# Preparation and Properties of Waterborne Polyurethane and SBS Composite-Modified Emulsified Asphalt
## 3 Results and Discussion
### Surface Free Energy Analysis
#### 3.6.2 Analysis of Adhesion Energy and Compatibility Indicators  
The fundamental cause of water damage in asphalt mixtures is the separation of the asphalt film from the aggregate caused by moisture. During this process, the adhesion energy (\(\Delta G_{wet}^{a}\)) between aggregate and asphalt in the presence of water is usually negative, indicating that water will spontaneously cause asphalt to peel off the surface of the aggregate.  
Some researchers suggest using the indicator \(ER_{1}\) to reflect the water stability of asphalt mixtures. The calculation equation for \(ER_{1}\) is shown in Equation (9). When \(ER_{1}\) is greater than 1, the adhesion energy between asphalt and aggregate in the absence of water is greater than that in the presence of water, indicating better water damage resistance. When \(ER_{1}\) equals 1, it serves as a threshold for evaluating the water sensitivity of asphalt mixtures. The larger the compatibility index, the better the water damage resistance of the asphalt mixture.  
Additionally, for a given aggregate surface, asphalt with higher wettability will have better adhesion energy, which is related to the cohesive energy of asphalt and aggregate. The larger the difference \(\left(\left|\Delta G_{dry}^{a}-\Delta G_{dry}^{c}\right|\right)\) between them, the stronger the wettability of asphalt. This can be represented by the index \(ER_{2}\), and the calculation method is shown in Equation (10). A higher \(ER_{2}\) value indicates stronger water damage resistance of the mixture.  
Figure 18 shows the adhesion energy between four types of asphalt and aggregate. Whether for diabase or limestone, the adhesion energy of the three dosages of PU+ was significantly higher than that of SEA. Among them, PU+3 had the highest adhesion energy, slightly higher than that of PU+6, and PU+6 had a slightly higher adhesion energy than PU+9. For both diabase and limestone, the adhesion energy of PU+3 was increased by 11.49% compared to that of SEA. Additionally, for both diabase and limestone, the adhesion energy of PU+3 was increased by 0.77% compared to that of PU+6 and by 2.12% compared to that of PU+9. This indicates that the addition of PU+ significantly improves the adhesion performance between asphalt and aggregate.  
Figures 19 and 20 show the compatibility indicators \(ER_{1}\) and \(ER_{2}\) of four types of asphalt, respectively. For the same aggregate, the \(ER_{1}\) and \(ER_{2}\) of the four types of asphalt exhibited the following patterns:  
* For diabase: \(\circ\) SEA had the highest \(ER_{1}\) and \(ER_{2}\) among the four types; \(\circ\) PU+9 had the lowest \(ER_{1}\) and \(ER_{2}\) among the four types; \(\circ\) PU+6 had the highest \(ER_{1}\) and \(ER_{2}\) among the three dosages of PU+.
* For limestone: \(\circ\) SEA had the highest \(ER_{1}\) and \(ER_{2}\) among the four types;  
Figure 18: Adhesion energies of four types of asphalt with diabase and limestone.  
SEA exhibited the best water stability, and the addition of the waterborne polymer PU+ reduced the water stability of asphalt and decreases its resistance to water damage. Among the PU+modified asphalts, PU+6 showed superior water damage resistance compared to PU+3 and PU+9.