## 3 Results and Discussion
### Fundamental Thermodynamic Principles for Efficient Carbon Nanotube Dispersion
So, the contradiction between increasing the number of microscopic states and the less favorable change in \(\Delta G\) can be explained by the fact that the enthalpic costs of dispersion are too high, and the entropy contribution cannot fully compensate for these costs. Properties Characterizing the Stability of the Structure and Storage Stability Polymer Nanomodified Binder  
When studying the fundamental thermodynamic foundations of the effective dispersion of MWCNTs and the formation of stable dispersed systems with the studied \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name of Hydrocarbon Plasticizer** & **Content of WCNT, \%** & \(\Delta H\) & \(\Delta S_{total}\) (\(\approx\)\(\Delta S_{mixing}\))** & \(T,\mathbf{K}\) & \(\Delta G\) \\ \hline \multirow{3}{*}{Industrial Oil Grade I-40A} & 5\(\cdot\)10\({}^{-4}\) & 12.56 & 0.690 & 371.15 & \(-\)243.53 \\  & 5\(\cdot\)10\({}^{-3}\) & 123.09 & 0.690 & 379.05 & \(-\)138.45 \\  & 5\(\cdot\)10\({}^{-2}\) & — & — & & \\ \hline \multirow{3}{*}{II Vacuum Distillate} & 5\(\cdot\)10\({}^{-4}\) & 23.70 & 0.665 & 408.43 & \(-\)247.91 \\  & 5\(\cdot\)10\({}^{-3}\) & 210.15 & 0.665 & 427.59 & \(-\)74.20 \\  & 5\(\cdot\)10\({}^{-2}\) & 2000.32 & 0.665 & 431.28 & 1713.52 \\ \hline \multirow{3}{*}{Selective Purification Extract, Distillate} & 5\(\cdot\)10\({}^{-4}\) & 41.98 & 0.648 & 403.84 & \(-\)219.71 \\  & 5\(\cdot\)10\({}^{-3}\) & 380.16 & 0.648 & 423.33 & 105.84 \\  & 5\(\cdot\)10\({}^{-2}\) & 3730.79 & 0.648 & 429.5 & 3452.47 \\ \hline \multirow{3}{*}{Selective Purification Extract, Residue} & 5\(\cdot\)10\({}^{-4}\) & 44.34 & 0.666 & 415.87 & \(-\)232.63 \\  & 5\(\cdot\)10\({}^{-3}\) & 451.15 & 0.666 & 426.75 & 166.93 \\ \cline{1-1}  & 5\(\cdot\)10\({}^{-2}\) & 2756.54 & 0.666 & 440.53 & 2463.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Influence of hydrocarbon plasticizers on the total entropy value. hydrocarbon plasticizers, it was found that at a concentration of MWCNTs of 5\(\cdot\)10\({}^{-2}\)%, a stable structure is not provided in all the studied dispersed systems. Therefore, further studying the effect of stable dispersed systems containing multilayer nanotubes, the studied compositions of polymer-modified binders were adjusted. Previously, the base composition corresponding to the requirements of Russian State Standard GOST R 52056.2003 [52] was selected for each investigated hydrocarbon plasticizer. Where the SBS polymer content was 3.5% for all compositions, and the plasticizer content was 3%. The updated compositions of polymer nanomodified binders (PNB) are presented in Table 8.  
The compositions of PNB presented in Table 8 allow us to evaluate the effect of different concentrations of the MWCNT and SBS polymer (the possibility of its reduction) on the properties of PNBs for each type of hydrocarbon plasticizer. The results of determining the effect of dispersed systems containing MWCNTs on the stability of the structure and storage stability of nanomodified binders are presented in Table 9.  
The analysis of results regarding the thermodynamic parameters of the dispersion systems \"multi-walled carbon nanotubes--hydrocarbon plasticizer\" and their influence on the properties of polymer nanomodified binders (PNB) requires a comparison of changes in free energy, enthalpy, and entropy with the practical characteristics of the finished materials (Tables 7-9). There is a connection between entropy, enthalpy, and the structural stability of PNB. The study of thermodynamic parameters (Table 7) showed that dispersion systems with different plasticizers demonstrate various values of mixing entropy (\(\Delta S_{mixing}\)) and enthalpy (\(\Delta H\)). Specifically, the entropy of disordering (\(\Delta S_{disordering}\)) was found to be insignificant compared to the mixing entropy, indicating that the primary change in disorder arises from the mixing of hydrocarbon plasticizers with multi-walled carbon nanotubes (MWCNTs), rather than from the breakdown of MWCNT aggregates under ultrasound.