Fractals dimension calculation

Chapter 13 - It was shown, that limiting conversion (in the given case - imidization) degree is defined by purely structural parameter - macromolecular coil fraction, subjected evolution (transformation) in chemical reaction course. This fraction can be correctly estimated within the framework of fractal analysis. For this purpose were offered two methods of macromolecular coil fractal dimension calculation, which gave coordinated results. 

TABLE 4 The comparison of macromolecular coil fractal dimensions calculated by different methods, for polyarylates. 

TABLE 15 The literary values of parameters and the fractal dimension calculated values Dl-... 

FIGURE 75 Comparison of the dependences of excluded volume factor on macromolecular coil fractal dimension calculated according to the Eqs. (6) (1) and (39)... 

FIGURE 49 The dependences of macromolecular coil fractal dimension calculated according to the Eq. (17), on formal contents cform for APESF (1), CP-OFD-lO/OSF-10 (2) and CP-OFD-lO/P-1 (3). 

FIGURE 10 The comparison of the heptylbenzoate molecule fractal dimension, calculated according to the Eq. (18)ofChapter2D andEq. (76) of Chapter 1 ]jy... 

This review has illustrated various applications of fractal concepts to the description of adsorption/desorption processes on environmental materials. The surface fractal dimension A can be determined by several independent methods, among which those based on adsorption measurements are shown to be the most convenient and straightforward. However, a comparison of fractal dimensions calculated from different approaches was shown to be problematic therefore, the need for further studies in this field is evident. 

Using this method. Park et al. [81] analysed TEM images of diesel particles and showed that the projected area equivalent diameter nearly equals the mobility diameter in the mobility size range from 50 to 220 nm. Doubly charged particles and possible fragments were observed for the DMA-classified particles. The fractal dimension calculated from the TEM images of mobility-classified aggregates was 1.75. The... 

FIGURE 8.7 The dependences of fracture surface fractal dimension calculated according... 

FIGURE 10.9 The dependence of fracture surface fractal dimension calculated according to the Eq. (5.16), on sample width B for HOPE [21],... 

Table 1 Fractal Dimension Calculated Via Image Analysis Compared to Fractal Dimension Calculated Via Rheology Using the Weak-Link Theory ... 

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