Humidity-driven nonlinear modulation of graphene reflectivity via interfacial wetting behavior

Humidity-driven nonlinear modulation of graphene reflectivity via interfacial wetting behavior | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Humidity-driven nonlinear modulation of graphene reflectivity via interfacial wetting behavior Cheng Li, Yang Liu, Zhen Wan, Tiantian Ma, Wei Zhou, Shang-Chun FAN This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7814470/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Graphene’s moisture absorption significantly impacts its optical reflectivity, leading to measurement errors in graphene-based optoelectronic devices. The mechanism underlying this humidity effect remains unclear. Here we developed a portable fiber optic Fabry–Perot (F–P) probe with a 10-layer graphene film to in situ investigate the non-monotonic changes in reflectivity across varying humidity conditions. The probe showed a 49.8% modulation range in reflectivity between 8 and 67.5% relative humidity (RH). Wetting experiments and COMSOL simulations reveal that humidity-driven changes in graphene reflectivity are due to droplet diameter growth. From 7.5 to 31.3% RH, increasing droplet size enhances scattering with weak absorption, resulting in a positive reflectivity-humidity correlation. From 31.3 to 66.3% RH, larger droplets reduce scattering and increase absorption, shifting the correlation to negative. We establish a quadratic relationship between reflectivity and humidity, allowing for a corrective method that narrows the operational range to 53.9–58.9% RH, minimizing humidity-induced reflectivity fluctuations. This method defines optimal humidity conditions for stable operation of graphene-based optoelectronic devices and offers a feasible route for probing humidity-sensitive behaviors in other two-dimensional materials. Physical sciences/Materials science/Nanoscale materials/Graphene/Optical properties and devices Physical sciences/Nanoscience and technology/Graphene/Optical properties and devices Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction As a monolayer of sp 2 -hybridized carbon atoms, graphene is the fundamental building block of carbon allotropes and offers exceptional optical, electrical, mechanical, and thermal properties, making it a promising material for transistors, transparent electrodes, and sensors. 1 – 5 However, the humidity absorption characteristics of graphene, driven by the inevitable adsorption of ambient water vapor, significantly affect the performance of graphene-based devices particularly in optoelectronics. 5 – 8 These characteristics lead to changes in graphene’s reflectivity, which directly impacts the functionality of devices such as sensors and modulators. For instance, a 50% variation in graphene's reflectivity can lead to a 22% change in the sensitivity of Fabry–Perot (F–P) acoustic sensors, a 50% shift in light modulator output, and a 50% change in photodetector responsivity (detailed analysis in Supplementary Note 1, Supporting Information). 9 – 13 To improve device reliability, it is essential to disclose the humidity-reflectivity relationship and the mechanism behind graphene's wetting behavior. However, the relationship between humidity and reflectivity has not been previously reported. Most studies on graphene reflectivity use optical microscopy, Raman spectroscopy and Fourier transform infrared spectroscopy. 14 – 16 For example, Nair et al. analyzed the transmittance of suspended graphene with varying layers using optical microscopy and found that the reflectivity of monolayer graphene is just 0.01%. 15 Microscopic instruments limit in-situ reflectivity measurements under varying humidity. F–P interference spectroscopy offers a portable and miniaturized probe for measuring reflectivity in humid environments, 17 overcoming conventional technique limitations for few-layered graphene. Building on this, our group has developed a platform utilizing the F–P probe for accurate reflectivity testing. 18 Under humid conditions, graphene's reflectivity is influenced by its wetting behavior and the state of droplets on its surface. Mie theory has been used to calculate optical parameters such as extinction and scattering efficiencies for spherical water droplets, revealing how reflectivity depends on temperature and droplet size. 19 However, accurately measuring the refractive index of micro-scale droplets remains challenging. Recent advances, such as a non-contact method combining digital image correlation and an inverse approach, enable high-precision analysis of both the refractive index and concentration of micro-droplets. 20 Most studies focus on suspended droplets, 19–21 with few addressing droplets adsorbed on graphene surfaces, where reflectivity is influenced by both the droplet’s intrinsic properties and the substrate. Droplet shape modified by surface energy and hydrophobicity changes with varying contact angle (CA), which is also affected by humidity. 22 , 23 However, the combined effect of adsorbed droplets and substrate on humidity-driven reflectivity remains unexplored. In this paper, we present a portable fiber-optic F–P probe integrated with 10-layer graphene, enabling in situ measurement of a quadratic relationship between ambient humidity and graphene reflectivity. Micro-characterizations using environmental scanning electron microscopy (ESEM) and optical microscopy were performed to establish a quantitative relationship between graphene's wettability behavior and humidity levels. Wetting experiments and COMSOL simulations demonstrate that droplet diameter and adsorption density primarily govern the modulation of graphene reflectivity. Humidity-driven nonlinearity arises from competing mechanisms of droplet light absorption and scattering. Leveraging this correlation, we propose a correction method that defines an operational range of 53.9% relative humidity (RH) to 58.9% RH, minimizing the humidity-induced effects on graphene optoelectronic devices. This integrated microanalysis-simulation approach is broadly applicable to other two-dimensional (2D) materials. Results and Discussion Structure and Characteristics of the F–P Probe The proposed portable, miniaturized F–P probe consists of a 10-layer graphene diaphragm, two ferrules, a sleeve, and a single-mode fiber (Fig. 1 a). In detail, a ferrule is covered with graphene to form a suspended diaphragm with a diameter of 125 µm, while the other ferrule is utilized to fix the single-mode fiber. To obtain suspended graphene in absence of contamination for accurate CA measurements, a polymer-free transfer method was employed (Fig. S1 , Supporting Information). 24 The side hole of the sleeve enabled direct contact between the graphene diaphragm and the external environment, thereby achieving humidity sensing. The air cavity between the graphene and the end face of the single-mode fiber forms the F–P cavity. In this case, the reflectivity of the graphene diaphragm can be determined by fitting the F–P interference spectrum obtained by an optical spectrum analyzer (OSA) (refer to Supplementary Note 2, Supporting Information, for details). Correspondingly, the image of the as-fabricated F–P probe is presented (Fig. 1 b). The scanning electron microscope (SEM) image illustrates that the residual impurities have been completely removed and that the center hole of the ferrule has been covered intacted (Fig. 1 c). Following structural characterization, the suspended graphene's quality was evaluated through Raman spectroscopy (Fig. 1 d). 25 – 27 The Raman spectrum shows the high crystallinity of the graphene diaphragm. Specifically, the absence of the D peak (1350 cm – 1 ) in the Raman spectrum represents the low concentration of defects in graphene. The intensity ratio of the G (1580 cm – 1 ) and 2D (2700 cm – 1 ) peaks is approximately 2.76, which is higher than that (0.3) of monolayer graphene. 28 – 30 For observing a more accurate thickness of graphene, an atomic force microscope (AFM) characterization was performed. The thickness of graphene is measured to be 3.3 nm (Fig. 1 e), which is close to the theoretical thickness of 10-layer graphene. It should be noted that there is a slight deviation between the measured thickness and the typical thickness (10-layer) of the commercial graphene. This discrepancy can be attributed to the inevitable inconsistency of the chemical vapor deposition process and the measurement accuracy of AFM. 31 The Influence of Humidity on Graphene Reflectivity By means of the reflectivity-humidity experimental setup (Fig. 2 a; Fig. S2, Supporting Information), the optical reflectivity of suspended graphene on four F–P probes was measured under various RH at room temperature. Figure 2 b displays the F–P interference spectra under different humidity conditions. These data visually illustrate the impact of humidity on the amplitude and wavelength shift of the F–P interference spectra. Notably, a remarkable 8-nm red-shift of the peak wavelength is observed (Fig. 2 b), attributed to the corresponding increase in the F–P interference length (0.29 µm, Supplementary Note 3, Supporting Information). The primary reason for this phenomenon is the high sensitivity of ultrathin graphene to additional mass induced by water adsorption. 8 – 10 Correspondingly, the suspended graphene also experiences sinking. Moreover, variations in the F–P interference contrast, which are directly related to graphene reflectivity, can be visually observed under different RH levels. As shown in Fig. 2 c, with increasing relative humidity, the reflectivity of graphene initially rises before subsequently decreasing. Specifically, as the humidity increases from 8.0% RH to 30.8% RH, the reflectivity of graphene rises from 0.48% to 0.60%. Conversely, as the humidity increases from 30.8% RH to 67.5% RH, the reflectivity drops from 0.60% to 0.34%. Notably, the relative change in average reflectivity is 49.8%, indicating that environmental humidity is a key factor influencing the commercial application of graphene-based optoelectronic devices. Wetting Experiments of Graphene To gain a deeper understanding of the mechanism by which air humidity affects the optical reflectivity of graphene, the wetting behavior of graphene was first characterized using optical microscopy and ESEM. Note that all the micro-characterizations were conducted on the suspended graphene to exclude substrate interference. An optical characterization platform equipped with humidity control and digital image processing (HCDIP) was constructed (Fig. S3, Supporting Information) to perform in situ measurements of droplet diameter and attachment density in humid environments. After optical microscopy captured images of micro-droplets adsorbed on the graphene surface, the images were processed using the Canny algorithm and binary segmentation. Referring to the processed images (Fig. 3 a), the boundary between droplets and graphene can be clearly delineated. Accordingly, the ρ d and the average diameter of droplets can be determined (Fig. 3 b). With an increase in ambient humidity from ~ 7% RH to ~ 66% RH, the ρ d increase from 0% to 18.4%; and the average diameters increase from 0 µm to 2.50 µm. This phenomenon is related to enhanced hygroscopic growth caused by increased humidity. 32 , 33 Besides the ρ d and diameter, the CA of the micron-sized droplets on suspended graphene is also observed via ESEM (the experimrntal setup can be found in Fig. S4, Supporting Information). Unfortunately, the heat effect of the electron beam at extremely high magnification in ESEM can lead to evaporation of the droplets during the experiment. 34 Therefore, the maximum magnification of the ESEM was set from 800 × to 2500 ×. Concurrently, only fully intact droplets were selected for CA measurements. Typically, the droplet within a yellow box depicted in Fig. 3 c is selected, while the droplet below it has shown clear evidence of volatilization. The diameter (16 µm) and the CA (59.03 °) of the selected droplet are shown in Fig. 3 d, e, respectively. Similarly, the diameters and CA of a total of 17 full droplets are measured (Fig. S5, Supporting Information). The CA of droplets decrease with the increase in diameter (Fig. 3 f). It is noteworthy that the measured CA of droplets, ranging from 49.18° to 91.46°, are generally consistent with previously reported results, 35 confirming the validity of our measurements. From the data shown in Fig. 3 f, the relationship between CA and diameter can be determined to be y = − 15.92ln( x ) + 102.96 through the least squares fitting. Therefore, for the droplet diameters measured in Fig. 3 b (ranging from 1.37 µm to 2.50 µm), the corresponding CA can be predicted to be between 88.37° and 97.97° (Fig. S6, Supporting Information). We thus conclude that the hygroscopic growth induced by high RH promotes an increase in both the distribution density and the size of droplets on graphene. Meanwhile, the CA of the droplets decreases with the increase in droplets size. Simulation of the Nonlinear Modulation Mechanism of Humidity on the Reflectivity Based on the wetting behavior of graphene measured before, a finite element method (FEM) model was established via COMSOL to validate the effect of humidity on reflectivity and to understand its underlying mechanisms (Fig. 4 a; Fig. S7, Supporting Information). Given that the correlation indices ( R 2 ) are all equal to 1 (Fig. S8, Supporting Information), a strict linear dependence of reflectivity on wavelength (from 1555 nm to 1605 nm) can be inferred. Due to the averaging effect of the reflectivity fitting method (refer to Supplementary Note 2, Supporting Information, for details), the wavelength in the FEM simulation is set at a median value of 1580 nm to reduce computational complexity. Utilizing the ρ d , diameter, and CA of droplets on the graphene surface under varying humidity conditions presented in Fig. 3 , the simulated reflectivity for the graphene-droplet coupling system corresponding to humidity is obtained (Fig. 4 b). Both simulated and measured reflectivity increase as the RH rises from 7.5% to 31.3%, and decrease with further the RH increase. Thus, the simulated values closely align with the experimental values, validating the accuracy of the simulations. To investigate the mechanisms by which the CA, ρ d , and diameter of the droplet affect reflectivity, we first simulated the reflectivity of the system with CA ranging from 88° to 98° (Fig. S9, Supporting Information). According to Fig. S9, the relative changes in reflectivity for four representative droplet densities and sizes (3.3%, 1.37 µm; 6.8%, 1.72 µm; 11.2%, 1.94 µm; 18.4%, 2.50 µm) induced by variations in CA are all less than 1.3%. Hence, the influence of CA on reflectivity can be considered negligible. In this case, the CA was set to a median value of 93°, and the effects of varying ρ d (2% to 20%) and diameters (1.0 µm to 2.6 µm) on graphene reflectivity were simulated (Fig. 4 c). The results presented in Fig. 4 c indicate that as the droplet diameter increases from 1.0 µm to 2.6 µm, the reflectivity first increases and then decreases, with a maximum value occurring near a diameter of 1.8 µm. Additionally, higher droplet ρ d lead to a greater maximum and a smaller minimum in the diameter-reflectivity relationship. This phenomenon is primarily attributed to the enhanced influence of droplet diameter with increased ρ d . Notably, this explains why the slope of the reflectivity-humidity curve in Fig. 4 b is lower during the ascent than during the descent. Subsequently, the graphene width was set to 40 µm, substantially larger than the droplet diameter, isolating the non-monotonic effect of droplet diameter on reflectivity for investigation. To visually illustrate the reflection characteristics of the graphene-droplet-air system, near-field maps showing the electric field intensity as a function of droplet diameter (1 to 2.5 µm) are presented (Fig. 4 d). The weak localized electric fields inside the droplet are a result of light absorption. Furthermore, the localized enhanced electric fields beneath the droplet near the central axis arise from its convex lens effect. 36 According to Fresnel equations, 37 the field enhancement near the graphene interface within the droplet can be attributed to the increased incidence angle caused by this lens effect, resulting in an enhanced reflectivity of graphene. Remarkably, as the droplet diameter increases, the electric field intensity beneath the droplet in both graphene and air gradually intensifies (indicated by the red box in Fig. 4 d). For quantitative analysis, the average electric field energy in the region directly below the droplet is calculated (Fig. 4 e). The average electric energy increases from 9.14 × 10 –15 J to 9.18 × 10 –15 J as the droplet diameter rises from 1 µm to 2.5 µm. This phenomenon is attributed to droplet size-dependent light scattering. 19 , 38 , 39 In other words, as the droplet size increases, more light passes through it rather than being scattered. Consequently, humidity-induced nonlinear modulation of graphene reflectivity stems from competition mechanisms between droplet-mediated light scattering and absorption. Specifically, across 7.5–31.3% RH, reflectivity enhancement primarily originates from higher light scattering at the air-droplet interface. Concurrently, enhanced reflectivity due to elevated incidence angles at the water-graphene interface occurs while droplets remain too small to absorb this enhanced reflected light. Subsequently, as humidity rises from 31.3% to 66.3% RH, increasing droplet size augments absorption while reducing scattering, thereby reducing graphene reflectivity. Correction Method for the Optimal Operating Range Based on the Reflectivity-Humidity Curve Given the challenges in achieving low-humidity conditions in practical applications, this study established a correction method based on the quadratic relationship between graphene reflectivity and relative humidity. Specifically, using the reflectivity at the humidity level constructed by anhydrous CaCl 2 as a reference, another data point with identical reflectivity was identified on the quadratic fitting curve of reflectivity versus humidity. At this data point, a reflectivity error interval was constructed to determine the optimal operational humidity range for the device. To enhance the applicability of the results, we prepared three additional F–P probes, designated as Probe 2, Probe 3, and Probe 4, using the same method as described for Probe 1. The relative humidity and reflectivity corresponding to these four F–P probes are shown in Fig. 5 a, b, respectively. Notably, all four F–P probes exhibit the same nonlinear relationship between reflectivity and humidity. Quadratic fitting of the mean experimental results from the aforementioned four probes yielded the curve (Fig. 5 c): y = − 0.00019 x 2 + 0.01181 x + 0.41905 where x is RH, and y is reflectivity. For the low-humidity environment constructed with anhydrous CaCl 2 , the mean reflectivity is 0.48%. Correspondingly, the other data point on the fitting curve with identical reflectivity corresponds to 56.5% RH. Using a reflectivity of 0.48% as the baseline, the corresponding humidity ranges for the error bands are as follows: ±5% error band from 53.9% RH to 58.9% RH (optimal operating range), ± 10% error band from 50.9% RH to 61.0% RH, and ± 20% error band from 42.9% RH to 65.0% RH. Thus, 53.9–58.9% RH can be identified as the optimal RH range for the stable operation of graphene-based optoelectronic devices. Conclusions In conclusion, a humidity-dependent optical reflectivity was demonstrated in 10-layer graphene using a miniaturized F–P probe. We observe a non-monotonic relationship with reflectivity increasing from 0.48 to 0.60% as humidity rises from 8.0 to 30.8% RH, then decreasing to 0.34% at 67.5% RH, yielding a 49.8% modulation effect. Optical microscopy shows that droplet attachment density increases from 0 to 18.4%, and droplet diameter expands from 0 to 2.50 µm with humidity. ESEM analysis establishes a relationship between the CA and droplet diameter, showing that the CA increases logarithmically with droplet size. COMSOL simulations further explain that reflectivity modulation arises from competing light scattering and absorption mechanisms: initial enhancement is due to increased scattering, while later reduction is linked to higher absorption. We thus propose a correction method between reflectivity and humidity, identifying an optimal operating range (53.9–58.9% RH) with minimal influence on reflectivity, ensuring stable conditions for graphene-based optoelectronics. This work provides a theoretical foundation and correction framework to better understand the impact of humidity on the performance of optoelectronic devices. Additionally, the method developed for studying humidity-induced reflectivity changes can be applied to other 2D materials, expanding its broader applicability. Methods Materials The 10-layer copper-based graphene used in this study was purchased from Nanjing Jicang Nano Technology Co., Ltd. (Nanjing, China). Epoxy resin adhesive (14270) was obtained from Devcon (USA). Single-mode fiber was purchased from Haiyu Optical (Shenzhen, China). Mineral salts, including anhydrous CaCl 2 , LiCl, MgCl 2 , NaBr, and NaCl, were supplied by Aladdin Biochemical Technology Co., Ltd. (Shanghai, China). The sealed glass chamber was fabricated by Shaorui Quartz Products Co., Ltd. (Lianyungang, China). SiO 2 bonding material was sourced from Beijing GIN KOO MEMS Scientific & Technological Co., Ltd. (Beijing, China). Coverslips were acquired from Citotest Labware Manufacturing Co., Ltd. (Jiangsu, China). Transmission electron microscope (TEM) grids were obtained from Zhong Jing Ke Yi Co., Ltd. (Beijing, China). The 45° sample holder was machined by Keso Precision Machinery Co., Ltd. (Beijing, China). Graphene Transfer The transfer process of the commercially available copper-based 10-layer graphene, as described in previous studies, 40,41 involves three main steps. First, the copper-graphene film was cut into square pieces with a width of 1 mm and then etched in a 5% FeCl 3 solution. Once the copper was completely etched away, the FeCl 3 solution was diluted with deionized water until it became transparent. Finally, the pure graphene diaphragms were transferred onto the center hole of the ferrule and onto a TEM grid, respectively, using van der Waals forces. It is important to note that the ferrule and TEM grid with pure graphene were used for reflectivity measurements and micro-characterization, respectively. F–P Probe Fabrication The ferrule covered with pure graphene and a clean ferrule were placed at each end of the sleeve, as shown in Fig. 1 a. A single-mode fiber was inserted through the clean ferrule, establishing F–P interference. This configuration ensures precise alignment between the single-mode fiber and the graphene. The F–P interference length was determined to be approximately 58 µm, based on the interference spectrum obtained using an OSA (Yokogawa, AQ6370C, Japan) and a broadband light source (Amonics, ALS-CL-17, China). To maintain the stability of the F–P interference length, the end of the clean ferrule was sealed with epoxy resin adhesive. Graphene Characterization The thickness of the commercial 10-layer graphene diaphragm was measured using AFM (FSM, FM-Nanoview 6800, China). The microstructure of the graphene diaphragm was characterized through SEM (JEOL, JMC7000, Japan). Raman spectroscopy was performed by using a Raman spectrometer (LabRAM, HR Evolution, France). Measurement To measure the reflectivity of graphene under varying ambient RH, a reflectivity-humidity measurement setup was established (Figs. 2 a and Supplementary Note 2). Adjustable RH conditions were generated using saturated salt solutions, with humidity levels ranging from 7.5% RH to 66.3% RH, achieved through anhydrous CaCl 2 , LiCl, MgCl 2 , NaBr, and NaCl. RH was monitored using a commercial hygrometer (MIAOXIN, TH20BL-EX, China) with an accuracy of ± 2% RH. Before each reflectivity measurement, the F–P probe was exposed for 30 min to stabilize droplet adsorption. 8 Prior to changing RH levels, the F–P probe was first exposed to a dry environment using CaCl 2 for recovery. For droplet diameter and adhesion density in situ measurements, an optical characterization platform equipped with HCDIP was set up (Fig. S3, Supporting Information). This platform consists of a optical characterization section and a digital image processing section. In the optical characterization section, RH (7.5–66.3%) was adjusted using saturated salt solutions, with stability ensured by sealing gaskets and fastening bolts. Then, micro-characterization was performed using a TEM grid with graphene, positioned on the stage of the glass chamber. A coverslip was attached with SiO 2 bonding material to facilitate clear imaging. Each graphene sample was exposed for 30 min at each RH level. In the digital image processing section, continuous, smooth profile of droplets were obtained using the Canny edge detection algorithm. When a closed profile detected by the Canny algorithm exhibits high global smoothness and its average curvature value was significantly higher than that of the background, the contour segment was identified as a droplet edge. Subsequently, binary segmentation was applied to mark the interior of the closed profile as black and the background as white. By analyzing the number of droplets, the background area, and the droplet area, the average droplet diameter and adhesion density were derived. For CA measurements, condensation was observed using ESEM (Thermo Fisher, Quattro ESEM, USA) with an acceleration voltage of 25 kV (Fig. S4, Supporting Information). The temperature of the graphene sample and RH were controlled via a Peltier stage and vapor pressure. 24 , 35 The TEM grid with graphene was mounted on a 45° sample holder and placed on the Peltier stage. The stage was set to − 0.8°C, ensuring that the graphene sample reached near 0°C after heat transfer. Once the air pressure in the vacuum chamber was reduced to 133 Pa, saturated vapor injection began with vapor pressure increased at 50 Pa·min – 1 until saturation. For enhanced RH control accuracy, the vapor pressure increase rate was then reduced to 1 Pa·min – 1 . When the vapor pressure reached 830 Pa, the first visible droplet appeared. The droplets continued to grow at a steady rate, and CA was measured using the ImageJ DropSnake plugin from ESEM images of droplets on the suspended graphene. 35 , 42 FEM Simulation To analyze the influence of air humidity on the reflectivity of suspended graphene, the optical properties of graphene coupled with a droplet-laden air environment were studied over the 1555–1605 nm wavelength range using COMSOL Multiphysics wave optics simulation. The FEM model shown in Fig. S7 (Supporting Information) incorporates the wave optics physics field with a 2D mesh defined by free triangular elements. Given the approximate uniform distribution of droplets on the suspended graphene, periodic boundary conditions were applied to the side boundaries of the model, forming multiple unit cells. This approach significantly reduces computational time and resources. 43 In the simulation, light entered the model through the incident port and exits via the output port (Fig. 4 a). To mitigate the effects of unwanted reflections from the boundary, perfectly matched layers (PMLs) were employed. 44 The simulation parameters included a real refractive index of 3, an imaginary refractive index of 1.15, 45 a graphene thickness of 10 layers, and an incident light power of 1 W·m – 1 . The droplet coverage density ( ρ d ) was set between 2% and 20%, consistent with the measured values in Fig. 3 b. For the modeled unit cell (Figs. 4 a and S8, Supporting Information), the relationship between ρ d and droplet diameter was expressed in Eq. S-19 (refer to Supplementary Note 4, Supporting Information, for details). Additional details on the shape and size of water droplets on graphene are provided in the Supporting Information. Declarations Credit Authorship Contribution Statement Y.L. conceived the idea, conducted the experiments, and wrote the manuscript. C.L. analyzed the data and revised the original draft. Z.W. analyzed the data and supervised the work. T.M. analyzed the data. W.Z. conceived the idea and revised the original draft. S.F. supervised the study. All the authors discussed the results and revised the final manuscript. Conflict of Interest The authors declare no conflict of interest. Acknowledgments This work was supported by the National Natural Science Foundation of China (62173021, U23A20638). Data Availability Statement The data for all the work is available from the corresponding authors based on reasonable requests. References Dai H, Wang Y, Liu Z, Liu Y, Guo Y, Liu D (2025) Interlayer phononic energy dissipation in the friction of graphene layers. Sci Adv 11:eadu2880 Seki R, Takamatsu H, Suzuki Y, Oya Y, Ohba T (2021) Hydrophobic-to-hydrophilic affinity change of sub-monolayer water molecules at water-graphene interfaces. Colloids Surf A-Physicochemical Eng Aspects 628:127393 Kim L, Kim S, Jha PK, Brar VW, Atwater HA (2021) Mid-infrared radiative emission from bright hot plasmons in graphene. Nat Mater 20:805 Zhao J, Ji PX, Li YQ, Li R, Zhang KM, Tian H, Yu KC, Bian BY, Hao LZ, Xiao X, Griffin W, Dudeck N, Moro R, Ma L (2024) Heer, W. A. Ultrahigh-mobility semiconducting epitaxial graphene on silicon carbide. Nature 625:60de Geim AK, Graphene (2009) Status and prospects. Science 324:1530 Zheng HL, He P, Yang SW, Ding G (2025) Q. Thermally conductive graphene-based films for high heat flux dissipation. Carbon 233:119908 Zhao YX, Lin L (2024) Graphene, beyond lab benches. Science 386:144 Xiao X, Li C, Fan SC, Liu YJ, Liu Y (2023) Optical-thermally actuated graphene mechanical resonator for humidity sensing. Sens Actuators B-Chemical 374:132851 Ding X, Chen XD, Chen XP, Zhao X, Li N (2018) A QCM humidity sensor based on fullerene/graphene oxide nanocomposites with high quality factor. Sens Actuators B-Chemical 266:534 Zhang DZ, Wang DY, Li P, Zhou XY, Zong XQ, Dong GK (2018) Facile fabrication of high-performance QCM humidity sensor based on layer-by-layer self-assembled polyaniline/graphene oxide nanocomposite film. Sens Actuators B-Chemical 255:1869 Melios C, Centeno A, Zurutuza A, Panchal V, Giusca CE, Spencer S, Silva SRP, Kazakova O (2016) Effects of humidity on the electronic properties of graphene prepared by chemical vapour deposition. Carbon 103:273 Smith AD, Elgammal K, Niklaus F, Delin A, Fischer AC, Vaziri S, Forsberg F, Råsander M, Hugosson H, Bergqvist L, Schröder S, Kataria S, Östling M (2015) Lemme, M. C. Resistive graphene humidity sensors with rapid and direct electrical readout. Nanoscale 7:19099 Shehzad K, Shi TJ, Qadir A, Wan X, Guo HW, Ali A, Xuan WP, Xu H, Gu ZZ, Peng XS, Xie J, Sun LT, He QY, Xu Z, Gao C, Rim YS, Dan YP, Hasan T, Tan PH, Li EP, Yin WY, Cheng ZY, Yu B, Xu Y, Luo JK (2017) Duan, X. F. Designing an efficient multimode environmental sensor based on graphene-silicon heterojunction. Adv Mater Technol 2:1600262 Liu Y, Li C, Li BX, Lu SS, Fan SC, Dong SX, Wan Z, Shen MX (2023) Ultrasensitive acoustic detection using an enlarged Fabry–Perot cavity with a graphene diaphragm. ACS Appl Mater Interfaces 15:51390 Liu M, Yin XB, Ulin-Avila E, Geng BS, Zentgraf T, Ju L, Wang F, Zhang X (2011) A graphene-based broadband optical modulator. Nature 474:64 Koepfli SM, Baumann M, Gadola R, Nashashibi S, Koyaz Y, Rieben D, Güngör AC, Doderer M, Keller K, Fedoryshyn Y, Leuthold J (2024) Controlling photothermoelectric directional photocurrents in graphene with over 400 GHz bandwidth. Nat Commun 15:7351 Sennary M, Shah J, Yuan M, Mahjoub A, Pervak V, Golubev NV, Hassan MT (2025) Light-induced quantum tunnelling current in graphene. Nat Commun 16:4335 Hu AQ, Tian HJ, Liu QL, Wang L, Wang L, He XY, Luo Y, Guo X (2019) Graphene on self-assembled InGaN quantum dots enabling ultrahighly sensitive photodetectors. Adv Opt Mater 7:1801792 Barrett JC (1985) The optical properties of water droplets in the infrared. J Phys D 18:753 Tan XY, Chen JB, Yan SH, Zhang HY, Sun C (2025) Dynamic refractive index measurement method for droplets based on digital image correlation and inverse method. Meas Sci Technol 36:065015 Price CL, Bain A, Wallace BJ, Preston TC, Davies JF (2020) Simultaneous retrieval of the size and refractive index of suspended droplets in a linear quadrupole electrodynamic balance. J Phys Chem A 124:1811 Shih CJ, Strano MS, Blankschtein D (2013) Wetting translucency of graphene. Nat Mater 12:866 Kim E, Kim D, Kwak K, Nagata Y, Bonn M, Cho M (2022) Wettability of graphene, water contact angle, and interfacial water structure. Chem 8:1187 Zhang JC, Jia KC, Huang YF, Liu XT, Xu QH, Wang WD, Zhang R, Liu BY, Zheng LM, Chen H, Gao P, Meng S, Lin L, Peng HL, Liu Z (2022) F. Intrinsic wettability in pristine graphene. Adv Mater 34:2103620 Ferrari AC, Basko DM (2013) Raman spectroscopy as a versatile tool for studying the properties of graphene. Nat Nanotechnol 8:235 Gupta A, Chen G, Joshi P, Tadigadapa S, Eklund PC (2006) Raman scattering from high-frequency phonons in supported-graphene layer films. Nano Lett 6:2667 Ling X, Zhang J (2011) Interference phenomenon in graphene-enhanced Raman scattering. J Phys Chem C 115:2835 Sun ZZ, Yan Z, Yao J, Beitler E, Zhu Y, Tour JM (2010) Growth of graphene from solid carbon sources. Nature 468:549 Li XS, Cai WW, An JH, Kim S, Nah J, Yang DX, Piner R, Velamakanni A, Jung I, Tutuc E, Banerjee SK, Colombo L, Ruoff RS (2009) Large-Area synthesis of high-quality and uniform graphene films on copper foils. Science 324:1312 Tiwari RN, Ishihara M, Tiwari JN, Yoshimura M (2012) Transformation of polymer to graphene films at partially low temperature. Polym Chem 3:2712 Munoz R, Gomez-Aleixandre C (2013) Review of CVD synthesis of graphene. Chem Vap Deposition 19:297 Mitchem L, Buajarern J, Hopkins RJ, Ward AD, Gilham RJJ, Johnston RL, Reid JP (2006) Spectroscopy of growing and evaporating water droplets: Exploring the variation in equilibrium droplet size with relative humidity. J Phys Chem A 110:8116 Feng Y, Marchal T, Sperry T, Yi H (2020) Influence of wind and relative humidity on the social distancing effectiveness to prevent COVID-19 airborne transmission: A numerical study. J Aerosol Sci 147:105585 Yuan PY, Wu JY, Ogletree DF, Urban JJ, Dames C, Ma YB (2020) Adapting the electron beam from SEM as a quantitative heating source for nanoscale thermal metrology. Nano Lett 20:3019 Wang HD, Orejon D, Song DX, Zhang X, McHale G, Takamatsu H, Takata Y, Sefiane K (2022) Non-wetting of condensation-induced droplets on smooth monolayer suspended graphene with contact angle approaching 180 degrees. Commun Mater 3:75 Zhang CX, Li TJ, Yuan Y, Wang FQ, Tan HP (2020) Effects of droplets in the air on light transmission in target optical detection. Opt Lasers Eng 128:106044 Born M, Wolf E (1999) Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light (7th Edition) Cambridge University Press Yu IG, Kim YJ, Kim HJ, Lee C, Lee W (2011) I. Size-dependent light-scattering effects of nanoporous TiO spheres in dye-sensitized solar cells. J Mater Chem 21:532 Bohren CF, Huffman DR (2008) Absorption and scattering of light by small particles (Wiley-VCH Liu Y, Li C, Yu LX, Wu ZW, Fan SC, Lv RT (2024) Ultra-high sensitivity fiber optic microphone with corrugated graphene-oxide diaphragm for voice recognition. Nano Res 17:7593 Yu FF, Liu QW, Gan X, Hu MX, Zhang TY, Li C, Kang FY, Terrones M, Lv RT (2017) Ultrasensitive pressure detection of few-layer MoS 2 . Adv Mater 29:1603266 Stalder AF, Kulik G, Sage D, Barbieri L, Hoffmann P (2006) A snakebased approach to accurate determination of both contact points and contact angles. Colloids Surf A 286:92 Gao RX, He YL, Zhang DM, Sun GY, He JX, Li JF, Li MD, Yang ZL (2023) Gigahertz optoacoustic vibration in Sub-5 nm tip-supported nano-optomechanical metasurface. Nat Commun 14:485 Kumar A, Tan YJ, Navaratna N, Gupta M, Pitchappa P, Singh R (2024) Slow light topological photonics with counter-propagating waves and its active control on a chip. Nat Commun 15:926 Bruna M, Borini S (2009) Optical constants of graphene layers in the visible range. Appl Phys Lett 94:031901 Additional Declarations There is NO Competing Interest. Supplementary Files SupportingInformation.docx Humidity-driven nonlinear modulation of graphene reflectivity via interfacial wetting behavior Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7814470","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":531223068,"identity":"26b2cff4-79a1-424e-a231-faa429455c7d","order_by":0,"name":"Cheng Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0ElEQVRIiWNgGAWjYBACPmYGNhAtZwDhMxPWwgbVYkyCFgaIlsQNxGthZ3724OOO2vTtEskPPzBUWCc2sJ89QMBhbOaGM88cz905I81YguFMemIDT14CAS08bNK8bcdyN9xIMJBgbDuc2CDBY0BYy9+2Y+kGN9I//2D8R6wWxraaBIMbOWYSjA1EaWEzk+xtO2C4s+dNmUXCsXTjNp4c/Fr4+Q8/k/jZVidvzp6++caHGmvZfvYz+LVAwWEIlcAAjSYiQB2R6kbBKBgFo2BEAgCE+z2ZVt4WHgAAAABJRU5ErkJggg==","orcid":"","institution":"Beihang University","correspondingAuthor":true,"prefix":"","firstName":"Cheng","middleName":"","lastName":"Li","suffix":""},{"id":531223069,"identity":"78d67f64-cf2d-41b1-b9a5-63ec8dc9a2b4","order_by":1,"name":"Yang Liu","email":"","orcid":"","institution":"Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Yang","middleName":"","lastName":"Liu","suffix":""},{"id":531223070,"identity":"07c6753e-3cdc-4acb-b9ad-185e5033cc0a","order_by":2,"name":"Zhen Wan","email":"","orcid":"","institution":"Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Zhen","middleName":"","lastName":"Wan","suffix":""},{"id":531223071,"identity":"05c450cd-5009-4680-8af8-f896e51e267f","order_by":3,"name":"Tiantian Ma","email":"","orcid":"","institution":"School of Chemistry, Beijing Advanced Innovation Center for Biomedical Engineering, Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology, Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Tiantian","middleName":"","lastName":"Ma","suffix":""},{"id":531223072,"identity":"ea7ec3f2-9c28-4faa-b20d-8c6b3561309b","order_by":4,"name":"Wei Zhou","email":"","orcid":"https://orcid.org/0000-0003-0659-7824","institution":"Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Zhou","suffix":""},{"id":531223073,"identity":"6ca6f552-c7ab-4f50-89cc-b65896a87bc3","order_by":5,"name":"Shang-Chun FAN","email":"","orcid":"","institution":"Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Shang-Chun","middleName":"","lastName":"FAN","suffix":""}],"badges":[],"createdAt":"2025-10-09 07:46:00","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7814470/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7814470/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93935531,"identity":"daece276-3435-4a61-9dd5-6cf1616c25a6","added_by":"auto","created_at":"2025-10-20 12:44:57","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":8764554,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.docx","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/52b2ef628c87729842fa02ad.docx"},{"id":93935529,"identity":"93033ac4-f1ce-4178-8c16-46fc02bb9849","added_by":"auto","created_at":"2025-10-20 12:44:57","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":7479,"visible":true,"origin":"","legend":"","description":"","filename":"NCOMMS2580666.json","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/7e6224c7da32e0790460cf49.json"},{"id":93935546,"identity":"0f3faa44-05a7-42e3-bb42-ca1c21221e67","added_by":"auto","created_at":"2025-10-20 12:44:58","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":20692158,"visible":true,"origin":"","legend":"","description":"","filename":"SupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/969fdd673f2483b207353449.docx"},{"id":93936905,"identity":"3938c67c-8a7f-480b-823f-cfc0790f418a","added_by":"auto","created_at":"2025-10-20 13:00:57","extension":"xml","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":111861,"visible":true,"origin":"","legend":"","description":"","filename":"NCOMMS25806660enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/cb68347acf485c645ad4dee6.xml"},{"id":93935829,"identity":"4d249b9e-dba2-4999-bfef-02f686796077","added_by":"auto","created_at":"2025-10-20 12:52:58","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":108083,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/5ae3927dbf7ccfa08ee7b664.png"},{"id":93935827,"identity":"e22605ef-de22-4a84-a340-60fc09659d21","added_by":"auto","created_at":"2025-10-20 12:52:57","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":74037,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/8d88e01d7c0e3a750371dace.png"},{"id":93935830,"identity":"86cc8845-f5b5-46fb-b26c-0b26383bb25c","added_by":"auto","created_at":"2025-10-20 12:52:58","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":455635,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/f4605bdca7a1a190c280df32.png"},{"id":93935543,"identity":"7516a0fd-2701-4133-b404-05982200f005","added_by":"auto","created_at":"2025-10-20 12:44:58","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":131915,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/0695df503ec7d624408905ee.png"},{"id":93935540,"identity":"4f744394-63fd-4a80-be06-a37ef2cfad5f","added_by":"auto","created_at":"2025-10-20 12:44:58","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":127742,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/6033ad85671a807d627126ac.png"},{"id":93935828,"identity":"cb1a172c-57a4-45c0-9435-19bd2ee0aae8","added_by":"auto","created_at":"2025-10-20 12:52:57","extension":"xml","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":110858,"visible":true,"origin":"","legend":"","description":"","filename":"NCOMMS25806660structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/665ff9414eade7c47ec20b21.xml"},{"id":93935542,"identity":"46d6305b-3abb-4514-a47f-f66d75ccceaf","added_by":"auto","created_at":"2025-10-20 12:44:58","extension":"html","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":117461,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/6c703f415b4ce6334e262070.html"},{"id":93935530,"identity":"1c73612c-955e-4fef-b443-fa084a384518","added_by":"auto","created_at":"2025-10-20 12:44:57","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":517008,"visible":true,"origin":"","legend":"\u003cp\u003ePreparation of the F–P probe with large–area suspended graphene for humidity sensitive. (a) Illustration of the F–P probe realizing the humidity sensitive. (b) Picture of the fabricated F–P probe. (c) SEM image of the suspended graphene diaphragm. (d) Typical Raman spectrum for the graphene diaphragm. (e) AFM image of the graphene diaphragm.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/5edc0dd78525293535d6b311.jpeg"},{"id":93935824,"identity":"977e12b4-083c-4089-b9fc-866f51c3ffeb","added_by":"auto","created_at":"2025-10-20 12:52:57","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":393299,"visible":true,"origin":"","legend":"\u003cp\u003eReflectivity-humidity test results of the proposed F–P probe. (a) Schematic for measuring reflectivity of graphene under various RH conditions. (b) Typical interference spectrum under different RH conditions. (c) Calculated graphene reflectivity in response to different RH.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/8cd1983715a65ab330e5a8b1.jpeg"},{"id":93935825,"identity":"3b36bcfd-aad6-481e-9df8-a075afffd5f1","added_by":"auto","created_at":"2025-10-20 12:52:57","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2730021,"visible":true,"origin":"","legend":"\u003cp\u003eWetting behavior of graphene measured by optical microscopy and ESEM. (a) Microscopic images and corresponding binary segmentation results of water droplets on the suspended graphene under different RH conditions. (The diameters of each view area are all 120 µm) (b) The distribution density and average diameter of water droplets in response to RH. (c) Typical ESEM image of water droplets on the surface of suspended graphene. (d) The diameter and (e) the CA of water droplet shown in Fig. 3c. (f) The fit results of the CA with different diameters. Inset: zoom-in 1.3 µm to 2.6 µm.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/d9398a859f394e8700c5fb9d.png"},{"id":93935533,"identity":"f27699b1-f640-409a-95b6-2ece2562acd8","added_by":"auto","created_at":"2025-10-20 12:44:57","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":598328,"visible":true,"origin":"","legend":"\u003cp\u003eThe results of wave optics simulation using COMSOL Multiphysics. (a) Established FEM model of the system of suspended graphene with droplets coupled air environment. (b) Measured values and simulated values of graphene reflectivity versus RH. (c) The effect of \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e and diameter of droplets on simulated reflectivity of graphene with droplets. (d) The spatial distribution of the simulated electric field norm changes with diameter. (e) The average electric energy directly beneath the droplet varies with the diameter.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/62dc36fd1a8ea129a61c4172.jpeg"},{"id":93935536,"identity":"9af4efd2-4ace-4ab7-b5a8-fecdb3d69504","added_by":"auto","created_at":"2025-10-20 12:44:57","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":570256,"visible":true,"origin":"","legend":"\u003cp\u003eExperimentally determined optimal RH range. (a) The measured RH values of the environments constructed using different saturated salt solutions. (b) Calculated graphene reflectivity in response to different RH. (c) The mean values of the experimental results shown in Fig. 5b.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/6790bb285371f36e69e2092d.png"},{"id":93937688,"identity":"5ab0b8d4-3d51-4bea-8834-a57a1abca9b7","added_by":"auto","created_at":"2025-10-20 13:09:13","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5671332,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/1287fa6f-8b05-4c6e-a2bc-37b07d04f7eb.pdf"},{"id":93935544,"identity":"e9011480-d577-4417-942d-09249b84b4aa","added_by":"auto","created_at":"2025-10-20 12:44:58","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":20692158,"visible":true,"origin":"","legend":"Humidity-driven nonlinear modulation of graphene reflectivity via interfacial wetting behavior","description":"","filename":"SupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-7814470/v1/5a304e3ac96872a61f7d3f18.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Humidity-driven nonlinear modulation of graphene reflectivity via interfacial wetting behavior","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAs a monolayer of sp\u003csup\u003e2\u003c/sup\u003e-hybridized carbon atoms, graphene is the fundamental building block of carbon allotropes and offers exceptional optical, electrical, mechanical, and thermal properties, making it a promising material for transistors, transparent electrodes, and sensors.\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3 CR4\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e However, the humidity absorption characteristics of graphene, driven by the inevitable adsorption of ambient water vapor, significantly affect the performance of graphene-based devices particularly in optoelectronics.\u003csup\u003e\u003cspan additionalcitationids=\"CR6 CR7\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e These characteristics lead to changes in graphene\u0026rsquo;s reflectivity, which directly impacts the functionality of devices such as sensors and modulators. For instance, a 50% variation in graphene's reflectivity can lead to a 22% change in the sensitivity of Fabry\u0026ndash;Perot (F\u0026ndash;P) acoustic sensors, a 50% shift in light modulator output, and a 50% change in photodetector responsivity (detailed analysis in Supplementary Note 1, Supporting Information).\u003csup\u003e\u003cspan additionalcitationids=\"CR10 CR11 CR12\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e To improve device reliability, it is essential to disclose the humidity-reflectivity relationship and the mechanism behind graphene's wetting behavior.\u003c/p\u003e\u003cp\u003eHowever, the relationship between humidity and reflectivity has not been previously reported. Most studies on graphene reflectivity use optical microscopy, Raman spectroscopy and Fourier transform infrared spectroscopy.\u003csup\u003e\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e For example, Nair et al. analyzed the transmittance of suspended graphene with varying layers using optical microscopy and found that the reflectivity of monolayer graphene is just 0.01%.\u003csup\u003e15\u003c/sup\u003e Microscopic instruments limit in-situ reflectivity measurements under varying humidity. F\u0026ndash;P interference spectroscopy offers a portable and miniaturized probe for measuring reflectivity in humid environments,\u003csup\u003e17\u003c/sup\u003e overcoming conventional technique limitations for few-layered graphene. Building on this, our group has developed a platform utilizing the F\u0026ndash;P probe for accurate reflectivity testing.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\u003cp\u003eUnder humid conditions, graphene's reflectivity is influenced by its wetting behavior and the state of droplets on its surface. Mie theory has been used to calculate optical parameters such as extinction and scattering efficiencies for spherical water droplets, revealing how reflectivity depends on temperature and droplet size.\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e However, accurately measuring the refractive index of micro-scale droplets remains challenging. Recent advances, such as a non-contact method combining digital image correlation and an inverse approach, enable high-precision analysis of both the refractive index and concentration of micro-droplets.\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e Most studies focus on suspended droplets,\u003csup\u003e19\u0026ndash;21\u003c/sup\u003e with few addressing droplets adsorbed on graphene surfaces, where reflectivity is influenced by both the droplet\u0026rsquo;s intrinsic properties and the substrate. Droplet shape modified by surface energy and hydrophobicity changes with varying contact angle (CA), which is also affected by humidity.\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e However, the combined effect of adsorbed droplets and substrate on humidity-driven reflectivity remains unexplored.\u003c/p\u003e\u003cp\u003eIn this paper, we present a portable fiber-optic F\u0026ndash;P probe integrated with 10-layer graphene, enabling \u003cem\u003ein situ\u003c/em\u003e measurement of a quadratic relationship between ambient humidity and graphene reflectivity. Micro-characterizations using environmental scanning electron microscopy (ESEM) and optical microscopy were performed to establish a quantitative relationship between graphene's wettability behavior and humidity levels. Wetting experiments and COMSOL simulations demonstrate that droplet diameter and adsorption density primarily govern the modulation of graphene reflectivity. Humidity-driven nonlinearity arises from competing mechanisms of droplet light absorption and scattering. Leveraging this correlation, we propose a correction method that defines an operational range of 53.9% relative humidity (RH) to 58.9% RH, minimizing the humidity-induced effects on graphene optoelectronic devices. This integrated microanalysis-simulation approach is broadly applicable to other two-dimensional (2D) materials.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eStructure and Characteristics of the F\u0026ndash;P Probe\u003c/h2\u003e\u003cp\u003eThe proposed portable, miniaturized F\u0026ndash;P probe consists of a 10-layer graphene diaphragm, two ferrules, a sleeve, and a single-mode fiber (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). In detail, a ferrule is covered with graphene to form a suspended diaphragm with a diameter of 125 \u0026micro;m, while the other ferrule is utilized to fix the single-mode fiber. To obtain suspended graphene in absence of contamination for accurate CA measurements, a polymer-free transfer method was employed (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e, Supporting Information).\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e The side hole of the sleeve enabled direct contact between the graphene diaphragm and the external environment, thereby achieving humidity sensing. The air cavity between the graphene and the end face of the single-mode fiber forms the F\u0026ndash;P cavity. In this case, the reflectivity of the graphene diaphragm can be determined by fitting the F\u0026ndash;P interference spectrum obtained by an optical spectrum analyzer (OSA) (refer to Supplementary Note 2, Supporting Information, for details). Correspondingly, the image of the as-fabricated F\u0026ndash;P probe is presented (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). The scanning electron microscope (SEM) image illustrates that the residual impurities have been completely removed and that the center hole of the ferrule has been covered intacted (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFollowing structural characterization, the suspended graphene's quality was evaluated through Raman spectroscopy (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed).\u003csup\u003e\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e The Raman spectrum shows the high crystallinity of the graphene diaphragm. Specifically, the absence of the D peak (1350 cm\u003csup\u003e\u0026ndash;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) in the Raman spectrum represents the low concentration of defects in graphene. The intensity ratio of the G (1580 cm\u003csup\u003e\u0026ndash;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) and 2D (2700 cm\u003csup\u003e\u0026ndash;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) peaks is approximately 2.76, which is higher than that (0.3) of monolayer graphene.\u003csup\u003e\u003cspan additionalcitationids=\"CR29\" citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e For observing a more accurate thickness of graphene, an atomic force microscope (AFM) characterization was performed. The thickness of graphene is measured to be 3.3 nm (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee), which is close to the theoretical thickness of 10-layer graphene. It should be noted that there is a slight deviation between the measured thickness and the typical thickness (10-layer) of the commercial graphene. This discrepancy can be attributed to the inevitable inconsistency of the chemical vapor deposition process and the measurement accuracy of AFM.\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eThe Influence of Humidity on Graphene Reflectivity\u003c/h3\u003e\n\u003cp\u003eBy means of the reflectivity-humidity experimental setup (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea; Fig. S2, Supporting Information), the optical reflectivity of suspended graphene on four F\u0026ndash;P probes was measured under various RH at room temperature. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb displays the F\u0026ndash;P interference spectra under different humidity conditions. These data visually illustrate the impact of humidity on the amplitude and wavelength shift of the F\u0026ndash;P interference spectra. Notably, a remarkable 8-nm red-shift of the peak wavelength is observed (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb), attributed to the corresponding increase in the F\u0026ndash;P interference length (0.29 \u0026micro;m, Supplementary Note 3, Supporting Information). The primary reason for this phenomenon is the high sensitivity of ultrathin graphene to additional mass induced by water adsorption.\u003csup\u003e\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e Correspondingly, the suspended graphene also experiences sinking. Moreover, variations in the F\u0026ndash;P interference contrast, which are directly related to graphene reflectivity, can be visually observed under different RH levels. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, with increasing relative humidity, the reflectivity of graphene initially rises before subsequently decreasing. Specifically, as the humidity increases from 8.0% RH to 30.8% RH, the reflectivity of graphene rises from 0.48% to 0.60%. Conversely, as the humidity increases from 30.8% RH to 67.5% RH, the reflectivity drops from 0.60% to 0.34%. Notably, the relative change in average reflectivity is 49.8%, indicating that environmental humidity is a key factor influencing the commercial application of graphene-based optoelectronic devices.\u003c/p\u003e\n\u003ch3\u003eWetting Experiments of Graphene\u003c/h3\u003e\n\u003cp\u003eTo gain a deeper understanding of the mechanism by which air humidity affects the optical reflectivity of graphene, the wetting behavior of graphene was first characterized using optical microscopy and ESEM. Note that all the micro-characterizations were conducted on the suspended graphene to exclude substrate interference. An optical characterization platform equipped with humidity control and digital image processing (HCDIP) was constructed (Fig. S3, Supporting Information) to perform \u003cem\u003ein situ\u003c/em\u003e measurements of droplet diameter and attachment density in humid environments. After optical microscopy captured images of micro-droplets adsorbed on the graphene surface, the images were processed using the Canny algorithm and binary segmentation. Referring to the processed images (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea), the boundary between droplets and graphene can be clearly delineated. Accordingly, the \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e and the average diameter of droplets can be determined (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). With an increase in ambient humidity from ~\u0026thinsp;7% RH to ~\u0026thinsp;66% RH, the \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e increase from 0% to 18.4%; and the average diameters increase from 0 \u0026micro;m to 2.50 \u0026micro;m. This phenomenon is related to enhanced hygroscopic growth caused by increased humidity.\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eBesides the \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e and diameter, the CA of the micron-sized droplets on suspended graphene is also observed via ESEM (the experimrntal setup can be found in Fig. S4, Supporting Information). Unfortunately, the heat effect of the electron beam at extremely high magnification in ESEM can lead to evaporation of the droplets during the experiment.\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e Therefore, the maximum magnification of the ESEM was set from 800 \u0026times; to 2500 \u0026times;. Concurrently, only fully intact droplets were selected for CA measurements. Typically, the droplet within a yellow box depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec is selected, while the droplet below it has shown clear evidence of volatilization. The diameter (16 \u0026micro;m) and the CA (59.03 \u0026deg;) of the selected droplet are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed, e, respectively. Similarly, the diameters and CA of a total of 17 full droplets are measured (Fig. S5, Supporting Information). The CA of droplets decrease with the increase in diameter (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef). It is noteworthy that the measured CA of droplets, ranging from 49.18\u0026deg; to 91.46\u0026deg;, are generally consistent with previously reported results,\u003csup\u003e35\u003c/sup\u003e confirming the validity of our measurements. From the data shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef, the relationship between CA and diameter can be determined to be \u003cem\u003ey\u003c/em\u003e = \u0026minus;\u0026thinsp;15.92ln(\u003cem\u003ex\u003c/em\u003e)\u0026thinsp;+\u0026thinsp;102.96 through the least squares fitting. Therefore, for the droplet diameters measured in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb (ranging from 1.37 \u0026micro;m to 2.50 \u0026micro;m), the corresponding CA can be predicted to be between 88.37\u0026deg; and 97.97\u0026deg; (Fig. S6, Supporting Information). We thus conclude that the hygroscopic growth induced by high RH promotes an increase in both the distribution density and the size of droplets on graphene. Meanwhile, the CA of the droplets decreases with the increase in droplets size.\u003c/p\u003e\n\u003ch3\u003eSimulation of the Nonlinear Modulation Mechanism of Humidity on the Reflectivity\u003c/h3\u003e\n\u003cp\u003eBased on the wetting behavior of graphene measured before, a finite element method (FEM) model was established via COMSOL to validate the effect of humidity on reflectivity and to understand its underlying mechanisms (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea; Fig. S7, Supporting Information). Given that the correlation indices (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) are all equal to 1 (Fig. S8, Supporting Information), a strict linear dependence of reflectivity on wavelength (from 1555 nm to 1605 nm) can be inferred. Due to the averaging effect of the reflectivity fitting method (refer to Supplementary Note 2, Supporting Information, for details), the wavelength in the FEM simulation is set at a median value of 1580 nm to reduce computational complexity. Utilizing the \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e, diameter, and CA of droplets on the graphene surface under varying humidity conditions presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the simulated reflectivity for the graphene-droplet coupling system corresponding to humidity is obtained (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). Both simulated and measured reflectivity increase as the RH rises from 7.5% to 31.3%, and decrease with further the RH increase. Thus, the simulated values closely align with the experimental values, validating the accuracy of the simulations.\u003c/p\u003e\u003cp\u003eTo investigate the mechanisms by which the CA, \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e, and diameter of the droplet affect reflectivity, we first simulated the reflectivity of the system with CA ranging from 88\u0026deg; to 98\u0026deg; (Fig. S9, Supporting Information). According to Fig. S9, the relative changes in reflectivity for four representative droplet densities and sizes (3.3%, 1.37 \u0026micro;m; 6.8%, 1.72 \u0026micro;m; 11.2%, 1.94 \u0026micro;m; 18.4%, 2.50 \u0026micro;m) induced by variations in CA are all less than 1.3%. Hence, the influence of CA on reflectivity can be considered negligible. In this case, the CA was set to a median value of 93\u0026deg;, and the effects of varying \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e (2% to 20%) and diameters (1.0 \u0026micro;m to 2.6 \u0026micro;m) on graphene reflectivity were simulated (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). The results presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec indicate that as the droplet diameter increases from 1.0 \u0026micro;m to 2.6 \u0026micro;m, the reflectivity first increases and then decreases, with a maximum value occurring near a diameter of 1.8 \u0026micro;m. Additionally, higher droplet \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e lead to a greater maximum and a smaller minimum in the diameter-reflectivity relationship. This phenomenon is primarily attributed to the enhanced influence of droplet diameter with increased \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e. Notably, this explains why the slope of the reflectivity-humidity curve in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb is lower during the ascent than during the descent.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSubsequently, the graphene width was set to 40 \u0026micro;m, substantially larger than the droplet diameter, isolating the non-monotonic effect of droplet diameter on reflectivity for investigation. To visually illustrate the reflection characteristics of the graphene-droplet-air system, near-field maps showing the electric field intensity as a function of droplet diameter (1 to 2.5 \u0026micro;m) are presented (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). The weak localized electric fields inside the droplet are a result of light absorption. Furthermore, the localized enhanced electric fields beneath the droplet near the central axis arise from its convex lens effect.\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e According to Fresnel equations,\u003csup\u003e37\u003c/sup\u003e the field enhancement near the graphene interface within the droplet can be attributed to the increased incidence angle caused by this lens effect, resulting in an enhanced reflectivity of graphene. Remarkably, as the droplet diameter increases, the electric field intensity beneath the droplet in both graphene and air gradually intensifies (indicated by the red box in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). For quantitative analysis, the average electric field energy in the region directly below the droplet is calculated (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee). The average electric energy increases from 9.14 \u0026times; 10\u003csup\u003e\u0026ndash;15\u003c/sup\u003e J to 9.18 \u0026times; 10\u003csup\u003e\u0026ndash;15\u003c/sup\u003e J as the droplet diameter rises from 1 \u0026micro;m to 2.5 \u0026micro;m. This phenomenon is attributed to droplet size-dependent light scattering.\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e In other words, as the droplet size increases, more light passes through it rather than being scattered. Consequently, humidity-induced nonlinear modulation of graphene reflectivity stems from competition mechanisms between droplet-mediated light scattering and absorption. Specifically, across 7.5\u0026ndash;31.3% RH, reflectivity enhancement primarily originates from higher light scattering at the air-droplet interface. Concurrently, enhanced reflectivity due to elevated incidence angles at the water-graphene interface occurs while droplets remain too small to absorb this enhanced reflected light. Subsequently, as humidity rises from 31.3% to 66.3% RH, increasing droplet size augments absorption while reducing scattering, thereby reducing graphene reflectivity.\u003c/p\u003e\n\u003ch3\u003eCorrection Method for the Optimal Operating Range Based on the Reflectivity-Humidity Curve\u003c/h3\u003e\n\u003cp\u003eGiven the challenges in achieving low-humidity conditions in practical applications, this study established a correction method based on the quadratic relationship between graphene reflectivity and relative humidity. Specifically, using the reflectivity at the humidity level constructed by anhydrous CaCl\u003csub\u003e2\u003c/sub\u003e as a reference, another data point with identical reflectivity was identified on the quadratic fitting curve of reflectivity versus humidity. At this data point, a reflectivity error interval was constructed to determine the optimal operational humidity range for the device. To enhance the applicability of the results, we prepared three additional F\u0026ndash;P probes, designated as Probe 2, Probe 3, and Probe 4, using the same method as described for Probe 1. The relative humidity and reflectivity corresponding to these four F\u0026ndash;P probes are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea, b, respectively. Notably, all four F\u0026ndash;P probes exhibit the same nonlinear relationship between reflectivity and humidity.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eQuadratic fitting of the mean experimental results from the aforementioned four probes yielded the curve (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec):\u003c/p\u003e\u003cp\u003e\u003cem\u003ey\u003c/em\u003e = \u0026minus;\u0026thinsp;0.00019\u003cem\u003ex\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;+\u0026thinsp;0.01181\u003cem\u003ex\u003c/em\u003e\u0026thinsp;+\u0026thinsp;0.41905\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003ex\u003c/em\u003e is RH, and \u003cem\u003ey\u003c/em\u003e is reflectivity. For the low-humidity environment constructed with anhydrous CaCl\u003csub\u003e2\u003c/sub\u003e, the mean reflectivity is 0.48%. Correspondingly, the other data point on the fitting curve with identical reflectivity corresponds to 56.5% RH. Using a reflectivity of 0.48% as the baseline, the corresponding humidity ranges for the error bands are as follows: \u0026plusmn;5% error band from 53.9% RH to 58.9% RH (optimal operating range), \u0026plusmn;\u0026thinsp;10% error band from 50.9% RH to 61.0% RH, and \u0026plusmn;\u0026thinsp;20% error band from 42.9% RH to 65.0% RH. Thus, 53.9\u0026ndash;58.9% RH can be identified as the optimal RH range for the stable operation of graphene-based optoelectronic devices.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn conclusion, a humidity-dependent optical reflectivity was demonstrated in 10-layer graphene using a miniaturized F\u0026ndash;P probe. We observe a non-monotonic relationship with reflectivity increasing from 0.48 to 0.60% as humidity rises from 8.0 to 30.8% RH, then decreasing to 0.34% at 67.5% RH, yielding a 49.8% modulation effect. Optical microscopy shows that droplet attachment density increases from 0 to 18.4%, and droplet diameter expands from 0 to 2.50 \u0026micro;m with humidity. ESEM analysis establishes a relationship between the CA and droplet diameter, showing that the CA increases logarithmically with droplet size. COMSOL simulations further explain that reflectivity modulation arises from competing light scattering and absorption mechanisms: initial enhancement is due to increased scattering, while later reduction is linked to higher absorption. We thus propose a correction method between reflectivity and humidity, identifying an optimal operating range (53.9\u0026ndash;58.9% RH) with minimal influence on reflectivity, ensuring stable conditions for graphene-based optoelectronics. This work provides a theoretical foundation and correction framework to better understand the impact of humidity on the performance of optoelectronic devices. Additionally, the method developed for studying humidity-induced reflectivity changes can be applied to other 2D materials, expanding its broader applicability.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003eMaterials\u003c/h2\u003e\u003cp\u003eThe 10-layer copper-based graphene used in this study was purchased from Nanjing Jicang Nano Technology Co., Ltd. (Nanjing, China). Epoxy resin adhesive (14270) was obtained from Devcon (USA). Single-mode fiber was purchased from Haiyu Optical (Shenzhen, China). Mineral salts, including anhydrous CaCl\u003csub\u003e2\u003c/sub\u003e, LiCl, MgCl\u003csub\u003e2\u003c/sub\u003e, NaBr, and NaCl, were supplied by Aladdin Biochemical Technology Co., Ltd. (Shanghai, China). The sealed glass chamber was fabricated by Shaorui Quartz Products Co., Ltd. (Lianyungang, China). SiO\u003csub\u003e2\u003c/sub\u003e bonding material was sourced from Beijing GIN KOO MEMS Scientific \u0026amp; Technological Co., Ltd. (Beijing, China). Coverslips were acquired from Citotest Labware Manufacturing Co., Ltd. (Jiangsu, China). Transmission electron microscope (TEM) grids were obtained from Zhong Jing Ke Yi Co., Ltd. (Beijing, China). The 45\u0026deg; sample holder was machined by Keso Precision Machinery Co., Ltd. (Beijing, China).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eGraphene Transfer\u003c/h2\u003e\u003cp\u003eThe transfer process of the commercially available copper-based 10-layer graphene, as described in previous studies,\u003csup\u003e40,41\u003c/sup\u003e involves three main steps. First, the copper-graphene film was cut into square pieces with a width of 1 mm and then etched in a 5% FeCl\u003csub\u003e3\u003c/sub\u003e solution. Once the copper was completely etched away, the FeCl\u003csub\u003e3\u003c/sub\u003e solution was diluted with deionized water until it became transparent. Finally, the pure graphene diaphragms were transferred onto the center hole of the ferrule and onto a TEM grid, respectively, using van der Waals forces. It is important to note that the ferrule and TEM grid with pure graphene were used for reflectivity measurements and micro-characterization, respectively.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eF\u0026ndash;P Probe Fabrication\u003c/h2\u003e\u003cp\u003eThe ferrule covered with pure graphene and a clean ferrule were placed at each end of the sleeve, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea. A single-mode fiber was inserted through the clean ferrule, establishing F\u0026ndash;P interference. This configuration ensures precise alignment between the single-mode fiber and the graphene. The F\u0026ndash;P interference length was determined to be approximately 58 \u0026micro;m, based on the interference spectrum obtained using an OSA (Yokogawa, AQ6370C, Japan) and a broadband light source (Amonics, ALS-CL-17, China). To maintain the stability of the F\u0026ndash;P interference length, the end of the clean ferrule was sealed with epoxy resin adhesive.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eGraphene Characterization\u003c/h2\u003e\u003cp\u003eThe thickness of the commercial 10-layer graphene diaphragm was measured using AFM (FSM, FM-Nanoview 6800, China). The microstructure of the graphene diaphragm was characterized through SEM (JEOL, JMC7000, Japan). Raman spectroscopy was performed by using a Raman spectrometer (LabRAM, HR Evolution, France).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eMeasurement\u003c/h2\u003e\u003cp\u003eTo measure the reflectivity of graphene under varying ambient RH, a reflectivity-humidity measurement setup was established (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea and Supplementary Note 2). Adjustable RH conditions were generated using saturated salt solutions, with humidity levels ranging from 7.5% RH to 66.3% RH, achieved through anhydrous CaCl\u003csub\u003e2\u003c/sub\u003e, LiCl, MgCl\u003csub\u003e2\u003c/sub\u003e, NaBr, and NaCl. RH was monitored using a commercial hygrometer (MIAOXIN, TH20BL-EX, China) with an accuracy of \u0026plusmn;\u0026thinsp;2% RH. Before each reflectivity measurement, the F\u0026ndash;P probe was exposed for 30 min to stabilize droplet adsorption.\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e Prior to changing RH levels, the F\u0026ndash;P probe was first exposed to a dry environment using CaCl\u003csub\u003e2\u003c/sub\u003e for recovery.\u003c/p\u003e\u003cp\u003eFor droplet diameter and adhesion density \u003cem\u003ein situ\u003c/em\u003e measurements, an optical characterization platform equipped with HCDIP was set up (Fig. S3, Supporting Information). This platform consists of a optical characterization section and a digital image processing section. In the optical characterization section, RH (7.5\u0026ndash;66.3%) was adjusted using saturated salt solutions, with stability ensured by sealing gaskets and fastening bolts. Then, micro-characterization was performed using a TEM grid with graphene, positioned on the stage of the glass chamber. A coverslip was attached with SiO\u003csub\u003e2\u003c/sub\u003e bonding material to facilitate clear imaging. Each graphene sample was exposed for 30 min at each RH level. In the digital image processing section, continuous, smooth profile of droplets were obtained using the Canny edge detection algorithm. When a closed profile detected by the Canny algorithm exhibits high global smoothness and its average curvature value was significantly higher than that of the background, the contour segment was identified as a droplet edge. Subsequently, binary segmentation was applied to mark the interior of the closed profile as black and the background as white. By analyzing the number of droplets, the background area, and the droplet area, the average droplet diameter and adhesion density were derived.\u003c/p\u003e\u003cp\u003eFor CA measurements, condensation was observed using ESEM (Thermo Fisher, Quattro ESEM, USA) with an acceleration voltage of 25 kV (Fig. S4, Supporting Information). The temperature of the graphene sample and RH were controlled via a Peltier stage and vapor pressure.\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e The TEM grid with graphene was mounted on a 45\u0026deg; sample holder and placed on the Peltier stage. The stage was set to \u0026minus;\u0026thinsp;0.8\u0026deg;C, ensuring that the graphene sample reached near 0\u0026deg;C after heat transfer. Once the air pressure in the vacuum chamber was reduced to 133 Pa, saturated vapor injection began with vapor pressure increased at 50 Pa\u0026middot;min\u003csup\u003e\u0026ndash;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e until saturation. For enhanced RH control accuracy, the vapor pressure increase rate was then reduced to 1 Pa\u0026middot;min\u003csup\u003e\u0026ndash;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. When the vapor pressure reached 830 Pa, the first visible droplet appeared. The droplets continued to grow at a steady rate, and CA was measured using the ImageJ DropSnake plugin from ESEM images of droplets on the suspended graphene.\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003eFEM Simulation\u003c/h2\u003e\u003cp\u003eTo analyze the influence of air humidity on the reflectivity of suspended graphene, the optical properties of graphene coupled with a droplet-laden air environment were studied over the 1555\u0026ndash;1605 nm wavelength range using COMSOL Multiphysics wave optics simulation. The FEM model shown in Fig. S7 (Supporting Information) incorporates the wave optics physics field with a 2D mesh defined by free triangular elements. Given the approximate uniform distribution of droplets on the suspended graphene, periodic boundary conditions were applied to the side boundaries of the model, forming multiple unit cells. This approach significantly reduces computational time and resources.\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e In the simulation, light entered the model through the incident port and exits via the output port (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). To mitigate the effects of unwanted reflections from the boundary, perfectly matched layers (PMLs) were employed.\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\u003cp\u003eThe simulation parameters included a real refractive index of 3, an imaginary refractive index of 1.15,\u003csup\u003e45\u003c/sup\u003e a graphene thickness of 10 layers, and an incident light power of 1 W\u0026middot;m\u003csup\u003e\u0026ndash;\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. The droplet coverage density (\u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e) was set between 2% and 20%, consistent with the measured values in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb. For the modeled unit cell (Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea and S8, Supporting Information), the relationship between \u003cem\u003eρ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e and droplet diameter was expressed in Eq. S-19 (refer to Supplementary Note 4, Supporting Information, for details). Additional details on the shape and size of water droplets on graphene are provided in the Supporting Information.\u003c/p\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003eCredit Authorship Contribution Statement\u003c/h2\u003e\u003cp\u003eY.L. conceived the idea, conducted the experiments, and wrote the manuscript. C.L. analyzed the data and revised the original draft. Z.W. analyzed the data and supervised the work. T.M. analyzed the data. W.Z. conceived the idea and revised the original draft. S.F. supervised the study. All the authors discussed the results and revised the final manuscript.\u003c/p\u003e\u003c/div\u003e\u003ch2\u003eConflict of Interest\u003c/h2\u003e\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e\u003cp\u003eThis work was supported by the National Natural Science Foundation of China (62173021, U23A20638).\u003c/p\u003e\u003ch2\u003eData Availability Statement\u003c/h2\u003e\u003cp\u003eThe data for all the work is available from the corresponding authors based on reasonable requests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eDai H, Wang Y, Liu Z, Liu Y, Guo Y, Liu D (2025) Interlayer phononic energy dissipation in the friction of graphene layers. Sci Adv 11:eadu2880\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSeki R, Takamatsu H, Suzuki Y, Oya Y, Ohba T (2021) Hydrophobic-to-hydrophilic affinity change of sub-monolayer water molecules at water-graphene interfaces. Colloids Surf A-Physicochemical Eng Aspects 628:127393\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKim L, Kim S, Jha PK, Brar VW, Atwater HA (2021) Mid-infrared radiative emission from bright hot plasmons in graphene. Nat Mater 20:805\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhao J, Ji PX, Li YQ, Li R, Zhang KM, Tian H, Yu KC, Bian BY, Hao LZ, Xiao X, Griffin W, Dudeck N, Moro R, Ma L (2024) Heer, W. A. Ultrahigh-mobility semiconducting epitaxial graphene on silicon carbide. Nature 625:60de\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGeim AK, Graphene (2009) Status and prospects. Science 324:1530\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZheng HL, He P, Yang SW, Ding G (2025) Q. Thermally conductive graphene-based films for high heat flux dissipation. Carbon 233:119908\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhao YX, Lin L (2024) Graphene, beyond lab benches. Science 386:144\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXiao X, Li C, Fan SC, Liu YJ, Liu Y (2023) Optical-thermally actuated graphene mechanical resonator for humidity sensing. Sens Actuators B-Chemical 374:132851\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDing X, Chen XD, Chen XP, Zhao X, Li N (2018) A QCM humidity sensor based on fullerene/graphene oxide nanocomposites with high quality factor. Sens Actuators B-Chemical 266:534\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhang DZ, Wang DY, Li P, Zhou XY, Zong XQ, Dong GK (2018) Facile fabrication of high-performance QCM humidity sensor based on layer-by-layer self-assembled polyaniline/graphene oxide nanocomposite film. Sens Actuators B-Chemical 255:1869\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMelios C, Centeno A, Zurutuza A, Panchal V, Giusca CE, Spencer S, Silva SRP, Kazakova O (2016) Effects of humidity on the electronic properties of graphene prepared by chemical vapour deposition. Carbon 103:273\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSmith AD, Elgammal K, Niklaus F, Delin A, Fischer AC, Vaziri S, Forsberg F, R\u0026aring;sander M, Hugosson H, Bergqvist L, Schr\u0026ouml;der S, Kataria S, \u0026Ouml;stling M (2015) Lemme, M. C. Resistive graphene humidity sensors with rapid and direct electrical readout. Nanoscale 7:19099\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eShehzad K, Shi TJ, Qadir A, Wan X, Guo HW, Ali A, Xuan WP, Xu H, Gu ZZ, Peng XS, Xie J, Sun LT, He QY, Xu Z, Gao C, Rim YS, Dan YP, Hasan T, Tan PH, Li EP, Yin WY, Cheng ZY, Yu B, Xu Y, Luo JK (2017) Duan, X. F. Designing an efficient multimode environmental sensor based on graphene-silicon heterojunction. Adv Mater Technol 2:1600262\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLiu Y, Li C, Li BX, Lu SS, Fan SC, Dong SX, Wan Z, Shen MX (2023) Ultrasensitive acoustic detection using an enlarged Fabry\u0026ndash;Perot cavity with a graphene diaphragm. ACS Appl Mater Interfaces 15:51390\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLiu M, Yin XB, Ulin-Avila E, Geng BS, Zentgraf T, Ju L, Wang F, Zhang X (2011) A graphene-based broadband optical modulator. Nature 474:64\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKoepfli SM, Baumann M, Gadola R, Nashashibi S, Koyaz Y, Rieben D, G\u0026uuml;ng\u0026ouml;r AC, Doderer M, Keller K, Fedoryshyn Y, Leuthold J (2024) Controlling photothermoelectric directional photocurrents in graphene with over 400 GHz bandwidth. Nat Commun 15:7351\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSennary M, Shah J, Yuan M, Mahjoub A, Pervak V, Golubev NV, Hassan MT (2025) Light-induced quantum tunnelling current in graphene. Nat Commun 16:4335\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHu AQ, Tian HJ, Liu QL, Wang L, Wang L, He XY, Luo Y, Guo X (2019) Graphene on self-assembled InGaN quantum dots enabling ultrahighly sensitive photodetectors. Adv Opt Mater 7:1801792\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBarrett JC (1985) The optical properties of water droplets in the infrared. J Phys D 18:753\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTan XY, Chen JB, Yan SH, Zhang HY, Sun C (2025) Dynamic refractive index measurement method for droplets based on digital image correlation and inverse method. Meas Sci Technol 36:065015\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePrice CL, Bain A, Wallace BJ, Preston TC, Davies JF (2020) Simultaneous retrieval of the size and refractive index of suspended droplets in a linear quadrupole electrodynamic balance. J Phys Chem A 124:1811\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eShih CJ, Strano MS, Blankschtein D (2013) Wetting translucency of graphene. Nat Mater 12:866\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKim E, Kim D, Kwak K, Nagata Y, Bonn M, Cho M (2022) Wettability of graphene, water contact angle, and interfacial water structure. Chem 8:1187\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhang JC, Jia KC, Huang YF, Liu XT, Xu QH, Wang WD, Zhang R, Liu BY, Zheng LM, Chen H, Gao P, Meng S, Lin L, Peng HL, Liu Z (2022) F. Intrinsic wettability in pristine graphene. Adv Mater 34:2103620\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFerrari AC, Basko DM (2013) Raman spectroscopy as a versatile tool for studying the properties of graphene. Nat Nanotechnol 8:235\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGupta A, Chen G, Joshi P, Tadigadapa S, Eklund PC (2006) Raman scattering from high-frequency phonons in supported-graphene layer films. Nano Lett 6:2667\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLing X, Zhang J (2011) Interference phenomenon in graphene-enhanced Raman scattering. J Phys Chem C 115:2835\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSun ZZ, Yan Z, Yao J, Beitler E, Zhu Y, Tour JM (2010) Growth of graphene from solid carbon sources. Nature 468:549\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi XS, Cai WW, An JH, Kim S, Nah J, Yang DX, Piner R, Velamakanni A, Jung I, Tutuc E, Banerjee SK, Colombo L, Ruoff RS (2009) Large-Area synthesis of high-quality and uniform graphene films on copper foils. Science 324:1312\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTiwari RN, Ishihara M, Tiwari JN, Yoshimura M (2012) Transformation of polymer to graphene films at partially low temperature. Polym Chem 3:2712\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMunoz R, Gomez-Aleixandre C (2013) Review of CVD synthesis of graphene. Chem Vap Deposition 19:297\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMitchem L, Buajarern J, Hopkins RJ, Ward AD, Gilham RJJ, Johnston RL, Reid JP (2006) Spectroscopy of growing and evaporating water droplets: Exploring the variation in equilibrium droplet size with relative humidity. J Phys Chem A 110:8116\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFeng Y, Marchal T, Sperry T, Yi H (2020) Influence of wind and relative humidity on the social distancing effectiveness to prevent COVID-19 airborne transmission: A numerical study. J Aerosol Sci 147:105585\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYuan PY, Wu JY, Ogletree DF, Urban JJ, Dames C, Ma YB (2020) Adapting the electron beam from SEM as a quantitative heating source for nanoscale thermal metrology. Nano Lett 20:3019\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang HD, Orejon D, Song DX, Zhang X, McHale G, Takamatsu H, Takata Y, Sefiane K (2022) Non-wetting of condensation-induced droplets on smooth monolayer suspended graphene with contact angle approaching 180 degrees. Commun Mater 3:75\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhang CX, Li TJ, Yuan Y, Wang FQ, Tan HP (2020) Effects of droplets in the air on light transmission in target optical detection. Opt Lasers Eng 128:106044\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBorn M, Wolf E (1999) \u003cem\u003ePrinciples of optics: Electromagnetic theory of propagation, interference and diffraction of light (7th Edition)\u003c/em\u003eCambridge University Press\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYu IG, Kim YJ, Kim HJ, Lee C, Lee W (2011) I. Size-dependent light-scattering effects of nanoporous TiO spheres in dye-sensitized solar cells. J Mater Chem 21:532\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBohren CF, Huffman DR (2008) \u003cem\u003eAbsorption and scattering of light by small particles\u003c/em\u003e (Wiley-VCH\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLiu Y, Li C, Yu LX, Wu ZW, Fan SC, Lv RT (2024) Ultra-high sensitivity fiber optic microphone with corrugated graphene-oxide diaphragm for voice recognition. Nano Res 17:7593\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYu FF, Liu QW, Gan X, Hu MX, Zhang TY, Li C, Kang FY, Terrones M, Lv RT (2017) Ultrasensitive pressure detection of few-layer MoS\u003csub\u003e2\u003c/sub\u003e. Adv Mater 29:1603266\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eStalder AF, Kulik G, Sage D, Barbieri L, Hoffmann P (2006) A snakebased approach to accurate determination of both contact points and contact angles. Colloids Surf A 286:92\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGao RX, He YL, Zhang DM, Sun GY, He JX, Li JF, Li MD, Yang ZL (2023) Gigahertz optoacoustic vibration in Sub-5 nm tip-supported nano-optomechanical metasurface. Nat Commun 14:485\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKumar A, Tan YJ, Navaratna N, Gupta M, Pitchappa P, Singh R (2024) Slow light topological photonics with counter-propagating waves and its active control on a chip. Nat Commun 15:926\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBruna M, Borini S (2009) Optical constants of graphene layers in the visible range. Appl Phys Lett 94:031901\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7814470/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7814470/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGraphene\u0026rsquo;s moisture absorption significantly impacts its optical reflectivity, leading to measurement errors in graphene-based optoelectronic devices. The mechanism underlying this humidity effect remains unclear. Here we developed a portable fiber optic Fabry\u0026ndash;Perot (F\u0026ndash;P) probe with a 10-layer graphene film to \u003cem\u003ein situ\u003c/em\u003e investigate the non-monotonic changes in reflectivity across varying humidity conditions. The probe showed a 49.8% modulation range in reflectivity between 8 and 67.5% relative humidity (RH). Wetting experiments and COMSOL simulations reveal that humidity-driven changes in graphene reflectivity are due to droplet diameter growth. From 7.5 to 31.3% RH, increasing droplet size enhances scattering with weak absorption, resulting in a positive reflectivity-humidity correlation. From 31.3 to 66.3% RH, larger droplets reduce scattering and increase absorption, shifting the correlation to negative. We establish a quadratic relationship between reflectivity and humidity, allowing for a corrective method that narrows the operational range to 53.9\u0026ndash;58.9% RH, minimizing humidity-induced reflectivity fluctuations. This method defines optimal humidity conditions for stable operation of graphene-based optoelectronic devices and offers a feasible route for probing humidity-sensitive behaviors in other two-dimensional materials.\u003c/p\u003e","manuscriptTitle":"Humidity-driven nonlinear modulation of graphene reflectivity via interfacial wetting behavior","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-20 12:44:52","doi":"10.21203/rs.3.rs-7814470/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"4876677d-0560-48d7-876c-aa0e63a3dd2e","owner":[],"postedDate":"October 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":56476260,"name":"Physical sciences/Materials science/Nanoscale materials/Graphene/Optical properties and devices"},{"id":56476261,"name":"Physical sciences/Nanoscience and technology/Graphene/Optical properties and devices"}],"tags":[],"updatedAt":"2026-03-21T08:55:31+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-20 12:44:52","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7814470","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7814470","identity":"rs-7814470","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}