# The Effect of Adsorbed Volatile Organic Compounds on an Ultrathin Water Film Measurement
## 3 Results and Discussion
### The Effect of Adsorption of VOCs on SPR Reflectance  
As Figure 1b,c show, the recorded images from SPRi are in grayscale (with pixel intensity values in the range of 0 to 4940). For the quantitative analysis of the results, it is required to normalize the images by converting the pixel intensity value into units of reflectivity (0-1). Reflectivity units show the ratio of reflected light from the prism into the incident light on the prism and allow comparison between the SPR theoretical model and the experimental result. The theoretical SPR reflectance can be modeled by solving the Fresnel equation for transverse magnetic light (p-polarized light) in a four-layer configuration BK7 prism, gold, water, and air as:  
\[R=\frac{r_{12}[1+\exp(-2i\:K_{2}d_{2})]+[r_{12}r_{23}+\exp(-2i\:K_{2}d_{2})]r_ {34}\exp(-2K_{3}d_{3})}{1+r_{12}r_{23}\exp(-2i\:K_{2}d_{2})+[r_{23}+r_{12}\exp (-2i\:K_{2}d_{2})]r_{34}\exp(-2K_{3}d_{3})} \tag{1}\]  
In this equation, the thickness of the air and the BK7 prism are considered infinity, and the thickness of the gold layer is 50 nm. In the case of SPRi of adsorbed VOCs on the surface, the thickness of the water layer is zero and Equation (1) reduces into the three-layer system. It is important to note that we assume the initial thickness of adsorbed VOCs on the surface is zero on the surface. For normalization of images, we introduced a scaling factor:  
\[S=\frac{I_{SPR,\:\max}-I_{SPR,\:\min}}{R_{t,\:\max}-R_{t,\:\min}} \tag{2}\]  
Figure 4: The sample stored in a desiccator (sample 3) allowed adsorption of fewer VOC molecules—a higher atomic percentage of Au—on its surface, as compared to the samples left in an open environment (sample 2) by desorbing the part of VOCs that has double oxygen bonds. At a wavelength of 550 nm, the \(R_{t,max}\) and \(R_{t,min}\) were, respectively, 0.778 (at \(\alpha\) = 42.0\({}^{\circ}\)) and 0.089 (at \(\alpha\) = 46.3\({}^{\circ}\)) from theoretical reflectance-angle plot. The reflectivity at each pixel can be calculated using:  
\[C=I_{SPR,\text{ max}}-S\;R_{t,\text{ min}} \tag{3}\]  
\[R=(1-C)/S+R_{t,\text{ min}} \tag{4}\]  
The reflectance-incident angle curves for samples 2 and 4 are shown in Figure 5a,b, respectively. The results show a good agreement between theoretical and experimental results. The real-time effects of adsorbed VOCs on the SPR reflectivity were measured by visualizing changes in the reflectivity of the surface at a fixed incident angle of 44.8\({}^{\circ}\). This angle is the same angle we used for observation of dropwise condensation. Figure 5a shows the reflectance changes with time for sample 2. The result indicates an odd behavior; initially, (for the first 43 h) reflectance dropped significantly (\(\sim\) 5%). In the next 70 h, reflectance gradually increased (1%). The SPRi was set up in such a way (incident angle of 44.8\({}^{\circ}\) and wavelength of 550 nm [5]) that any increase in the reflectance showed an increase in the thickness of the adsorbed layer and/or an increase in the refractive index of the adsorbed layer. Conversely, a decrease in the reflectance is an indicator of desorption and/or reduction in the refractive index of the adsorbed layer. As SPRi was performed under intensity modulation, it was not possible to deconvolute changes in the refractive index and the thickness of the adsorbed layer concurrently. Simultaneous measurement of refractive index and thickness of a film using SPRi is possible when SPRi with angle-scanning is performed at two different wavelengths. It is possible to determine refractive index and thickness of sample from Equation (1) using reflectance-incident angle curve at two wavelengths. More information regarding the simultaneous measurement of refractive index and thickness can be found in our previous work [24]. In this work, we used XPS data to observe the trend of the adsorbed layer thickness with time.