3.1.1. Geometric Method

The variation in the cross sections, given by the mean values of *a* and *b*, is shown in the histogram of Figure 2, with percentage frequency related to five arbitrary intervals. The variation in the cross sections, given by the mean values of *a* and *b*, is shown in the histogram of Figure 2, with percentage frequency related to five arbitrary intervals.

**Figure 2.** Frequency distribution of the average cross-section dimensions of ubim fibers. **Figure 2.** Frequency distribution of the average cross-section dimensions of ubim fibers.

The mean frequency of the cross-sectional dimensions for the investigated ubim fibers (Figure 2) reveals an almost normal distribution within the range of 510 to 620 µm. For each interval, the mean density was measured by dividing the mass by the volume before being statistically analyzed by the Weibull method. Table 1 presents the mean ubim fiber density values for each interval of the mean dimensions of the cross-sections shown in Figure 2. In this table, a trend of greater density for thinner fibers should be noted. Weibull statistical analysis was performed for densities measured by the geometric method. Table 1 presents the Weibull parameters provided by the WA software associated The mean frequency of the cross-sectional dimensions for the investigated ubim fibers (Figure 2) reveals an almost normal distribution within the range of 510 to 620 µm. For each interval, the mean density was measured by dividing the mass by the volume before being statistically analyzed by the Weibull method. Table 1 presents the mean ubim fiber density values for each interval of the mean dimensions of the cross-sections shown in Figure 2. In this table, a trend of greater density for thinner fibers should be noted. Weibull statistical analysis was performed for densities measured by the geometric method. Table 1 presents the Weibull parameters provided by the WA software associated with the shape parameter, scale parameter and precision fit (R<sup>2</sup> ). The quality of these measurements can be evaluated using the R<sup>2</sup> parameter; the closer to 1, the more reliable the data obtained.

with the shape parameter, scale parameter and precision fit (R2). The quality of these measurements can be evaluated using the R2 parameter; the closer to 1, the more reliable the data obtained. In Table 1 it is important to note that thinner ubim fibers, with lower diameters, display significantly higher density, while the thicker ones are much less dense. As compared to the cellulose, hemicellulose and lignin densities, ~1.6 g/cm<sup>3</sup> [21,23], the ubim fibers revealed an amount of porosity that increases markedly with the fiber diameter.


**Table 1.** Density of ubim fibers calculated for different intervals of cross-section dimension.
