Procedure for Obtaining the Analytical Distribution Function of Relaxation Times for the Analysis of Impedance Spectra using the Fox HH-function

The interpretation of electrochemical impedance spectroscopy data by fitting it to equivalent circuit models has been a standard method of analysis in electrochemistry. However, the inversion of the data from the frequency domain to a distribution function of relaxation times (DFRT) has gained considerable attention for impedance data analysis, as it can reveal more detailed information about the underlying electrochemical processes without requiring a priori knowledge. The focus of this paper is to provide a general procedure for obtaining analytically the DFRT from an impedance model, assuming an elemental Debye relaxation model as the kernel. The procedure consists of first representing the impedance function in terms of the Fox $H$-function, which possesses many useful properties particularly that its Laplace transform is again an $H$-function. From there the DFRT is obtained by two successive iterations of inverse Laplace transforms. In the passage, one can easily obtain an expression for the response function to a step excitation. The procedure is tested and verified on some known impedance models

Information Encoding/Decoding using the Memory Effect in Fractional-order Capacitive Devices

In this study, we show that the discharge voltage pattern of a fractional-order supercapacitor from the same initial steady-state voltage into a constant resistor is dependent on the past charging voltage profile. The charging voltage was designed to follow a power-law function, i.e. $v_c(t)=V_{cc} \left( {t}/{t_{ss}}\right)^p \;(0<t \leqslant t_{ss})$, in which $t_{ss}$ (charging time duration between zero voltage to the terminal voltage $V_{cc}$) and $p$ ($0<p<1$) act as two variable parameters. We used this history-dependence of the dynamic behavior of the device to uniquely retrieve information pre-coded in the charging waveform pattern. Furthermore, we provide an analytical model based on fractional calculus that explains phenomenologically the information storage mechanism. The use of this intrinsic material memory effect may lead to new types of methods for information storage and retrieval.Comment: 5 pages, 3 figures, Submitted on Jan 28, 2021 to ACS Applied Electronic Materials - Manuscript ID: el-2021-00092

On the Electrochemical Discharges for Nanoparticles Synthesis

The electrochemical discharge phenomenon is a high current density electrochemical process with intrinsic physicochemical properties suitable for the synthesis of nanosized materials. At this mesoscopic range of physics, matter takes on drastically new properties and activities different from its bulk counterpart, which explains the dynamic research activity in building nano-structures. This thesis focuses on the macroscopic and microscopic descriptions of the electrochemical discharges and on the application of the phenomenon for the synthesis of nanoparticles. It starts by establishing the leading variables to control the process from the perspective of entropy production. The nonequilibrium thermodynamics analysis is successfully adapted to the process to extract a global expression for its entropy balance. Based on the excess entropy production in the system, the conjugated thermal and electrochemical fluxes and forces are the hierarchically top constraints affecting the process and its stability. This approach is supported by experimental evidences on the dynamic analysis of the electrochemical system which is performed through a designed wavelet-based signal processing algorithm. The gas film, covering and insulating the electrode during the process from the rest of the solution, has a life-time and building-time which are respectively an increasing and decreasing positive definite functions of the applied terminal voltage and the bulk temperature. With the successful synthesis of nickel and platinum nanoparticles, characterized morphologically, chemically and electrochemically, the second part of this thesis presents a comprehensive methodological procedure to apply the process in nanoparticles manufacturing. Two synthesis mechanisms of nano-materials by the electrochemical discharges and supported by the experiment are treated in detail. The first one involves the continuous competition of direct reduction of metal ions by the hydrated electron, e^–_{aq}, the hydrogen radical, H·, and secondary generated species, versus the back reaction of oxidation by the hydroxide radical OH·. The second mechanism is based on electrode sputtering physics by which the positively charged ions are accelerated in the gas film gap and strike the outermost atoms at the electrode surface to be diffused afterwards in the bulk solution. Zero-valent atoms will then undergo time-dependent nucleation and crystal growth processes to form colloidal suspension of nano-sized particles in the bulk solution. The performances of the synthesized nickel oxide nano-materials by electrochemical discharges as supercapacitors for energy storage applications are investigated and discussed. It is shown that the pseudocapacitance behavior and consequently the energy and power densities are size-dependent

Possibility of information encoding/decoding using the memory effect in fractional-order capacitive devices

In this study, we show that the discharge voltage pattern of a supercapacitor exhibiting fractional-order behavior from the same initial steady-state voltage into a constant resistor is dependent on the past charging voltage profile. The charging voltage was designed to follow a power-law function, i.e. [Formula: see text], in which [Formula: see text] (charging time duration between zero voltage to the terminal voltage [Formula: see text]) and p ([Formula: see text]) act as two variable parameters. We used this history-dependence of the dynamic behavior of the device to uniquely retrieve information pre-coded in the charging waveform pattern. Furthermore, we provide an analytical model based on fractional calculus that explains phenomenologically the information storage mechanism. The use of this intrinsic material memory effect may lead to new types of methods for information storage and retrieval

Time-Domain and Frequency-Domain Mappings of Voltage-to-Charge and Charge-to-Voltage in Capacitive Devices

In this work, we aim to show that there are generally four possible mapping functions that can be used to map the time-domain or frequency-domain representations of an applied voltage input to the resulting time-domain or frequency-domain electrical charge output; i.e. when the capacitive device is voltage-charged. Alternatively, there are four more possible combinations when the device is current-charged. The dual relationship between each pair of functions for the case of voltage or charge input are provided in terms of single or double Fourier transforms. All eight system functions coincide with each other if and only if a constant time- and frequency-independent capacitance is considered

Non-Debye impedance and relaxation models for dissipative electrochemical capacitors

Electrochemical capacitors are a class of energy devices in which complex mechanisms of accumulation and dissipation of electric energy take place when connected to a charging or discharging power system. Reliably modeling their frequency-domain and time-domain behaviors is crucial for their proper design and integration in engineering applications, knowing that electrochemical capacitors in general exhibit anomalous tendency that cannot be adequately captured with traditional integer-order-based models. In this study we first review some of the widely used fractional-oder models for the description of impedance and relaxation functions of dissipative resistive-capacitive system, namely the Cole-Cole, Davidson-Cole, and Havriliak-Negami models. We then propose and derive new q-deformed models based on modified evolution equations for the charge or voltage when the device is discharged into a parallel resistive load. We verify our results on anomalous spectral impedance response and time-domain relaxation data for voltage and charge obtained from a commercial supercapacitor.Comment: 9 pages, 3 figure

Fractional Marcus-Hush-Chidsey-Yakopcic current-voltage model for redox-based resistive memory devices

We propose a circuit-level model combining the Marcus-Hush-Chidsey electron current equation and the Yakopcic equation for the state variable for describing resistive switching memory devices of the structure metal-ionic conductor-metal. We extend the dynamics of the state variable originally described by a first-order time derivative by introducing a fractional derivative with an arbitrary order between zero and one. We show that the extended model fits with great fidelity the current-voltage characteristic data obtained on a Si electrochemical metallization memory device with Ag-Cu alloy.Comment: 7 pages, 3 figure

Short-Time Fourier Transform Analysis of Current Charge/Discharge Response of Lithium-Sulfur Batteries

Measurements acquired on batteries in the form of time signals such as voltage-time and capacity-time to assess their cyclability performance can be supplemented by examining their frequency-domain response. This allows one to determine the global characteristics of the signals and the battery, but not the local behavior, which is very important for determining for example battery fading. In this study we examine the short-time Fourier transform for time-frequency deconstruction of galvanostatic charge/discharge signals of lithium-sulfur batteries, taken as an example. The results displayed in terms of spectrograms show how the frequency content of such signals (e.g. charge and voltage time series) evolve with the lifetime of the batteries allowing the detection of critical changes in the response that may lead to fading and eventually default

A superstatistics approach to memristor current-voltage modelling

Memristors are expected to form a major cornerstone in the upcoming renaissance of analog computing, owing to their very small spatial footprint and low power consumption. Due to the nature of their structure and operation, memristors are intrinsically stochastic devices. This characteristic is amplified by currently employed semiconductor fabrication processes, which introduce spatial inhomogeneities into the structural fabric that makes up the memristor. In this work, a Ag-Cu based synaptic memory cell is characterized by utilizing a superstatistical approach, resulting in a novel, $q$-deformed current-voltage model for memristors. We demonstrate that our model has a 4-14% lower error than the current state-of-the-art. Additionally, we show how the resulting $q$-parameter can be used to make statements about the internal makeup of the memristor, giving insights to spatial inhomogeneities.Comment: 10 pages, 4 figures, appendi