## 2 Materials and Methods
### Methods
#### 2.2.2 Determination of Entropy Change in the \"Carbon Nanotubes-Hydrocarbon Plasticizer\" System  
The molecular mass (Equation (10)) of multi-walled carbon nanotubes (MWCNTs) in an aggregate depends on the number of layers and the size of the aggregate. To calculate the molecular mass, it is necessary to determine the number of carbon atoms in the multi-walled nanotubes and convert this into molecular mass. In our study, \"molecular mass\" refers to the relative molecular mass of an individual MWCNT, calculated based on its geometric and physical properties. To obtain the absolute molecular mass, this value would need to be multiplied by the atomic mass unit (approximately 1.66 \(\times\) 10\({}^{-27}\) kg). We acknowledge that this distinction is critical for clarity, and the terminology is used accordingly in our calculations. According to the manufacturer, the Taunit-MD multi-walled carbon nanotubes have the following characteristics: external diameter (\(D_{ext}\)) of MWCNTs is 18 nm, internal diameter (\(D_{int}\)) of MWCNTs is 10 nm, the number of graphene layers (nlayers) is 15, the thickness of one graphene layer (hlayers) is 0.34 nm, the length of MWCNTs (\(L_{\text{MWCNT}}\)) is 20 \(\upmu\)m, and the density of MWCNTs (\(\rho_{MWCNT}\)) is 1.4 g/cm\({}^{3}\). The atomic mass of carbon (\(M_{\text{C}}\)) is 12 g/mol. MWCNTs are hollow cylinders, so the volume of one MWCNT is calculated as the difference between the volumes of the outer and inner cylinders:  
\[V_{MWCNT}=\pi L_{MWCNT}\Bigg{(}\left(\frac{D_{ext}}{2}\right)^{2}-\left(\frac {D_{int}}{2}\right)^{2}\Bigg{)} \tag{13}\]  
Next, the mass of one MWCNT can be found as follows:  
\[m_{MWCNT}=V_{MWCNT}\cdot\rho_{MWCNT}, \tag{14}\]  
To determine the number of MWCNTs in the total mass of MWCNTs:  
\[N_{MWCNT}=\frac{m_{total}}{m_{MWCNT}}, \tag{15}\]  
where \(m_{total}\)--the total mass of the multi-walled carbon nanotubes introduced into the \"multi-walled carbon nanotubes-hydrocarbon plasticizer\" system. To determine the molecular mass, it is important to calculate how many carbon atoms are in a single MWCNT. This can be completed by dividing the mass of one MWCNT by the atomic mass of carbon:  
\[n_{c\ in\ MWCNT}=\frac{m_{MWCNT}}{Mc}, \tag{16}\]  
This expression allows us to find the number of moles of carbon in a single MWCNT. A mole of carbon is the number of atoms equal to Avogadro's number (approximately 6.022 \(\times\) 10\({}^{23}\) atoms per mole). Therefore, the number of carbon atoms can be found using the following equation:  
\[N_{atoms\ in\ MWCNT}=n_{c\ in\ MWCNT}\cdot N_{A}, \tag{17}\]  
The relative molecular mass of a single MWCNT can then be found using the following equation:  
\[M_{MWCNT}=N_{atoms\ in\ MWCNT}\cdot M_{C}, \tag{18}\]To convert this into absolute molecular mass in kilograms, the result must be multiplied by the atomic mass unit (approximately 1.6610\({}^{-27}\)). The total molecular mass of multi-walled carbon nanotubes can be calculated using the following equation:  
\[M_{total}=N_{atoms\ in\ MWCNT}\cdot M_{\rm C}\cdot N_{MWCNT}, \tag{19}\]  
The relative molecular mass calculations for MWCNTs and data analysis were carried out using Python software. To calculate the molecular mass of hydrocarbon plasticizers, which are various petroleum fractions, [PERSON]'s formula [50] is used.