## 2 Materials and Methods
### Test Methods
#### 2.4.2 Nano-Morphological Parameters  
Based on the analysis of nano-morphology of bitumen, three nano-morphological parameters, such as the area ratio of bee-like structure, the roughness, and the maximum amplitude, are proposed in this paper. A brief explanation is as follows.  
\(\bullet\) The Area Ratio of Bee-like Structure  
The bee-like structure is a unique nanostructure of bitumen, and its quantity and area may be related to the technical indexes of bitumen. In this paper, the area ratio of the bee-like structure in the AFM image was measured and calculated by the following methods: Firstly, the bee-like structure in the AFM image is removed by using Photoshop software as shown in Figure 7a,b [41]; Secondly, the measure function of Image-Pro-Plus software is used to encode the bee-like structure and read the pixel points \(P_{i}\), as shown in Figure 7c,d [42; 43]; Finally, the area ratio of the bee-like structure can be calculated according to Equation (1). All the images in this paper are \(256\times 256\) pixels, and the pixels are not changed during image processing.  
\[P_{BSA}=\sum_{1}^{i}P_{i}/P,\ \% \tag{1}\]  
where \(P_{BSA}\) is the area ratio of bee-like structure; \(P_{i}\) is the area of bee-like structure which is encoded number \(i\); \(P\) is the total area of the AFM image.  
Figure 6: Height curves of representative areas in bitumen atomic force microscope (AFM) images (**a**) area selection; (**b**) height curves; (1) away from bee-like structure area; (2) bee-like structure and adjacent area; (3) and (4) bee-like structures.  
\(\bullet\) The Maximum Amplitude  
In the bitumen AFM image, the height of the bee-like structure fluctuates along its major axis [44]. It is not difficult to find that the surface height of the bee-like structure fluctuates in the form of waves, and the wavelength is basically the same, but the wave crest and wave trough are different. The maximum height difference between the wave crest and wave trough is defined as amplitude, as shown in Figure 8.  
Amplitude response is the intensity of fluctuation of bee-like structure, and it is also a parameter to describe the development of the bee-like structure. The maximum amplitude of bee-like structure can be obtained by measuring all bee-like structures in the AFM image.  
\(\bullet\) The Roughness  
The area ratio of the bee structure can be described as the proportion of the area of the bee structure in the two-dimensional image. The degree of the single bee structure development can be described by the amplitude. However, in the three-dimensional image, the surface area of the bee structure needs to include the two-dimensional area and three-dimensional amplitude of the bee structure. Fortunately, the roughness just meets these two requirements. In this paper, the root means square roughness is  
Figure 7: Bee-like structure area measurement. (**a**) two-dimensional bitumen atomic force microscope (AFM) image; (**b**) bee-like structure removal image; (**c**) calculation image of bee-like structure area; (**d**) partial enlargement image of calculation results of bee-like structure).  
used to describe the surface structure characteristics of bitumen. The calculation method is shown in Equation (2) [44].  
\[R_{q}=\left(\frac{\iint\left[h(x,\ y)-h_{0}\right]^{2}dA}{\iint dA}\right)^{1/2} \tag{2}\]  
where \(A\) is the scanning area, 10 um \(\times\) 10 um in this paper; \(h(x,\ y)\) is the height equation, nm; \(h_{0}\) is the reference height, and its equation is shown in Equation (3) [45].  
\[h_{0}=\frac{\iint h(x,\ y)dA}{\iint dA} \tag{3}\]