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Abstract
Putrescine and cadaverine are significant volatile indicators used to assess the degree of food spoilage. Herein, we propose a micro-nano multi cavity structure for surface-enhanced Raman spectroscopy (SERS) to analyze the volatile gas putrescine and cadaverine in decomposing food. The MoS2 nano-flowers are inserted into a PVDF micro-cavity through in-situ growth, followed by vacuum evaporation technology of Ag nanoparticles to form an Ag/MoS2 nano-flower cavity/PVDF micron-bowl cavity (FIB) substrate. The micro-nano multi cavity structure can improve the capture capacity of both light and gas, thereby exhibiting high sensitivity (EF = 7.71 × 107) and excellent capability for gas detection of 2-naphthalenethiol. The SERS detections of the putrescine and cadaverine are achieved in the spoiled pork samples with the FIB substrate. Therefore, this substrate can provide an efficient, accurate, and feasible method for the specific and quantitative detection in the food safety field.
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1. Introduction
With the remarkable improvement of living standards, food safety and quality have been paid more and more attention [1–4]. As is known to all, spoiled meat gives off a distinctive odor, primarily due to the production of gases such as cadaverine and putrescine, which poses serious risks to human health, such as inducing cough, nausea, vomiting, and even death [5–8]. Currently, traditional methods for detecting biogenic amines mainly include high-performance liquid chromatography (HPLC) and gas chromatography coupled with mass spectrometry (GC-MS), which has the disadvantages of expensive equipment, tedious sample pretreatment, and the requirement for professional technicians [9].
As nondestructive analytical technique, surface enhanced Raman spectroscopy (SERS) can provide specific information about compound molecules with excellent detection sensitivity and distinctive fingerprint effect [10–15]. In general, it is widely accepted that the SERS enhancement mechanism mainly includes the electromagnetic mechanism (EM) induced by localized surface plasmon resonance (LSPR) and the chemical mechanism (CM) caused by the charge transfer between the adsorbed molecules and the substrate [16–21]. Different from the solid and liquid molecules, gas molecules have higher kinetic energy but lower number density, which is hard to be captured by the “hot spots”. In other words, gas molecules near the SERS “hot spots” are not easily adsorbed because of their low affinity, resulting in poor selectivity. Therefore, it is still challenging to detect gas molecules with the SERS [22–25].
The cavity structures have been attached more and more attention to enhance the SERS performance over the years. Cavity structures are of great interest due to their larger surface area and light-focusing properties, which benefits in capturing the laser, increasing the light path, and further promoting the interactions between photons and absorbed molecules [26–29]. Tian et al. prepared the bottom bowl-shaped silver cavity film on polystyrene microsphere template by electrodeposition, and assessed the significant enhancement, repeatability and practical applicability for protein [30]. Wang et al. transformed rigid Anodized Aluminum Oxide (AAO) into flexible AAO thin films through aluminum-based etching, producing SF-AAO-Au ultra-thin cavities to construct efficient dual-functional SERS wearable sensors [31]. Gao et al. designed a 4-inch ultrasensitive micro-nano porous structure of Ag/Si/Ag substrate for SERS characterization of gaseous aldehyde, realizing a real sense of use in auxiliary diagnosis of early lung cancer [32]. Nevertheless, there is limited application of cavity structures in gas detection, primarily due to the low affinity and poor adsorption capacity of gas molecules to simple cavity structures. To enhance the substrate to capture gas molecules, it is necessary to combine other structures or noble metals to generate more SERS “hot spots”, thereby introducing effective plasmonic coupling.
Herein, we propose a micro-nano multi cavity substrate with Ag/MoS2 nano-flower cavity/PVDF micron-bowl cavity (FIB) structure. MoS2 nano-flower cavity is grown on PVDF micron-bowl cavity membrane by hydrothermal method and silver nanoparticles (Ag NPs) are deposited on the substrate to form micro-nano multi cavity structure. This structure not only can provide a larger surface area, but also can effectively enhance the light-trapping effect, thus significantly enhancing plasmonic couple effect. Rhodamine 6 G (R6 G) and crystal violet (CV) are detected successfully, with detection concentration low to 10−10 M. The micro-nano multi cavity structure also provides more adsorption sites for gas molecules, so that gaseous molecules 2-naphthalenethiol (2-NAT) can be successfully detected with a detection limit of 10−5 M. After 4-Mercaptobenzoic acid (4-MBA) molecular modification on the FIB substrate, we successfully achieve the specific detection of cadaverine and putrescine to assess the freshness of pork samples. This work indicates that the FIB substrate possesses great potential in gas molecular detection.
2. Results and discussion
To fabricate the FIB substrate, we adopt a one-step hydrothermal method, with the preparation process in Fig. 1 and the details is presented in Supplement 1. The morphologies of the substrate are observed and characterized by scanning electron microscopy (SEM). As shown in Fig. 2(a), the SEM image of the polystyrene (PS) microsphere template exhibits a neat, smooth, and ordered array structure, which can greatly improve the uniformity of the substrate. Figure 2(b) displays the SEM image of the PVDF micron-bowl cavity membrane prepared from the Ag-PS microsphere template, showing a well-arranged micron-bowl cavity structure with clear edges and complete morphology, which is beneficial for the obtaining stable SERS signal. After 7 h of hydrothermal treatment, the uniform growth of MoS2 nano-flower in the PVDF micron-bowl cavity membrane can be observed, and the vertical MoS2 exhibits closely aligned flake-like structure, while the interlacing nanosheets form a new cavity shown in Fig. 2(c). Such structure can effectively capture incident light and improve the utilization of light. To enable the substrate with SERS activity, the Ag film is deposited on the obtained substrate to form Ag NPs (Fig. 2(d)), which can generate dense SERS “hot spots”, providing a possibility for improving SERS activity. Figure 2(e) displays the Raman spectra of MoS2 on the FIB structure, where two typical vibrational peaks at about 378 and 406 cm-1 are found corresponding to the in-plane vibration of Mo and S atoms ($\textrm{E}_{\textrm{2g}}^\textrm{1}$) and the out-of-plane lattice vibration of S atoms (${\textrm{A}_{\textrm{1g}}}$), respectively. Additionally, the energy dispersive spectroscopy (EDS) elemental mapping of the sample, as depicted in Supplement 1, Fig. S1, clearly reveals the presence of Mo (purple) and S (orange) elements within the substrate. To explore the size distribution of MoS2 nanosheets and Ag NPs, they are characterized in detail and the results are shown in Supplement 1, Fig. S2. The average length of the MoS2 nanosheets is determined to be 107 nm, while the average size of the Ag NPs is about 18 nm. In order to analyze the elemental composition and substrate state changes, we conduct qualitative and quantitative analysis using X-ray photoelectron spectroscopy (XPS) on the FIB substrate. In Fig. 2(f), the XPS survey spectra of the FIB substrate reveal the presence of Mo, S, and Ag elements, in addition to C 1s (285.0 eV) and O 1s (532.5 eV). High-resolution spectra for the Mo 3d, S 2p, and Ag 3d regions of the FIB substrate are presented in Fig. 2(g-i). Two characteristic peaks at 229.15 and 232.36 eV are detected as shown in Fig. 2(g), namely to the Mo 3d5/2 and Mo 3d3/2 orbitals, indicating that the predominant oxidation state of Mo in the MoS2 matrix is IV (Mo4+) [10]. Additionally, the S 2s peak at 226.34 eV and the Mo6+ peak at 236.08 eV is primarily attributed to surface oxidation of MoS2 [33]. Meanwhile, in the high-resolution S 2p spectrum shown in Fig. 2(h), we observe two separate peaks at 163.19 and 162.09 eV associated with the S 2p1/2 and S 2p3/2 orbitals of divalent sulfide ions (S2-), respectively [34]. Besides, the presence of Ag NPs is supported by two peaks at 368.46 eV and 374.45 eV for Ag 3d5/2 and Ag 3d3/2, respectively in Fig. 2(i). All of these characterizations provide clear evidence for the successful synthesis of the FIB substrate.
Fig. 1. Illustration diagram of the fabrication process for the Ag/MoS2 nano-flower cavity/PVDF micron-bowl cavity (FIB) substrate.
Fig. 2. Scanning electron microscope (SEM) images of (a) PS microsphere array template, (b) PVDF micron-bowl cavity membrane, (c) MoS2 nano-flower cavity/PVDF micron-bowl cavity substrate, (d) Ag/MoS2 nano-flower cavity/PVDF micron-bowl cavity substrate (FIB). (e) Surface enhanced Raman scattering (SERS) spectra of the MoS2 on MoS2/PVDF substrate. (f) X-ray photoelectron spectroscopy (XPS) spectra. High-resolution XPS spectra of (g) Mo 3d, (h) S 2p, and (i) Ag peaks.
To optimize the SERS effect of the FIB structure, we deposit different thicknesses of Ag layers on the substrate surface, as shown in Fig. 3(a-f). As the thickness of the deposited Ag NPs gradually increased, the morphology of the Ag NPs transition from irregular sizes and relatively disperse distribution to uniform sizes and dense coverage, ultimately achieving complete coverage and top aggregation. It is evident from the above SEM results that with the increasing thickness of the Ag layer, the MoS2 nano-flower cavity structure is gradually filled with the thick Ag, which is a critical factor affecting the morphology and SERS performance of the FIB substrate. Additionally, the SERS effect of FIB substrates with different thicknesses of silver is compared as shown in Fig. 3(g-i). In Fig. 3(g), it can be seen that as the thickness add from 10 to 20 nm, the strength of the Raman peaks increases firstly as the formation of denser Ag NPs, which can produce more “hot spots”. However, as the thickness further increase to 30 nm, the intensity decreases for the aggregation of Ag NPs leading to a weakening of plasmonic couple. Therefore, it can be concluded that the optimal SERS performance is achieved at a thickness of 20 nm.
Fig. 3. (a) SEM image of MoS2 nano-flower cavity/PVDF micron-bowl cavity substrate. (b)-(f) SEM image of the FIB substrate with different Ag thickness at 10, 15, 20, 25, 30 nm. (g) Raman spectra of R6 G alcoholic solution (10−5 M) detected on the FIB substrate with different Ag thickness. (h), (i) Variation of the SERS intensity at peaks of 613 and 774 cm-1 with the change of Ag thickness.
To better comprehend the enhancement mechanism and demonstrate the advantage of the FIB substrate for SERS performance, we collected the Raman spectra on different substrates, including Ag/PVDF, micron-bowl cavity Ag/PVDF, Ag/MoS2/PVDF and FIB substrates. It is worth noting that, as shown in Fig. 4(a), the intensity of the SERS spectral collected on the micron-bowl cavity Ag/PVDF is higher than that of the Ag/PVDF. The reason for this phenomenon may be the introduction of the micron-bowl cavity, which can effectively enhance the interaction between light and Ag NPs by virtue of the light-trapping effect, resulting in a stronger local enhanced electric field [35]. The intensity of the SERS spectral on the FIB substrate is highest compared with the former two cases, primarily attributed to the synergistic effect of the PVDF micron-bowl cavity and MoS2 nano-flower cavity structures. As we mentioned above, this micro-nano multi cavity structure not only can significantly increase the specific surface area, providing more adsorption sites for molecular, but also can effectively enhance the light-trapping effect [36,37]. To further investigate the optical properties of the proposed substrates, the reflectance spectra were collected and shown in Fig. 4(b), where we can see clearly that the reflectance of the micron-bowl cavity Ag/PVDF substrate is significantly lower than that of the Ag/PVDF substrate, validating the exceptional light-focusing capabilities of the micron-bowl structures [38,39]. After the in-situ growth of MoS2 nanoflower cavities within the PVDF micron-bowl, the reflectance further reduces, indicating the light trapping capacity of the micro-nano multi cavity structures.
Fig. 4. (a) Raman spectra of R6 G alcoholic solution (10−5 M) recorded on the FIB, Ag/PVDF micron-bowl cavity, Ag/MoS2/PVDF, and Ag/PVDF substrate. (b) Reflectance spectra of the substrates mentioned above. (c) Simulated vertical electric field distribution of Ag/PVDF, Ag/MoS2/PVDF, Ag/PVDF micron-bowl cavity and FIB substrate.
To visualize the intensity and distribution for the electromagnetic field, we employed Finite-Difference Time-Domain (FDTD) simulations. The sizes of MoS2 nanosheets and Ag NPs required for modeling are set based on the actual dimensions obtained from scanning electron microscopy, as shown in Supplement 1, Fig. S2. We can observe that the electric field is focused within the Ag/PVDF micron-bowl cavity substrate, exhibiting a typical resonant cavity effect in Fig. 4(c) and its local electric field intensity is stronger than that of Ag/PVDF substrate, resulting in higher SERS activity [40]. Compared with that on the Ag/MoS2/PVDF substrate, it can be observed that the electric field intensity of the FIB substrate is improved about 100 folds, which can attribute to the synergistic effect of the micro-nano multi cavity structure [41,42]. Additionally, for the case of the FIB substrate, “hot spots” not only distributes between Ag NPs but also on the top of the nanosheets, which is much beneficial for the achievement of the outstanding SERS performance [43].
To quantify the SERS performance of FIB substrates, the EF was assessed using the formula listed below [44–46]:
The calculated EF for the 613 cm-1 characteristic peak is 7.71 × 107 with ISERS = 216, CSERS = 10−10 M, IRS = 28, and CRS = 10−3 M. The reference data for Raman spectra of R6 G alcohol solution in FIB (10−10 M) and PVDF membrane (10−3 M) are shown in Supplement 1, Fig. S3. The calculated EF value is slightly higher than the simulated FDTD value, which may be attributed to the following reasons: (1) In the experimental setup, the laser spot is approximately 1 µm, which covers not just one but multiple PVDF micron-bowl cavities due to their smaller individual diameters (approximately 750 nm). In contrast, the simulation model only considers a single cavity and does not account for interactions between neighboring cavities. (2) The synergistic effects of numerous MoS2 nano-flower cavities may be influencing the SERS performance. In fact, within a single PVDF micron-bowl cavity, there are many intertwined MoS2 nanosheets, while the simulation model only considers nine neatly arranged MoS2 nanosheets. These factors highlight the complexities and interactions present in the actual experimental system, which may lead to differences between the calculated and simulated enhancement factors.
Sensitivity, quantitative detection ability, uniformity, and stability is crucial for evaluating the performance of SERS substrates. Therefore, the suitability of the FIB substrate for SERS is investigated. Figure 5(a) displays the Raman signals obtained from the FIB substrate at different concentrations (10−10 -10−5 M) of R6 G. The inset in Fig. 5(a) shows the characteristic peaks even at the detection limit of 10−10 M, indicating that the FIB substrate the well sensitivity. Besides, the FIB substrate also exhibits outstanding detection capabilities for other molecules, as shown in Fig. 5(b), where the detection limit for CV is also 10−10 M, demonstrating the universality. Subsequently, the intensity of the characteristic peaks at 613, 774, and 1650 cm-1 for R6 G is used to illustrate the relationship between intensity and concentration on a logarithmic scale (Fig. 5(c)). The relationships between the intensities of these three characteristic peaks and concentration can be expressed by the equations $\textrm{Log}(\textrm{I} )\textrm{ = 0}\textrm{.35Log}(\textrm{C} )\textrm{ + 5}\textrm{.80}$, $\textrm{Log}(\textrm{I} )\textrm{ = 0}\textrm{.31Log}(\textrm{C} )\textrm{ + 5}\textrm{.27}$, and $\textrm{Log}(\textrm{I} )\textrm{ = 0}\textrm{.37Log}(\textrm{C} )\textrm{ + 5}\textrm{.51}$, respectively, with average correlation coefficients of 0.994, 0.986, and 0.972, indicating a good linear relationship. Similarly, as shown in Fig. 5(d), we chose the characteristic peaks of CV molecules at 913, 1175, and 1620 cm-1 to obtain linear fitting relationships expressed as $\textrm{Log}(\textrm{I} )\textrm{ = 0}\textrm{.28Log}(\textrm{C} )\textrm{ + 4}\textrm{.62}$, $\textrm{Log}(\textrm{I} )\textrm{ = 0}\textrm{.31Log}(\textrm{C} )\textrm{ + 4}\textrm{.78}$, and $\textrm{Log}(\textrm{I} )\textrm{ = 0}\textrm{.30Log}(\textrm{C} )\textrm{ + 4}\textrm{.66}$, with R2 values of 0.978, 0.986, and 0.979, respectively. This demonstrates that the FIB substrate has excellent quantitative detection capability for probe molecules. To evaluate the uniformity of the SERS signal on the FIB substrate, an area of 1 × 1 µm2 with 10−7 M R6 G is selected, and mapping spectra are obtained (Fig. 5(e)). The relative standard deviation (RSD) is found to be 8.95%, with an RSD of less than 20%, which is generally considered relatively uniform compared to various influencing factors in SERS technology [47]. To test the stability of the FIB substrate, we collect SERS spectra (R6 G, 10−6 M) from ten randomly selected points on the same FIB substrate after storage of one day, ten days, twenty days, and thirty days. The average intensities of the characteristic peaks at 613, 714, and 1650 cm-1 only slightly decrease after thirty days (Fig. 5(f)), which may be attributed to the close contact between MoS2 and Ag nanoparticles to some extent preventing the oxidation of Ag. This indicates that the FIB substrate possesses excellent stability.
Fig. 5. (a) Raman spectra of R6 G alcoholic solution from 10−10 to 10−5 M recorded on the FIB substrate. The inset is an enlarged view of the Raman spectra of the R6 G solution (10−10 M) detected by the FIB substrate. (b) Raman spectra of CV alcoholic solution from 10−10 to 10−5 M recorded on the FIB SERS substrate. (c) The relationship between the peak intensity of 613, 774 and 1650 cm-1 and the logarithmic concentration. (d) The relationship between the peak intensity of 913 and 1620 cm-1 and the logarithmic concentration. (e) Raman mapping of 10−7 M R6 G measured at 774 cm-1. (f) The intensity of three main characteristic peaks (10−6 M) detected on the FIB SERS substrate per 10 days.
As we mentioned above, the SERS detection for gas molecule analytes still presents a significant challenge. It requires capturing and detecting diffusive molecules while maximizing their escape time from the substrate. In this study, 2-NAT molecule was employed to preliminarily explore the capability of FIB substrates for capturing and SERS detecting gas molecules. First, 1 milliliter of 2-NAT alcohol solution at different concentrations (10−5-10−1 M) was separately dispensed into 4-milliliter centrifuge tubes. Simultaneously, FIB substrates were fixed to the inner surface of the centrifuge tube caps. Subsequently, all centrifuge tubes were heated in a water bath at 60 °C for 1 hour, causing the gradual evaporation of the 2-NAT solution, leading to the formation of gas molecules that were captured by the FIB substrates. The use of FIB substrates enabled the capture of the evaporated 2-NAT molecules within intricate micro-nano multi cavity structures, facilitating sensitive SERS detection of gas molecules, as shown in Fig. 6(a). Remarkably, even for a 2-NAT solution with a concentration as low as 10−5 M, the clear characteristic peaks can also be detected, which indicates the excellent gas molecule detection capabilities of FIB substrates. The intensity of the 2-NAT characteristic peak at 1381 cm-1 was employed to illustrate the relationship between intensity and concentration, as shown in Fig. 6(b). The relationship between the intensity of the 1381 cm-1 characteristic peak and concentration can be expressed by the formula: $\textrm{Log}(\textrm{I} )\textrm{ = 0}\textrm{.34Log}(\textrm{C} )\textrm{ + 3}\textrm{.5}$. The average correlation coefficient was 0.957, indicating a strong linear relationship. This suggests that FIB substrates also possess outstanding quantitative detection capabilities for 2-NAT molecules. To further evaluate the ability of different structural substrates to detect gas molecules, we employed the same method to analyze the Raman spectra of Ag/PVDF, micron-bowl cavity Ag/PVDF, Ag/MoS2/PVDF, and FIB substrates with a 10−2 M 2-NAT solution. Figure 6(c) illustrates that the FIB substrate exhibits the highest Raman peak intensity. This is primarily attributed to the synergistic effect of MoS2 nanosheets and PVDF micron-bowl cavities, enhancing the detection performance. Particularly, the micro-nano cavity structures can promote the aggregation of gas molecules and provide additional enhancement of SERS signals. In summary, FIB substrates exhibit excellent capabilities for the detection of gas molecules.
Fig. 6. (a) Raman spectra of 2-NAT with the concentration ranging from 10−5 to 10−1 M on the FIB substrate. (b) The relationship between the peak intensity of 1381 cm-1 and the logarithmic concentration. (c) Raman spectra of 2-NAT (10−2 M) as the probe molecule on four substrates. (d-e) Schematic representation of the detection of putrescine and cadaverine using 4-MBA functionalized FIB substrate. (f) Raman spectra of 4-MBA with the concentration ranging from 10−7 to 10−4 M on the FIB substrate. (g) Photograph of storage container for detection of putrescine and cadaverine using 4-MBA functionalized FIB substrate. (h) SERS spectra measured from FIB substrate by varying the reaction time of putrescine and cadaverine from 0 to 24 h. (i) SERS spectra measured from FIB substrate after reaction with diverse gaseous molecules.
Cadaverine and putrescine are gas indicators of food spoilage, and their presence can cause serious harm to human health. Therefore, there is an urgent need for a fast and accurate detection method to monitor their existence. Currently, there is still a lack of cadaverine and putrescine detection methods based on SERS. As demonstrated above, the FIB substrates have excellent gas capturing capabilities and can be used to detect cadaverine and putrescine generated in daily life. For more accurate detection, the FIB substrate is modified with 4-MBA. It can act as a specific receptor for Raman probe molecules and react with volatile amine molecules through the Schiff base reaction to produce p-mercapto-N-(4-amino butylidene) aniline and p-mercapto-N-(5-amino pentylidene) aniline, respectively (Fig. 6(e-f)) [48,49]. Figure 6(d) displays the Raman signals obtained from the FIB substrate at different concentrations (10−7-10−4 M) of 4-MBA. The intensity of the characteristic peak varies with the concentration, while the location of the peak remains unchanged. After placing the fresh pork at the bottom of the container, the FIB substrate containing 2 µL of 4-MBA (10−2 M) alcohol solution is fixed to the container lid and then places in 37 °C incubator, as shown in Fig. 6(g). According to the presentation in Fig. 6(h), the typical SERS peaks at 1640 cm-1 gradually increased in intensity over a time range of 0 to 20 hours, indicating that the gas molecules of cadaverine and putrescine were continuously generated and reacted with 4-MBA on the substrate. However, after 20 hours, the typical SERS peak intensity remained unchanged, indicating that the signal had reached a stationary state and the SERS substrate surface had been saturated with molecules. Raman spectrum comparison with 4-MBA shows that a new characteristic peak appeared at 1640 cm-1, corresponding to C-N stretching in imine, indicating that a new chemical bond is formed between the -NH2 groups in cadaverine and putrescine and the -CHO groups in 4-MBA [50]. This indicates that the modified substrate can detect cadaverine and putrescine produced during pork deterioration, and the intensity of the new characteristic peak increases with the extension of reaction time. Except for the two gases mentioned above, several other gas molecules, such as H2S, MeOH, N-hexane and dichloromethane, are related to pork spoilage. To explore the specificity of this method, SERS detection is conducted on these molecules, which displays when cadaverine and putrescine are detected, a characteristic peak of 1640 cm-1 appears, while other volatile gases do not (Fig. 6(i)), which further proves that the 4-MBA modified substrate is feasible for the specific detection of cadaverine and putrescine. The FIB substrate realizes the specificity and high sensitivity detection of volatile amine molecules produced by pork spoilage under complex environment, and provides a new SERS method for gas molecular detection.
3. Conclusion
In summary, the FIB substrate has been developed via growing MoS2 nano-flower cavity in PVDF micron-bowl cavity membrane and applied in food spoilage detection. The SERS detection results indicate that the detection limit of R6 G and CV molecules in the solution is up to 10−10 M, and the detection limit of 2-NAT gas molecules is up to 10−5 M. The micro-nano multi cavity structure not only can significantly increase the specific surface area, providing more adsorption sites for molecular, but also can effectively enhance the light-trapping effect. After 4-MBA modification, the FIB substrate can achieve the specific detection of cadaverine and putrescine molecules, so as to complete the evaluation of pork freshness. It is anticipated that FIB substrates can be used for the detection of various gas molecules, and will be widely applied to food quality detection, environmental monitoring, disease diagnosis and so on.
Funding
National Natural Science Foundation of China (12174229, 11974222, 11904214, 12004226); Taishan Scholars Program of Shandong Province (tsqn202306152); Qingchuang Science and Technology Plan of Shandong Province (2021KJ006); Natural Science Foundation of Shandong Province (ZR2022YQ02); China Postdoctoral Science Foundation (2019M662423).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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