Based on the article: Structural dependence of the transferred charge density in triboelectric nanogenerators: analytical and numerical study.  I have simulated the Open-circuit voltage distribution (OCVD) for 2 of the structures in that study with COMSOL. (COMSOL is a finite element method (FEM) modeling) and then analyzed the data with a C++ program and ROOT. The goal was to get a visual representation of the OCVD and calculate the transferred charge.
TENG is a way to harvest mechanical energy such as vibrations, sliding and more from the environment. TENG is using contact electrification and electrostatic induction. TENGs today are commonly categorized in two: contact-mode and sliding-mode. The article  is looking on contact-mode. They say in their own introduction that Utilizing finite-element methods (FEMs), a relationship between the transferred surface charge and one side of the rectangular rod of TENGs structure is derived. The computed results show that the volume of each rectangular rod should be maximized under the fixed total volume of the structures in order to enhance the amount of transferred charges.  I simulated with FEM (COMSOL) two of the six structures. The description of the structure is: it is 60x60 µm in the x-y plane. The pitch between the rectangular rods (rods thickness are 4,6,8,10,15,18 µm and height 10µm) are 20 µm, thickness of top and bottom Al layer is 2µm with a distance of 25µm between them. The layers between the two Al layers are PTFE. On Top of the bottom Al layer you got one layer of PTFE that is 2µm thick then the rods. I simulated this without the rods and did the two control simulations witch are one without rods only 2µm PTFE between the Al layers and one with a layer of 12µm between the Al layers. This is done with the thought from above that the volume of each rod should be maximized, and then lead to higher transferred charge from the thick one then the thin PTFE layer. This thought will be shown as to simplistic and wrong later.
With the exported files from my FEM simulations done in COMSOL which is the two files:txt file with data for thick PTFE txt file with data for thin PTFE
I did a 2D histogram plot of the data to show the voltage distribution along the z axis which is the axis perpendicular to the Al and PTFE players. The program:Code that generates the two histograms
Gives out two histograms one for the thin 2µm PTFE layer and one for the Thick 12µm PTFE layer.
As you can see and expected for the thick the voltage distribution is around 0 from the bottom of the Al layer (starts on Z= -2 µm) to around end of PTFE layer (stops at Z= 12 µm). Before it increases to bottom of top Al layer (Z= 25 µm). Similar for the Thinn one just that it starts to increase earlier since the layer is lower (starts to increase at top PTFE layer at Z= 2 µm). This also is what my own representation sown in figure under for thick and thin PTFE layer.
From the link over the most important to get to calculate transferred charge is that from equation (5) is V1 that is argumented to be voltage difference between the two Al layers. The rest of the symbols in the equation is known variables and constants. So if you solve for Qi, Qtot equation (9) will be Qi since you only have one region (since you do not have rods) n=1 and m=0. Hence you got the transferred charge.
This equation Qi is the transferred charge. V1 gets calculated with an average of the charges at z=0 and z=25 and subtract the lover from the top. X in that equation is distance between top Al and top PTFE layer. S is area bottom Al layer, d2 is PTFEs thickness, E0 is Relative Permittivity = 1 and E2 is the same just for PTFE which is 2. Sigma is the triboelectric charge density which is -1x10^-6 C/m^2.
The calculation of V1 and the calculation of Qi for thin and thick PTFE is done in the file under and results in picture under there.Code that calculates transfered charge
As you can see the transferred charge is really close to 0. This shows that it is not only pure volume of the rod that contributes to the transferred charge.
As stated in the introduction we can now see that the thought that the higher the PTFE layer is the more transferred charge we will get is wrong. The transferred charge without rods is 0. This hints that the edges have a lot to say when it comes to transferred charge and to harvest energy with a TENG.
I would like to thank: - Boris Wagner and Ladislav Kocbach, for useful tips and guidance.
SeongMin Kim, Jaewook Ha, Jin-Baek Kim,:Structural dependence of the transferred charge density in triboelectric nanogenerators: analytical and numerical study