5.1 Model Building and Simulation Process
The research results show that 10 wt% OAPS modified insulating paper had higher tensile strength, better dielectric properties, and excellent thermal stability. On this basis, the cellulose model of OAPS modified insulating paper was built by simulation, and the mechanism of modification and promotion was studied and analyzed using molecular simulation technology.
Insulating paper is mainly composed of cellulose (Zheng et al. 2021). Cellulose exists in the form of crystalline area and amorphous area in insulating paper. However, many researches show that the aging of cellulose insulating paper mainly occurred in the amorphous region (Zhu et al. 2015). In order to ensure that the constructed model could reflect the physical and chemical properties of real materials, and in view of the time cost of molecular simulation and the difficulty of model optimization, the cellulose molecular chain with polymerization degree of 10 was built. The actual value of transformer insulating paper, 1.5 g/cm3, was taken as the molecular density of the model. The temperature was set as 298 K, the charge distribution method was Forcefield assigned, and the force field was COMPASS force field. After the model was built, its structure went through optimization and annealing. The model with optimal energy convergence and structure was selected for molecular dynamics simulation under NVT and NPT ensemble successively. Finally, the model was calculated and analyzed. See Reference (Du et al. 2021) for specific parameter setting and operation procedures. The molecular model and simulation calculation process are shown in Fig. 5 and Fig. 6.
5.2 Tensile Strength Improvement Mechanism
Cellulose is composed of multiple glucose units β-(1, 4) the linear structure formed by the connection of glycosidic bonds, in which a large number of active hydroxyl groups are distributed, so it is easy to form hydrogen bond interaction between internal molecular chains. as shown in Fig. 7a.
The generation of hydrogen bond will increase the bonding strength between cellulose chains, which has a strong impact on the tensile strength of insulating paper. calculation of the hydrogen bonds in the cellulose model of OAPS modified insulating paper shows that, in addition to the hydrogen bonds formed within and between cellulose molecules, a large number of hydrogen bonds were also formed between OAPS and cellulose chains, as shown in Fig. 7b.
Compared with pure cellulose, the number of hydrogen bonds formed in the model of OAPS modified insulating paper cellulose increases, which makes the interaction between the molecules closer, thus increasing the tensile strength of insulating paper. This explains the reason for the increase of tensile strength of OAPS modified cellulose insulating paper in Fig. 3a and Fig. 4a from the perspective of energy.
5.3 Dielectric Property Improvement Mechanism
Under the influence of external electric field, the original haphazardly distributed inherent dipoles in the dielectric deflect along the direction of the electric field, resulting in a gradual convergence of arrangements. In this process, the induced dipole moment is generated. As a result, the sum of the macroscopic dipole moments is no longer zero. This process is the polarization of the dielectric (Freitas et al. 2021). For polar polymers, the relationship between dielectric response and polarization can be described by Clausius-Mossotti equation, as shown below,
\(\frac{{\epsilon }_{r}-1}{{\epsilon }_{r}+2}=\frac{N}{\left(3{\epsilon }_{0}\right)\left({\alpha }_{e}+{\alpha }_{a}+{\alpha }_{d}\right)}\) (5 − 1)
\({\alpha }_{d}=\frac{{\mu }^{2}}{3kT}\) (5 − 2)
In the equation, \({\alpha }_{e}\) is the electronic polarizability, \({\alpha }_{a}\) is the ionic polarizability, \({\alpha }_{d}\) is the turning polarizability, \(\mu\) is the induced dipole moment, \(T\) is the temperature,
\(N\) is the number of molecules per unit volume, \(k\) and \({\epsilon }_{0}\) are the Boltzmann constant and relative dielectric constant of vacuum respectively. As the electronic and ionic polarizability of cellulose insulating paper at 50 Hz is negligible and \(N\) can be obtained by measuring the mass of insulating paper, the \({\epsilon }_{r}\) of insulating paper at 50 Hz is only related to \({\alpha }_{d}\). The \({\alpha }_{d}\) of dielectric is proportional to the polarization intensity P. The greater the polarization intensity, the greater the turning polarizability. P is the vector sum of molecular dipole moment µ in a unit volume, and can be calculated using the formula below:
\(P=\frac{{\sum }_{i=1}^{n}\mu }{\varDelta V}\) (5 − 3)
Therefore, the dielectric properties of insulating paper could be reflected through calculation of dipole moment and polarizability in the model. The dipole moments calculation results are shown in the Fig. 8. The polarizability was calculated according to the total moment of dipole are shown in Table 2.
Table 2
Polarizability of the models
Model | Volume(Å3) | Dipole Moments(D) | Polarizability/(D·Å−3) |
Pure cellulose | 27598.83 | 142.41 | 5.16×10− 3 |
OAPS modified cellulose | 23617.60 | 31.45 | 1.33×10− 3 |
It can be seen from Fig. 8 and Table 2 that the moment of dipole and polarizability of OAPS modified cellulose model decreased drastically. The reason was, on the one hand, OAPS has a low dielectric constant (Lee et al. 2005). When it is doped into cellulose, the overall dielectric constant of the system would decrease and the polarizability would also decrease. On the other hand, though OAPS is of nano scale, its molecular weight is much greater than that of the hydroxide radical in the side group of cellulose chain. The binding effect of this macromolecule hinders the turnover of cellulose chain, which makes it difficult for the dipole in the system to deflect and reduces the polarizability of the whole system. Moreover, as OAPS is of a hollow structure (Hu et al. 2022), its particularity of this structure would result in a greater porosity of the model, higher air content, and lower polarizability of cellulose. Under the joint action of the above factors, the polarizability of the OAPS modified insulating paper system decreased significantly, which further resulted in a lower relative dielectric constant and better dielectric properties of the insulating paper.
5.4 Thermal Stability Improvement Mechanism
The chain motion intensity of cellulose chain is an important parameter reflecting the thermal stability of cellulose insulating paper. At the same temperature, the more intense the motion of cellulose chain, the worse the thermal stability of insulating paper. In order to compare the strength of cellulose chain motion in different models, it can be characterized by its Mean Square Displacement (MSD). MSD is directly proportional to the motion intensity of cellulose chain, so the larger MSD is, the worse the thermal stability of cellulose insulating paper are (Qi et al. 2022).
In order to study the overall movement of the molecular chain centroid of each model, the analysis tool of Forcite module was used to calculate the Mean Square Displacement (MSD) of each model under the actual operating temperature of transformer (343K). The calculation results are shown in Fig. 9.
It can be seen from the Fig. 9 that the MSD of the OAPS modified model is significantly lower than that of the pure cellulose model, and the intensity of chain motion is significantly weakened. The reason is, on the one hand, the doping of OAPS filled the gap between cellulose chains to a certain extent. On the other hand, OAPS is of a nano size. Its nano-size effect allowed the OAPS matrix to be more closely bound with the polymer. This way, the thermal stability of the insulating paper was improved.