# Adhesion Evaluation of Asphalt-Aggregate Interface Using Surface Free Energy Method
## 3 Properties of Raw Materials
### Surface Free Energy of Raw Materials  
There are many methods for testing the surface free energy of different materials, including the capillary method, rings method, drop weight method, Wilhelmy plate method, sessile drop method, atomic force microscopy and the nuclear magnetic resonance method. [PERSON] and [PERSON] [19] measured the surface free energy components of asphalt pavement materials using the sessile drop method. [PERSON] et al. presented a sessile drop device for measuring the surface energy components of both asphalt binders and aggregates [20; 21]. In this manuscript, a sessile drop device is employed to measure contact angles on the surface of raw materials. The surface energy components of raw materials are calculated using the measured contact angles.  
The test liquids are distilled water, glycerin and formamide. The surface free energy components [22] of all test liquids are known in advance, as shown in Figure 4.  
The sessile drop method was conducted to test contact angles between the surface of the raw materials and test liquids. Based on the simplified matrix formula of the Young-Dupre Equation (see Equation (1)) [23; 24] the surface free energy components of raw materials are calculated, as shown in Table 2.  
\[\left[\begin{array}{ccc}\sqrt{\gamma_{L1}^{LW}}&\sqrt{\gamma_{L1}^{+}}&\sqrt {\gamma_{L1}^{-}}\\ \sqrt{\gamma_{L2}^{LW}}&\sqrt{\gamma_{L2}^{+}}&\sqrt{\gamma_{L2}^{-}}\\ \sqrt{\gamma_{L3}^{LW}}&\sqrt{\gamma_{L3}^{+}}&\sqrt{\gamma_{L3}^{-}}\\ \end{array}\right]\left[\begin{array}{ccc}\sqrt{\gamma_{d}^{LW}}\\ \sqrt{\gamma_{d}^{-}}\\ \sqrt{\gamma_{d}^{+}}\\ \end{array}\right]=\left[\begin{array}{ccc}\frac{\gamma_{L1}(1+\cos\theta _{1})}{2}\\ \frac{\gamma_{L2}(1+\cos\theta_{2})}{\gamma_{L3}(1+\cos\theta_{3})}\\ \frac{\gamma_{L3}(1+\cos\theta_{3})}{2}\\ \end{array}\right] \tag{1}\]  
where \(\gamma_{L1}\), \(\gamma_{L2}\), \(\gamma_{L3}\)--the surface free energy of distilled water, glycerin, and formamide, respectively; \(\gamma_{L1}^{LW}\), \(\gamma_{L2}^{LW}\), \(\gamma_{L3}^{LW}\)--the nonpolar part of surface free energy of distilled water, glycerin, and formamide, respectively; \(\gamma_{L1}^{+}\), \(\gamma_{L2}^{+}\), \(\gamma_{L3}^{+}\)--the acidic effect part of surface free energy of distilled water, glycerin, and formamide, respectively; \(\gamma_{L1}^{-}\), \(\gamma_{L2}^{-}\), \(\gamma_{L3}^{-}\)--the basic effect part of surface free energy of distilled water, glycerin, and formamide, respectively; \(\theta_{1}\), \(\theta_{2}\), \(\theta_{3}\)--the contact angle between raw material and distilled water, glycerin, and formamide, respectively; the rest of the parameters are the same as above.  
Figure 4: The Surface Free Energy Components of Test Liquids (mJ/m\({}^{2}\)) (Note: \(\gamma\)L—the surface free energy of test liquid; \(\gamma\)L\({}^{\text{LW}}\)—the nonpolar part of the surface free energy of test liquid; \(\gamma\)L\({}^{\text{AB}}\)—the polar part of the surface free energy of test liquid; \(\gamma\)L\({}^{+}\)—the acidic effect part of the surface free energy of test liquid; \(\gamma\)L\({}^{-}\)—the basic effect part of the surface free energy of test liquid.).  
The method proposed by [PERSON] is applied to further verify the validity of the test methods and results [25,26]. [PERSON] pointed out that there is a good linear relationship between \(\gamma_{L}\cos\theta\) and \(\gamma_{L}\) of test liquid. If the correlation coefficient is higher than 0.95, it indicates that the test method and results are effective. However, when the correlation coefficient is lower than 0.95, the test method and results are ineffective. In this paper, the correlation coefficients of \(\gamma_{L}\cos\theta\) and \(\gamma_{L}\) of test liquid are all above 0.95, which indicates that using the sessile drop method to test the surface free energy components of raw materials is feasible.