**3. Dielectric properties of PI/nanocomposites and their modeling**

To simulate the electrical field distribution in PI/nanocomposites, COMSOL-MATLAB Live link and image processing tools were used to build the PI/SIO2 (NPI) 3D model. The boundary conditions and geometry of the model were obtained from TEM/SEM images of laboratory-produced samples, as shown in

*Synthesis Process Optimization of Polyimide Nanocomposite Multilayer Films, Their Dielectric… DOI: http://dx.doi.org/10.5772/intechopen.91206*

**Figure 10.** *(a) TEM image of PI/SiO2 and (b) model in COMSOL using MATLAB Live Link.*

**Figure 10a**, and its respectfully constructed model, as shown in **Figure 10b**. The positions of nanoparticle coordinates (*x*, *y*) in the model were taken from TEM/ SEM images after converting the image into binary. For *z*-axis information, there are two possible ways to estimate the *z*-axis parameter. Either we can assume color intensity level from SEM/TEM images of **Figure 10a** as the depth (*z*-axis) of nanoparticles to construct 3D model or we can use SEM cross-sectional view information (if particle size is viewable from SEM/TEM) to find the depth of nanoparticles inside the bulk of samples to build model. For our samples, we have used the color intensity technique to obtain the *z*-axis parameter and create a 3D model. To construct the model, we picked a clear TEM/SEM image, applied an image processing to remove background noise, and finally converted it into the binary. To select the required data from the binary image, we adjusted the image to binary conversion threshold, nanoparticles size, and circularity level. The data contained different information about the particle size and shape (*x*, *y*) coordinates. The *z*-axis related to the depth of each particle is obtained using a small code in MATLAB according to the intensity level of each particle. In this simulation model, the dielectric permittivity of the PI matrix is taken to be *ε*1 = 3.4, and that of the silica nanoparticles is *ε*2 = 3.6. The nanoparticles were assumed to have a spherical shape of 10 nm radiuses calculated after image processing. The top surface of the 3D model was applied by the constant electric potential of (*V* = 10 V), and the bottom surface was grounded to 0 V. The volume fraction of nanoparticles is constant and set at 1% for single and multilayer insulation structures. The details to construct the model are presented in **Figure 11**.

After constructing the continuum model in COMSOL, the finite element method (FEM) was utilized to observe the nonlinear electric field distribution, as shown in **Figure 12**. The nanodielectric modeling with FEM can be used to predict its dielectric strength based on electric field distribution. FEM was used to calculate the electric field enhancement factor and polarization charge density, as shown in **Figure 13a** and **b**, respectively. Single and multilayers of PI/silica nanocomposite models were simulated with altered nanoparticle permittivity and position. The analysis is focused on calculating the peak electric field enhancement factor (peak EFEF) in the sample from Eq. (3).

Incanaaning une peak encecurne neu enumerament factor (peak from Eq. (3)).

\*\*Peak EFFF\*\* =  $\frac{\text{maximum electric field (kV/mm)}}{\text{applied electric field (kV/mm)}}}
\tag{3}$ 

The simulation results from **Figure 13** show that the electric field enhancement factor (EFEF) and polarization charge density vary with the increase in nanoparticle permittivity, and lesser EFEF is observed in three-layer PI films compared with single-layer models such as top agglomeration and bottom agglomeration. As shown in the simulation solution of **Figure 12**, the maximum electric field exists at the surface between the nanoparticles and the PI matrix in the direction of the *z*-axis, while the linear electric field is observed in the remaining area of PI/nanocomposite model.

The uniform dispersion of nanoparticle models improved the electric field distribution and reduced the electric field localization as happened in single-layer agglomerated models. The highest electric field and polarization density were obtained in a single-layer top agglomeration model. One of the main reasons for this enhancement can be the change in equivalence capacitance of the sample due to the agglomeration of the nanoparticles, which influence the effective permittivity of the overall sample. The electric field is also influenced due to the shape of the outer surface of nanoparticles because if agglomeration happens, there is a chance that the *Synthesis Process Optimization of Polyimide Nanocomposite Multilayer Films, Their Dielectric… DOI: http://dx.doi.org/10.5772/intechopen.91206*

### **Figure 12.**

*(a) Top agglomeration, (b) bottom agglomeration, (c) three-layer homogenous dispersion, and (d) three-layer original homogenous distribution.*

combined particles may change the circularity level and transform the shape into the sharp edges, which increase the local electric field around those edges. Another reason for higher EFEF in agglomeration models can be due to a decrease in the interparticle distance.

To verify the simulation results, electrical characterizations such as the space charge are also determined through the experimental results for single and

### **Figure 14.**

*TS current after applying different temperatures and electric fields: (a) single-layer NPI samples and (b) two-layer PI-NPI samples.*

*Synthesis Process Optimization of Polyimide Nanocomposite Multilayer Films, Their Dielectric… DOI: http://dx.doi.org/10.5772/intechopen.91206*

multilayer PI nanocomposite films [19]. For space charge measurements, the experiments are conducted using the thermal step method (TSM) to detect the capacity of these new insulating materials to accumulate/release space charges after thermoelectric poling, close to the practical applications. An electric field between 5 and 40 kV/mm is applied at 50, 100, and 150°C for 1 h [19]. The results presented in **Figure 14(a)** for single-layer NPI films and **Figure 14(b)** for double-layer PI-NPI films illustrate that the amplitude of the TSM current acquired for double-layer PI-NPI films is lesser than the single-layer NPI films at all electric fields and temperature conditions. The lower amplitude of TSM current is due to a lower level of space charge accumulation. Moreover, two opposite TSM current signs correspond to different dominant charges. The current sign changes from positive to negative from low temperature 50°C to higher temperature 150°C, especially for single-layer NPI samples. The sign of current corresponds to the same dominant charge injected from the electrode and shows an increase in accumulated space charge when the poling applied field increases. A thin layer of NPI on PI samples highlights lower TSM currents, and this behavior is more visible at higher electric fields because the signal-to-noise ratio is improved at the higher electric field. Thus, the coating of thin NPI on PI acts as a barrier and reduces the charge injection from electrodes. These coated layers are discharged resistive and increase the charge dissipation rate to reduce the space charge accumulation. Adding nanoparticles in the form of multistructure improves its dispersion by reducing the layer thickness and therefore leads to better dielectric properties, as presented in results.
