherent stiffness of the PTS device and incorporating these dimensional parameters, the actual 3D in-plane shear modulus of the monolayer Ti3C2Tx was calculated to be ~278.8 GPa. In the second stage, a gradual decrease in the actual shear stiffness of the sample was observed (as indicated by the green arrow). However, the sample did not exhibit the expected wrinkling instability behavior of 2D material, and still maintained strong wrinkle resistance. In the third stage, the monolayer Ti3C2Tx was further subjected to shear loading, and the effective shear modulus eventually stabilized at ~110.7 GPa. Ultimately, the sustained shear load led to brittle fracture of the sample starting from the position marked with a purple asterisk, after which the probe began to unload. It should be noted that the effective shear modulus in this context denotes a representative engineering shear modulus derived from the actual experimental conditions. Through SEM snapshots of the samples before and after shear testing, the maximum shear strain of the monolayer Ti3C2Tx can be obtained to be 8.9% (Fig. 3b), which illustrates the potential of Ti3C2Tx in device applications. Determining the shear modulus of monolayer Ti3C2Tx nanosheets remains highly challenging, as it is essential to ensure the integrity and high quality of the monolayer 2D material during the transfer process. Although multiple monolayer Ti3C2Tx nanosheets were used in our study, only seven tests were successfully performed. This is primarily due to the inherently fragile structure of monolayer 2D materials, which makes them highly susceptible to damage during the transfer process. Additionally, surface contamination is often introduced during transfer, which can adversely affect the material’s properties and compromise the accuracy of subsequent test results. Therefore, the key to improving the success rate and reproducibility of testing 2D materials lies in the ability of researchers to select the appropriate material transfer technique based on the specific properties of the material, ensure sample cleanliness, avoid sample damage, precisely secure the sample, and choose suitable testing methods. Table 1 summarizes the geometry, shear modulus, maximum shear strain, and shear fracture strength of the tested samples with a width of 5.5 μm. The average shear modulus in the first stage is 278.8±7.4 GPa, the average shear modulus in the third stage remains at 110.7±9.7 GPa, and the average shear fracture strength is 18.6±2.0 GPa. Notably, in conventional wet-transfer methods with polymer protection layers, 2D materials are anchored onto nanomechanical devices through van der Waals interactions. Pre-strain is often introduced due to capillary contraction, surface tension during the dissolution of the polymer protection layer, and the interfacial van der Waals forces. In contrast, in this work, monolayer Ti3C2Tx was dry-transferred using a micromanipulator under SEM, enabling precise pickup and release of the flakes. The subsequent localized Pt fixation at the sample edges imposed minimal disturbance on the suspended area, thereby substantially reducing pre-strain effects. Prior to the formal tests, a small cyclic load was applied to release the pre-strain introduced during the transfer and fixation processes. Specifically, sample #4 was subjected to 19 loading cycles at 8–10% of the maximum load (Supplementary Fig. 13), which effectively eliminated the pre-strain. The obtained results were consistent with those of the other three samples, confirming that pre-strain had no effect on the measurements. Furthermore, STEM imaging and geometric phase analysis (GPA) mapping of the samples prior to testing also verified the absence of pre-strain (Supplementary Fig. 14).

Methods
Sample preparation for shear tests
Due to the size requirement of the test area of the PTS device and the size loss during the transfer process, the improved minimally intensive layer delamination (MILD) method is required to synthesize large-size monolayer Ti3C2Tx nanosheets (Supplementary Fig. 1). Specifically, we selected 200 mesh (74 μm) of MAX phase Ti3AlC2, and used the mild etching method of HCl + LiF: 40 ml of 6 mol/L HCl and 1.6 g LiF were mixed in a polytetrafluoroethylene (PTFE) beaker, stirred with a magnetic stirrer for 15 min to completely dissolve, then slowly add 1 g Ti3AlC2, seal the beaker with a sealing film. The PTFE beaker was sealed with sealing film, and several small holes were pricked on the surface to exclude the gas escaping from the reaction. The Ti3AlC2 was etched in a water bath at 35 °C for 30 h. After the reaction was completed, the solution was washed twice with 1 mol/L HCl to remove the excess LiF, and then washed several times with deionized water until the pH of the solution was neutral. The obtained solution was subjected to vacuum-assisted filtration, the precipitate was collected, and dried in vacuum at 50 °C for 12 h. The dried multilayer Ti3C2Tx powder was redispersed with 50 ml of deionized water, and the solution was treated with a spin shaker for 30 min, and centrifuged at 684.8 × g for 30 min. The dark green upper colloid solution was taken out, which was the high-quality and large-size monolayer Ti3C2Tx suspension.

In situ SEM shear testing
In situ shear tests of monolayer Ti3C2Tx nanosheets were carried out in the chamber of Carl Zeiss CossBeam 340 SEM, utilizing the Bruker s-Hysitron PI88 pic indenter (Supplementary Fig. 22a) to load the hemispherical indenter of the PTS device (Supplementary Fig. 22b). Prior to testing, an air calibration of the PI88 was required, followed by pushing force applied to the PTS device using a displacement control of 10 nm/s. The PTS device converts pushing force into shear force on the sample through four springs. During testing, the Pico-Indenter applied force electrostatically while simultaneously measuring displacement capacitively, enabling load and displacement data to be recorded with sub-μN and sub-nm resolution, respectively. The integrated controller provided feedback stability and high-speed data acquisition, allowing real-time synchronization of load-displacement curves with in situ SEM movie imaging. The PTS device also acted as a strain sensor and energy buffer, ensuring accurate strain measurement during tensile loading. The accuracy of the mechanical parameters was ensured by minimizing instrument compliance, thermal drift, and alignment errors. The load-displacement data in the experiment were recorded by the mechanical sensors on the PI88 probe, and the in situ shearing process was also recorded in real time by movie, and the shear strain of the sample could be measured directly from the in situ shearing movie. The boundary conditions of the tested specimen are illustrated in Supplementary Fig. 23, where the locations of the Pt strips are clearly specified, including the no-slip positions and the defined testing area. The slope of the load-displacement curve experimentally determined is the total shear stiffness of the sample and the PTS device. By subtracting the inherent stiffness of the PTS device, the calculation of the monolayer Ti3C2Tx shear performance can be achieved. Specifically, the 3D shear modulus of the monolayer Ti3C2Tx sample: G3D = C * W / (b * h), C, W, b, and h in the formula represent the shear stiffness of the sample in the test area, the gap length of the PTS device, width, and thickness of the sample, respectively. Here, the PTS gap length W is 4.5 μm, and the sample width b is 5.5 μm. The thickness of the sample is selected as the nominal thickness of 0.98 nm for monolayer Ti3C2Tx, which is supported by STEM and DFT theoretical models, and is consistent with the thickness selection principle of the monolayer graphene. The shear strength: τ = F / (b * h), and shear strain: γ = δ / W, F in the formula is the shear force applied to the sample, and δ is the relative displacement on both sides of the sample. It can be calculated that the ultimate shear strength is ~18.6 GPa and the maximum shear strain is ~8.6%. The 2D shear modulus G2D of monolayer Ti3C2Tx is listed in Supplementary Table 4. In practical applications, the effect of thickness plays a crucial role in determining the mechanical performance. Therefore, adopting the 3D shear modulus G3D provides a more comprehensive representation of the mechanical properties of monolayer Ti3C2Tx. Accordingly, the 3D shear modulus G3D is employed in the present discussion.

Molecular dynamics (MD) simulation
To verify the mechanical behavior of the monolayer Ti3C2Tx sample during shear loading and to understand the reasons for the slight decrease in the shear modulus, we use MD simulations to reproduce the experimental phenomenon. All simulations are performed on a large-scale atomic/molecule massively parallel simulator (LAMMPS). The modeling sizes of the monolayer Ti3C2Tx are 400 Å × 320 Å, and the upper and lower edges of the monolayer Ti3C2Tx are fixed to apply shear strain at a constant rate of 0.001 ps−1. The temperature is maintained at 300 K, and the temperature rise during loading is within 10 K. The COMB3 potential function is used to set the interaction forces between atoms in the Ti3C2Tx model. The Open Visualization Tool (OVITO) is used to visualize the results of in situ shear simulations of monolayer Ti3C2Tx.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "General comments: This study examines the shear properties of 2D Mexene sheet, deriving its shear modulus and fracture strength based on push to shear devices installed in SEM. The authors claim that they standardized the testing method for the intrinsic shear modulus of 2D materials. However, I cannot accept this claim without reservations. In recent work reported in Nat Commun (2024, 15,4033) by Hou et al., similar testing facilitates were employed, and they indicated that there was significant measurement errors associated with this method, even for monolayer MoS2 sheet. Thus, it is unclear how these critical issues were overcome in the current work. The results summarized in Table 1 ( 3 samples) are consistent, but no visible development of periodic wrinkle patterns was observed during shear deformation process. Therefore, it is uncertain whether the stress -strain curve obtained in this work relate to the actual shear deformation of 2D sheet. Furthermore, although the state-of-art of nanomechanical testing methods are discussed, none of the cited references (e.g. 13-18) are closely related to the shear deformation of 2D materials, except for Ref 35. The second paragraph of the introduction part is somewhat irrelevant to the present work. As this study focused on the intrinsic parameter test of 2D materials, it will be useful for future researchers to investigate the effects of pre-strain, crystalline orientation, deformation rate, boundary conditions and dose of ion beam on the derived shear modulus of 2D materials. The force-displacement curve exhibited a nonlinear profile, where was classified it into three regions by the authors. The absence of visible wrinkle patters suggest that the derived modulus may be influenced by factors beyond material itself, as previously mentioned.\nSpecific comments:\n1. The use of shear modulus of monolayer graphene sheet in this study may not present a compelling argument for discussion. It might be more effective to consider materials such as TMD for this discourse.\n2. It is strongly suggested that the authors revise the second paragraph of their paper, as its content appears to be peripheral to the main subject matter of the work.\n3. In standard shear testing, the deformation is expected to be symmetrical. However, due to the constraints of the PTP device, the shear deformation becomes asymmetrical, which could potentially influence derived parameter. A comment addressing this issuce would be appreciated.\n4. Dose the sample’s geometry have any bearing on the test results?\n5. The author conducted MD simulration for the MXene sheet. What was the outcome of the force displacement curve based on MD simulation?\n6. The shear modulus of Mxene sheet was derived from region I, yielding an exceptionally high shear modulus (~300 GPa). How can the effect of prestrain can be mitigated in stage I?", "reviewer_2": "This study aims to investigate the shear properties of monolayer Ti3C2Tx nanosheets through direct in-situ shear testing. Utilizing a push-to-shear approach within a scanning electron microscope, the shear modulus and the shear strength of monolayer Ti3C2Tx were directly measured. Additionally, the high shear modulus endows monolayer Ti3C2Tx with stable wrinkle resistance. These findings underscore the potential of Ti3C2Tx to maintain device performance and reliability. However, some issues need to be addressed prior to publication.\n1. In section 2.3, the authors stated that “In the third stage, continuous shear loading caused the sample to experience brittle fracture, starting from the purple star. The probe then began to unload, and the effective shear modulus of the monolayer Ti3C2Tx decreased slightly, stabilizing at ~111.7 GPa.” Can you explain whether the fracture continued throughout the third stage? When did unloading performed? Why was the effective modulus used and what is the definition of the “effective modulus”?\n2. In the in-situ shear test, the authors should provide more experimental details, For example, the authors should explain how to obtain coordinate parameters (Load and Displacement in Fig.3) and describe the corresponding experimental setup? The accuracy of these parameters should also be determined. Moreover, a more detailed description of the boundary conditions should be provided. The position of the Pt strip should be specified, as well as the no slippage position and the range of the testing area.\n3. The variations in the slope of the load-displacement curves observed in Figure 3 for single-layer Ti₃C₂Tₓ reflect different deformation mechanisms in stages 1, 2, and 3, each of which necessitates a comprehensive elucidation. Table 1 provides the shear modulus values for the sample at stage 1 and stage 3, respectively, but why the shear modulus in stage 2 is absent?\n4. In the PTS strategy employed in this study, the specimen is placed within the side gap of the push-to-pull device. Given the asymmetrical nature of the structure when shear load is applied, it is crucial for the authors to evaluate whether the specimen experiences pure shear deformation under this loading condition. It is worth noting that the PTS device was originally designed to accommodate unidirectional tensile loading, commonly referred to as push-to-pull loading. The utilization of this device for shear loading, particularly for measuring the high shear strength of single-layer Ti₃C₂Tₓ, introduces a unique set of considerations. The paper should therefore include a discussion on whether this specific loading method has any implications for the performance of the PTS device.\n5. The authors assert in the article that they synthesized high-quality monolayer Ti3C2Tx nanosheets. However, local transmission electron microscope images alone are insufficient to support this claim. The authors are encouraged to provide additional evidence to support the quality and characteristics of the synthesized nanosheets?6. The author used molecular dynamics simulations to reveal the mechanism behind the Ti3C2Tx's resistance to wrinkling. Could molecular dynamics simulations be used to provide more results for comparison with experiments, such as shear modulus, shear strength and stress-strain curve?\n7. In the molecular dynamics simulation, the COMB3 potential function is used to set the interaction forces between atoms in the Ti3C2Tx model. Is there any basis for choosing this potential function?\n8. The authors should provide a detailed description of the methodology used to determine the nominal thickness value of the monolayer Ti3C2Tx, which was reported as 0.98 nm in this study.\n9. In the article, the shear modulus of the material in the first stage was 278 GPa and the Young's modulus is around 484 GPa. Therefore, if we assume that the monolayer Ti3C2Tx is isotropic material, the Poisson's ratio of the material for the first stage can be estimated as -0.129, which indicated that the material was a negative Poisson's ratio material? Is this reasonable?\n10. The comparison of the shear properties between monolayer Ti₃C₂Tₓ and monolayer graphene, as presented in the article, warrants careful consideration. While the study claims that Ti₃C₂Tₓ exhibits superior shear properties compared to graphene, the structural differences between the two materials introduce complexities that affect the validity of such a direct comparison.\n11. In section 3, the authors claim that “Our research uncovers the performance enhancement mechanism at the smallest unit of the material microstructure.” However, this statement is not appropriate, as the study does not provide a detailed enhancement mechanism at the smallest unit of the material microstructure.", "reviewer_3": "The article titled “Shear Properties and Stable Wrinkle Resistance in 2D Ti3C2Tx MXene Monolayers” by Rong et al. presents a groundbreaking study that addresses a critical gap in the characterization of 2D materials. The development of a novel in-situ push-to-shear strategy using a scanning electron microscope represents a significant methodological advancement, allowing for the first direct measurement of intrinsic in-plane shear properties of monolayer Ti3C2Tx. The reported exceptionally high shear modulus and strength, along with stable wrinkle resistance, challenge previous assumptions about the performance of 2D materials. While the results are intriguing and significant, several points require clarification and improvement:\n1. Given that this study focuses on the in-plane mechanical properties of 2D materials, it would be better to use the 2D shear modulus (in N/m) rather than the 3D one (in GPa). This is because 2D values are independent of the material's thickness, more accurately reflecting the in-plane properties.\n2. One of the most challenging aspects of the molecular dynamics (MD) simulation of MXene is constructing the appropriate atomic models to represent Tx, the terminal groups with differing concentrations. Many previous density functional theory (DFT) studies have demonstrated that these terminal groups can impact their in-plane mechanical properties. It is well known that manipulating the terminal groups on MXene in experiments is difficult. However, it is unclear how the atomic model for the MD simulation was constructed. It would be beneficial to elaborate on how the Ti3C2Tx model was developed in the main text or supporting information.\n3. Many details regarding the MD simulation are missing.\n4. It is unnecessary to mention nitrides in the first sentence of the abstract, as they were not included in this study.\n5. Could the authors provide the main structural differences of Ti3C2X2 across the three different stages? If these differences cannot be observed through experimental characterizations, can the MD simulations offer insights? Such information may help explain the reduced in-plane shear modulus value at Stage 3.\n6. The authors note, “Although multiple monolayer Ti3C2Tx nanosheets were used in our study, only three tests were successfully performed.” Could they briefly discuss why these experiments are so challenging? This information might help other researchers attempt similar studies."}, "author_response": "Response to Reviewers\nReviewer #1\nGeneral comments: This study examines the shear properties of 2D MXene sheet,\nderiving its shear modulus and fracture strength based on push to shear devices\ninstalled in SEM. The authors claim that they standardized the testing method for the\nintrinsic shear modulus of 2D materials. However, I cannot accept this claim without\nreservations. In recent work reported in Nat Commun (2024, 15,4033) by Hou et al.,\nsimilar testing facilitates were employed, and they indicated that there was significant\nmeasurement errors associated with this method, even for monolayer MoS sheet.\nresults summarized in Table 1 (3 samples) are consistent, but no visible development\nof periodic wrinkle patterns was observed during shear deformation process.\nTherefore, it is uncertain whether the stress -strain curve obtained in this work relate\nto the actual shear deformation of 2D sheet. Furthermore, although the state-of-art of\nnanomechanical testing methods are discussed, none of the cited references (e.g. 13-\n18) are closely related to the shear deformation of 2D materials, except for Ref 35.\nThe second paragraph of the introduction part is somewhat irrelevant to the present\nwork. As this study focused on the intrinsic parameter test of 2D materials, it will be\nuseful for future researchers to investigate the effects of pre-strain, crystalline\norientation, deformation rate, boundary conditions and dose of ion beam on the\nderived shear modulus of 2D materials. The force-displacement curve exhibited a\nnonlinear profile, where was classified it into three regions by the authors. The\nabsence of visible wrinkle patters suggest that the derived modulus may be influenced\nby factors beyond material itself, as previously mentioned.\nResponse: We are grateful for the reviewer’s kind comments and suggestions.\nThe scientific nature of this paper was improved, especially on the legitimacy of\nPTS device and the reliability of experimental results, by absorbing the\nsuggestions. It is worth noting that the study in Nat. Commun. (2024, 15, 4033)\ninvestigated the wrinkle instability of monolayer graphene and MoS ,\n2\ndemonstrating that the wrinkle instability of materials affects their mechanical\nproperties. However, this instability can also be quantitatively controlled.\nMeanwhile, Hou et al. measured the shear modulus of monolayer graphene to be\n~70 GPa using the PTS device, without specifying whether this device introduces\nsignificant measurement errors. In our shear tests of monolayer Ti C T\n3 2 x\nnanosheets, the material exhibited exceptional resistance to wrinkling due to its\nintrinsic properties, which is why the measurement results are consistent.\nAdditionally, we excluded external factors other than the material itself that might\naffect the experimental results. Below are addressed all the comments point by\npoint:\n1. The use of shear modulus of monolayer graphene sheet in this study may not\npresent a compelling argument for discussion. It might be more effective to\nconsider materials such as TMD for this discourse.\nResponse: We appreciate the reviewer’s suggestion. We chose to discuss the\nshear modulus of monolayer graphene based on the following three\nconsiderations:\n(1) Practical application scenarios of 2D materials: The excellent electrical\nconductivity, mechanical properties, and solution processability of Ti C T\n3 2 x\nMXene make it one of the most promising alternatives to graphene. Specifically,\nthe large-scale fabrication of nanomaterials into self-supporting films with high\nconductivity and outstanding mechanical properties is crucial for advancing\nvarious applications in flexible electronics, electromagnetic interference shielding,\nand supercapacitors. However, the core challenge in achieving this goal lies in\nfinding nanomaterials with both intrinsic high strength and excellent conductivity.\n(Advanced Materials 2020, 32, 2001093) Among various 2D materials,\nhexagonal boron nitride is non-conductive, transition metal dichalcogenides\n(TMDs, such as MoS ) have relatively low conductivity, while graphene\n2\npossesses both extremely high conductivity and strength, making it widely\nregarded as the strongest material known to date. Graphene has been applied in\nflexible electronics, energy storage, and electromagnetic shielding. However, its\npoor dispersion during processing limits its large-scale applications. In the search\nfor 2D materials with excellent elasticity and conductivity, Ti C T is the first and\n3 2 x\nmost widely studied MXene material discovered. It exhibits higher conductivity\nthan graphene prepared via solution methods, along with excellent\nelectrochemical properties, showing great potential in energy storage and flexible\nelectronics. Monolayer Ti C T nanosheets are considered the material of choice\n3 2 x\nfor future flexible electronics, energy storage, and electromechanical nanodevices.\nIn contrast, the low conductivity of TMDs limits their widespread use, so\ncomparing Ti C T with TMDs is of little significance.\n3 2 x\n(2) Graphene as a prototype system for the study of 2D material mechanical\nproperties: Graphene is commonly viewed as a prototype system for studying\nthe mechanical properties of 2D materials, and its mechanical properties are\nrepresentative and universal. In other research works, the mechanical properties\nof 2D materials with different atomic layer structures are typically compared to\ngraphene, which does not affect the validity of the comparison. (Science\nAdvances 2018, 4, eaat0491; Nature Communications 2024, 15, 1566;\nAdvanced Electronic Materials 2020, 1901382) This is because graphene is\nconsidered the material with the strongest known mechanical properties, and its\nmechanical properties are typically used as a benchmark.\n(3) The shear properties of monolayer graphene have been extensively\nstudied, while the shear mechanical properties of TMDs have not been fully\nexplored: Currently, only the in-plane shear mechanical properties of monolayer\ngraphene have been extensively reported in both experimental and simulation\nstudies. Due to the limitations of testing techniques, in-plane shear tests on\nmonolayer 2D materials are still in the early stages. As a result, the shear modulus\nof TMDs has not been determined, and the shear properties of TMDs have not\nbeen fully explored. Therefore, a comparison of the shear properties of Ti C T\n3 2 x\nMXene and TMDs is not yet possible. Our future work may further expand to\ndiscuss the relevant properties of TMDs materials.\nFor the reasons outlined above, we have selected monolayer graphene as a\nreference in this study and conducted a comparative analysis with monolayer\nTi C T . To strengthen the discussion of the shear modulus of monolayer\n3 2 x\ngraphene in this study, we have added supplementary content to the original\ndiscussion to highlight the performance advantages of Ti C T and support our\n3 2 x\nresearch argument:\n“In this study, the shear modulus of monolayer graphene is chosen as the\nreference, based on the practical application scenarios of 2D materials, and\ngraphene is also a typical benchmark in the research of the mechanical\nproperties of 2D materials. Specifically, the large-scale fabrication of\nnanomaterials into self-supporting films with both high electrical conductivity\nand excellent mechanical properties is key to advancing the development of\nvarious applications, such as flexible electronics, electromechanical nano-devices,\nsupercapacitors, sensors, and electromagnetic interference shielding51,52.\nHowever, the core challenge in achieving this goal lies in finding nanomaterials\nthat combine both high strength and excellent conductivity53. Among existing 2D\nmaterial systems, hexagonal boron nitride is non-conductive54, and transition\nmetal dichalcogenides (TMDs, such as MoS ) have relatively low conductivity55.\nstrength, and is widely regarded as the strongest known material to date, making\nit applicable in flexible electronics, energy storage, and electromagnetic\nshielding56. However, the poor dispersion of graphene during processing limits its\nlarge-scale applications57. In the exploration of other 2D materials with excellent\nelasticity and conductivity, MXenes have emerged as ideal candidates. Among\nthem, Ti C T is the earliest discovered and most extensively studied MXene\n3 2 x\nmaterial. Solution-processed Ti C T exhibits conductivity significantly higher\n3 2 x\nthan that of graphene and demonstrates outstanding electrochemical\nperformance, offering great potential for applications in energy storage and\nflexible electronics. Monolayer Ti C T nanosheets are excellent building blocks\n3 2 x\nfor constructing micro-/nanoelectromechanical devices and wearable\nelectronics58,59. In the realm of 2D materials, the robust mechanical properties,\nand solution processability of Ti C T MXene make it a promising alternative to\n3 2 x\n2D materials such as graphene. It is worth emphasizing that monolayer graphene\nis often regarded as a “prototype system” in the research of 2D materials, as its\nmechanical properties are representative and universal, making it suitable as a\ncomparative benchmark27,29,60. Based on the aforementioned reasons, we selected\nmonolayer graphene as the reference in this study and performed a comparative\nanalysis with monolayer Ti C T to highlight the performance advantages of\n3 2 x\nTi C T and support the research discussion.”\n3 2 x\n2. It is strongly suggested that the authors revise the second paragraph of their\npaper, as its content appears to be peripheral to the main subject matter of the\nwork.\nResponse: We thank the reviewer for this feedback. We have supplemented the\nsecond paragraph of the paper to enhance the narrative logic. In fact, the key\npoint we aim to convey is that previous research in the field of 2D material\nmechanics has mainly focused on studying the shear properties at the\nsurface/interface. However, the interface often obscures the intrinsic shear\ncharacteristics of 2D materials, and these methods do not directly measure the\nintrinsic shear properties of the materials themselves. Therefore, new testing\ntechnologies are needed to study the intrinsic shear mechanical properties of 2D\nmaterials. This work overcomes the limitations of conventional micro- and\nnanomechanical techniques, which can only measure the surface-interfacial shear\nmodulus and interlayer shear stress of 2D materials (Physical Review Letters\n2017, 119, 036101; Nature Nanotechnology 2019, 14, 567; Nature\nCommunications 2022, 13, 3898). We have further revised the second paragraph:\n“Currently, the related work primarily focuses on investigating the interfacial\nshear modulus and interlayer shear stress of monolayer 2D materials, including\ntip-based adhesion measurement13,14, pressurized bubbling method15,16, and\natomic force microscopy (AFM) nanoindentation strategy17,18. However, these\nmethods make it difficult to reveal the in-plane shear behavior of 2D materials\nand obscure their intrinsic shear properties. Specifically, the tip-based adhesion\nmeasurement relies on the interaction between the probe with the sample surface.\nGuo’s team systematically studied the shear mechanical properties of the surface\nand interface of 2D materials using graphite-wrapped AFM probes, but could not\ndirectly measure the shear mechanical properties of the 2D materials\nthemselves19. The pressurized bubbling method employs uniform bubbles on the\nsurface of 2D materials to assess the shear mechanical properties. For instance,\nan interfacial shear stress of 1.64 MPa was determined by bubble loading\nmonolayer graphene on a silicon oxide substrate20. This technique, however, is\naffected by the unstable interfacial force between the 2D material and the\nsubstrate, necessitating an accurate assessment of the airtightness of the 2D\nmaterial. Additionally, the inhomogeneity of bubble expansion and stress\nconcentration impacts the measurement accuracy21. The AFM nanoindentation\nstrategy involves loading different layers of 2D materials suspended on a porous\nsubstrate, with the interlayer shear force determined by comparing and analyzing\nthe load-displacement curves22. However, nanoindentation method induces both\nuneven shear stress and tensile stress in the transverse test area of the 2D\nmaterial, and different indenter sizes and indentation locations contribute to\nsignificant uncertainty in the results23. In general, due to the limitations of\ncurrent testing techniques, the intrinsic shear properties and mechanical\nbehavior of 2D materials under in-plane shear loading are often overlooked. As\nhighlighted in recent in-plane shear studies, internal shear deformation plays a\ncrucial role in dictating both the mechanical stability and functional properties of\natomically thin materials24. Nevertheless, quantitative investigations of solution-\nprocessed Ti C T remain scarce. Therefore, there is an urgent need for a direct,\n3 2 x\nquantitative, and reliable approach to study the in-plane shear properties of\nmonolayer Ti C T nanosheets.”\n3 2 x\n3. In standard shear testing, the deformation is expected to be symmetrical.\nHowever, due to the constraints of the PTP device, the shear deformation\nbecomes asymmetrical, which could potentially influence derived parameter. A\ncomment addressing this issue would be appreciated.\nResponse: Thank you very much for your valuable comments. We have\nvalidated the effectiveness of the PTS nano-mechanical device under shear\nloading, ensuring that the Ti C T sample experiences pure shear deformation. In\n3 2 x\nthe in-plane shear test for 2D materials, it is crucial to keep one side of the sample\nfixed while applying a parallel tangential displacement on the opposite side,\nwhich the PTS device achieves efficiently. We will first explain this from the\nperspective of the testing principle of the PTS device, as shown in Figure a-b\nbelow. The PTS device consists of a movable plate (purple area) and a fixed plate\n(gray area). When the hemispherical indenter is loaded, the purple movable plate\nmoves downward to apply force to the sample. During the loading process, the\nentire area beneath the hemispherical indenter constitutes the effective testing\narea of the sample (orange box), while the surrounding springs ensure the\nstability of the PTS device. Throughout the loading, the gap width remains\nunchanged (Figure c), allowing one side of the sample to remain fixed while the\nother side undergoes tangential displacement.\nIt is worth noting that the PTS device was originally designed for uniaxial\ntensile loading (commonly referred to as Push-to-Pull loading). In previous studies of\nuniaxial tensile tests on 1D nanowires (Science Advances 2016, 2, e1501382;\nNature Communications 2025, 16, 3265; Nano Letters 2011, 11, 3207) and 2D\nnanosheets (Nature Communications 2020, 11, 284; Journal of the Mechanics\nand Physics of Solids 2025, 200, 106151; Cell Reports Physical Science 2020, 1,\n100172), the samples in the testing region were well subjected to uniaxial tension,\nwithout any lateral displacement, which verified that the gap width remains\nunchanged during loading (Figure c). Additionally, recent studies have used the\nPTS device to probe the shear properties of monolayer graphene (Nature\nCommunications 2024, 15, 4033), further confirming that the device is suitable\nfor the study of in-plane shear properties of 2D materials.\nThe SEM images of the Ti C T sample during our experimental process (Figure\n3 2 x\nd) show that the gap width remains unchanged, confirming that the sample\nundergoes pure shear deformation, consistent with the testing conditions where\none side of the sample is fixed while the opposite side undergoes parallel\ntangential displacement. Moreover, our MD simulation results (The shear\nmodulus Gstage1 is ~294 GPa, and the shear fracture strength τ is ~19.7 GPa)\nmatch the experimental results (The shear modulus Gstage1 is ~279 GPa, and\nthe shear fracture strength τ is ~18.6 GPa), further validating the effectiveness of\nthe shear test.\nTo avoid confusion for reviewers and readers, we have provided an explanation in\nthe manuscript:\nSupplementary Fig. 2 Validation of the effectiveness of PTS nanomechanical\ndevices in shear loading. (a) Schematic 3D illustration showing the working\nmechanism of the PTS nano-device. The device is divided into two regions: the\npurple region corresponds to the movable plate, while the gray region represents\nthe fixed plate. (b) Upon loading of the movable plate, the region beneath the\nhemispherical indenter is defined as the effective testing area of the sample,\nwhereas the springs around the device maintain its stability. (c) Enlarged view of\nthe sample testing area. During the loading process, the gap width remains\nunchanged, enabling one side of the sample to be fixed while applying a\ntangential displacement on the opposite side. As a result, the tested sample\nundergoes pure shear deformation. (d) The SEM image of the tested sample\nduring the experiment shows that the gap width remains unchanged, confirming\nthat the sample was subjected to pure shear deformation, consistent with the\ntesting condition in which one side of the sample is fixed while a parallel\ntangential displacement is applied to the opposite side.\n“It is worth noting that the PTS device was originally designed for uniaxial\ntensile loading (commonly referred to as push-to-pull loading). Here, it is\nemployed to perform shear loading on monolayer Ti C T for shear strength\n3 2 x\nmeasurement, with a discussion on the validity of the shear testing to demonstrate\nthat the specimen experienced pure shear deformation. As shown in\nSupplementary Fig. 2a-b, the PTS device consists of a movable plate (purple\nregion) and a fixed plate (gray region). When the hemispherical indenter is\nloaded, the purple movable plate translates downward to apply force on the\nspecimen. Under loading, the entire region beneath the hemispherical indenter\nconstitutes the effective testing area of the specimen (the boxed orange region),\nwhile the surrounding springs ensure the stability of the device. During the\nloading process, the gap width remains unchanged (Supplementary Fig. 2c),\nenabling one side of the specimen to be fixed while a tangential displacement is\napplied to the opposite side. Consequently, the specimen at the device side gap\nundergoes pure shear deformation. SEM images taken during the test further\nshow that the gap width does not change (Supplementary Fig. 2d), confirming\nthat the specimen experiences pure shear deformation, consistent with the testing\nrequirement of fixing one side while applying a parallel tangential displacement\nto the other side.”\n4. Dose the sample’s geometry have any bearing on the test results?\nResponse: We thank the reviewer for the constructive suggestion. Indeed, in the\nmechanical testing of 2D materials, increasing the sample size typically reduces\nthe influence of geometric size effects and allows for a closer approximation of\nthe material’s true mechanical properties. In fact, during our actual testing process,\nwe chose a monolayer Ti C T sample with an actual size of 4.5 μm in length\n3 2 x\n(which also corresponds to the gap size of the PTS device testing area) and 5.5\nμm in width, and this choice is well-founded. The selection of this sample size\nwas based on our preliminary experimental results. We compared the test results\nof samples with different sizes (with widths of 3.5 μm, 4.5 μm, 5.5 μm, and 6.5\nμm), as well as the simulation results (with Width-to-Length ratios b/W of 0.5,\n0.75, 1, 1.25, 1.5, and 2), and found that when the sample width exceeded 5 μm,\nthe results were closer to the material’s true shear properties. In the formal\nexperiment, considering factors such as the validity of the test results, the initial\nsize of the monolayer Ti C T , size loss during the experiment (due to Pt fixing\n3 2 x\nand FIB milling), and the difficulty of transferring larger samples (the larger the\nsample, the harder the transfer), we selected a sample with a width of 5.5 μm for\nthe formal test. We have also explained this point in the manuscript:\n“In mechanical testing of 2D materials, enlarging the lateral dimensions of the\nspecimen (while keeping the thickness constant) generally mitigates size-\ndependent effects and yields measurements that better reflect the intrinsic\nmechanical properties33. To validate this, we performed preliminary experiments\nand simulations on samples with varying widths, and found that the measured\nshear response approached the intrinsic behavior when the sample width\nexceeded 5 μm (Supplementary Fig. 11-12, Supplementary Table 1-2).\nConsidering the reliability of the measurements, the initial dimensions of\nmonolayer Ti C T , the inevitable size loss during the experimental process, and\n3 2 x\nthe challenges associated with transfer. The actual dimensions of the sample in\nthe test area were 4.5 μm in length and 5.5 μm in width, with a monolayer\nthickness of 0.98 nm.”\nSupplementary Fig. 11 Experimental investigation of the geometric size effect\non the shear properties of monolayer Ti C T MXene nanosheets. (a) Shear\n3 2 x\nmodulus Gstage1 values of monolayer Ti C T samples with different widths. (b)\n3 2 x\nShear fracture strength τ values of monolayer Ti C T samples with different\n3 2 x\nwidths. The tested sample with a width of (c) 3.5 μm, (d) 4.5 μm, (e) 5.5 μm, (f)\n6.5 μm.\nSupplementary Fig. 12 MD simulation investigation of the geometric size effect\non the shear properties of monolayer Ti C T MXene nanosheets. (a) The\n3 2 x\ncorresponding stress-strain curve in Figure 4c. (b) Shear modulus Gstage1 values\nof monolayer Ti C T samples with different b/W ratios. (c) Shear fracture\n3 2 x\nstrength τ values of monolayer Ti C T samples with different b/W ratios. The\n3 2 x\ntested sample with a b/W ratio of (d) 0.5, (e) 0.75, (f) 1, (g) 1.25, (h) 1.5, (i) 2.\nSupplementary Table 1. Experimental shear properties of monolayer Ti C T of\n3 2 x\ndifferent geometric sizes under in-plane shear loading.\nSample Width Length Shear Shear Fracture Fracture\n# modulus modulus strain strength\nb W\n𝑺𝒕𝒂𝒈𝒆𝟏 𝑺𝒕𝒂𝒈𝒆𝟑\n𝑮 (GPa) 𝑮 (GPa)\n𝟑𝑫 𝟑𝑫 γ τ\n(μm) (μm)\n(%) (GPa)\n1 3.5 4.5 162.4 73.6 9.3 10.6\n2 4.5 4.5 261.3 91.5 8.9 16.1\n3 6.5 4.5 281.2 112.3 8.3 18.6\nSupplementary Table 2. MD simulation results of the shear properties of\nmonolayer Ti C T of different sizes under in-plane shear loading.\n3 2 x\nSample Width/Length Shear Fracture\n# modulus strength\n(b/W)\n𝑺𝒕𝒂𝒈𝒆𝟏\n𝑮 (GPa)\n𝟑𝑫 τ\n(GPa)\n1 1/2 79.1 11.4\n2 3/4 186.2 16.2\n3 1 276.5 19.0\n4 5/4 293.6 19.5\n5 3/2 294.3 19.7\n6 2 294.5 19.8\n5. The author conducted MD simulation for the MXene sheet. What was the\noutcome of the force displacement curve based on MD simulation?\nResponse: We appreciate the reviewer’s suggestion. We have added the stress-\nstrain curve from the MD simulation in the manuscript. The curve obtained from\nthe simulation shows a slight decreasing trend in shear modulus, which is similar\nto the experimental results. The simulated values of shear modulus and shear\nstrength also align with the experimental results. It is important to note that the\nmain purpose of the MD simulation is to understand the mechanism behind the\nslight decrease in the shear modulus of monolayer Ti C T , rather than simply to\n3 2 x\naccurately replicate the force-displacement curve measured in experiments.\nAchieving perfect agreement between the experimental and simulation curves is\nnot the primary goal of this work. Therefore, in the MD simulation, we focus only\non the intrinsic shear modulus of monolayer Ti C T (Gstage1) and the shear\n3 2 x\nfracture strength (τ). We have provided this additional explanation in the\nmanuscript:\n“This phenomenon is further corroborated by the stress-strain curve from MD\nsimulations: at the onset of shear loading, the monolayer Ti C T underwent\n3 2 x\nuniform shear deformation, with a simulated shear modulus of ~294 GPa,\nmaintaining a high shear modulus consistent with the experimental observations\n(Supplementary Table 2). As the loading progressed, however, the atoms in the\nTi C T lattice were severely compressed, localized strain emerged\n3 2 x\n(Supplementary Fig. 16), and the shear modulus of the monolayer Ti C T\n3 2 x\nexhibited a slight decline (Supplementary Fig. 12a), in agreement with the\nexperimental trend.”\nSupplementary Fig. 12a. The stress-strain curve corresponding to the MD\nsimulation in Figure 4c.\n6. The shear modulus of MXene sheet was derived from region I, yielding an\nexceptionally high shear modulus (~300 GPa). How can the effect of prestrain\ncan be mitigated in stage I?\nResponse: We really appreciate this insightful question, which greatly improved\nthe quality of this work. As the reviewer mentioned, in previous studies,\nresearchers have indeed introduced pre-strain by using polymer-protected wet\ntransfer techniques. However, we effectively avoid this problem by using a\nmanipulator for dry transfer.\nTraditional wet transfer involves first transferring CVD-grown 2D materials onto\na metal substrate, followed by spin-coating a polymer protection layer onto the\nsurface of the 2D material. Then, metal etchants are used to remove the metal\nsubstrate. Next, the 2D material with the polymer protection layer is transferred\nto the nano-mechanical device, and the polymer layer is removed using organic\nsolvents to complete the process. The 2D material is fixed to the nano-mechanical\ndevice by van der Waals forces. However, due to capillary shrinkage, the surface\ntension from the removal process of the polymer protection layer, and the van der\nWaals forces between the sample and the device, pre-strain is usually introduced.\nIn contrast, we use a manipulator for the dry transfer of monolayer Ti C T ,\n3 2 x\nwhich allows precise picking and releasing of the 2D material under SEM. The\nboundaries of the sample are then precisely fixed with Pt, minimizing the effect\non the suspended portion. This greatly reduces the influence of pre-strain.\nIt is well known that applying a small cyclic load to the sample before formal\ntesting can release the pre-strain potentially introduced during the transfer and\nfixation process. Therefore, we applied a maximum load of 8%~10% to sample\n#4 and cycled it 19 times to eliminate any pre-strain effects before testing. The\nfinal results matched those of the other three samples #1~#3, confirming that pre-\nstrain had no effect on the test results. Additionally, STEM images and the\ncorresponding geometric phase analysis (GPA) mapping of the samples before\ntesting further confirmed the absence of pre-strain.\nWe have also provided a detailed explanation of this in the manuscript:\n“Notably, in conventional wet-transfer methods with polymer protection layers,\n2D materials are anchored onto nano-mechanical devices through van der Waals\ninteractions. Pre-strain is often introduced due to capillary contraction, surface\ntension during the dissolution of the polymer protection layer, and the interfacial\nvan der Waals forces36. In contrast, in this work, monolayer Ti C T was dry-\n3 2 x\ntransferred using a micromanipulator under SEM, enabling precise pickup and\nrelease of the flakes. The subsequent localized Pt fixation at the sample edges\nimposed minimal disturbance on the suspended area, thereby substantially\nreducing pre-strain effects. Prior to the formal tests, a small cyclic load was\napplied to release the pre-strain introduced during the transfer and fixation\nprocesses. Specifically, sample #4 was subjected to 19 loading cycles at 8~10% of\nthe maximum load (Supplementary Fig. 13), which effectively eliminated the pre-\nstrain. The obtained results were consistent with those of the other three samples,\nconfirming that pre-strain had no effect on the measurements. Furthermore,\nSTEM imaging and geometric phase analysis (GPA) mapping of the samples\nprior to testing also verified the absence of pre-strain (Supplementary Fig. 14).”\nSupplementary Fig. 13 Before the formal testing, a small cyclic load (8%~10%\nof the maximum load, 19 cycles) was applied to monolayer Ti C T sample #4 to\n3 2 x\nrelease the pre-strain potentially introduced by the transfer and fixation processes.\nTable 1. Shear properties of monolayer Ti C T under in-plane shear loading.\n3 2 x\nSample Width Length Shear Shear Fracture Fracture\n# modulus modulus strain strength\nb W\n𝑺𝒕𝒂𝒈𝒆𝟏 𝑺𝒕𝒂𝒈𝒆𝟑\n𝑮 (GPa) 𝑮 (GPa)\n𝟑𝑫 𝟑𝑫 γ τ\n(μm) (μm)\n(%) (GPa)\n1 5.5 4.5 274.1 103.8 8.9 17.2\n2 5.5 4.5 284.9 117.3 8.7 19.3\n3 5.5 4.5 276.5 114.0 8.2 19.9\n4 5.5 4.5 279.8 107.5 8.7 17.9\nAverage 278.8±7.4 110.7±9.7 8.6±0.5 18.6±2.0\nSupplementary Fig. 14 Characterization of monolayer Ti C T nanosheets\n3 2 x\nbefore the shear testing. (a) STEM images of monolayer Ti C T samples, and (b)\n3 2 x\nthe corresponding fast Fourier transform (FFT) patterns, and (c) the\ncorresponding geometric phase analysis (GPA) mapping confirmed the absence\nof pre-strain in the sample before testing.\nReviewer #2\nThis study aims to investigate the shear properties of monolayer Ti C T nanosheets\n3 2 x\nthrough direct in-situ shear testing. Utilizing a push-to-shear approach within a\nscanning electron microscope, the shear modulus and the shear strength of monolayer\nTi C T were directly measured. Additionally, the high shear modulus endows\n3 2 x\nmonolayer Ti C T with stable wrinkle resistance. These findings underscore the\n3 2 x\npotential of Ti C T to maintain device performance and reliability. However, some\n3 2 x\nissues need to be addressed prior to publication.\nResponse: We sincerely thank the reviewer for careful review and the\nconstructive suggestions towards improving our manuscript. The point-by-point\nresponses are shown below:\n1. In section 2.3, the authors stated that “In the third stage, continuous shear\nloading caused the sample to experience brittle fracture, starting from the purple\nstar. The probe then began to unload, and the effective shear modulus of the\nmonolayer Ti C T decreased slightly, stabilizing at ~111.7 GPa.” Can you\n3 2 x\nexplain whether the fracture continued throughout the third stage? When did\nunloading performed? Why was the effective modulus used and what is the\ndefinition of the “effective modulus”?\nResponse: Thank you very much for your comments, and I apologize for the\nconfusion caused. In fact, in the third stage, the monolayer Ti C T begins to\n3 2 x\nfracture at the purple asterisk, and prior to this, the sample has been under load.\nThe fracture of the sample does not occur continuously throughout the entire third\nstage; unloading occurs at the purple asterisk.\nAdditionally, in the field of mechanical testing of 2D materials, the effective\nmodulus is the representative engineering equivalent modulus measured under\nactual experimental conditions, a concept that has been widely used in other\nresearch works on the mechanical properties of 2D materials (Nature\nCommunications 2020, 11, 284; Science Advances 2018, 4, eaat0491). To avoid\nconfusion for reviewers and readers, we have provided an explanation in the\nmanuscript and made modifications to Figure 3a:\n“In the third stage, the monolayer Ti C T was further subjected to shear\n3 2 x\nloading, and the effective shear modulus eventually stabilized at ~110.7 GPa.\nUltimately, the sustained shear load led to brittle fracture of the sample starting\nfrom the position marked with a purple asterisk, after which the probe began to\nunload. It should be noted that the effective shear modulus in this context denotes\na representative engineering shear modulus derived from the actual experimental\nconditions.”\nFig. 3 Shear properties of monolayer Ti C T nanosheets. (a) The measured\n3 2 x\nload-displacement curves during shear loading, inserted into the formula (see\nSection 4.2 for details) can be used to calculate the 2D and 3D shear modulus G\nof the nanosheets, and the shear fracture strength τ, where C, W, b, h, δ, γ are the\nshear stiffness, the gap length of the PTS device, width, and thickness of the\nsample, relative displacement, and shear strain, respectively. (b) The tested\nsamples are sheared in-plane until fracture with a maximum strain at fracture of\n8.9 %.\n2. In the in-situ shear test, the authors should provide more experimental details.\nFor example, the authors should explain how to obtain coordinate parameters\n(Load and Displacement in Fig.3) and describe the corresponding experimental\nsetup? The accuracy of these parameters should also be determined. Moreover, a\nmore detailed description of the boundary conditions should be provided. The\nposition of the Pt strip should be specified, as well as the no slippage position and\nthe range of the testing area.\nResponse: We appreciate this precious suggestion by the reviewer, which has\nbeen very helpful in improving the manuscript. We have provided more\nexperimental details and a detailed description of the boundary conditions. These\nadditions have been included in the manuscript:\n“As shown in Supplementary Fig. 2a-b, the PTS device consists of a movable\nplate (purple region) and a fixed plate (gray region). When the hemispherical\nindenter is loaded, the purple movable plate translates downward to apply force\non the specimen. Under loading, the entire region beneath the hemispherical\nindenter constitutes the effective testing area of the specimen (the boxed orange\nregion), while the surrounding springs ensure the stability of the device. During\nthe loading process, the gap width remains unchanged (Supplementary Fig. 2c),\nenabling one side of the specimen to be fixed while a tangential displacement is\napplied to the opposite side.”\nSupplementary Fig. 2 Validation of the effectiveness of PTS nanomechanical\ndevices in shear loading. (a) Schematic 3D illustration showing the working\nmechanism of the PTS nano-device. The device is divided into two regions: the\npurple region corresponds to the movable plate, while the gray region represents\nthe fixed plate. (b) Upon loading of the movable plate, the region beneath the\nhemispherical indenter is defined as the effective testing area of the sample,\nwhereas the springs around the device maintain its stability. (c) Enlarged view of\nthe sample testing area. During the loading process, the gap width remains\nunchanged, enabling one side of the sample to be fixed while applying a\ntangential displacement on the opposite side. As a result, the tested sample\nundergoes pure shear deformation.\n“In situ shear tests of monolayer Ti C T nanosheets were carried out in the\n3 2 x\nchamber of Carl Zeiss CossBeam340 SEM, utilizing the Brukers-Hysitron PI88\npicindenter (Supplementary Fig. 18a) to load the hemispherical indenter of the\nPTS device (Supplementary Fig. 18b). Prior to testing, an air calibration of the\nPI88 was required, followed by pushing force applied to the PTS device using a\ndisplacement control of 10 nm/s. The PTS device converts pushing force into\nshear force on the sample through four springs. During testing, the Pico-Indenter\napplied force electrostatically while simultaneously measuring displacement\ncapacitively, enabling load and displacement data to be recorded with sub-μN\nand sub-nm resolution, respectively. The integrated controller provided feedback\nstability and high-speed data acquisition, allowing real-time synchronization of\nload-displacement curves with in-situ SEM video imaging. The PTS device also\nacted as a strain sensor and energy buffer, ensuring accurate strain measurement\nduring tensile loading. The accuracy of the mechanical parameters was ensured\nby minimizing instrument compliance, thermal drift, and alignment errors. The\nload-displacement data in the experiment were recorded by the mechanical\nsensors on the PI88 probe, and the in-situ shearing process was also recorded in\nreal time by video, and the shear strain of the sample could be measured directly\nfrom the in situ shearing video. The boundary conditions of the tested specimen\nare illustrated in Supplementary Fig. 19, where the locations of the Pt strips are\nclearly specified, including the no-slip positions and the defined testing area.”\nSupplementary Fig. 19 The boundary conditions of the monolayer Ti C T\n3 2 x\nsamples are described, specifying the position of the Pt strip, the no-slip position,\nand the range of the testing area.\n3. The variations in the slope of the load-displacement curves observed in Figure\n3 for single-layer Ti C T reflect different deformation mechanisms in stages 1,\n3 2 x\nand 3, each of which necessitates a comprehensive elucidation. Table 1 provides\nthe shear modulus values for the sample at stage 1 and stage 3, respectively, but\nwhy the shear modulus in stage 2 is absent?\nResponse: We thank the reviewer for the constructive suggestion. We have\nprovided a comprehensive explanation of the deformation mechanisms for each\nstage, combining experiments, simulations, and characterizations.\nThe shear modulus is derived from the slope of the force-displacement curve. The\nsecond stage curve is in the transition region between the first and third stages.\nTherefore, the effective shear modulus in the second stage lies between those of\nthe first and third stages, similar to the yield point in conventional mechanical\ntesting. For example, the shear modulus in Stage 1 is 278.8 GPa, and in Stage 3 it\nis 110.7 GPa, so the shear modulus in Stage 2 lies between 110.7 and 278.8 GPa.\nFor this reason, we did not list its specific value. We have also provided an\nexplanation of this in the manuscript:\n“Before shear loading, the surface of the monolayer Ti C T was flat, and no\n3 2 x\nlocalized strain was observed (Supplementary Fig. 14). In stage 1, the overall\nstructure of monolayer Ti C T undergoes uniform shear deformation, with no\n3 2 x\nnoticeable localized strain, which reliably reflects the intrinsic shear modulus of\nthe sample. In stage 2, after localized strain generation (Supplementary Fig. 15),\nthe shear modulus of the monolayer Ti C T decreased to a certain extent. But the\n3 2 x\nshear modulus still remained at a high level until shear fracture in stage 3, and\nno structural instability occurred. Notably, the effective shear modulus in stage 2\nlies between that of stage 1 and stage 3, analogous to the yield point in\nconventional mechanical tests. In stage 3, with continued shear loading, the\nstrong bonding between the atomic layers of Ti C T effectively redistributes the\n3 2 x\nlocalized stress, preventing macroscopic wrinkles triggered by large-scale energy\naccumulation, until shear fracture. This phenomenon is further corroborated by\nthe stress-strain curve from MD simulations: at the onset of shear loading, the\nmonolayer Ti C T underwent uniform shear deformation, with a simulated shear\n3 2 x\nmodulus of ~294 GPa, maintaining a high shear modulus consistent with the\nexperimental observations (Supplementary Table 2). As the loading progressed,\nhowever, the atoms in the Ti C T lattice were severely compressed, localized\n3 2 x\nstrain emerged (Supplementary Fig. 16), and the shear modulus of the monolayer\nTi C T exhibited a slight decline (Supplementary Fig. 12a), in agreement with\n3 2 x\nthe experimental trend.”\nSupplementary Fig. 14 Characterization of monolayer Ti C T nanosheets\n3 2 x\nbefore the shear testing. (a) STEM images of monolayer Ti C T samples, and (b)\n3 2 x\nthe corresponding fast Fourier transform (FFT) patterns, and (c) the\ncorresponding geometric phase analysis (GPA) mapping confirmed the absence\nof pre-strain in the sample before testing.\nSupplementary Fig. 15 Characterization of monolayer Ti C T nanosheets after\n3 2 x\ncompleting the shear testing. (a) STEM images of monolayer Ti C T samples,\n3 2 x\nand (b) the corresponding FFT patterns, and (c) the corresponding geometric\nphase analysis (GPA) mapping confirmed the presence of global shear strain and\nlocalized lattice shear strain in the sample after testing.\nSupplementary Fig. 16 MD simulations of monolayer Ti C T under shear\n3 2 x\nloading. (a) MD simulation results of monolayer Ti C T under shear loading,\n3 2 x\nwith color changes showing the localized strain distribution on the sample\nsurface. Zoomed-in atomic structure images of localized strain in (b) Area 1, (c)\nArea 2, (d) Area 3, (e) Area 4 in (a).\n4. In the PTS strategy employed in this study, the specimen is placed within the\nside gap of the push-to-pull device. Given the asymmetrical nature of the\nstructure when shear load is applied, it is crucial for the authors to evaluate\nwhether the specimen experiences pure shear deformation under this loading\ncondition. It is worth noting that the PTS device was originally designed to\naccommodate unidirectional tensile loading, commonly referred to as push-to-\npull loading. The utilization of this device for shear loading, particularly for\nmeasuring the high shear strength of single-layer Ti C T , introduces a unique set\n3 2 x\nof considerations. The paper should therefore include a discussion on whether\nthis specific loading method has any implications for the performance of the PTS\ndevice.\nResponse: Thank you very much for your valuable comments. We have validated\nthe effectiveness of the PTS nano-mechanical device under shear loading, ensuring\nthat the Ti C T sample experiences pure shear deformation. In the in-plane shear\n3 2 x\ntest for 2D materials, it is crucial to keep one side of the sample fixed while\napplying a parallel tangential displacement on the opposite side, which the PTS\ndevice achieves efficiently. We will first explain this from the perspective of the\ntesting principle of the PTS device, as shown in Figure a-b below. The PTS\ndevice consists of a movable plate (purple area) and a fixed plate (gray area).\nWhen the hemispherical indenter is loaded, the purple movable plate moves\ndownward to apply force to the sample. During the loading process, the entire\narea beneath the hemispherical indenter constitutes the effective testing area of\nthe sample (orange box), while the surrounding springs ensure the stability of the\nPTS device. Throughout the loading, the gap width remains unchanged (Figure\nc), allowing one side of the sample to remain fixed while the other side undergoes\ntangential displacement.\nIt is worth noting that the PTS device was originally designed for uniaxial\ntensile loading (commonly referred to as Push-to-Pull loading). In previous studies of\nuniaxial tensile tests on 1D nanowires (Science Advances 2016, 2, e1501382;\nNature Communications 2025, 16, 3265; Nano Letters 2011, 11, 3207) and 2D\nnanosheets (Nature Communications 2020, 11, 284; Journal of the Mechanics\nand Physics of Solids 2025, 200, 106151; Cell Reports Physical Science 2020, 1,\n100172), the samples in the testing region were well subjected to uniaxial tension,\nwithout any lateral displacement, which verified that the gap width remains\nunchanged during loading (Figure c). Additionally, recent studies have used the\nPTS device to probe the shear properties of monolayer graphene (Nature\nCommunications 2024, 15, 4033), further confirming that the device is suitable\nfor the study of in-plane shear properties of 2D materials.\nThe SEM images of the monolayer Ti C T sample during our experimental\n3 2 x\nprocess (Figure d) show that the gap width remains unchanged, confirming that\nthe sample undergoes pure shear deformation, consistent with the testing\nconditions where one side of the sample is fixed while the opposite side\nundergoes parallel tangential displacement. Moreover, our MD simulation results\n(The shear modulus Gstage1 is ~294 GPa, and the shear fracture strength τ is ~19.7\nGPa) match the experimental results (The shear modulus Gstage1 is ~279 GPa, and\nthe shear fracture strength τ is ~18.6 GPa), further validating the effectiveness of\nthe shear test.\nTo avoid confusion for reviewers and readers, we have provided an explanation in\nthe manuscript:\nSupplementary Fig. 2 Validation of the effectiveness of PTS nanomechanical\ndevices in shear loading. (a) Schematic 3D illustration showing the working\nmechanism of the PTS nano-device. The device is divided into two regions: the\npurple region corresponds to the movable plate, while the gray region represents\nthe fixed plate. (b) Upon loading of the movable plate, the region beneath the\nhemispherical indenter is defined as the effective testing area of the sample,\nwhereas the springs around the device maintain its stability. (c) Enlarged view of\nthe sample testing area. During the loading process, the gap width remains\nunchanged, enabling one side of the sample to be fixed while applying a\ntangential displacement on the opposite side. As a result, the tested sample\nundergoes pure shear deformation. (d) The SEM image of the tested sample\nduring the experiment shows that the gap width remains unchanged, confirming\nthat the sample was subjected to pure shear deformation, consistent with the\ntesting condition in which one side of the sample is fixed while a parallel\ntangential displacement is applied to the opposite side.\n“It is worth noting that the PTS device was originally designed for uniaxial\ntensile loading (commonly referred to as push-to-pull loading). Here, it is\nemployed to perform shear loading on monolayer Ti C T for shear strength\n3 2 x\nmeasurement, with a discussion on the validity of the shear testing to demonstrate\nthat the specimen experienced pure shear deformation. As shown in\nSupplementary Fig. 2a-b, the PTS device consists of a movable plate (purple\nregion) and a fixed plate (gray region). When the hemispherical indenter is\nloaded, the purple movable plate translates downward to apply force on the\nspecimen. Under loading, the entire region beneath the hemispherical indenter\nconstitutes the effective testing area of the specimen (the boxed orange region),\nwhile the surrounding springs ensure the stability of the device. During the\nloading process, the gap width remains unchanged (Supplementary Fig. 2c),\nenabling one side of the specimen to be fixed while a tangential displacement is\napplied to the opposite side. Consequently, the specimen at the device side gap\nundergoes pure shear deformation. SEM images taken during the test further\nshow that the gap width does not change (Supplementary Fig. 2d), confirming\nthat the specimen experiences pure shear deformation, consistent with the testing\nrequirement of fixing one side while applying a parallel tangential displacement\nto the other side.”\n5. The authors assert in the article that they synthesized high-quality monolayer\nTi C T nanosheets. However, local transmission electron microscope images\n3 2 x\nalone are insufficient to support this claim. The authors are encouraged to provide\nadditional evidence to support the quality and characteristics of the synthesized\nnanosheets?\nResponse: Thank you very much for your valuable comments. We have added\nboth the overall and local TEM, mapping, and corresponding SAED of the\nmonolayer Ti C T nanosheets. Additionally, we have included STEM images of\n3 2 x\nthe monolayer Ti C T nanosheets before testing to support the quality and\n3 2 x\ncharacteristics of the synthesized nanosheets.\n“Prior to sample transfer, the high quality of the suspended Ti C T was\n3 2 x\nverified using transmission electron microscopy (TEM) and EDS mapping\n(Supplementary Fig. 7-8). The corresponding selected area electron diffraction\n(SAED) pattern confirming the single-crystal nature of Ti C T (Fig. 2d,\n3 2 x\nSupplementary Fig. 9).”\nSupplementary Fig. 7 Dark-field TEM and elemental mapping of monolayer\nTi C T MXene nanosheets, and the corresponding SAED pattern.\n3 2 x\nSupplementary Fig. 8 Bright-field TEM and elemental mapping of monolayer\nTi C T MXene nanosheets, and the corresponding SAED pattern.\n3 2 x\nSupplementary Fig. 9 TEM image of monolayer Ti C T MXene nanosheets, and\n3 2 x\nthe corresponding SAED pattern.\nSupplementary Fig. 14 Characterization of monolayer Ti C T nanosheets\n3 2 x\nbefore the shear testing. (a) STEM images of monolayer Ti C T samples, and (b)\n3 2 x\nthe corresponding fast Fourier transform (FFT) patterns, and (c) the\ncorresponding geometric phase analysis (GPA) mapping confirmed the absence\nof pre-strain in the sample before testing.\n6. The author used molecular dynamics simulations to reveal the mechanism\nbehind the Ti C T ’s resistance to wrinkling. Could molecular dynamics\n3 2 x\nsimulations be used to provide more results for comparison with experiments,\nsuch as shear modulus, shear strength and stress-strain curve?\nResponse: We appreciate the reviewer’s insightful suggestion. We have added the\nstress-strain curve from the MD simulation in the manuscript. The curve obtained\nfrom the simulation shows a slight decreasing trend in shear modulus, which is\nsimilar to the experimental results. The simulated values of shear modulus and\nshear strength also align with the experimental results. It is important to note that\nthe main purpose of the MD simulation is to understand the mechanism behind\nthe slight decrease in the shear modulus of monolayer Ti C T , rather than simply\n3 2 x\nto accurately replicate the force-displacement curve measured in experiments.\nAchieving perfect agreement between the experimental and simulation curves is\nnot the primary goal of this work. Therefore, in the MD simulation, we focus only\non the intrinsic shear modulus of monolayer Ti C T (Gstage1) and the shear\n3 2 x\nfracture strength (τ). We have provided this additional explanation in the\nmanuscript:\n“This phenomenon is further corroborated by the stress-strain curve from MD\nsimulations: at the onset of shear loading, the monolayer Ti C T underwent\n3 2 x\nuniform shear deformation, with a simulated shear modulus of ~294 GPa,\nmaintaining a high shear modulus consistent with the experimental observations\n(Supplementary Table 2). As the loading progressed, however, the atoms in the\nTi C T lattice were severely compressed, localized strain emerged\n3 2 x\n(Supplementary Fig. 16), and the shear modulus of the monolayer Ti C T\n3 2 x\nexhibited a slight decline (Supplementary Fig. 12a), in agreement with the\nexperimental trend.”\nSupplementary Fig. 12a. The stress-strain curve corresponding to the MD\nsimulation in Figure 4c.\nSupplementary Fig. 12 MD simulation investigation of the geometric size effect\non the shear properties of monolayer Ti C T MXene nanosheets. (a) The\n3 2 x\ncorresponding stress-strain curve in Figure 4c. (b) Shear modulus Gstage1 values\nof monolayer Ti C T samples with different b/W ratios. (c) Shear fracture\n3 2 x\nstrength τ values of monolayer Ti C T samples with different b/W ratios. The\n3 2 x\ntested sample with a b/W ratio of (d) 0.5, (e) 0.75, (f) 1, (g) 1.25, (h) 1.5, (i) 2.\nSupplementary Table 2. MD simulation results of the shear properties of\nmonolayer Ti C T of different sizes under in-plane shear loading.\n3 2 x\nSample Width/Length Shear Fracture\n# modulus strength\n(b/W)\n𝑺𝒕𝒂𝒈𝒆𝟏\n𝑮 (GPa)\n𝟑𝑫 τ\n(GPa)\n1 1/2 79.1 11.4\n2 3/4 186.2 16.2\n3 1 276.5 19.0\n4 5/4 293.6 19.5\n5 3/2 294.3 19.7\n6 2 294.5 19.8\n7. In the molecular dynamics simulation, the COMB3 potential function is used\nto set the interaction forces between atoms in the Ti C T model. Is there any\n3 2 x\nbasis for choosing this potential function?\nResponse: Thank you very much for your comments. In fact, the COMB3\npotential function was chosen for the simulation of Ti C T in the molecular\n3 2 x\ndynamics study due to its ability to effectively model the interactions in\nheterogeneous systems, including both short-range and long-range interactions.\nCOMB3 is a third-generation potential from the charge-optimized many-body\n(COMB) potential family, which integrates variable charge electrostatics and\nbond order concepts to simulate complex bonding environments. The COMB\npotential family, including COMB3, is specifically designed to model materials\nwith mixed bonding types (metallic, ionic, covalent, and van der Waals) in the\nsame system, making it well-suited for MXenes like Ti C T , which involve\n3 2 x\ndifferent bonding characteristics. It also includes corrections for long-range\nelectrostatic interactions and van der Waals forces, which are crucial for the\naccurate modeling of surface and interface properties in materials like Ti C T .\n3 2 x\nThe COMB3 potential uses self-consistent charge equilibration (QEq) to\ndynamically adjust atomic charges, which is particularly beneficial in systems\nwith varying charge distributions like MXenes. This ability to adaptively model\nthe charge environment enhances the accuracy of simulations, especially for\nmaterials that undergo functionalization. Thus, the choice of COMB3 for the\nTi C T model is well-supported by its proven ability to handle multi-component,\n3 2 x\nmulti-functional systems with variable charge dynamics, making it an appropriate\nchoice for simulating MXenes. In addition, the COMB3 potential function has\nbeen applied in other studies on the mechanical properties of MXenes (Applied\nSurface Science 2021, 566, 150633; Materials Science and Engineering R 2013,\n74, 255-279; Nature Communications 2024, 15, 1566).\n8. The authors should provide a detailed description of the methodology used to\ndetermine the nominal thickness value of the monolayer Ti C T , which was\n3 2 x\nreported as 0.98 nm in this study.\nResponse: We thank the reviewer for the constructive suggestion. In fact, the\nnominal thickness value of 0.98 nm for monolayer Ti C T has been widely used\n3 2 x\nin other relevant research works (Science Advances 2018, 4, eaat0491; Nature\nCommunications 2024, 15, 1566; Journal of the American Chemical Society\n2015, 137, 2715-2721). We have provided a detailed description of the\nmethodology used to determine the nominal thickness of monolayer Ti C T as\n3 2 x\n0.98 nm in the manuscript.\n“Specifically, we employed STEM to obtain high-resolution images of the\ncross-section of monolayer Ti C T . By analyzing the distinct boundary of the\n3 2 x\nmonolayer Ti C T in the STEM images, we were able to precisely measure its\n3 2 x\nthickness, confirming that the material’s thickness is approximately 0.98 nm. To\nfurther validate the result obtained from the STEM images, we combined a\ntheoretical model to derive the thickness of the monolayer Ti C T . The model\n3 2 x\npredictions were consistent with the experimental results, further supporting the\nthickness value of 0.98 nm. Notably, this value has been widely used in the\nliterature10,27,32. Therefore, this value is supported by both STEM measurements\nand theoretical models (Fig. 2f).”\n9. In the article, the shear modulus of the material in the first stage was 278 GPa\nand the Young’s modulus is around 484 GPa. Therefore, if we assume that the\nmonolayer Ti C T is isotropic material, the Poisson's ratio of the material for the\n3 2 x\nfirst stage can be estimated as -0.129, which indicated that the material was a\nnegative Poisson's ratio material? Is this reasonable?\nResponse: Thank you very much for your valuable comments. The concept of\nPoisson’s ratio was first introduced by Siméon Poisson in 1829, initially to study\nthe mechanical behavior of isotropic homogeneous bulk materials, such as steel,\nrubber, metals, and wood. The formula for calculating Poisson’s ratio is widely\nused in traditional 3D isotropic materials (E/2G1). However, monolayer\n2D materials are composed of specific chemical bonding between atoms. For\nexample, monolayer Ti C T is a 2D material formed by arranging three Ti atoms\n3 2 x\nand two C atoms in a specific pattern, with strong Ti-C covalent bonds between\nTi and C. Therefore, monolayer 2D materials often exhibit significant differences\nin properties within the plane and perpendicular to the plane, and the Poisson’s\nratio formula (E/2G1) is not applicable to monolayer 2D materials.\nTi C T MXenes and other 2D nanomaterials exhibit strong transverse orthotropy\n3 2 x\nin their mechanical properties. For example, the fracture strength of MoS was\n2\nmeasured to be ~1 GPa along the basal plane (Nanoscale 2017, 9(26), 9119),\nwhile in the direction perpendicular to the plane, this value increases to 23 GPa\n(ACS Nano 2011, 5(12), 9703). A similar behavior has been reported for\nmonolayer graphene, where its experimental tensile strength ranges from 2 to 10\nGPa (Nature Communications 2014, 5, 3782), and the intrinsic strength\nmeasured by AFM is 130 GPa (Science 2008, 321, 385). In the case of actual\ncalculations for monolayer 2D materials, more complex models and derived\nformulas are typically required to calculate the Poisson’s ratio. This may involve\nseparately considering the elastic modulus and shear modulus parallel to the\nmaterial’s plane and perpendicular to the plane.\nIn addition, the Poisson’s ratio of graphene is 0.165 (Journal of Applied Physics\n1970, 41, 3373), and its Young’s modulus E is 920 GPa (Nature\nCommunications 2020, 11, 284). Using the formula E/2G1, the shear\nmodulus G is calculated to be approximately 395 GPa. However, in actual\nexperiments, the shear modulus of monolayer graphene has been measured to be\n~70 GPa (Nature Communications 2024, 15, 4033). This discrepancy further\nvalidates that the calculation formula is not applicable to monolayer 2D materials.\n10. The comparison of the shear properties between monolayer Ti C T and\n3 2 x\nmonolayer graphene, as presented in the article, warrants careful consideration.\nWhile the study claims that Ti C T exhibits superior shear properties compared\n3 2 x\nto graphene, the structural differences between the two materials introduce\ncomplexities that affect the validity of such a direct comparison.\nResponse: Thank you very much for your comment. We chose to discuss the\nshear modulus of monolayer graphene based on the following three\nconsiderations:\n(1) Practical application scenarios of 2D materials: The excellent electrical\nconductivity, mechanical properties, and solution processability of Ti C T\n3 2 x\nMXene make it one of the most promising alternatives to graphene. Specifically,\nthe large-scale fabrication of nanomaterials into self-supporting films with high\nconductivity and outstanding mechanical properties is crucial for advancing\nvarious applications in flexible electronics, electromagnetic interference shielding,\nand supercapacitors. However, the core challenge in achieving this goal lies in\nfinding nanomaterials with both intrinsic high strength and excellent conductivity.\n(Advanced Materials 2020, 32, 2001093) Among various 2D materials,\nhexagonal boron nitride is non-conductive, transition metal dichalcogenides\n(TMDs, such as MoS ) have relatively low conductivity, while graphene\n2\npossesses both extremely high conductivity and strength, making it widely\nregarded as the strongest material known to date. Graphene has been applied in\nflexible electronics, energy storage, and electromagnetic shielding. However, its\npoor dispersion during processing limits its large-scale applications. In the search\nfor 2D materials with excellent elasticity and conductivity, Ti C T is the first and\n3 2 x\nmost widely studied MXene material discovered. It exhibits higher conductivity\nthan graphene prepared via solution methods, along with excellent\nelectrochemical properties, showing great potential in energy storage and flexible\nelectronics. Monolayer Ti C T nanosheets are considered the material of choice\n3 2 x\nfor future flexible electronics, energy storage, and electromechanical nanodevices.\nIn contrast, the low conductivity of other 2D materials such as TMDs limits their\nwidespread use, so comparing Ti C T with other 2D materials is of little\n3 2 x\nsignificance.\n(2) Graphene as a prototype system for the study of 2D material mechanical\nproperties: Graphene is commonly viewed as a prototype system for studying\nthe mechanical properties of 2D materials, and its mechanical properties are\nrepresentative and universal. In other research works, the mechanical properties\nof 2D materials with different atomic layer structures are typically compared to\ngraphene, which does not affect the validity of the comparison. (Science\nAdvances 2018, 4, eaat0491; Nature Communications 2024, 15, 1566;\nAdvanced Electronic Materials 2020, 1901382) This is because graphene is\nconsidered the material with the strongest known mechanical properties, and its\nmechanical properties are typically used as a benchmark.\n(3) The shear properties of monolayer graphene have been extensively\nstudied, while the shear mechanical properties of other 2D materials have\nnot been fully explored: Currently, only the in-plane shear mechanical properties\nof monolayer graphene have been extensively reported in both experimental and\nsimulation studies. Due to the limitations of testing techniques, in-plane shear\ntests on monolayer 2D materials are still in the early stages. As a result, the shear\nmodulus of many 2D materials has not been determined, and their shear\nproperties have not been comprehensively explored. Therefore, a comparison of\nthe shear properties of Ti C T MXene and other 2D materials is not yet possible.\n3 2 x\nOur future work may further expand to discuss the relevant properties of other 2D\nmaterials.\nFor the reasons outlined above, we have selected monolayer graphene as a\nreference in this study and conducted a comparative analysis with monolayer\nTi C T . To strengthen the discussion of the shear modulus of monolayer\n3 2 x\ngraphene in this study, we have added supplementary content to the original\ndiscussion to highlight the performance advantages of Ti C T and support our\n3 2 x\nresearch argument:\n“In this study, the shear modulus of monolayer graphene is chosen as the\nreference, based on the practical application scenarios of 2D materials, and\ngraphene is also a typical benchmark in the research of the mechanical\nproperties of 2D materials. Specifically, the large-scale fabrication of\nnanomaterials into self-supporting films with both high electrical conductivity\nand excellent mechanical properties is key to advancing the development of\nvarious applications, such as flexible electronics, electromechanical nano-devices,\nsupercapacitors, sensors, and electromagnetic interference shielding51,52.\nHowever, the core challenge in achieving this goal lies in finding nanomaterials\nthat combine both high strength and excellent conductivity53. Among existing 2D\nmaterial systems, hexagonal boron nitride is non-conductive54, and transition\nmetal dichalcogenides (TMDs, such as MoS ) have relatively low conductivity55.\nstrength, and is widely regarded as the strongest known material to date, making\nit applicable in flexible electronics, energy storage, and electromagnetic\nshielding56. However, the poor dispersion of graphene during processing limits its\nlarge-scale applications57. In the exploration of other 2D materials with excellent\nelasticity and conductivity, MXenes have emerged as ideal candidates. Among\nthem, Ti C T is the earliest discovered and most extensively studied MXene\n3 2 x\nmaterial. Solution-processed Ti C T exhibits conductivity significantly higher\n3 2 x\nthan that of graphene and demonstrates outstanding electrochemical\nperformance, offering great potential for applications in energy storage and\nflexible electronics. Monolayer Ti C T nanosheets are excellent building blocks\n3 2 x\nfor constructing micro-/nanoelectromechanical devices and wearable\nelectronics58,59. In the realm of 2D materials, the robust mechanical properties,\nand solution processability of Ti C T MXene make it a promising alternative to\n3 2 x\n2D materials such as graphene. It is worth emphasizing that monolayer graphene\nis often regarded as a “prototype system” in the research of 2D materials, as its\nmechanical properties are representative and universal, making it suitable as a\ncomparative benchmark27,29,60. Based on the aforementioned reasons, we selected\nmonolayer graphene as the reference in this study and performed a comparative\nanalysis with monolayer Ti C T to highlight the performance advantages of\n3 2 x\nTi C T and support the research discussion.”\n3 2 x\n11. In section 3, the authors claim that “Our research uncovers the performance\nenhancement mechanism at the smallest unit of the material microstructure.”\nHowever, this statement is not appropriate, as the study does not provide a\ndetailed enhancement mechanism at the smallest unit of the material\nmicrostructure.\nResponse: We are very grateful to the reviewer for this precious suggestion. We\nhave made revisions to this sentence accordingly.\n“Our research confirms that monolayer Ti C T can indeed enhance the\n3 2 x\nmechanical properties and stability of structural membranes.”\nReviewer #3\nThe article titled “Shear Properties and Stable Wrinkle Resistance in 2D Ti C T\n3 2 x\nMXene Monolayers” by Rong et al. presents a groundbreaking study that addresses a\ncritical gap in the characterization of 2D materials. The development of a novel in-situ\npush-to-shear strategy using a scanning electron microscope represents a significant\nmethodological advancement, allowing for the first direct measurement of intrinsic in-\nplane shear properties of monolayer Ti C T . The reported exceptionally high shear\n3 2 x\nmodulus and strength, along with stable wrinkle resistance, challenge previous\nassumptions about the performance of 2D materials. While the results are intriguing\nand significant, several points require clarification and improvement:\nResponse: We thank the reviewer for the positive assessment and constructive\nsuggestions of our work. The point-by-point responses are shown below:\n1. Given that this study focuses on the in-plane mechanical properties of 2D\nmaterials, it would be better to use the 2D shear modulus (in N/m) rather than the\n3D one (in GPa). This is because 2D values are independent of the material's\nthickness, more accurately reflecting the in-plane properties.\nResponse: We thank the reviewer for the valuable feedback. We acknowledge\nthat the use of the 2D shear modulus G (in N/m) can more accurately reflect the\n2D\nin-plane mechanical properties, and in theory, it provides a more precise\nrepresentation of the intrinsic in-plane behavior. Therefore, we have\nsupplemented the manuscript with the values of the 2D shear modulus G .\n2D\nIn fact, our use of the 3D shear modulus G (in GPa) in the manuscript is based\n3D\non the consideration of practical applications of 2D materials, where the effect of\nthickness plays a key role in determining the mechanical performance. Thus,\nadopting the 3D shear modulus G (in GPa) provides a more comprehensive\n3D\ncharacterization of the mechanical properties of the monolayer Ti C T . We have\n3 2 x\nfurther clarified this point in the revised manuscript to help readers better\nunderstand our research methodology and results. It is worth noting that other\nstudies investigating the mechanical properties of 2D materials have also taken\nthickness into account (e.g., Figure 3b in Science Advances 2018, 4, eaat0491;\nTable 1 in Nature Communications 2024, 15, 1566; Table 1 in Advanced\nMaterials 2016, DOI: 10.1002/adma.201604201; Nature Communications 2020,\n11, 284; Figure 6i in Advanced Electronic Materials 2020, 1901382; Table 1 in\nNano Letters 2020, 20, 5900-5908).\n“The 2D shear modulus G of monolayer Ti C T is listed in Supplementary\n2D 3 2 x\nTable 3. In practical applications, the effect of thickness plays a crucial role in\ndetermining the mechanical performance. Therefore, adopting the 3D shear\nmodulus G provides a more comprehensive representation of the mechanical\n3D\nproperties of monolayer Ti C T . Accordingly, the 3D shear modulus G is\n3 2 x 3D\nemployed in the present discussion.”\nSupplementary Table 3. 2D shear properties of monolayer Ti C T under in-\n3 2 x\nplane shear loading.\nSample Length Width Shear modulus Shear modulus\n# 𝑮 𝑺𝒕𝒂𝒈𝒆𝟏 (N/m) 𝑮 𝑺𝒕𝒂𝒈𝒆𝟑 (N/m)\nb W 𝟐𝑫 𝟐𝑫\n(μm) (μm)\n1 5.5 4.5 268.6 101.7\n2 5.5 4.5 279.2 115.0\n3 5.5 4.5 271.0 111.7\n4 5.5 4.5 274.2 105.4\nAverage 273.7±7.3 108.5±9.6\n2. One of the most challenging aspects of the molecular dynamics (MD)\nsimulation of MXene is constructing the appropriate atomic models to represent\nTx, the terminal groups with differing concentrations. Many previous density\nfunctional theory (DFT) studies have demonstrated that these terminal groups can\nimpact their in-plane mechanical properties. It is well known that manipulating\nthe terminal groups on MXene in experiments is difficult. However, it is unclear\nhow the atomic model for the MD simulation was constructed. It would be\nbeneficial to elaborate on how the Ti C T model was developed in the main text\n3 2 x\nor supporting information.\nResponse: We really appreciate this insightful question, which has been very\nhelpful in improving the manuscript. We have supplemented the discussion on\nthe influence of different terminal group concentrations on the shear properties of\nmonolayer Ti C T . In addition, we have elaborated in detail the construction\n3 2 x\nprocess of the monolayer Ti C T model in the manuscript.\n3 2 x\n“As is well known, manipulating terminal groups on MXenes in experimental\nsettings is challenging. To address this issue, we employed MD simulations to\ninvestigate the shear properties of monolayer Ti C T with different terminal\n3 2 x\ngroup concentrations (Supplementary Fig. 17). Despite variations in terminal\ngroup concentrations, the shear modulus and fracture strength of monolayer\nTi C T remain within reasonable ranges, consistent with experimental values.”\n3 2 x\nSupplementary Fig. 17 MD simulation of the shear properties of monolayer\nTi C T with different terminal group concentrations. (a) Shear modulus Gstage1\n3 2 x\nvalues of monolayer Ti C T samples with different terminal group concentrations.\n3 2 x\n(b) Shear fracture strength τ values of monolayer Ti C T samples with different\n3 2 x\nterminal group concentrations. The tested sample with a terminal group\nconcentration of (c) 100%, (d) 80%, (e) 60%, (f) 40%, (g) 20%, (h) 0%.\n“All simulations are performed on a large-scale atomic/molecule massively\nparallel simulator (LAMMPS). The crystal structure of Ti C T belongs to the\n3 2 x\nhexagonal crystal system. The initial lattice structure of monolayer Ti C was\n3 2\nobtained through theoretical calculations (DFT) and experimental\ncharacterization. The atomic structure and lattice constants of Ti C are well-\n3 2\nknown, and based on this, the Ti C T model is constructed. The basic structure of\n3 2 x\nTi C consists of the arrangement of Ti atoms and C atoms. Ti C typically\n3 2 3 2\nconsists of three Ti atoms and two C atoms, arranged in a layered structure. The\nTi atoms are covalently bonded with the C atoms. In constructing the Ti C T\n3 2 x\nmodel, oxygen functional groups (-O) are selected to attach to the surface of Ti\natoms, forming chemical bonds with the Ti atoms. To simulate the atomic\ninteractions in Ti C T , this study employs the COMB3 potential function\n3 2 x\n(Charge-Optimized Many-Body Potentials). The COMB3 potential function is\ncapable of adapting to the interactions of different chemical bonds in the material,\nsuch as metallic, covalent, and ionic bonds, making it particularly suitable for\ndescribing MXenes, which are surface-functionalized materials. COMB3 allows\nfor dynamic charge adjustment based on the local environment of each atom,\nwhich is crucial for simulating MXene materials. The charge transfer between the\nsurface termination groups and Ti atoms is captured through this charge\noptimization process, enabling a more accurate simulation of the chemical\nbehavior of Ti C T .”\n3 2 x\n3. Many details regarding the MD simulation are missing.\nResponse: Thank you very much for your comments. We have supplemented the\ndetails of the MD simulations.\n“In the simulation of Ti C T , periodic boundary conditions (PBC) are typically\n3 2 x\nconsidered to ensure seamless connections between the samples, thus avoiding\nboundary effects that may interfere with the results. To simulate real physical\nstrain, the upper and lower boundary atoms of Ti C T are usually fixed, and\n3 2 x\nshear strain is applied to model the deformation of the material under external\nforces. This shear strain can be analyzed through stress-strain curves to assess\nthe mechanical properties of Ti C T . The commonly used ensemble is the NPT\n3 2 x\nensemble (isothermal-isobaric ensemble) to ensure the thermodynamic stability of\nthe system. In summary, the construction of the Ti C T atomic model begins by\n3 2 x\ndetermining the basic lattice structure of Ti C and adding the surface\n3 2\ntermination group -O on its surface. Subsequently, the COMB3 potential function\nis used to simulate the interactions between Ti, C, and O atoms, and molecular\ndynamics simulations are employed to minimize the system’s energy and apply\nshear strain. The modeling sizes of the monolayer Ti C T are 400 Å×320 Å\n3 2 x\n(b/W=1.25), 160 Å×320 Å (b/W=0.5), 240 Å×320 Å (b/W=0.75), 320 Å×320 Å\n(b/W=1), 480 Å×320 Å (b/W=1.5), 640 Å×320 Å (b/W=2), and the upper and\nlower edges of the monolayer Ti C T are fixed to apply shear strain at a constant\n3 2 x\nrate of 0.001ps-1.”\n4. It is unnecessary to mention nitrides in the first sentence of the abstract, as they\nwere not included in this study.\nResponse: Many thanks for your precise observation. We are sorry that the\nmentioned nitrides have confused the reviewer. In fact, MXenes have a general\nformula of M X T , where M represents a transition metal (Ti, Zr, V, Nb, Ta, Cr,\nn+1 n x\nMo, Sc, etc.), X is carbon or nitrogen, and n = 1, 2, or 3. This chemical synthesis\nof MXenes adds surface functionalities such as fluorine, oxygen, and hydroxyl\ngroups, denoted as T in the MXenes’ general formula. Since 2011, when the first\nx\nTi C T MXene was discovered, MXenes has been defined as two-dimensional\n3 2 x\n(2D) carbides and nitrides. Of course, we understand the reviewer’s concern,\nwhich may confuse readers, so we revised “and” to “or”, making it more accurate\nfor our research while still meeting the definition of MXenes.\n“Two-dimensional (2D) transition metal carbides or nitrides (MXenes)”\n5. Could the authors provide the main structural differences of Ti C T across the\n3 2 x\nthree different stages? If these differences cannot be observed through\nexperimental characterizations, can the MD simulations offer insights? Such\ninformation may help explain the reduced in-plane shear modulus value at Stage3.\nResponse: We thank the reviewer for the constructive suggestion. We have\ncomprehensively elaborated on the structural deformation mechanisms at each\nstage of the monolayer Ti C T shear tests by integrating experiments,\n3 2 x\ncharacterizations, and simulations.\n“Before shear loading, the surface of the monolayer Ti C T was flat, and no\n3 2 x\nlocalized strain was observed (Supplementary Fig. 14). In stage 1, the overall\nstructure of monolayer Ti C T undergoes uniform shear deformation, with no\n3 2 x\nnoticeable localized strain, which reliably reflects the intrinsic shear modulus of\nthe sample. In stage 2, after localized strain generation (Supplementary Fig. 15),\nthe shear modulus of the monolayer Ti C T decreased to a certain extent. But the\n3 2 x\nshear modulus still remained at a high level until shear fracture in stage 3, and\nno structural instability occurred. Notably, the effective shear modulus in stage 2\nlies between that of stage 1 and stage 3, analogous to the yield point in\nconventional mechanical tests. In stage 3, with continued shear loading, the\nstrong bonding between the atomic layers of Ti C T effectively redistributes the\n3 2 x\nlocalized stress, preventing macroscopic wrinkles triggered by large-scale energy\naccumulation, until shear fracture. This phenomenon is further corroborated by\nthe stress-strain curve from MD simulations: at the onset of shear loading, the\nmonolayer Ti C T underwent uniform shear deformation, with a simulated shear\n3 2 x\nmodulus of ~294 GPa, maintaining a high shear modulus consistent with the\nexperimental observations (Supplementary Table 2). As the loading progressed,\nhowever, the atoms in the Ti C T lattice were severely compressed, localized\n3 2 x\nstrain emerged (Supplementary Fig. 16), and the shear modulus of the monolayer\nTi C T exhibited a slight decline (Supplementary Fig. 12a), in agreement with\n3 2 x\nthe experimental trend.”\nSupplementary Fig. 14 Characterization of monolayer Ti C T nanosheets\n3 2 x\nbefore the shear testing. (a) STEM images of monolayer Ti C T samples, and (b)\n3 2 x\nthe corresponding fast Fourier transform (FFT) patterns, and (c) the\ncorresponding geometric phase analysis (GPA) mapping confirmed the absence\nof pre-strain in the sample before testing.\nSupplementary Fig. 15 Characterization of monolayer Ti C T nanosheets after\n3 2 x\ncompleting the shear testing. (a) STEM images of monolayer Ti C T samples,\n3 2 x\nand (b) the corresponding FFT patterns, and (c) the corresponding geometric\nphase analysis (GPA) mapping confirmed the presence of global shear strain and\nlocalized lattice shear strain in the sample after testing.\nSupplementary Fig. 16 MD simulations of monolayer Ti C T under shear\n3 2 x\nloading. (a) MD simulation results of monolayer Ti C T under shear loading,\n3 2 x\nwith color changes showing the localized strain distribution on the sample\nsurface. Zoomed-in atomic structure images of localized strain in (b) Area 1, (c)\nArea 2, (d) Area 3, (e) Area 4 in (a).\n6. The authors note, “Although multiple monolayer Ti C T nanosheets were used\n3 2 x\nin our study, only three tests were successfully performed.” Could they briefly\ndiscuss why these experiments are so challenging? This information might help\nother researchers attempt similar studies.\nResponse: We appreciate the reviewer’s suggestion. We have added a discussion\non the challenges related to the mechanical testing of 2D materials in the\nmanuscript:\n“This is primarily due to the inherently fragile structure of monolayer 2D\nmaterials, which makes them highly susceptible to damage during the transfer\nprocess. Additionally, surface contamination is often introduced during transfer,\nwhich can adversely affect the material’s properties and compromise the\naccuracy of subsequent test results. Therefore, the key to improving the success\nrate and reproducibility of testing 2D materials lies in the ability of researchers\nto select the appropriate material transfer technique based on the specific\nproperties of the material, ensure sample cleanliness, avoid sample damage,\nprecisely secure the sample, and choose suitable testing methods34,35.”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The manuscript has been somewhat enhanced. Nevertheless, my stance remains that the methodology employed in this study cannot be classified as a method for deriving the shear modulus of 2D materials. In contrast to Hou’s previous work, which primarily focused on the emergency and evolution of instability patterns under shear strategy, the present study conducted mechanical testing to extract specific shear parameters. During the deformation process, it is expected that coupled shear and bending modes will occur due to the atomic thickness of the film. However, the lower amplitude and larger wavelength of out-of-plane instability during shear render it unresolvable due to the low resolution in the Z direction in SEM. Consequently, the authors did not consider the contribution from bending term.\nThe derivation of shear strength from the current experiment setup presents significant challenges. The sample fractured at the edge, implying an effect of stress concentration. While the response from stress-strain curve does correlate with the membrane’s response, larger strain levels induced tension due to edge effect has been taken into account. Consequently, it is difficult to ascertain I the shear strength using the current methodology.\nThe stress-strain curves form MD simulation as depicted in Fig S12a, exhibit notable difference when compared to those obtained experimentally. This divergence suggests that the observed shear deformation in the experiment may be intertwined both with bending and shear phenomena.\nThe GPA was employed to characterize the strain and its distribution within the sample. Fig S14 confirms the absence of pre-strain in the sample as indicated by GPA. Fig S15 illustrates the presence of both local and global shear deformation of sample after shear testing. It is important to note how one can derive the result showing in Fig S15 without knowledge of the preceding stages. Furthermore, the pre-strain effect can be evaluated on a case by case basis.", "reviewer_2": "The author has addressed the reviewers' comments. I recommend acceptance of the paper.", "reviewer_3": "The authors have successfully addressed all the issues I raised.", "reviewer_4": "This study investigates the shear properties of monolayer Ti3C2Tx using a push-to-shear device installed in SEM. Although the push-to-shear device has been reported before, the key factor enabling accurate measurements is the dry transfer technique, which eliminates the pretension, reporting an exceptionally high shear modulus and fracture strain. While the results are intriguing and significant, the accuracy of the measurements and the mechanism behind the stable wrinkle resistance behavior-which is related to the bending stiffness-require more thorough discussion and validation.\n1.The reported shear modulus exceeds half of the Young’s modulus, which contradicts the theoretical prediction. Therefore, the accuracy of the measurements should be carefully verified, or the potential influence of geometry measurement, pretension and anisotropy should be considered. A comparison with first-principles calculations would help clarify this discrepancy.\n2.The formation of wrinkles is governed by the bending modulus and geometry of materials, rather than the shear modulus. For instance, in Nat Commun (2024, 15,4033) by Hou et al., wrinkling in monolayer graphene and MoS2 arises due to its low bending rigidity resulting from atomic-scale thickness. The authors should provide evidence that, under the same geometry condition, the bending modulus of monolayer Ti3C2Tx is sufficiently large to suppress wrinkle formation.\n3.The transition mechanism from stage 1 to 3 remains unclear. The authors demonstrate that ‘ in stage 2, a localized strain generation, and in stage 3, the strong bonding between the atomic layers of Ti3C2Tx effectively redistributes the localized stress’. How does this happen? Fig.3b shows a change of the sample transparency, it seems an irregular corrugation emerges in the middle. So the authors should demonstrate that the strain field remains purely in-plane as any out-of-plane displacement would compromise the validity of the shear properties measured in stage 3.\n4.The MD simulations show asymmetric strain distributions during the shearing process, this could potentially be an artifact arising from an excessively high strain rate or temperature used in the simulations. Besides, a color bar must be provided for those figures.\n5.A summary is needed to discuss the types of 2D materials for which the push-to-shear technique provides accurate results, and what key material characteristics are required. This is crucial for demonstrating the broad applicability of the method beyond the specific material studied here."}, "author_response": "Response to Reviewers\nReviewer #1\nThe manuscript has been somewhat enhanced. Nevertheless, my stance remains that\nmy stance remains that the methodology employed in this study cannot be classified as a method for deriving\nthe shear modulus of 2D materials. In contrast to Hou’s previous work, which\nprimarily focused on the emergency and evolution of instability patterns under shear\nstrategy, the present study conducted mechanical testing to extract specific shear\nparameters. During the deformation process, it is expected that coupled shear and\nbending modes will occur due to the atomic thickness of the film. However, the lower\namplitude and larger wavelength of out-of-plane instability during shear render it\nunresolvable due to the low resolution in the Z direction in SEM. Consequently, the\nauthors did not consider the contribution from bending term.\nThe derivation of shear strength from the current experiment setup presents\nsignificant challenges. The sample fractured at the edge, implying an effect of stress\nconcentration. While the response from stress-strain curve does correlate with the\nmembrane’s response, larger strain levels induced tension due to edge effect has been\ntaken into account. Consequently, it is difficult to ascertain I the shear strength using\nthe current methodology.\nThe stress-strain curves form MD simulation as depicted in Fig S12a, exhibit notable\ndifference when compared to those obtained experimentally. This divergence suggests\nthat the observed shear deformation in the experiment may be intertwined both with\nbending and shear phenomena.\nThe GPA was employed to characterize the strain and its distribution within the\nsample. Fig S14 confirms the absence of pre-strain in the sample as indicated by GPA.\nFig S15 illustrates the presence of both local and global shear deformation of sample\nafter shear testing. It is important to note how one can derive the result showing in Fig\nS15 without knowledge of the preceding stages. Furthermore, the pre-strain effect can\nbe evaluated on a case by case basis.\nResponse: Thank you very much for your comments, which are helpful in\nimproving the manuscript quality. We are happy to discuss these with you. The\nmaterial properties of the monolayer Ti C T MXene studied in our work are\n3 2 x\ndifferent from those of the materials investigated in Hou’s work (Nature\nCommunications 2024, 15, 4033). Hou’s previous research focused on\nmonolayer graphene and monolayer MoS , both of which were synthesized via\n2\nthe CVD method and required copper foil or polymer protection (such as\nPMMA). These materials are inherently soft and lack the self-supporting\nindependence. As a result, Hou’s work mainly concentrated on the emergency\nand evolution of instability patterns under shear strategies. In contrast, monolayer\nTi C T MXene is a free-standing nanosheet obtained through etching of\n3 2 x\nmultilayer ceramic MAX phases and mechanical exfoliation, without requiring\nany external protection. Furthermore, the free-standing monolayer Ti C T\n3 2 x\nMXene nanosheets can be transferred by dry transfer using a manipulator. These\nphenomena indicate that monolayer Ti C T possesses a strong resistance to out-\n3 2 x\nof-plane bending. Notably, a comparison of the bending stiffness (resistance to\nout-of-plane bending deformation) of these three materials further validates this.\nThe bending stiffness of monolayer Ti C T is 23.69 nN nm (Nature 2025, 647,\n3 2 x\n80), that of monolayer MoS is 1.54 nN nm (Nanotechnology 2013, 24, 435705),\n2\nand that of monolayer graphene is 0.192 nN nm (Journal of Physics D: Applied\nPhysics 2009, 42, 102002). The bending stiffness of monolayer Ti C T is ~15.4\n3 2 x\ntimes and ~123.4 times greater than that of monolayer MoS and monolayer\n2\ngraphene, respectively. This indicates that the bending stiffness of monolayer\nTi C T is sufficiently large to suppress the formation of wrinkles.\n3 2 x\nSupplementary Fig. 17 Comparison of bending stiffness for two 2D materials:\ngraphene1, MoS 2, and Ti C T 3. The bending stiffness of monolayer Ti C T is\n2 3 2 x 3 2 x\n~123.4 times greater than that of monolayer Graphene. The bending stiffness of\nmonolayer Ti C T is ~15.4 times greater than that of monolayer MoS .\n3 2 x 2\nDuring the deformation process, if the material’s surface undergoes bending, it is\neasily observable, as seen in Hou’s work where periodic wrinkling patterns\nappeared on the surface of monolayer graphene. These wrinkling patterns would\ndisappear upon unloading. In our shear loading experiments on monolayer\nTi C T , we did not observe similar periodic wrinkling patterns. Regarding the\n3 2 x\nreviewer’s comment about the lower resolution in the Z-direction, with lower\namplitude and larger wavelength, making it difficult to distinguish, wavelength is\ntypically associated with periodic phenomena and refers to the distance between\ntwo adjacent wave peaks or troughs in a periodic fluctuation. Wavelength is\nusually used to describe repetitive, cyclic oscillations or vibrations. However,\nboth the shear experiments on monolayer Ti C T and the MD simulation results\n3 2 x\nconfirm that no periodic wrinkling patterns exist on the surface of the sample,\nmaking this hypothesis unlikely. Additionally, we compared the monolayer\nTi C T from a sectional side view using MD simulations. As shown in Figures\n3 2 x\n16a-c, there is no displacement perpendicular to the plane before and after the\napplication of shear load on the monolayer Ti C T . This is attributed to the\n3 2 x\nextremely high bending stiffness and strong atomic interlayer bonding\ninteractions of the monolayer Ti C T , which endows it with the ability to resist\n3 2 x\nout-of-plane deformation. In contrast, the monolayer graphene exhibits\nsignificant displacement perpendicular to the plane after the application of shear\nload (Figures 16d). In addition, the irregular corrugation observed in the sample\nin Figure 3b are attributed to in-plane lattice distortion caused by the compression\nbetween atomic layers. As a result, these corrugations do not disappear after\nbrittle fracture, which contrasts with the out-of-plane wrinkling recovery\nobserved in monolayer graphene (Nature Communications 2024, 15, 4033).\nTherefore, it is reasonable to derive the shear strength of monolayer Ti C T\n3 2 x\nbased on the current experimental setup.\nSupplementary Fig. 16 Comparison of the side view of the cross-sectional MD\nsimulation for monolayer Ti C T and monolayer graphene under shear load.\n3 2 x\nWe have mitigated the influence of edge stress concentration by studying the size\neffect. As the material size increases, the edge stress concentration effect becomes\nrelatively smaller. This is because, in larger materials, the edge effect has a lesser\nimpact on the overall stress distribution, and the stress is more uniformly\ndistributed within the material. We compared the test results of samples with\ndifferent sizes (with widths of 3.5 μm, 4.5 μm, 5.5 μm, and 6.5 μm), as well as\nthe simulation results (with Width-to-Length ratios b/W of 0.5, 0.75, 1, 1.25, 1.5,\nand 2), and found that when the sample width exceeded 5 μm, the results were\ncloser to the material’s true shear properties.\nAdditionally, the brittle fracture of monolayer Ti C T occurs within a very short\n3 2 x\ntime, and no delayed or unbroken regions are observed during the fracture\nprocess. Therefore, no larger strain levels due to edge effects are present. Thus, it\nis reasonable to determine the shear strength of monolayer Ti C T using the\n3 2 x\npush-to-shear strategy. In Fig. S12a, the curve obtained from the MD simulation\nshows a slight decreasing trend in shear modulus, which is similar to the\nexperimental results. The simulated values of shear modulus and shear strength\nalso align with the experimental results. It is important to note that the main\npurpose of the MD simulation is to understand the mechanism behind the slight\ndecrease in the shear modulus of monolayer Ti C T , rather than simply to\n3 2 x\naccurately replicate the force-displacement curve measured in experiments.\nAchieving perfect agreement between the experimental and simulation curves is\nnot the primary goal of this work. The discrepancy between the simulation curve\nand the experimental curve is reasonable, as it has been observed in many other\nstudies (Science Advances 2023, 9, eadf7075; PNAS 2025, 122, e2424124122;\nPNAS 2020, 117(44), 27154). It is important to note that, from the cross-\nsectional side view of the MD simulation, no out-of-plane bending phenomenon\nwas observed. Therefore, there is no overlap of bending and shear phenomena.\nThis work involves in situ shear mechanical experiments conducted under SEM,\nrather than in situ TEM experiments. Based on this, we performed TEM\ncharacterization and comparison of the sample before and after testing.\nAdditionally, the SEM morphology after fracture reveals in-plane lattice\ndistortion on the sample surface, which was further confirmed by TEM. This\ncontrasts with the recoverable out-of-plane wrinkling morphology of soft\nmonolayer graphene. It is worth noting that this issue has also been highlighted\nin recent paper (Nature Materials 2025, 24, 1554-1560), where the tested\nsamples were loaded onto the MEMS device in the SEM chamber, rather than\nbeing loaded in the TEM chamber. Direct in-situ observation of monolayer\nnanosheets with lateral dimensions of approximately a few micrometers using\nTEM is highly challenging. Therefore, researchers in this study have only\nperformed HRTEM characterization on the samples before and after testing. In\naddition, we have applied small cyclic loads to the samples prior to formal testing\nto release any pre-strain that might have been introduced during the transfer and\nfixation process. This has been confirmed through STEM and the corresponding\nGPA diagram, which verify that the effects of pre-strain have been eliminated.\nReviewer #2\nThe author has addressed the reviewers’ comments. I recommend acceptance of the\npaper.\nResponse: We sincerely thank you for the helpful suggestions and recommending\nour article for acceptance.\nReviewer #3\nThe authors have successfully addressed all the issues I raised.\nResponse: We sincerely thank for your careful review.\nReviewer #4\nThis study investigates the shear properties of monolayer Ti C T using a push-to-\n3 2 x\nshear device installed in SEM. Although the push-to-shear device has been reported\nbefore, the key factor enabling accurate measurements is the dry transfer technique,\nwhich eliminates the pretension, reporting an exceptionally high shear modulus and\nfracture strain. While the results are intriguing and significant, the accuracy of the\nmeasurements and the mechanism behind the stable wrinkle resistance behavior-\nwhich is related to the bending stiffness-require more thorough discussion and\nvalidation.\nResponse: We thank you for the positive assessment and constructive\nsuggestions for our work. The point-by-point responses as follows:\n1. The reported shear modulus exceeds half of the Young’s modulus, which\ncontradicts the theoretical prediction. Therefore, the accuracy of the\nmeasurements should be carefully verified, or the potential influence of geometry\nmeasurement, pretension and anisotropy should be considered. A comparison\nwith first-principles calculations would help clarify this discrepancy.\nResponse: We thank the reviewer for the valuable feedback. In conventional\nisotropic linear elasticity theory, the material constants satisfy the fixed relation:\nE/2G1. In this case, the shear modulus G must be less than or equal to\nE/2. Notably, the concept of Poisson’s ratio was first introduced by Siméon\nPoisson in 1829, initially to study the mechanical behavior of isotropic\nhomogeneous bulk materials, such as steel, rubber, metals, and wood. The\nformula for calculating Poisson’s ratio is widely used in traditional 3D isotropic\nmaterials (E/2G1). However, monolayer 2D materials are composed of\nspecific chemical bonding between atoms. For example, monolayer Ti C T is a\n3 2 x\n2D material formed by arranging three Ti atoms and two C atoms in a specific\npattern, with strong Ti-C covalent bonds between Ti and C. Therefore, monolayer\n2D materials often exhibit significant differences in properties within the plane\nand perpendicular to the plane, and the Poisson’s ratio formula (E/2G1)\nis not applicable to monolayer 2D materials.\nTi C T MXenes and other 2D nanomaterials exhibit strong transverse orthotropy\n3 2 x\nin their mechanical properties. For example, the fracture strength of MoS was\n2\nmeasured to be ~1 GPa along the basal plane (Nanoscale 2017, 9(26), 9119),\nwhile in the direction perpendicular to the plane, this value increases to 23 GPa\n(ACS Nano 2011, 5(12), 9703). A similar behavior has been reported for\nmonolayer graphene, where its experimental tensile strength ranges from 2 to 10\nGPa (Nature Communications 2014, 5, 3782), and the intrinsic strength\nmeasured by AFM is 130 GPa (Science 2008, 321, 385). In the case of actual\ncalculations for monolayer 2D materials, more complex models and derived\nformulas are typically required to calculate the Poisson’s ratio. This may involve\nseparately considering the elastic modulus and shear modulus parallel to the\nmaterial’s plane and perpendicular to the plane.\nIn addition, the Poisson’s ratio of graphene is 0.165 (Journal of Applied Physics\n1970, 41, 3373), and its Young’s modulus E is 920 GPa (Nature\nCommunications 2020, 11, 284). Using the formula E/2G1, the shear\nmodulus G is calculated to be approximately 395 GPa. However, in actual\nexperiments, the shear modulus of monolayer graphene has been measured to be\n~70 GPa (Nature Communications 2024, 15, 4033). This discrepancy further\nvalidates that the calculation formula is not applicable to monolayer 2D materials.\n(1) We have carefully verified the accuracy of the measurements:\nWe have validated the effectiveness and accuracy of the PTS nano-mechanical\ndevice under shear loading. In the in-plane shear test for 2D materials, it is crucial\nto keep one side of the sample fixed while applying a parallel tangential\ndisplacement on the opposite side, which the PTS device achieves efficiently. We\nwill first explain this from the perspective of the testing principle of the PTS\ndevice, as shown in Figure a-b below. The PTS device consists of a movable\nplate (purple area) and a fixed plate (gray area). When the hemispherical indenter\nis loaded, the purple movable plate moves downward to apply force to the\nsample. During the loading process, the entire area beneath the hemispherical\nindenter constitutes the effective testing area of the sample (orange box), while\nthe surrounding springs ensure the stability of the PTS device. Throughout the\nloading, the gap width remains unchanged (Figure c), allowing one side of the\nsample to remain fixed while the other side undergoes tangential displacement.\nIt is worth noting that the PTS device was originally designed for uniaxial\ntensile loading (commonly referred to as Push-to-Pull loading). In previous studies of\nuniaxial tensile tests on 1D nanowires (Science Advances 2016, 2, e1501382;\nNature Communications 2025, 16, 3265; Nano Letters 2011, 11, 3207) and 2D\nnanosheets (Nature Communications 2020, 11, 284; Journal of the Mechanics\nand Physics of Solids 2025, 200, 106151; Cell Reports Physical Science 2020, 1,\n100172), the samples in the testing region were well subjected to uniaxial tension,\nwithout any lateral displacement, which verified that the gap width remains\nunchanged during loading (Figure c). Additionally, recent studies have used the\nPTS device to probe the shear properties of monolayer graphene (Nature\nCommunications 2024, 15, 4033), further confirming that the device is suitable\nfor the study of in-plane shear properties of 2D materials.\nThe SEM images of the monolayer Ti C T sample during our experimental\n3 2 x\nprocess (Figure d) show that the gap width remains unchanged, confirming that\nthe sample undergoes pure shear deformation, consistent with the testing\nconditions where one side of the sample is fixed while the opposite side\nundergoes parallel tangential displacement. Moreover, our MD simulation results\n(The shear modulus Gstage1 is ~294 GPa, and the shear fracture strength τ is ~19.7\nGPa) match the experimental results (The shear modulus Gstage1 is ~279 GPa, and\nthe shear fracture strength τ is ~18.6 GPa), further validating the effectiveness of\nthe shear test.\nTo avoid confusion for reviewers and readers, we have provided an explanation in\nthe manuscript:\nSupplementary Fig. 2 Validation of the effectiveness of PTS nanomechanical\ndevices in shear loading. (a) Schematic 3D illustration showing the working\nmechanism of the PTS nano-device. The device is divided into two regions: the\npurple region corresponds to the movable plate, while the gray region represents\nthe fixed plate. (b) Upon loading of the movable plate, the region beneath the\nhemispherical indenter is defined as the effective testing area of the sample,\nwhereas the springs around the device maintain its stability. (c) Enlarged view of\nthe sample testing area. During the loading process, the gap width remains\nunchanged, enabling one side of the sample to be fixed while applying a\ntangential displacement on the opposite side. As a result, the tested sample\nundergoes pure shear deformation. (d) The SEM image of the tested sample\nduring the experiment shows that the gap width remains unchanged, confirming\nthat the sample was subjected to pure shear deformation, consistent with the\ntesting condition in which one side of the sample is fixed while a parallel\ntangential displacement is applied to the opposite side.\n(2) We have carefully considered the potential effects of geometric\nmeasurements, pre-tension, and anisotropy:\nThe lateral dimensions of the monolayer Ti C T sample were precisely defined\n3 2 x\nduring the FIB operation and can be clearly observed in the SEM. The sample\nthickness was determined to be 0.98 nm. In fact, the nominal thickness value of\n0.98 nm for monolayer Ti C T has been widely used in other relevant research\n3 2 x\nworks (Science Advances 2018, 4, eaat0491; Nature Communications 2024, 15,\n1566; Journal of the American Chemical Society 2015, 137, 2715-2721). We\nhave provided a detailed description of the methodology used to determine the\nnominal thickness of monolayer Ti C T as 0.98 nm in the manuscript.\n3 2 x\n“Specifically, we employed STEM to obtain high-resolution images of the cross-\nsection of monolayer Ti C T . By analyzing the distinct boundary of the\n3 2 x\nmonolayer Ti C T in the STEM images, we were able to precisely measure its\n3 2 x\nthickness, confirming that the material’s thickness is approximately 0.98 nm. To\nfurther validate the result obtained from the STEM images, we combined a\ntheoretical model to derive the thickness of the monolayer Ti C T . The model\n3 2 x\npredictions were consistent with the experimental results, further supporting the\nthickness value of 0.98 nm. Notably, this value has been widely used in the\nliterature10,27,32. Therefore, this value is supported by both STEM measurements\nand theoretical models (Fig. 2f).”\nWe use a manipulator for the dry transfer of monolayer Ti C T , which allows\n3 2 x\nprecise picking and releasing of the 2D material under SEM. The boundaries of\nthe sample are then precisely fixed with Pt, minimizing the effect on the\nsuspended portion. This greatly reduces the influence of pre-tension.\nIt is well known that applying a small cyclic load to the sample before formal\ntesting can release the pre-strain potentially introduced during the transfer and\nfixation process. Therefore, we applied a maximum load of 8%~10% to sample\n#4 and cycled it 19 times to eliminate any pre-strain effects before testing. The\nfinal results matched those of the other three samples #1~#3, confirming that pre-\nstrain had no effect on the test results. Additionally, STEM images and the\ncorresponding geometric phase analysis (GPA) mapping of the samples before\ntesting further confirmed the absence of pre-tension.\nWe have also provided a detailed explanation of this in the manuscript:\n“Notably, in conventional wet-transfer methods with polymer protection layers,\n2D materials are anchored onto nano-mechanical devices through van der Waals\ninteractions. Pre-strain is often introduced due to capillary contraction, surface\ntension during the dissolution of the polymer protection layer, and the interfacial\nvan der Waals forces36. In contrast, in this work, monolayer Ti C T was dry-\n3 2 x\ntransferred using a micromanipulator under SEM, enabling precise pickup and\nrelease of the flakes. The subsequent localized Pt fixation at the sample edges\nimposed minimal disturbance on the suspended area, thereby substantially\nreducing pre-strain effects. Prior to the formal tests, a small cyclic load was\napplied to release the pre-strain introduced during the transfer and fixation\nprocesses. Specifically, sample #4 was subjected to 19 loading cycles at 8~10% of\nthe maximum load (Supplementary Fig. 13), which effectively eliminated the pre-\nstrain. The obtained results were consistent with those of the other three samples,\nconfirming that pre-strain had no effect on the measurements. Furthermore,\nSTEM imaging and geometric phase analysis (GPA) mapping of the samples\nprior to testing also verified the absence of pre-strain (Supplementary Fig. 14).”\nSupplementary Fig. 13 Before the formal testing, a small cyclic load (8%~10%\nof the maximum load, 19 cycles) was applied to monolayer Ti C T sample #4 to\n3 2 x\nrelease the pre-strain potentially introduced by the transfer and fixation\nprocesses.\nSupplementary Fig. 14 Characterization of monolayer Ti C T nanosheets\n3 2 x\nbefore the shear testing. (a) STEM images of monolayer Ti C T samples, and (b)\n3 2 x\nthe corresponding fast Fourier transform (FFT) patterns, and (c) the\ncorresponding geometric phase analysis (GPA) mapping confirmed the absence\nof pre-strain in the sample before testing.\nWe have also carefully considered the effect of sample orientation:\nSupplementary Table 5. MD simulation results of the shear properties of\nmonolayer Ti C T of different orientations under in-plane shear loading.\n3 2 x\nSample Width/Length Orientation Shear Fracture\n# modulus strength\n(b/W)\n𝑺𝒕𝒂𝒈𝒆𝟏\n𝑮 (GPa)\n𝟑𝑫 τ\n(GPa)\n1 5/4 Zigzag 293.6 19.5\n2 5/4 Armchair 293.1 19.2\n(3) We have verified the results through first-principles calculations, the\nexperimental results are consistent with the DFT calculation results:\nSupplementary Fig. 20 DFT calculation results of the shear properties of\nmonolayer Ti C T . (a) The top view and (b) side view models of monolayer\n3 2 x\nTi C T under in-plane shear loading, before and after deformation. (c) The\n3 2 x\ncorresponding stress-strain curve results.\nSupplementary Table 3. DFT results of the shear properties of monolayer\nTi C T .\n3 2 x\nSample Shear modulus 𝑮 𝑺𝒕𝒂𝒈𝒆𝟏 (GPa) Fracture strength τ (GPa)\n𝟑𝑫\nTi C T 306.1 19.5\n3 2 x\n2. The formation of wrinkles is governed by the bending modulus and geometry\nof materials, rather than the shear modulus. For instance, in Nat Commun (2024,\n15,4033) by Hou et al., wrinkling in monolayer graphene and MoS2 arises due to\nits low bending rigidity resulting from atomic-scale thickness. The authors should\nprovide evidence that, under the same geometry condition, the bending modulus\nof monolayer Ti C T is sufficiently large to suppress wrinkle formation.\n3 2 x\nResponse: We really appreciate this insightful question, which has been very\nhelpful in improving the manuscript. The bending stiffness of monolayer Ti C T\n3 2 x\nis 23.69 nN nm (Nature 2025, 647, 80), that of monolayer MoS is 1.54 nN nm\n2\n(Nanotechnology 2013, 24, 435705), and that of monolayer graphene is 0.192 nN\nnm (Journal of Physics D: Applied Physics 2009, 42, 102002). The bending\nstiffness of monolayer Ti C T is ~15.4 times and ~123.4 times greater than that\n3 2 x\nof monolayer MoS and monolayer graphene, respectively. This indicates that the\n2\nbending stiffness of monolayer Ti C T is sufficiently large to suppress the\n3 2 x\nformation of wrinkles. Furthermore, both monolayer graphene and monolayer\nMoS require a copper foil or polymer substrate for protection and do not possess\n2\nself-supporting properties. In contrast, monolayer Ti C T is directly etched and\n3 2 x\nmechanically exfoliated from multilayer MAX phases, requiring no additional\nsubstrate for protection, making it a self-supporting, independent nanosheet. This\nalso confirms the ability of monolayer Ti C T to resist out-of-plane wrinkling\n3 2 x\ndeformation.\nSupplementary Fig. 17 Comparison of bending stiffness for two 2D materials:\ngraphene1, MoS 2, and Ti C T 3. The bending stiffness of monolayer Ti C T is\n2 3 2 x 3 2 x\n~123.4 times greater than that of monolayer Graphene. The bending stiffness of\nmonolayer Ti C T is ~15.4 times greater than that of monolayer MoS .\n3 2 x 2\n3. The transition mechanism from stage 1 to 3 remains unclear. The authors\ndemonstrate that ‘in stage 2, a localized strain generation, and in stage 3, the\nstrong bonding between the atomic layers of Ti C T effectively redistributes the\n3 2 x\nlocalized stress’. How does this happen? Fig.3b shows a change of the sample\ntransparency, it seems an irregular corrugation emerges in the middle. So the\nauthors should demonstrate that the strain field remains purely in-plane as any\nout-of-plane displacement would compromise the validity of the shear properties\nmeasured in stage 3.\nResponse: We thank the reviewer for the constructive suggestion. The transition\nfrom stage 1 to stage 3 involves a gradual decrease in the shear modulus due to\nthe onset of localized strain during shear loading, but the material does not\nexhibit wrinkling instability, unlike other 2D materials such as monolayer\ngraphene. In stage 1, monolayer Ti C T undergoes uniform shear deformation\n3 2 x\nwith no noticeable localized strain, effectively reflecting the intrinsic shear\nmodulus of the sample. In stage 2, localized strain begins to develop, which leads\nto a slight reduction in shear modulus. However, the material continues to\nmaintain its structural integrity, and no significant instability or wrinkle formation\nis observed. Finally, in stage 3, shear loading continues, and the shear modulus\nstabilizes at a lower value, but the strong interlayer bonding between Ti C T\n3 2 x\nlayers prevents large-scale wrinkles or structural collapse, which ultimately leads\nto brittle fracture.\nThe charge density distribution shown in Figure 15a reveals that, in the\nmonolayer Ti C T structure, charge is concentrated around the atoms (darker\n3 2 x\ncolors indicate higher electron density), suggesting strong bonding interactions\nbetween the atomic layers in the monolayer Ti C T . Upon application of in-plane\n3 2 x\nshear load, some Ti-C bonds shorten, while others elongate, allowing for effective\nredistribution of local stress within the in-plane atomic layers (Figure 15b). The\nrigid structural framework of the monolayer Ti C T itself can dissipate the shear\n3 2 x\nload energy without the need for out-of-plane buckling, thus effectively\npreventing macroscopic wrinkling caused by large-scale energy accumulation.\nSupplementary Fig. 15 Differential charge density distribution map of the\nmonolayer Ti C T structure. Upon applying shear strain, the distances of some\n3 2 x\nC-Ti bonds shorten, with bonding charge significantly accumulating, leading to\nstrengthened bonding and the generation of forces that resist shear.\nWe compared the monolayer Ti C T from a sectional side view using MD\n3 2 x\nsimulations. As shown in Figures 16a-c, there is no displacement perpendicular\nto the plane before and after the application of shear load on the monolayer\nTi C T . This is attributed to the extremely high bending stiffness and strong\n3 2 x\natomic interlayer bonding interactions of the monolayer Ti C T , which endows it\n3 2 x\nwith the ability to resist out-of-plane deformation. In contrast, the monolayer\ngraphene exhibits significant displacement perpendicular to the plane after the\napplication of shear load (Figures 16d). In addition, the irregular corrugation\nobserved in the sample in Figure 3b are attributed to in-plane lattice distortion\ncaused by the compression between atomic layers. As a result, these corrugations\ndo not disappear after brittle fracture, which contrasts with the out-of-plane\nwrinkling recovery observed in monolayer graphene (Nature Communications\n2024, 15, 4033).\nSupplementary Fig. 16 Comparison of the side view of the cross-sectional MD\nsimulation for monolayer Ti C T and monolayer graphene under shear load.\n3 2 x\n4. The MD simulations show asymmetric strain distributions during the shearing\nprocess, this could potentially be an artifact arising from an excessively high\nstrain rate or temperature used in the simulations. Besides, a color bar must be\nprovided for those figures.\nResponse: Thank you very much for your comments. In this MD simulations,\nthe temperature is set at room temperature, maintained at 300 K, which is within\na reasonable range. Other studies in this field also commonly adopt a temperature\nsetting of 300 K (Computational Materials Science 2023, 227, 112268;\nNanotechnology 2015, 26, 265705; Applied Surface Science 2021, 566,\n150633). The shear strain is applied with a rate of 0.001 ps-1. The shear strain rate\nis within a reasonable range (Nature Communications 2024, 15, 1566; Applied\nSurface Science 2021, 566, 150633; Nanotechnology 2015, 26, 265705), and\nother studies in this field have also used strain rates on the order of ns-1 (Nature\nCommunications 2020, 11, 284; Applied Surface Science 2020, 532, 147380).\nTherefore, the strain rate (the order of magnitude of ps-1) used in this work is not\nexcessively high. In addition, the corresponding color bars for the MD simulation\nresults have been provided.\n5. A summary is needed to discuss the types of 2D materials for which the push-\nto-shear technique provides accurate results, and what key material characteristics\nare required. This is crucial for demonstrating the broad applicability of the\nmethod beyond the specific material studied here.\nResponse: We thank the reviewer for the constructive suggestion. We have added\ninformation in the main text of the manuscript regarding the types of 2D materials\nsuitable for the push-to-shear technique and the acquisition of accurate results:\n“It is noteworthy that the classical Ti C T MXene is just one of many 2D\n3 2 x\nmaterials prepared via solution methods. This precise push-to-shear technique is\napplicable to free-standing nanosheets derived from exfoliating layered precursor\nmaterials, such as transition metal tellurides (TMTs)66, and emerging 2D high-\nentropy MXene nanosheets67. Unlike monolayer graphene and monolayer MoS ,\n2\nthese 2D materials do not require additional copper foils or polymers as\nsupports, indirectly suggesting that the free-standing nanosheets possess a\ncertain resistance to out-of-plane bending. This indicates their potential for being\nsuitable for the push-to-shear shear technique, yielding accurate results. Our\nstandardized experimental strategy serves as a guideline for determining the\nshear properties of numerous other solution-processable 2D materials.”\nResponse to Reviewers\nReviewer #1\nMost comments have been addressed by the authors, although the free-bending mode\nis supported only by MD rather than experimental evidence. I have an additional\ncomment on the revised version. The authors state in Line 456 that they developed\nstandard experimental strategy to determine the shear properties of solution-\nprocessable 2D materials. In my opinion, however, a second material is necessary to\nvalidate the universality of the current strategy.\nResponse: We appreciate your careful review and constructive suggestions on\nour manuscript. The scientific nature of this paper was improved by absorbing the\nsuggestions. We have added a note in the discussion section regarding the\nlimitations of the free-bending mode without experimental support, and removed\nthe claim about the material’s generalizability mentioned in line 456.\nReviewer #4\nThe authors have successfully addressed all the issues I raised. I recommend\nacceptance of the paper.\nResponse: We thank for your review and acceptance of our article."}, {"round": 3, "reviewer_comments": {"reviewer_1": "Most comments have been addressed by the authors, although the free-bending mode is supported only by MD rather than experimental evidence. I have an additional comment on the revised version. The authors state in Line 456 that they developed standard experimental strategy to determine the shear properties of solution-processable 2D materials. In my opinion, however, a second material is necessary to validate the universality of the current strategy.", "reviewer_4": "The authors have successfully addressed all the issues I raised. I recommend acceptance of the paper."}, "author_response": "Response to Reviewers\nReviewer #1\nMost comments have been addressed by the authors, although the free-bending mode\nis supported only by MD rather than experimental evidence. I have an additional\ncomment on the revised version. The authors state in Line 456 that they developed\nstandard experimental strategy to determine the shear properties of solution-\nprocessable 2D materials. In my opinion, however, a second material is necessary to\nvalidate the universality of the current strategy.\nResponse: We appreciate your careful review and constructive suggestions on\nour manuscript. The scientific nature of this paper was improved by absorbing the\nsuggestions. We have added a note in the discussion section regarding the\nlimitations of the free-bending mode without experimental support, and removed\nthe claim about the material’s generalizability mentioned in line 456.\nReviewer #4\nThe authors have successfully addressed all the issues I raised. I recommend\nacceptance of the paper.\nResponse: We thank for your review and acceptance of our article."}]

Decision letter