## 2 Materials and Methods
### Icephobic Behavior Assessment  
Three laboratory tests were used to evaluate the icephobic behavior of materials:  
* The centrifugal force adhesion test (CAT);
* The push-off test; and
* The freezing delay test. The CAT apparatus consists of a centrifuge developed at the Anti-Icing Material International Laboratory (AMIL) as seen in Figure 1.  
Figure 1: Overview of the centrifuge apparatus. Equipped with an accelerometer, the iced beam is rotated until the ice is detached and captured by the pan. The ice adhesion strength is the centrifugal shear stress exerted on the ice sample at the time of detachment. A CAT sampling consists of six different coating samples that are compared to six reference blank aluminum sheets. All samples are subjected to icing simultaneously under freezing drizzle conditions set at \(-8\)\({}^{\circ}\)C and tested at \(-10.0\)\({}^{\circ}\)C. Afterwards, samples are rotated at an acceleration speed of 300 rpm/s until the ice is detached by centrifugal force. This acceleration creates a strain rate of approximately \(10^{-6}\) s\({}^{-1}\). The rotational speed is controlled during the acceleration phase by the AMIL-made software, which records and plots the angular velocity in real time with data from installed sensors. An accelerometer sensor located on the wall of the centrifuge is used to determine the exact time of ice detachment. This time corresponds to a sharp increase in the vibration signal. The centrifugal force is calculated using the following equation:  
\[F_{c}=mr\omega^{2} \tag{1}\]  
where:  
\(F_{c}=\) centrifugal force;  
\(\omega=\) ice detachment velocity;  
\(m=\) mass of ice; and  
\(r=\) beam radius at the center of the sample. The ice adhesion shear stress is then obtained as follows:  
\[\tau_{ia}=\frac{F_{c}}{A} \tag{2}\]  
where:  
\(\tau_{ia}=\) ice adhesion shear stress;  
\(F_{c}=\) centrifugal force; and  
\(A=\) iced area in contact with the coating. The adhesion reduction factor (ARFs) of coating \(i\) is calculated as follows:  
\[ARF_{i}=\frac{\tau_{bA}}{\tau_{bi}} \tag{3}\]  
where:  
\(ARF_{i}=\) adhesion reduction factor of coating \(i\);  
\(\tau_{bA}=\) bulk shear stress of the aluminum; and  
\(\tau_{bi}=\) bulk shear stress of coating \(i\). The push-off test is conducted by first placing a thin 1 cm diameter cylindrical plastic mold onto a substrate. The mold is then filled with deionized water and placed together with the substrate into a cold chamber at \(-10.0\)\(\pm\) 0.2 \({}^{\circ}\)C for 24 h to form an ice cylinder. The test sample is placed onto the holder and fixed into position by a vacuum (using two specialty screws on the apparatus). In our test, a remote computer-controlled interface controlled the velocity of these specialty screws at a fixed rate of 0.05 mm\(\cdot\)s\({}^{-1}\) so that the sample holder gradually approached the force gauge. The force gauge was set to measure the shear force every Deci-second (one-tenth of a second) until the ice was detached. The adhesion stress was then calculated based on the maximum force and icing area. As previously stated, the adhesion reduction factors (ARF) of the coatings are obtained by dividing the bulk shear stress value of the uncoated aluminum sheets by the bulk shear stress of the coated sheets. Figure 2 illustrates the push-off apparatus. The two methods previously described were used to determine ice adhesion. The CAT is a method that uses simulated atmospheric ice, while the push-off test is a better representative of ice removal during actual operations. The use of the centrifugal force, however, allows for a direct comparison of coatings. The final method consists of measuring the water freezing delay on the coatings interface, namely the nucleation time. The experimental freezing device used allows for the precise determination of the time required for a water drop to solidify under controlled environmental conditions.