# Effect of Characteristics of Different Types of Bauxite Clinker on Adhesion
## 2 Materials and Methods
### Adhesion Test
#### 2.3.2 Surface Energy Property Test  
Contact angle measurements were used to determine the free energy of the asphalt samples (Table 9). The surface energies of three liquids (distilled water, glycerol, and ethylene glycol) and the calculated surface energies of asphalt are listed in Equations (5)-(7). The net absorption method was used to obtain the surface energy of the aggregate (Table 10), using a test procedure described in references [27; 28]. Three liquids (distilled water, hexane, and ethylene glycol) with known surface energies and the calculated surface energies of the aggregates are listed in Equations (5)-(7). The work between the bitumen (a) and aggregate (s) is given by Equation (4), peeling work is given by Equation (8), ER1 is given by Equation (9), and ER2 is given by Equation (10).  
\[w_{as}=2\left(\sqrt{r_{a}^{LW}r_{s}^{LW}}+\sqrt{r_{a}^{+}r_{s}^{-}}+\sqrt{r_{a}^{ -}r_{s}^{+}}\right) \tag{4}\]  
where \(r_{a}^{+}\) and \(r_{S}^{+}\) are the Lewis acid component; \(r_{a}^{-}\) and \(r_{s}^{-}\) are the Lewis base component; and \(r_{a}^{LW}\) and \(r_{s}^{LW}\) are the Lifshitz van der Waals component.  
Using the [PERSON] equation to form three continuous formulas (Equations (5)-(7)), the surface energy parameters of the materials to be measured were obtained.  
\[r_{L_{1}}(1+\cos\theta_{a_{1}}) = 2\left(\sqrt{r_{a}^{LW}r_{L_{1}}^{LW}}+\sqrt{r_{a}^{+}r_{L_{1}}^{ -}}+\sqrt{r_{a}^{-}r_{L_{1}}^{+}}\right) \tag{5}\] \[r_{L_{2}}(1+\cos\theta_{a_{2}}) = 2\left(\sqrt{r_{a}^{LW}r_{L_{2}}^{LW}}+\sqrt{r_{a}^{+}r_{L_{2}}^ {-}}+\sqrt{r_{a}^{-}r_{L_{2}}^{+}}\right)\] (6) \[r_{L_{3}}(1+\cos\theta_{a_{3}}) = 2\left(\sqrt{r_{a}^{LW}r_{L_{3}}^{LW}}+\sqrt{r_{a}^{+}r_{L_{3}}^ {-}}+\sqrt{r_{a}^{-}r_{L_{3}}^{+}}\right) \tag{7}\]  
where \(r_{L}^{+}\), \(r_{L}^{-}\), and \(r_{L}^{LW}\) are the surface energies parameters of three liquids (distilled water, glycerol, and ethylene glycol, respectively). The surface energies of the aggregates were obtained by Equations (5)-(7), and the contact angles were obtained by the capillary rise method.  
The work of debonding (Equation (8)) is the reduction in bond strength of a bitumen-aggregate system in the presence of moisture.  
\[w_{asw}^{wet}=\left[2\sqrt{r_{s}^{LW}r_{w}^{LW}}+2\sqrt{r_{s}^{ +}r_{w}^{-}}+2\sqrt{r_{s}^{-}r_{w}^{+}}+2\sqrt{r_{a}^{LW}r_{w}^{LW}}\right]\] \[+2\sqrt{r_{a}^{+}r_{w}^{-}}+2\sqrt{r_{a}^{-}r_{w}^{+}}-2r_{w}^{LW }-4\sqrt{r_{w}^{-}r_{w}^{+}}-2\sqrt{r_{s}^{LW}r_{a}^{LW}} \tag{8}\] \[-2\sqrt{r_{s}^{+}r_{a}^{-}}-2\sqrt{r_{s}^{-}r_{a}^{+}}\]  
Equations (9) and (10) were used to calculate the moisture compatibility ratios [16; 29; 30]. Higher ratio values suggest a higher resistance to moisture damage.  
\[ER_{1}=\left|\frac{w_{as}}{w_{asw}^{wet}}\right| \tag{9}\]  
\[ER_{2}=\left|\frac{w_{as}-w_{as}}{w_{asw}^{wet}}\right| \tag{10}\]  
The use of ER as an index to evaluate the water stability of asphalt mixtures is based on the fact that the water sensitivity of a mixture is directly proportional to the strength of adhesion between asphalt and aggregate in the anhydrous state and is inversely proportional to the exfoliation power in the aqueous state. However, ER1 does not consider the wettability of asphalt with respect to the aggregate. [PERSON] et al. further proposed the index ER2 by noting that the water damage resistance of an asphalt mixture is directly proportional to the wettability of asphalt with respect to the aggregate and inversely proportional to the exfoliation power [31].