Complex permittivity of a conducting, dielectric layer containing arbitrary binary Nernst–Planck electrolytes with applications to polymer films and cellulose acetate membranes

Abstract

The theory of Trukhan [Sov. Phys. Solid State (Engl. Trans/.), 1963, 4, 25601 for t h e calculation of the complex permittivity of a conducting dielectric film containing a binary 1 : 1 electrolyte is critically reviewed. It is shown that the final result of Trukhan is correct, in spite of some errors and odd procedures in the original derivation. The method of Trukhan is changed to a more concise procedure which is better suited to generalisations, and t h e theory is generalised to binary electrolytes of a n y charge type. The dimensionless excess impedance (over and above the Maxwell-Wagner-Sillars impedance) and t h e complex relative permittivity are functions of t h e type of electrolyte, the dimensionless frequency, t h e ratio of the ionic diffusion coefficients and t h e film thickness scaled by t h e Debye length. The complex relative permittivity has a Debye-like relaxation, but for very different values of t h e two diffusion coefficients and for films which are thin compared with the Debye length, one can clearly distinguish two dielectric relaxations, one for each ion. The peak in t h e dielectric loss corresponding to the ion of higher valency, is dominating in thin films. W h e n t h e film is thicker, (or when t h e electrolyte concentration is increased) t h e low-frequency peak diminishes relative to the high-frequency peak. The maximum in the loss tangent is positioned at higher frequencies t h a n the maximum in t h e dielectric loss. Therefore it is often an advantage to fit the loss tangents to actual measurements, since measurements at low frequencies are generally more difficult. Two applications of t h e theory are treated: the low-frequency dielectric relaxation of a dry copolymer of vinylidene cyanide and vinyl acetate with conducting ions (T. Furukawa, M. Date, K. Nakajima, T.

Conductivity of composite membrane-based poly(ether-ether-ketone) sulfonated (SPEEK) nanofiber mats of varying thickness

“…In our samples, we can observe two plateaus: one situated in the region of high frequencies associated with the protonic conductivity in the bulk SPEEK-PVA pure membrane, identical to the bulk conductivity s dc , reecting long-range proton transport, and the other in the region of low frequencies that can be associated to the proton conductivity trough of the SPEEK-PVB nanobers and also to the electrode polarization via the formation of electrochemical double layers and polymer relaxation. [54][55][56][57] Between the regions of high and low frequency, there is a decrease in the conductivity that can be explained as a Debye relaxation due to the macroscopic polarization of the ionic charges as a consequence of the applied electric eld. This relaxation is characterized by a relaxation time which is dependent on the temperature, the chemical structure of the membrane and its thickness.…”

Ionic conductivity and diffusion coefficients of lithium salt polymer electrolytes measured with dielectric spectroscopy

“…Also, we propose a method to estimate the values of cation and anion diffusion coefficients together with the free ion concentration assuming that the diffusion coefficient values for both the cation and anion of the dissolved salt are of the same order of magnitude, which is in agreement with reported measurements from other methods [16,17]. In this case, the tan δ data can be analyzed with the Trukhan model [4,5] and the diffusion coefficients and ionic concentration of free charge carriers can be estimated. The measurements are performed for temperatures ranging from 0 to 105°C and are check against different sample thicknesses.…”

“…With a varying degree, conductivity is also observed for other semi-crystalline phases below de glass transition temperature (t g ) [2]. Besides that in dielectric measurements, depending on the temperature, the separation between glass-rubber relaxation and relaxation due to free charges can be difficult due to their simultaneous presence [4][5][6]. From the experimental point of view, electrode effects caused by image charges in the electrodes can greatly contribute to obscure the measurements, especially at low frequencies [7].…”

Ion dynamics and relaxation behavior of NaPF6-doped polymer electrolyte systems

“…They can be obtained from dielectric spectra. The ion diffusivity is calculated from tan δ vs. log ω curve [17][18][19] using the following relation:…”