Absorbance/emissivity of the structure
To determine the average emissivity, we analyzed the spectral absorbance/emissivity characteristics of all four Ti3C2Tx MXene variants (Fig. 2). The thicknesses of VO2, SiO2 and Ti3C2Tx MXene are considered,\({\text{d}}_{{{\text{VO}}_{2} }} = 15\;{\text{nm}}\), \({\text{d}}_{{{\text{SiO}}_{2} }} = 1050\;{\text{nm}}\) and \({\text{d}}_{{{\text{MXene}}}} = 500\;{\text{nm}}\), respectively. The layers thicknesses are optimized for achieving a large contrast in emissivity between two different semiconductor and metallic states of VO2.
The optical properties of Ti3C2Tx can be precisely tuned by controlling its surface termination groups. In practical, this can be achieved by carefully selecting the etching solution composition and concentration. Moreover, the surface chemistry can be further optimized by adjusting etching parameters such as time and temperature, allowing for tailored optical responses in various applications16,44,45.
The absorbance/emissivity in the infrared wavelength region of 2–20 µm is plotted for structures with no terminal group (Fig. 2a) and with –F, –O–, and –OH terminal groups (Fig. 2b–d, respectively). The spectra show clear dependence on the MXene terminal group type. The absorbance/emissivity is examined across two different states of VO2 to discern the influence of VO2 phase transition on its behavior. At the semiconductor state, the thermal emitter shows the minimum average spectral value of 0.23 for absorbance/emissivity in Fig. 2c for VO2/SiO2/Ti3C2O2 MXene among other kinds of MXene in the structure. The average spectral absorbance/emissivity for VO2/SiO2/Ti3C2, VO2/SiO2/Ti3C2F2 and VO2/SiO2/Ti3C2(OH)2 in Fig. 2a,b,d is 0.35, 0.34 and 0.43, respectively. By considering the temperature above the critical temperature of TC = 68 °C, the spectral absorbance/emissivity of the thermal emitter increases for all four kinds of Ti3C2Tx MXene. The highest absorbance/emissivity in this state of VO2 occurs for VO2/SiO2/Ti3C2(OH)2 and VO2/SiO2/Ti3C2F2 and in Fig. 2b,d with the average values of 0.74 and 0.73, respectively. For the two others of MXene in the structure in Fig. 2a,c, the average spectral absorbance/emissivity is 0.68 and 0.56, respectively.
The optical absorption characteristics of the multilayer structures vary significantly based on the MXene surface terminations. Ti3C2F2 and Ti3C2(OH)2-based structures (VO2/SiO2/Ti3C2F2 and VO2/SiO2/Ti3C2(OH)2) demonstrate higher average absorptivity due to the larger imaginary permittivity component of these terminations in a wide range of the studied wavelength. In contrast, the VO2/SiO2/Ti3C2O2 configuration exhibits minimal average absorptivity, attributed to its smaller imaginary permittivity component16.
Figure 3 illustrates the electric field profile of the structure for all variants of Ti3C2Tx MXene incorporated into the structure. Figure 3a–d are attributed to the norm of electric field at the semiconductor state for the structures of VO2/SiO2/Ti3C2, VO2/SiO2/Ti3C2F2, VO2/SiO2/Ti3C2(O)2 and VO2/SiO2/Ti3C2(OH)2, respectively and figures (e, f, g and h) represent the norm of electric field for metallic state. We can see that the terminal group has effect on the electric field distribution of the structure under the incidence wavelength of 7.5 µm which leads to the change in light absorbance/emissivity as we studied in Fig. 2. The reason for choosing this wavelength is due to the big difference in absorbance/emissivity for semiconductor and metallic states of VO2 for all kinds of MXene.
Electric field distribution of the proposed thermal emitter VO2/SiO2/Ti3C2Tx MXene without and with different terminal groups of Ti3C2Tx MXene at both semiconductor and metallic states of VO2. The electric field distribution at the semiconductor state of VO2 for (a) VO2/SiO2/Ti3C2, (b) VO2/SiO2/Ti3C2F2, (c) VO2/SiO2/Ti3C2O2 and (d) VO2/SiO2/Ti3C2(OH)2 and the electric field distribution at the metallic state of VO2 for (e) VO2/SiO2/Ti3C2, (f) VO2/SiO2/Ti3C2F2, (g): VO2/SiO2/Ti3C2O2 and (h) VO2/SiO2/Ti3C2(OH)2. The thicknesses of VO2, SiO2 and Ti3C2Tx MXene are considered 15 nm, 1050 nm and 500 nm, respectively. The considered wavelengths is 7.5 µm.
Average emissivity of the thermal emitter
The reversible phase transition of VO2 provides an effective way to realize the tunable emissivity with thermal configurability and large contrast in emissivity in two different VO2 states.
The integration of VO2, which undergoes phase transition on femtosecond timescales46, with Ti3C2Tx MXene creates a hybrid structure capable of exceptional optical modulation. This combination enables dynamic emissivity control within specific temperature ranges. Additionally, the inherent flexibility of MXene can induce strain in the VO2 film during thermal cycling, influencing the overall optical response47.
In Fig. 4, the average emissivity of the thermal emitter is modeled as a function of temperature for both heating (red line) and cooling (blue line) processes in the temperature range of 28–100 °C (301–373 K) for four different kinds of Ti3C2Tx MXene in the structure.
Average emissivity of the proposed VO2/SiO2/Ti3C2Tx MXene thermal emitter with considering four kinds of Ti3C2Tx MXene in the structure. Average emissivity of (a) VO2/SiO2/Ti3C2, (b) VO2/SiO2/Ti3C2F2, (c) VO2/SiO2/Ti3C2(OH)2 and (d) VO2/SiO2/Ti3C2O2.
The proposed thermal emitter covers two distinct states; one state at low temperature which the VO2 is in semiconductor state and the thermal emitter shows low average emissivity. Another one occurs in the metallic state which in contrast to the semiconductor state, a high average emissivity occurs at high temperature.
In particular, by involving four kinds of Ti3C2Tx MXene in the structure, the maximum average emissivity of εH = 0.80 at high temperature is obtained by considering VO2/SiO2/Ti3C2F2 and VO2/SiO2/Ti3C2(OH)2 in Fig. 4b,d, respectively. At the low temperature, the minimum average emissivity of εL = 0.36 occurs for VO2/SiO2/Ti3C2 in Fig. 4a. Among all four kinds of Ti3C2Tx MXene in the structure, the maximum differential emissivity of Δε = 0.42 is achieved for VO2/SiO2/Ti3C2F2 which is a good candidate for thermal control applications working in the temperature range of 301–373 K. The minimum average emissivity of Δε = 0.33 is obtained for VO2/SiO2/Ti3C2(OH)2 in Fig. 4d and in the following, the average differential emissivity of Δε = 0.38 and Δε = 0.41 happens by consideration of VO2/SiO2/Ti3C2 and VO2/SiO2/Ti3C2(O)2 in Fig. 4a,c, respectively. The emissivity results for all kinds of Ti3C2Tx MXene are summarized in Table 1.
During cooling from 373 to 301 K, the thermal emitter’s emissivity response matches its heating behavior in both semiconductor and metallic states. The average emissivity, simulated in the 2–20 µm wavelength range, demonstrates clear hysteresis behavior. For all four Ti3C2Tx MXene variants, the hysteresis loop exhibits consistent temperature regions for both VO2 phase states and the phase transition period during heating and cooling cycles. The phase transition threshold temperatures during the hysteresis loop remain fixed at 325 K for cooling and 345 K for heating (indicated by dashed lines) across all Ti3C2Tx MXene variants in the structure. This hysteresis behavior enables dynamic emissivity control through precise temperature regulation. Table 1 summarizes the average emissivity values at low and high temperatures and the differential emissivity for all four Ti3C2Tx MXene variants.
By precisely controlling surface chemistry to manage emissivity in IR region, these structures can effectively regulate heat dissipation to the environment. This property makes them particularly valuable for spacecraft thermal management applications, where precise control over heat emission and absorption is crucial.
Size effects on the thermal emitter
Figure 5 demonstrates the thermal emitter’s emissivity for VO2 thicknesses of 25 nm and 35 nm. The thicknesses of SiO2 and Ti3C2Tx MXene are considered 1050 nm and 500 nm, respectively.
Average emissivity of the proposed VO2/SiO2/Ti3C2Tx MXene thermal emitter for different thicknesses of VO2 by considering four kinds of Ti3C2Tx MXene in the structure. Average emissivity of (a) VO2/SiO2/Ti3C2, (b) VO2/SiO2/Ti3C2F2, (c) VO2/SiO2/Ti3C2(OH)2 and (d) VO2/SiO2/Ti3C2O2.
The structure with inclusion of four kinds of Ti3C2Tx MXene; Ti3C2, Ti3C2F2, Ti3C2O2 and Ti3C2(OH)2 is investigated as shown in Fig. 5a–d, respectively. An increase in VO2 thickness leads to a decrease in differential emissivity between semiconductor and metallic states across all Ti3C2Tx MXene variants. For Ti3C2O2, the maximum differential average emissivity reaches Δε = 0.39 at 25 nm and Δε = 0.34 at 35 nm VO2 thickness, as shown in Fig. 5c. In the following, the minimum values of Δε = 0.26 (\({\text{d}}_{{{\text{VO}}_{2} }} = 25\;{\text{nm}}\)) and 0.17 (\({\text{d}}_{{{\text{VO}}_{2} }} = 35\;{\text{nm}}\)) is realized for VO2/SiO2/Ti3C2 (OH)2 in Fig. 5d due to the high average emissivity at the low temperature in comparison to other kinds of Ti3C2Tx MXene. For the two rest of Ti3C2Tx MXene in Fig. 5a,b; VO2/SiO2/Ti3C2 and VO2/SiO2/Ti3C2(F)2, the differential average emissivity, included the values between the minimum and maximum ones in Fig. 5c,d. In addition, the threshold temperature of the hysteresis loop during the heating and cooling processes occurs at the fixed temperature regions for all kinds of Ti3C2Tx MXene terminal groups. The details of emissivity with various VO2 thicknesses is shown in Table 2.
Figure 6 shows the emissivity of the thermal emitter under two different SiO2 thicknesses of \({\text{d}}_{{{\text{SiO}}_{2} }} = 900\;{\text{nm}}\) and 1200 nm for four kinds of Ti3C2Tx MXene in the structure. The thickness of VO2 and Ti3C2Tx are considered 15 nm and 500 nm, respectively.
Average emissivity of the proposed VO2/SiO2/Ti3C2Tx MXene thermal emitter for different thicknesses of SiO2 by considering four kinds of Ti3C2Tx MXene in the structure. Average emissivity of (a) VO2/SiO2/Ti3C2, (b) VO2/SiO2/Ti3C2F2, (c) VO2/SiO2/Ti3C2(OH)2 and (d) VO2/SiO2/Ti3C2O2.
The average emissivity for all cases of Ti3C2Tx MXene in the structure including Ti3C2, Ti3C2F2, Ti3C2(O)2 and Ti3C2(OH)2 is shown in Fig. 6a–d, respectively. Among four kinds of MXene, the maximum average emissivity of Δε = 0.41 is achieved for VO2/SiO2/Ti3C2F2 in Fig. 6b under considering both two different thicknesses. Also, this value of average emissivity happens for VO2/SiO2/Ti3C2(O)2 by considering \({\text{d}}_{{{\text{SiO}}_{2} }} = 1200\;{\text{nm}}\) in Fig. 6c. The minimum average emissivity of Δε = 0.22 and 0.32 occurs for the structure of VO2/SiO2/Ti3C2(OH)2 by considering \({\text{d}}_{{{\text{SiO}}_{2} }} = 900\;{\text{nm}}\) and 1200 nm, respectively in Fig. 6d. The threshold temperature of the hysteresis loop for the heating and cooling process occurs at the fixed regions for all kinds of Ti3C2Tx MXene. The details of average emissivity of two semiconductor and metallic states is summarized in Table 2.
The effect of Ti3C2Tx MXene thickness on the average emissivity of the proposed thermal emitter by considering VO2 and SiO2 thicknesses 15 nm and 1050 nm, respectively is investigated in Fig. 7 for four kinds of Ti3C2Tx MXene. The two different thicknesses of Ti3C2Tx MXene \({\text{d}}_{{{\text{MXene}}}} = 1\;\upmu {\text{m}}\) and 2 µm is studied in this part.
Average emissivity of the proposed VO2/SiO2/Ti3C2Tx MXene thermal emitter for different thicknesses of Ti3C2Tx MXene by considering four kinds of Ti3C2Tx MXene in the structure. Average emissivity of (a) VO2/SiO2/Ti3C2, (b) VO2/SiO2/Ti3C2F2, (c) VO2/SiO2/Ti3C2(OH)2 and (d) VO2/SiO2/Ti3C2O2.
The average emissivity measurements reveal interesting thickness-dependent behavior: variations in the thickness of Ti3C2F2 and Ti3C2(OH)2 MXene layers do not significantly affect the overall emissivity, maintaining consistent differential emissivity values of Δε = 0.42 and Δε = 0.30, respectively. The emissivity remains constant due to the significantly smaller electromagnetic penetration depth in Ti3C2F2 and Ti3C2(OH)2 compared to the film thickness. When the film thickness exceeds the penetration depth, additional material thickness does not contribute to radiative properties, resulting in unchanged emissivity. This phenomenon is consistent with the recent comprehensive analyses by Han et al.28 and Huang et al.16, which systematically examined infrared interactions in MXene materials.
For the two other kinds of Ti3C2Tx MXene; Ti3C2 and Ti3C2O2 in Fig. 7a,c, the differential emissivity decreases with increasing the thickness which the findings are summarized in Table 2. The temperature threshold of the hysteresis loop for the heating and cooling occurs at the fixed temperature similar to the VO2 and SiO2 size effects on the differential average emissivity which we investigated in Figs. 5 and 6.