## 3 Results and Discussion
### Entropy Change in the \"Multi Walled Carbon Nanotubes-Hydrocarbon Plasticizer\" System  
Entropy (\(\Delta S\)) is related to the order of the system, and its increase during dispersion helps reduce free energy. For successful dispersion, it is important to minimize enthalpy and maximize entropy. The total change in entropy in the system, associated with the breakdown of nanotube agglomerates and their more uniform distribution throughout the volume, is determined by the summation of the mixing entropy and the entropy from breaking down MWCNT aggregates. To find the mixing entropy (\(\Delta S_{mixing}\)), the entropy component related to the mixing of the two phases, it is necessary to determine the relative molecular masses of the multi-walled carbon nanotubes (Table 4) and the hydrocarbon plasticizers (Figure 6 (density, kg/m\({}^{3}\)), and Figure 7 (molecular mass, g/mol)). \begin{table}
\begin{tabular}{c c} \hline \hline
**Content of WCNT, \%** & **Relative Molecular Mass, g/mol** \\ \hline
5\(\cdot\)10\({}^{-4}\) & 4.5\(\cdot\)10\({}^{20}\) \\
5\(\cdot\)10\({}^{-3}\) & 4.5\(\cdot\)10\({}^{21}\) \\
5\(\cdot\)10\({}^{-2}\) & 4.5\(\cdot\)10\({}^{23}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Relative molecular mass of multi-walled carbon nanotubes in the studied dispersion systems. Figure 6: Density of hydrocarbon plasticizers in the studied dispersion systems. Based on the obtained values of relative molecular masses of MWCNTs and hydrocarbon plasticizers (Table 4, Figures 6 and 7), their molar fractions in the dispersion system were calculated (Formulas (9) and (10)), along with the first component of entropy--mixing entropy (Formula (8)). The results of the mixing entropy (\(\Delta S_{mixing}\)) determination are presented in Table 5.  
Mixing entropy is related to the process of mixing two phases: multi-walled carbon nanotubes and hydrocarbon plasticizers. This parameter depends on the molar fractions of the components (\(X_{1}\) and \(X_{2}\)) and the relative molecular masses of MWCNTs and plasticizers, as shown in Table 4, Figure 5. The data in Table 5 show that the molar fractions of MWCNTs in the mixture do not change with changes in their concentration. This can be explained by the fact that the relative molecular mass of MWCNTs (\(\approx\)4.5\(\cdot\)10\({}^{23}\) g/mol) is so large compared to the molecular mass of the hydrocarbon plasticizers (\(\approx\)200-900 g/mol) that even with changes in MWCNT concentration, the number of moles n1 remains extremely small compared to the number of moles of the plasticizer \(n_{2}\). In such a case, the contribution of MWCNTs to the overall molar fraction is minimal, and the MWCNT concentration may slightly alter the molar fraction of the system. Therefore, the molar fraction of MWCNTs may remain nearly the same across different concentrations in the studied dispersion systems. Systems with large molecules of MWCNTs and plasticizers create more opportunities for mixing (more microscopic states), which increases the mixing entropy. However, due to the vast difference in molecular masses between MWCNTs and plasticizers, the contribution of MWCNTs to the molar fraction is very small, and the plasticizer has the most influence on mixing entropy. As the molecular mass of the plasticizer increases, its molar fraction in the system decreases by the same mass. This leads to a reduction in the contribution of the component with the smaller molecular mass to the mixing entropy. For example, for the selective purification extract with a molecular mass of 938.3 g/mol, its molar fraction will be lower than that of Industrial Oil I-40A with a molecular mass of 248.2 g/mol, given