## 2 Experimental Approach  
### Experimental Setup  
Surface plasmon resonance (SPR) is a physical process where the electrons in the metal surface layer are excited by the incident light under a total internal reflection (TIR) condition. It is a sensitive, nonintrusive, and real-time detection tool to visualize the refractive index variation. It is known as a sensitive technique to detect the refractive index on the order of \(10^{-5}\)[26]. Kretschmann configuration has been widely used for SPRi. The index-matching liquid layer is used to optically couple the prism with a gold film-coatedglass substrate. Moreover, the reflectance can be predicted theoretically from the Fresnel equation for the p-polarized light in a four-layer SPRi system [27].  
\[R = \left|\frac{r_{1}+r_{2}\exp(-2 ik_{2}d_{2})+[r_{1}r_{2}+\exp(-2 ik_{2}d_{ 2})]r_{3}\exp(-2 ik_{3}d_{3})}{1+r_{1}r_{2}\exp(-2 ik_{2}d_{2})+[r_{2}+r_{1}\exp(- 2 ik_{2}d_{2})]r_{3}\exp(-2 ik_{3}d_{3})}\right|^{2} \tag{1}\]  
where, \(r_{i}\) indicates the reflection coefficient between the \(i\)-th and \((i+1)\)-th layer, \(k_{i}\) represents the waver vector, and \(d_{i}\) refers to the thickness of the \(i\)-th medium. Subscripts 1, 2, and 3 indicate prism, the gold film, and the test medium, respectively. The reflected light from the metal surface has the lowest intensity at the SPR angle, which changes only by the refractive index of the test medium with a fixed configuration of the prism, gold film thickness, and wavelength. By conducting the angular modulation (AM) process, the refractive index can be estimated based on the SPR angle.  
Figure 1a shows the SPRi experimental setup. Light irradiated from the LED light source (SugarCuBeTM Ultra LED Illuminators, Nathaniel Group, Inc.) is converted from a diverging light beam to a parallel light through the collimation lens array. A bandpass filter (632 \(\pm\) 5 nm, Edmund Optics) and a polarizer (Edmund Optics) are installed to convert the light into a single wavelength and p-polarized light. Mirror mounted on the rotation stage controls the incidence angle of the light to the dove prism (BK7 glass). Gold film (47 nm) is coated on a thin coverslip (0.5 mm) with a titanium adhesion layer (3 nm). A CCD camera (XImea) and CMOS camera (JENOPTIK) are used to detect the reflected light and visualize the droplet shape. Details of the calibration method for measuring reflectance based on the intensity of SPR images are explained in the previous studies [28; 29]. Figure 1b depicts a multi-layer film structure to measure the solid-liquid interface temperature of the droplet. The pNIPAM solution (5.4 \(\mu\)L) is sealed by insulation tape attached to the gold films to prevent vaporization of the pNIPAM solution. The de-ionized (DI) water droplet (1 \(\mu\)L) is deposited on the gold film located on the pNIPAM solution. Experiments are repeated three times for different surface temperature cases. The surface temperature is controlled using a heating plate from 27 to 29 \({}^{\circ}\)C, and the relative humidity is 10 \(\pm\) 3% at room temperature.  
To develop the temperature measurement method, we purchase pNIPAM with a number-average molecular weight of 30,000 g mol\({}^{-1}\) from Sigma-Aldrich. The pNIPAM aqueous solution is prepared with the following processes. The pNIPAM and de-ionized (DI) water are filled into a vial located on the microbalance (AND Co., LTD., Tokyo, Japan) to measure the exact quantities. After shaking the pNIPAM aqueous solutions an hour, it is kept in the fridge for a few days for the total dissolution [24]. At a concentration below 10 wt%, pNIPAM solution shows a small variation of refractive index depending on the temperature. On the other hand, the refractive index variations of the pNIPAM solution are too large above the 10 wt% that cannot be estimated with the current experimental setup. Thus, the pNIPAM solution with 10 wt% is used through the temperature sensitivity test with different concentrations.