Agamyrat Agambayev, et al., "Towards fractional-order capacitors with broad tunable constant phase angles: Multi-walled carbon nanotube-polymer composite as a case study." Journal of Physics D: Applied Physics 51(6), 2018, 065602.
In this study, multi-walled carbon nanotube (MWCNT) filled polyevinelidenefluoride-trifluoroethylene-chlorofluoroethylene composites are used to realize fractional-order capacitors (FOCs). A solution-mixing and drop-casting approach is used to fabricate the composite. Due to the high aspect ratio of MWCNTs, percolation regime starts at a small weight percentage (wt%), 1.00%.The distributed MWCNTs inside the polymer act as an electrical network of micro-capacitors and micro-resistors, which, in effect, behaves like a FOC. The resulting FOCs' constant phase angle (CPA) can be tuned from to by changing the wt% of the MWCNTs. This is the largest dynamic range reported so far at the frequency range from 150 kHz to 2 MHz for an FOC. Furthermore, the CPA and pseudo-capacitance are shown to be practically stable (with less than 1% variation) when the applied voltage is, changed between 500 µV and 5 V. For a fixed value of CPA, the pseudo-capacitance can be tuned by changing the thickness of the composite, which can be done in a straightforward manner via the solution-mixing and drop-casting fabrication approach. Finally, it is shown that the frequency of a Hartley oscillator built using an FOC is almost 15 times higher than that of a Hartley oscillator built using a conventional capacitor.