## 3 Results and Discussion
### Spontaneous Evaporation Rate Dependency on Surface Temperature  
To deal with the non-uniform temperature profile in the liquid phase, the thermostat region was divided into several bins with varying bin width, and the thermostat was applied to each bin separately to maintain the average desired temperature within each bin. The simulations were performed with different bin widths of 27.5, 18.4, 9.2, 6.1, and 3.1 A, which correspond to 2, 3, 6, 9, and 18 division bins in the liquid region, respectively. The temperature profiles shown in Figure 6 demonstrate that dividing the liquid phase into 2 bins with bin widths of 27.5 A already makes the temperature profile flatter in the  
Figure 5: A phase equilibria simulation temperature profile comparison with the temperature profiles obtained from the deletion vacuum simulation and the steady-state vacuum simulation. The vertical dotted lines represent the liquid/thermostat and vapor boundary positions of the right-side interface, respectively, while the blue dotted line represents the liquid surface position located at coordinate \(z^{*}=0\). Note: the deletion vacuum simulation temperature profile is slightly shifted so that the right-side interfaces from all three simulations would coincide. liquid phase, and the temperature at the surface is increased to 88.7 K compared to 87.55 K obtained in the one bin case (no division). However, Figure 6b shows that the further division into thinner bins is not as effective and has little impact on the surface temperature because the temperatures at the surface position group below desired temperature of 90 K in all bin width cases. Consequently, the division into 2 bins leads to increased spontaneous evaporation rates, with the evaporation coefficient values increasing by 11%, as shown in Figure 7, while the spontaneous evaporation rate increases by another 2.5% and reaches saturation value when bin size is reduced to 9.2 A. Since the energy is drawn from the liquid surface due to the evaporative heat sink, the evaporating surface temperature depends on the separation distance, through which the heat is conducted from the liquid film to the surface, i.e., the distance between the surface and the thermostat region boundaries. Thus, the temperature of the evaporating surface is below the desired temperature by several K with the separation distance of 27.5 A  
Figure 6: (**a**) The temperature profiles from simulations with different thermostat region division bin widths, and (**b**) the zoomed view of these profiles in the liquid region near the liquid surface. The black dotted lines denote the liquid/thermostat and vapor boundary positions \(z^{*}=-0.9\) and \(z^{*}=3\) for both left- and right-side interfaces, while the blue dotted line denote the liquid surface position \(z^{*}=0\). For comparison, the temperature profiles from the phase equilibria simulation and the steady-state vacuum simulation with no bin division are also plotted. Figure 7: (**a**) The spontaneous evaporation rate, and (**b**) the corresponding evaporation coefficient as a function of the liquid phase division bin width in steady-state vacuum simulations. The first point (55 Å bin width) represents the data point for simulations without the liquid phase division. (above cases), even when the liquid phase is divided into separately thermostated bins, which level out the temperature profiles in the liquid phase. Since there are no objective criteria to define the liquid phase and thermostat region boundary positions, we performed simulations with different thermostat region boundary positions at the right-side interface. The thermostat region boundary position of the left-side interface was set to \(z^{*}=-0.9\) as in previous cases, and the number of thermostated bins were set to 6.