Abstract
Polymer microspheres (PMs) are a kind of self-similar volume expansion particle, and their fractal dimension varies with hydration swelling. However, there is no unique fractal dimension calculation method for their characteristics. A new model is established in this paper, which is particular to calculate the fractal dimension of PMs. We carried out swelling hydration experiments and scanning electron microscope (SEM) experiments to verify the new model. The new model and the box-counting model were used to calculate the fractal dimensions of PMs based on the hydration experiment results. Then, a comparison of the calculation results of the two methods was used to verify the validity of the model. Finally, according to the new model calculation results, the fractal dimension characteristics of PMs were analyzed. The research results indicate that the new model successfully correlates the cumulative probability of the PMs dispersed system with the fractal dimension and makes fractal dimension calculation of PMs more accurate and convenient. Based on the experiment results, the new model was used to calculate the fractal dimension of PMs and the box-counting model, and its findings were all 2.638 at initial state hydration and 2.739 and 2.741 at hydration time as of day 1. This result verifies the correctness of the new model. According to the hydration swelling experiments and the new model calculation results, the fractal dimension is linear correlated to the average particle size of PMs and the standard deviation average particle size. This means the fractal dimension of PMs represents the space occupancy ability and space occupancy effectiveness.
Highlights
Polymer microspheres (PMs) are spherical polymer composite materials with diameters ranging from nanometers to micrometers, high specific surface area, high reactivity, and other unique physical, chemical, biological properties (Wang et al, 2019; Wang et al, 2018)
Hydration Swelling Experiment Results The particle size distribution of PMs dispersion system measured in the swelling hydration experiment at 1, 3, 5, 10, and 30 days are shown in Figure 2 and Table 1 (Li, 2015)
The PMs expanse in the process of hydration can be observed, which leads to the increase of average particle size
Summary
Polymer microspheres (PMs) are spherical polymer composite materials with diameters ranging from nanometers to micrometers, high specific surface area, high reactivity, and other unique physical, chemical, biological properties (Wang et al, 2019; Wang et al, 2018). The selection method of PMs is based mainly on the matching coefficient that comes from the ratio of the particle size with the throat diameter (Yang et al, 2017). A new method is needed to characterize the microsphere dispersion system and describe the particle distribution and particle size simultaneously. At this time, the self-similar characteristics of PMs have attracted the attention of researchers. For a disordered polymer system microspheres dispersed solution, the microstructure can be named self-similar portions present in a matrix called fractals (Sayan et al, 2018). That is because the system that satisfies the self-similar theory can study its particle size distribution rule according to fractal theory (Hu et al, 2006)
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