## 3 Results and Discussion
### Entropy Change in the \"Multi Walled Carbon Nanotubes-Hydrocarbon Plasticizer\" System
 \\ \hline \begin{tabular}{c} Industrial Oil \\ Grade I-40A \\ \end{tabular}  & \begin{tabular}{c} 0.0075 \\ 0.075 \\ 0.75 \\ 0.75 \\ \end{tabular}  & \begin{tabular}{c} 56.27 \\ 57.29 \\ \end{tabular}  & \begin{tabular}{c} \(e^{1.28\cdot 10^{2}}\) \\ \(e^{1.28\cdot 10^{2}}\) \\ \(-\) \(-\) \(-\) \\ \end{tabular}  & \begin{tabular}{c} \(e^{1.35\cdot 10^{2}}\) \\ \(1.38\cdot 10^{-15}\) \\ \end{tabular}  \\ \hline \ \begin{tabular}{c} II Vacuum \\ Distillate \\ \end{tabular}  &
\begin{tabular}{c} 0.0075 \\ 0.075 \\ 0.  
all tested systems after ultrasonic dispersion. For example, for Selective Purification Extract, Residue at 0.0075% MWCNT content with an average diameter of 21 nm before ultrasound \(W_{1}=e^{1.28\cdot 10^{12}}\) states, after ultrasound \(W_{2}=e^{7.64\cdot 10^{30}}\), over 8 orders of magnitude higher, indicating effective dispersion. This significant growth in \(W_{2}\) underscores the destruction of aggregates, allowing nanotubes to form more configurations in the dispersed state. 2. Entropy of Disordering (\(\Delta S_{disontering}\)). The transition from aggregated to dispersed states correlates with a rise in entropy (\(\Delta S_{disordering}\)) highlighting increased disorder within the system. At higher MWCNT concentrations, the increase in entropy is more pronounced. For instance, in Selective Purification Extract, Residue with a concentration of 0.0075 g, \(\Delta S_{disontering}=8.14\cdot 10^{-15}\), but as the concentration increases to 0.75 g, the value of \(\Delta S_{disontering}\) rises by two orders of magnitude. 3. Comparison of Plasticizers:  
- Industrial Oil Grade I-40A exhibits the smallest entropy increase and fewer microscopic states, especially at lower MWCNT concentrations (e.g., 0.0075%). This suggests poorer dispersion capability, likely due to weak interaction with nanotubes. This is likely due to the fact that the oil molecules do not wet the nanotubes well or do not penetrate between them effectively enough, which prevents complete dispersion. - II Vacuum Distillate displays better dispersion performance than industrial oil, particularly at higher MWCNT concentrations (e.g., 0.75%), likely due to enhanced compatibility with MWCNTs. - Selective Purification Extract (Distillate and Residual) outperforms other plasticizers, showing the highest increase in microscopic states and disordering entropy across all concentrations, indicating superior dispersion effectiveness. 4. Significance of Ultrasonic Dispersion. Ultrasonic treatment significantly increases the number of microscopic states (\(W_{2}\)) and entropy (\(\Delta S_{disontering}\)), demonstrating its effectiveness in breaking down MWCNT aggregates and promoting a more homogeneous dispersion. 5. Microscopic Nature of Entropy Changes. Despite the astronomically high numbers of microscopic states (\(W_{2}\)), the absolute entropy values are small because the disordering process occurs at the molecular level, and the logarithmic relationship between (\(W_{2}\)) and entropy compresses the scale of results. This underscores the localized nature of entropy changes compared to macroscopic processes such as phase mixing. The study confirms that the Selective Purification Extract is the most effective plasticizer for dispersing MWCNTs, leading to the greatest increase in system disorder and the most significant rise in entropy. Higher MWCNT concentrations amplify these effects, underlining the importance of optimizing plasticizer selection and concentration for targeted applications. These findings provide a quantitative framework for understanding dispersion mechanisms and pave the way for further optimization of MWCNT dispersion systems.