# Novel Microscopic Approach to Particle Size Evaluation in Colloidal Systems
## 3 Results and Discussion  
The x-axis in each graph represents the calculated area. The area was calculated using the ImageJ program (which gives us the major and minor axis of the particles) and the data software which returns an area calculated by approximating the particle to an ellipse. To reduce the error, particles with circularity < 0.3 were not taken into account (the formula for circularity is 4\(\pi\)(Area/Perimeter2) [35]. Once the area of the particles was calculated, it was divided into classes and the number of particles detected for each class was counted (class population). All the values reported on the y-axis of the following graphs are presented according to the fraction of solid particles present and dispersed in the colloidal system. This axis represents the abundance of the colloidal particles (asphaltenes). This abundance is a measure of the occurrence of each size range of the particles relative to the total particle number in the tested sample. The abundance was obtained by dividing the number of particles of a certain dimension by the total number of particles. On the y-axis, the population of the columns which have been divided by the total number (\(y=\frac{column\ population}{total\ number\ of\ area\ values}\)) is shown. The calculation of the abundance was repeated separately for each technique (and each thickness of the glass slides in the case of the optical microscope). The reason for choosing the area limits and the number of classes is explained below. Optical microscopy: From the photos taken, approximately 10,000 particles per photo are detected. Of these, those that are too small to be distinguished (smaller than 0.4 \(\mu\)m\({}^{2}\)) and those that are too large most likely from spots in the microscope lenses up to a maximum size of 4 \(\mu\)m are discarded. Confocal microscopy: Confocal microscope photos have a photo resolution of 0.3 \(\mu\)m\({}^{2}\)/pixel, therefore, we opted to group the particle count into 14 classes (this is a low resolution for a line graph, and is due to the poor resolution of the photos) thanks to the data software provided by our collaborator (Professor [PERSON] who is duly acknowledged in the footnotes). Atomic Force Microscopy: The procedure is the same, but since this technique has a high resolution, we did not consider the particles which are undetectable on the optical microscope (being the technique with the lowest resolution); for the same reason, the total number of particles per photo is very low (about a hundred). With regards to the trend lines in the graphs, the points that are graphed as in the previous explanations on the values plotted on x and y axes were then interpolated with fifth and sixth degree polynomial trend lines in Excel [36; 37]. The correlation with the number of data points and the degree of polynomial interpolation is explained below. _\"Generally, if we have n data points, there is exactly one polynomial of degree at most n\(-\)1 going through all the data points. The interpolation error is proportional to the distance between the data points to the power n. Furthermore, the interpolant is a polynomial and thus infinitely differentiable. So we see that polynomial interpolation overcomes most of the problems of linear interpolation\"._[38]  
In general, the graphs show the notable differences between the sizes of the particles and their frequency or distribution in general. It can thus be said that different particle size classes occurred in varying frequencies in this investigation. The virgin bitumen sample was initially analyzed using OM at the different thicknesses obtained, sequentially reducing the distance between the two glass slides starting from 21 \(\mu\)m all the way to 9 \(\mu\)m. From the graph, it can be seen that the thickness does not influence the dimensions of the asphaltenes present in the bitumen sample.