## 3 Results and Discussion
### Fundamental Thermodynamic Principles for Efficient Carbon Nanotube Dispersion
Transition to Macroscopic Properties of PNB: Thermodynamic parameters such as the change in Gibbs free energy are used to describe microscopic processes at the molecular level. However, when transitioning to the macroscopic properties of materials (e.g., PNB), other factors may arise that were not considered in the basic thermodynamic model. For example, even if \(\Delta G\) is positive at the level of the dispersion system, other factors such as the strength of intermolecular interactions, the rheological properties of the mixture, and interactions with the bitumen matrix can ensure the stability of the macroscopic structure of PNB. 2. Role of SBS Polymer: The SBS (styrene-butadiene-styrene) polymer present in all modified bitumen can significantly influence the overall structure and stability of the system. SBS is known to form three-dimensional polymer networks that can greatly enhance the structural stability of bitumen binders. This polymer ordering can compensate for the effect of positive \(\Delta G\), which indicates instability in purely thermodynamic calculations. Thus, the mechanical stability provided by the polymer network may dominate over the thermodynamic instability of the dispersion. 3. Influence of MWCNT Concentration: As evident from the results, at high concentrations of MWCNTs (e.g., 0.05%), \(\Delta G\) becomes positive, indicating thermodynamic instability. However, in practice, a high concentration of MWCNTs can lead to the formation of a more rigid and stable structure due to the dispersity of nanotubes and their mechanical influence on the viscosity and flow of bitumen. In other words, MWCNTs can enhance the structural properties of the system, providing mechanical stability despite the thermodynamic forecasts. 4. Unaccounted Factors in Thermodynamic Calculations: Thermodynamic calculations, such as the Gibbs equation, consider only idealized conditions and may not reflect the complex nature of real multicomponent systems. For instance, the neglect of interactions between MWCNT particles, plasticizer, and bitumen, as well as the influence of temperature and ultrasonic treatment, steric and electrostatic stabilization, the influence of local energy barriers, and non-traditional thermodynamic factors that may dominate in such cases, can affect the actual distribution and stability of the system. At the macro level, this can lead to a situation where even with positive \(\Delta G\), the system remains stable due to other physical effects not accounted for in the thermodynamic approach. 5. Kinetic Stability: A positive value of \(\Delta G\) indicates that the dispersion process may be thermodynamically unfavorable. However, the stability of PNB may be related to kinetic stability--that is, aggregation or phase separation processes in the dispersion system occur slowly enough that on the timescale of material use, the system remains sufficiently stable. In this case, macroscopic stability is ensured not so much by thermodynamic conditions as by slow kinetic processes that prevent the system from quickly reaching an equilibrium state. Understanding the thermodynamic fundamentals and dependencies in the system of carbon nanotubes and hydrocarbon plasticizers is crucial for developing effective methods for their dispersion and application in various materials and technologies. One notable application is in the enhancement of bitumen and asphalt concrete for road construction and maintenance. Incorporating dispersed multi-walled carbon nanotubes (MWCNTs) into bitumen can significantly improve its rheological and thermal properties, such as elasticity, resistance to deformation, and durability under extreme temperatures. This, in turn, enhances the performance and lifespan of asphalt pavements, making them more resistant to cracking, rutting, and weather-induced damage. These findings provide a basis for advancing the production of modified asphalt binders, paving the way for more sustainable and cost-effective road infrastructure solutions.