Strain-Induced Raman Band Shifts and Interlayer Stress Transfer

Changes of the Raman band position with strain in the center of MXene flakes were measured in situ, as shown in the schematic diagram in Figure ​Figure22a. The strain was applied to the PMMA beam using a four-point bending rig, and the spectra at 0 and 0.4% strain for the monolayer flake in Figure ​Figure11a are shown in Figure ​Figure22b. It can be seen that the position of the A_1g Raman band of the MXene undergoes a downshift, as a result of the stress being transferred from the matrix to the flake. The band positions were obtained by Lorentzian curve fitting, and the downshift of the A_1g band was found to be around −1.9 cm^–1 at a strain of 0.4%.

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Figure 2

(a) Schematic diagram of the strain-induced in situ Raman band shift experiment. The strain on the surface of the deformed beam is uniaxial tension. (b) Raman spectra of the monolayer at 0 and 0.4% strain, showing a band shift of −1.9 cm^–1/% at the A_1g peak. The peak was fitted using a Lorentzian curve and the strain was determined by a resistance strain gauge. (c) Strain-induced Raman band shift rate for all of the flakes with a range of different lateral sizes and thicknesses. The average value of the band shift rate was found to be 3.3 cm^–1/%. The color coding was based on the no. of the flakes shown in Table 1.

We performed similar measurements at the centers of 14 flakes, of which seven flakes were coated (nos. 1–7) with a thin layer of PMMA on the top and the other seven were uncoated (nos. 8–14). The normalized A_1g band positions are plotted against the applied strain for the 13 flakes measured in Figure ​Figure22c (flake no. 6 showed no band shift) and plotted individually in Figures S3 and S4. The full width at half-maximum (FWHM) of all of the flakes are tabulated in Table S1. As can be seen, the FWHM of the different flakes measured were found to be similar. Regarding flake no. 6, where no band shift was shown, the reason is believed due to the fact that a good interface might not have formed. Although the upper surface can easily be seen under the optical microscope (Figure S3f), the morphology of the flake underneath the surface could be complex, leading to a poor interface. Overall, the A_1g band peak positions shifted to lower wavenumbers with strain up to 0.4% with an average band shift rate (dω/dε) of −3.3 cm^–1/% over this strain range (Figure ​Figure22c). However, for higher strains from 0.4 to 0.6%, A_1g band positions became scattered, possibly due to interfacial slip at the higher strain. Similar behavior has also been seen during the deformation of thin flakes of other 2D materials.^29,44 The detailed results including the band shift rate, thickness of flakes, the lateral sizes of flakes, and the calculated Grüneisen parameter for the A_1g mode can be seen in Table 1.

Grüneisen Parameter

The Grüneisen parameter is used to describe how the change in volume of a crystal lattice affects its vibrational properties. In terms of strain engineering of 2D materials, the Grüneisen parameter can be calculated from the Raman band shifts, which reflects the rate of phonon shift under strain. The Grüneisen parameter for the A_1g mode can be evaluated from the Raman band shift rate using the equation⁵⁹

1

where (dω_A1g/dε) is the strain-induced Raman band shift rate, ω_A1g⁰ is the A_1g band position (~730 cm^–1), and ν is the Poisson’s ratio of the substrate (0.35 for PMMA). The Grüneisen parameter for the A_1g mode for uniaxial tension was calculated for all of the flakes measured in this work (listed in Table 1) and gave values mostly in the range between 0.6 and 0.8. If we take an average value of the measured band shift rate (−3.3 ± 0.5 cm^–1/%), then the Grüneisen parameter, γ_A1g, is given by 0.70 ± 0.15.

A previous study⁶⁰ by Zhang and co-workers upon subjecting Ti₃C₂T_x MXene to hydrostatic pressure reported a value of γ_A1g of 0.29. They determined the strain by undertaking measurements of the change in lattice parameters of the MXene under pressure and used the out-of-plane strain from the change in c lattice parameter for the calculation of the Grüneisen parameter. In our study, we subjected MXene flakes to in-plane strains and obtained a higher value of γ_A1g. It should be pointed out that at this stage that molecular crystals do not have a single value of γ_A1g. In fact, the Grüneisen parameter for molecular crystals should be represented as a tensor, in a similar way to three-dimensional stresses and strains.^61,62 This means that there are different components of γ_A1g, one for out-of-plane strains, determined by Zhang et al.,⁶⁰ and another for in-plane strains, determined in this presented study. Fortunately, Zhang et al. also measured the in-plane strains from the change in the a lattice parameter under pressure, which they found to be more than 3 times lower than the changes in the c lattice parameter. This leads to a value of γ_A1g for in-plane strains of more than 3 × 0.29 ≈ 0.9 for their pressurization study,⁶⁰ close to our value of 0.70 ± 0.15 determined from the present investigation by straining Ti₃C₂T_x MXene on a substrate.

Stress Transfer and Interfacial Shear Strength

By introducing our previous approach established for graphene,^27,29 it was also possible to monitor the stress transfer from the PMMA substrate to the MXene by mapping the strain distribution over a MXene flake. Herein, we focus on the two monolayers (flake nos. 13 and 14) for the analysis of interfacial stress transfer and the determination of the interfacial shear strength. As can be seen from Figure ​Figure33a–d, the contour maps of band positions mirror the profile of the flake, the optical micrograph of which is highlighted in Figure ​Figure33e. At 0% strain, the Raman wavenumbers of the A_1g band were at ~729 cm^–1 for most of the area of the flake. However, some areas in the central part of the flake displayed wavenumbers down to ~728 cm^–1, possibly due to variations in terminating groups that affect the vibration frequency of the radiated light slightly.⁵⁶ With increasing strain applied to the PMMA beam, the band positions of the flake central area shifted gradually to lower wavenumbers and finally down to around 727 cm^–1 at a strain of 0.4%. The direction of the applied strain is indicated in Figure ​Figure33e. When the strain was increased to 0.6%, however, the A_1g band did not undergo any further downshift relative to 0.4% strain, indicating possible interfacial slippage.⁶³ To convert band position mappings into the strain distribution within the flake, we normalized the band positions of 0.2, 0.4, and 0.6% strains to that of 0% strain by subtraction of the band positions at 0% strain. The strain of the MXene at a given location, ε_MXene, is given by

2

where ω_A1g^strain is the band position of the A_1g band at the strain of the measurement, ω_A1g⁰ is the band position of A_1g at the strain of 0%, and (dω_A1g/dε)_ref is the reference band shift rate (−3.7 cm^–1/% for flake no. 13 in Table 1). Hence, strain distributions across the MXene flake were obtained at 0.2, 0.4, and 0.6% and are shown in Figure ​Figure33f–h. It can be seen that the strain of the MXene flake builds up from the edges of the flake (left and right in the figures) and reaches a plateau value at the central area of the flake (with some scatter of the data).

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Figure 3

(a–d) Contour maps of A_1g band positions at strains of 0, 0.2, 0.4, and 0.6% for a monolayer MXene; (e) optical micrograph of the measured flake; the strain direction is indicated by the arrows, while the dashed line indicates the line mapping positions corresponding to Figure ​Figure44a,b; and (f–h) strain distribution at 0.2, 0.4, and 0.6% strains obtained by subtraction of band position mappings at 0.2, 0.4, and 0.6% to that of 0% based on eq 2. (This flake is no. 13 in Table 1.).

We were then able to analyze the stress transfer efficiency using the shear-lag theory adapted for 2D materials.^{27,29,30,32,40,44} The detailed strain distributions along the axial direction at 0.2 and 0.4% are plotted in Figure ​Figure44a as a function of position (shown by the dashed line in Figure ​Figure33e). The strain along the MXene flake (ε_M) can be fitted by the shear-lag theory and is given by²⁹

3

where ε_m is the strain of the matrix; , s and l are the aspect ratio and length of the flake; t is the thickness of the flake (~1 nm for monolayer)²⁵ and T is the thickness of the matrix surrounding the flake; G_m and E_M are the shear modulus of the matrix and the effective modulus of the MXene flake; and x refers to the axial position along the flake. It can be seen in Figure ​Figure44a that the experimental data can be fitted to eq 3 using an ns value of 20, which gives good agreement with the experimental data at both 0.2 and 0.4% strain. Another monolayer was also examined using the same method (shown in Figure ​Figure44c), and this gave an ns value of 25. It is known that a higher ns value represents better interfacial stress transfer from polymers to the 2D material.^29,30 Overall, we can conclude that the stress transfer efficiency from the polymer to the monolayer MXene is similar to that for monolayer graphene (ns ~ 20).²⁹

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Figure 4

(a) Strain distribution of the MXene flake no. 13 at 0.2 and 0.4% matrix strain; the data points are fitted by shear-lag theory (eq 3); and the ns value obtained is 20. (b) Interfacial shear stress against the position at 0.2 and 0.4% strains based on eq 4; the maximum interfacial shear stresses at the flake ends at 0.2 and 0.4% strain were found to be 1.5 and 3.0 MPa, respectively. (c) Strain distribution of the MXene flake no. 14, at 0.2% and 0.4% strain of the matrix; the data points are fitted by shear-lag theory (eq 3); and the ns value obtained is 25. (d) Interfacial shear stress against positions of the measurement at 0.2 and 0.4% strain based on eq 4; the maximum interfacial shear stress at the flake ends were obtained to be 2.0 and 4.0 MPa, respectively.

With the ns values determined, the interfacial shear stress, τ_i, at the flake ends can now be calculated using²⁹

4

where E_M can be taken as the modulus of the Ti₃C₂T_x MXene monolayer (330 GPa).²⁵ The value of n can be obtained from the ns value of 20. Using the aspect ratio, s (=l/t), n is determined to be 0.002 (flake no. 13 in Table 1), where the thickness t is taken as 1 nm for a monolayer. The interfacial shear stress values at the flake ends were estimated from the plots of eq 4 in Figure ​Figure44b to be 1.5 and 3.0 MPa for 0.2 and 0.4% strain, respectively. In addition, we performed the same analysis on another monolayer with an ns of 25 (Figure ​Figure44d and flake no. 14 in Table 1, n = 3.1 × 10^–3) mapped at 0.2 and 0.4% gave an interfacial shear stress of 2.0 and 4.0 MPa, respectively (Figure ​Figure44d). Thus, the interfacial shear stress of the monolayer MXene flakes on the PMMA substrate were slightly higher but of similar values compared with those of monolayer graphene at 0.4% (τ_i ~2.3 MPa).

Ian A. Kinloch acknowledges the Royal Academy of Engineering and Morgan Advanced Materials. Research on MXene composites at Drexel University was supported by the MSCA RISE NANO2DAY project, Grant Agreement No. 777810, funded by the European Commission under HORIZON-2020 program and through the Fluid Interface Reactions, Structures, and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences. All research data supporting this publication are available within this publication.