Schematic showing the charge density distribution, ρ, of a one-dimensional (1D) diffusion process in an insulating matrix.
Comparison of Sawada and Coelho7,20 diffusion models in a matrix with ɛ′matrix = 11, ɛ″matrix = 0.5, and n = 8 × 1018 ions/m3. Parameters used: (a) D = 9 × 10 −12 m2/s, d = 375 nm and (b) D = 9 × 10−12 m2/s, d = 3750nm.
A plot of F(R) versus R where F(R) consists of all the factors in the Sawada loss equation7 that contain the variable R.
Equivalent circuit of PC/P(VDF-HFP) layered films. Layered film can be modeled as equivalent to an ideal PC capacitor in series with a lossy P(VDF-HFP) capacitor.
Dielectric storage and loss permittivity as a function of frequency for P(VDF-HFP) (14 and 7 μm film thickness) and PC (14 μm film thickness) controls. (a) Storage permittivity at 25 °C, (b) storage permittivity at 100 °C, (c) loss permittivity at 25 °C, and (d) loss permittivity at 100 °C.
(a) Effect of a dc bias voltage on the dielectric loss of a P(VDF-HFP) 14 μm control at 100 °C. (b) Loss dielectric spectroscopy as a function of frequency for a 14 μm P(VDF-HFP) control at 100 °C initial measurement (blue circle), after applying a 100 V bias for 72 h (light orange circle), and 2 h after further annealing at 100 °C (green triangle). The dc conductivity contribution to the loss permittivity is plotted as the black line in the plot.
Loss permittivity as a function of frequency for the 50/50 PC/P(VDF-HFP) multilayered films with different layer thicknesses at 100 °C. As a consequence of the PC blocking electrodes, the magnitude of the layered films is much smaller than the P(VDF-HFP) control.
Loss permittivity as a function of frequency for a 32-layer 50/50 PC/P(VDF-HFP) film with 430 nm layers at 100 °C (green triangle) and the extracted P(VDF-HFP) component (red diamond).
Dielectric loss of extracted P(VDF-HFP) data (blue diamond) as compared to the fitted Sawada model (green circle) at 100 °C. (a) 7200 nm P(VDF-HFP) layers from 2 L film and the 7000 nm P(VDF-HFP) control, (b) 430 nm P(VDF-HFP) layers from 32 L film, (c) 190 nm P(VDF-HFP) layers from 32 L film, and (d) 50 nm P(VDF-HFP) layers from 256 L film.
Extrusion direction wide angle x-ray diffraction of (a) 7 μm thick P(VDF-HFP) control, (b) 2 L PC/P(VDF-HFP) with 7 μm layers, (c) 32 L PC/P(VDF-HFP) with 430 nm layers, and (d) 256 L PC/P(VDF-HFP) with 50 nm layers. Schematic in (e) shows the crystal orientations found in the layered films and control.
The diffusion coefficient, D, and ion concentration, n, in 50/50 PC/P(VDF-HFP) multilayered films and single layer controls. Values were obtained by fitting Sawada’s diffusion model to the experimental dielectric loss peak frequency, fpk, and amplitude, ɛpk, which was measured at 100 °C.
The crystallinity, melting temperature, and crystallization temperature of P(VDF-HFP) controls and 50/50 PC/P(VDF-HFP) layered films using DSC.
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