## 2 Materials and Methods
### Cyclic Fatigue Testing  
A customized static cyclic fatigue testing device was used [20] (Figure 1). The device ensured a standardized instrument insertion through a fixed block and the possibility to test the files at different inclinations. For this study, all instruments were tested at the standard position (0\({}^{\circ}\)). A simulated 16-mm-long ceramic canal was made by replicating the instrument's size and taper. It presented a curvature with a 5-mm radius (calculated at the internal concave surface of the artificial canal), a 60\({}^{\circ}\) angle of curvature assessed using the [PERSON]'s method [21], a center of curvature 5 mm from the end of the canal and a curved segment of 5 mm in length [14]. The ceramic artificial canal was milled in a zirconium oxide disc (Dental Zirconia Pre-Shaded Blank, Liaoning Upcera Co., Ltd., Shenzhen, Guangdong, China) using the milling machine Roland DWX-51D (Roland DG Mid Europe, AP, Italy). To permit the injection/expulsion of the liquid or gel sodium hypochlorite from the artificial canal, a cover formed by the superimposition of two Plexiglas slides was employed. A 1-mm diameter channel was built inside this cover in correspondence with the artificial canal to permit the irrigant flow in the system, ensuring the absence of contact between the syringe and the instrument or the zirconium canal. The insertion point of the irrigant syringe was placed at the beginning of this channel. Figure 1: The custom-made apparatus for cyclic fatigue tests with an OneCurve (OC) file and a preset temperature of 20 \({}^{\circ}\)C. (**a**) The fixed block in which the electric handpiece is inserted and (**b**) the mobile support on rails to allow the insertion/withdrawal of the file; (**c**) the ceramic canal with a 60 \({}^{\circ}\)angle and a 5-mm radius covered by the superimposition of two Plexiglas slides; (**d**) the hole made on the cover near the corresponding canal apex to permit the outflow of the solution during the test through an aspiration system; (**e**) the insertion point of the irrigant tip and (**f**) the channel built inside the cover to permit the irrigant flow during the test; (**g**) the thermostat which allowed the temperature adjustment through to a thermocouple (**h**) applied to the artificial canal. A small circular hole was made on the cover near the corresponding canal apex to ensure the outflow of the solution during the test by means of an aspiration system (Figure 2). Moreover, a thermostat was associated to the customized device to allow the temperature adjustment in the artificial canal. The temperature was kept constant during the test using a thermocouple applied to the artificial canal and which activated or deactivated the thermostatic resistance when the temperature decreased or reached the preset one respectively. In particular, the instruments were tested at room temperature (20 \({}^{\circ}\)C \(\pm\) 1 \({}^{\circ}\)C) and body temperature (37 \({}^{\circ}\)C \(\pm\) 1 \({}^{\circ}\)C). A 6:1 reduction handpiece (Sirona Dental Systems GmbH, Bensheim, Germany) activated by a torque-controlled motor (Silver Reciproc, VDW, Munich, Germany) was used to turn on 15 instruments of each system in continuous rotation (300 rpm) as indicated by the manufacturer. Torque was fixed at the maximum value provided (4.1 Ncm). Each instrument was located in the contra-angle handpiece and inserted into the canal at the same length (16 mm). The rotation started at the preset temperature, and this temperature was kept constant for the whole duration of the test. For groups 1 and 4 (control groups), the friction of the file on the artificial canal walls was reduced by employing a special high-flow synthetic oil (Super Oil, Singer Co Ltd., Elizabeth, NJ, USA) projected for lubrication of mechanical parts. Experimental protocols (for liquid and gel solutions) included a continuous and constant injection of irrigant for 10 s every 30 s of rotation of the instruments.