## 3 Results and Discussion
### Fundamental Thermodynamic Principles for Efficient Carbon Nanotube Dispersion  
The total entropy of the studied dispersion systems (presented in Table 7) is the sum of two components mixing entropy and disordering entropy. However, due to the negligible values of \(\Delta S_{disordering}\), indicating that the main change in disorder is due to the mixing (compatibility of hydrocarbon plasticizers with MWCNTs) rather than the destruction of MWCNT aggregates under ultrasound, we will use only the \(\Delta S_{mixing}\) data in calculating the total entropy. Thus, for the studied dispersion systems, the total system entropy is equal to the mixing entropy. Effective dispersion of multiwalled carbon nanotubes (MWCNTs) is critically important for achieving desired properties in composites based on them. The main thermodynamic parameters affecting the dispersion process are the change in Gibbs free energy (\(\Delta G\)), enthalpy (\(\Delta H\)), and entropy of mixing (\(\Delta S_{mixing}\)). When studying the influence of MWCNT concentration on the thermodynamic parameters of a dispersed system, contradictory results were obtained. Despite the fact that dispersed systems with Industrial Oil Grade I-40A and II Vacuum Distillate had larger diameter MWCNTs and fewer possible microscopic states, these systems showed the best results in terms of thermodynamic compatibility at MWCNT concentrations from 5\(\cdot\)10\({}^{-4}\)% to 5\(\cdot\)10\({}^{-3}\)%. \(\Delta G\) ranged from \(-\)247.53 kJ/mol to \(-\)74.20 kJ/mol. In contrast, systems with Extracts exhibited positive values of \(\Delta G\) for MWCNT content of 5\(\cdot\)10\({}^{-3}\)%, indicating strong limitations in thermodynamic compatibility. The contradictory results we observe may be related to several factors influencing the change in Gibbs free energy (\(\Delta G\)) in systems with different plasticizers and MWCNT concentrations. Systems where there is a greater number of microscopic states (\(W_{2}\)) tend to have less favorable changes in Gibbs free energy, contrary to expectations. Possible reasons include:  
1. Enthalpic contribution. From Tables 6 and 7, it can be seen that for plasticizers with the greatest number of microscopic states (e.g., selective purification extract, residue), enthalpy increases significantly. This means that the dispersion process requires significant energy expenditure. Despite an increase in entropy, high positive enthalpy can significantly worsen the overall result because Gibbs free energy (\(\Delta G\)) depends both on the entropic contribution and on the enthalpic one. If the costs associated with enthalpy exceed the gains from entropy, then \(\Delta G\) becomes positive, indicating a less favorable dispersion process. 2. Entropy of mixing (\(\Delta S_{mixing}\)). Although the number of microscopic states increases during dispersion, the value of \(\Delta S_{mixing}\) remains approximately constant for various plasticizers and does not demonstrate such significant growth as might be expected. This implies that the contribution of entropy to the Gibbs equation may be insufficient to compensate for the increased enthalpy. 3. Temperature dependence. Temperature (\(T\)) influences the entropic contribution to the change in Gibbs free energy through the product \(T\cdot\Delta S\). However, even at higher temperatures, the entropic contribution sometimes fails to offset the high enthalpy, leading to a positive value of \(\Delta G\), especially at high MWCNT contents. 4. Viscosity and structure of plasticizers. Some plasticizers, such as selective purification extracts, may have more complex structures and physicochemical properties that enhance their interaction with carbon nanotubes. These interactions can intensify intermolecular forces, resulting in a higher enthalpy value and consequently worse \(\Delta G\).