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14Complex Systems of Charged Particles and their Interactions with Electromagnetic Radiation 2019
UNDERSTANDING IONIC LOSSES IN ENERGY STORAGE FILMS
Elshad Allahyarov12,3
Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia Theoretical Chemistry, Duisburg-Essen University, Essen, Germany 3Physics Department, Case Western Reserve University, Cleveland OH, USA, e-mail: elshad.allahyarov@case.edu
Novel energy storage materials utilize polarization of their molecular dipoles to increase effective dielectric permittivity of the membrane. Electrostatic energy pumped into the polymer matrix, apart from its atomic polarization, is also spent on the orientation of molecular dipoles along the applied field. The molecular dipoles, such as SO2, are usually attached as side chains to the backbone of the polymer. The increase of the dipolar density, however, not always allows to store more energy in the film because of the following reasons. First, the correlation effects between dipoles might induce collective phenomena such as instantaneous flipping of neighboring dipoles resulting in the formation of larger dipolar domains. These domains require much higher fields to orient them along the field. Second, each individual dipole should not be strongly confined and keep fast response ability to external fields. Therefore, a bare increase of the dipolar density should be accompanied with compliant manipulation of the pore network in the membrane. Third, the high density of dipoles creates lower free energy for ions because of the attractive ion-dipole polarization effects. As a consequent, dipolar clusters behave like trapping centers for ions at low fields and temperatures and release them into the bulk at operating fields and temperatures.
Conducted experimental studies on the energy storage under ac-field shave shown that ionic losses degrade the integrity of the membrane and should be rigorously addressed. The BDS (broadband dielectric spectroscopy) experiments measure frequency dependent permittivity £r(a)=£r'(a)+£r"(a). Our aim was to use this data to calculate the concentration n(ro) and diffusion coefficients D(ro)of ions in the polarized middle layer. Because the fast-ion (impurity) conduction relaxation is superimposed with aC relaxation of dipoles, we implement Havriliak-Negami deconvolution method to separate different contributions,
ehn (m) = e— + £3=1-2—-—n-. Once the spectra of ions are defined, we use a combination of
7 (l+0^)1-av) ;
loop-based and least-square minimization approaches to match simulated ionic spectra with the deconvoluted one. For this purpose, we first define the voltage across the polarized layer without ionic currents. Then, using the Nernst-Planck diffusion equations for the ions and starting loops over n(ro) and D(ro)we calculate total charge distribution in the middle layer p(x). This quantity is then used to evaluate the polarization of the middle layer arising from the ion separation under the applied field, and thus the boundary charges at the membrane walls are defined. Next, the voltage across the layer is renewed and new ionic current, boundary charges and polarizations are recalculated until stable values for them are obtained. By analyzing the voltage drop across the middle layer we were able to predict the best working conditions (the voltage amplitude l o and frequency co) for the film.
6.4
6.0 5.8 We_2
4.5
10 ' ID1 1Dn 10' 10= II.' 10* 10fi
Frequency (Hz)
10' W1 10' 10; 10s 10* 10' 10' Frequency (Hz)
HTPC
200 nm 400 nm 200 nm
cation - anion
Figure. (A) Real (er') and (B) imaginary (er'') relative permittivities as a function of frequency at different temperatures for the HTPC/PVDF 50/50 33L film (11.55 ^m thickness).
References
[1] E. Allahyarov et al, Springer Nature 1-48 (2018), Nano/Micro-Structured Materials for Energy Applications.
[2] E. Allahyarov et al, Polymer 144, 150-158 (2018), Electroactuation in dielectric elastomer with prestrain.
