Distribution Of Relaxation Times Research Articles

Direct computations of viscoelastic moduli of biomolecular condensates.

In vitro facsimiles of biomolecular condensates are formed by different types of intrinsically disordered proteins including prion-like low complexity domains (PLCDs). PLCD condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model and information regarding intra- and inter-chain contacts that is extracted from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations. The key ingredient of the generalized Rouse model is the Zimm matrix that we compute from equilibrium MMC simulations. We compute two flavors of Zimm matrices, one referred to as the single-chain model that accounts only for intra-chain contacts, and the other referred to as a collective model, that accounts for inter-chain interactions. The single-chain model systematically overestimates the storage and loss moduli, whereas the collective model reproduces the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two models proves to be most accurate. In line with the theory of Rouse, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic versus dominantly viscous behaviors is influenced by the totality of the relaxation modes. Hence, our analysis suggests that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain distributions of relaxation times that underlie the dynamics within condensates.

Exploration of electrochemical behavior of Sb-based porous carbon composites anode for sodium-ion batteries

Sb-based materials are considered as promising anode materials for sodium-ion batteries (SIBs) due to their excellent sodium storage capacities and suitable potentials. However, the Sb-based anodes usually suffer from intense volume expansion and severe pulverization during the alloying-dealloying process, resulting in poor cycling performance. Herein, a composite anode with Sb/Sb2O3 nanoparticles embedded in N-doped porous carbon is prepared by the gas–solid dual template method. The volume change of the anode material is mitigated by the carbon layer enwrapping and the confinement of the porous structure. Nitrogen doping provides abundant sodium storage sites, thus enhancing the storage capacity of sodium ion. Furthermore, to gain the accurate kinetic interpretation of the electrochemical process, an ex-situ transmission electron microscope (TEM) characterization combined with distribution of relaxation times (DRT) is conducted. The Sb/Sb2O3@NPC-1.0 demonstrates excellent electrochemical performance, achieving 340.3 mAh g−1 at 1A g−1, and maintains a capacity of 86.7 % after 1000 cycles. This work paves the way for the practical application of SIBs with high-performance and long-life Sb-based anodes.

Rheological effect of particle volume fraction and chemical additives on tape casting slurry optimization for solid oxide fuel cells application

This study analyzes the impact of particle volume fraction and various chemical additives on tape-casting slurries from a rheological perspective. Tape casting, a method prevalently employed for fabricating substrates for fuel cells, dictates the morphological characteristics of the substrates contingent upon the slurry properties. These characteristics are modulated not solely by the intrinsic properties of the ceramic particles but also through the incorporation of chemical additives. The rheological properties of the slurry were scrutinized through various methodologies, with alterations in parameters and particle characteristics. Moreover, the relationship between the rheological properties and the green body was elucidated by examining mechanical properties, such as bending strength. Subsequently, leveraging the anode support generated through this methodology, a cell is fabricated. Performance evaluations substantiate a maximum power density of 2.41W/cm2 in a fuel cell (FC) mode, a current density of 0.84A/cm2 at 1.3V in electrolysis cell (EC) mode at 700 °C is evidenced, indirectly signifying adequate dispersion and the presence of pores at the anode support even without pore former. Next, electrochemical impedance spectroscopy (EIS) is conducted, followed by an in-depth analysis employing the distribution of relaxation times (DRT) technique. The findings confirm the successful fabrication of an electrochemically stable and robust fuel cell.

Demystifying the Distribution of Relaxation Times: A Simulation-Based Investigation into the Limits and Possibilities of Interpretation for Lithium-Ion Batteries

Interpreting impedance spectra of electrochemical systems using the distribution of relaxation times analysis remains an incompletely solved task. This study carefully examines various challenges related to the interpretation of resulting distributions of relaxation times using a closed-form lumped Doyle-Fuller-Newman model. First, the physical and phenomenological interpretation of peaks in the distribution of relaxation times are analyzed through a global sensitivity analysis. Second, the assignment of processes to specific ranges of time constants is investigated. Third, the use of half cells for the characterization of full cells is examined, and the clear limitations associated with the use of lithium metal counter electrodes are pointed out. Furthermore, the study provides first insights into the effects of distributed processes such as charge transfer, double-layer effects, and solid-state diffusion. Several prevailing interpretations in the literature are challenged and new insights and guidelines for interpreting distributions of relaxation times are offered.

Beyond Ridge Regression: Enhancing Distribution of Relaxation Times Deconvolution

The distribution of relaxation times (DRT) has emerged as a promising method for analyzing electrochemical impedance spectroscopy (EIS) data. The standard approach for reconstructing the DRT from measured impedances consists of regularized regression, which usually leverages the Euclidean norm. In this work, we show for the first time that the 1-norm is often more accurate than ridge regression and the infinity-norm. We also demonstrate that the 1-norm is more robust against discontinuities in the DRT and outliers in the impedance data. Overall, this work is expected to enhance regularized regression of non-parametric methods when analyzing EIS spectra.

Impact of Electrochemical Impedance Spectroscopy Dataset Curation on Solid Oxide Cell Degradation Assessment

Electrochemical impedance spectroscopy (EIS) has become a standard measurement technique for detecting degradation in single cells and stacks of solid oxide cells (SOCs). Depending on the experimental setup and test equipment, instabilities and unexpected results can be observed in EIS measurements. For example, in the low-frequency range, instabilities can be induced by feed gas flow fluctuations. Another phenomenon are parasitic, inductive impedances that degrade the high-frequency range. To compensate for such influences in large EIS data sets, we propose a specially developed EIS data curation pipeline. Based on the results of its application, we demonstrate the impact on the quantitative and qualitative attribution of electrochemical processes from EIS using equivalent circuit modeling and distribution of relaxation times. Furthermore, the substantial differences in the temporal evolution of the latter during long-term experiments are highlighted for EIS measurements obtained at the SOC stack and single cell level. In addition, the significant misestimation of aging rates, especially with respect to the fuel electrode and the high-frequency series resistance, is shown when comparing EIS measurements, few of which exhibit a parasitic inductive impedance.

Derivation and analysis of lattice Boltzmann form of the mild slope equation

The present study investigates the performance of the Lattice Boltzmann Method (LBM) as an alternative numerical method for simulating wave propagation in coastal zones. While formulations like the Mild-Slope Equation (MSE) remain efficient for coastal engineering applications due to their simplicity, LBM offers an explicit numerical solver for partial differential equations (PDEs). LBM utilizes local operations, making it well-suited for Graphics Processing Unit (GPU) acceleration and consequently efficient simulations. This study examines LBM's performance in several benchmark cases, including wave propagation behind a single breakwater, harbor resonance, refraction of long waves over a parabolic shoal, and wave propagation over an elliptic shoal. The Chapman-Enskog multi-scale expansion was used within a popular 2D LBM scheme to derive the relaxation time and equilibrium distribution function. The results showed a good agreement between LBM predictions and benchmark data. Furthermore, LBM demonstrated efficiency in reducing the computation time, achieving a notable 30–50% decrease in CPU time and an 85% reduction when utilizing a GPU.

In-situ electrochemical impedance analysis of a commercial SOFC stack fueled by real wood gas

The combination of solid oxide fuel cells (SOFCs) and wood gasification has the potential to significantly increase renewable electricity production and decrease emissions. Depending on the quality of the wood gas, degradation processes have a significant impact on the reliability and lifetime of the SOFC. Using electrochemical impedance spectroscopy (EIS) and subsequent distribution of relaxation times (DRT) analysis, the impact on the degradation of coupling wood gasification with a commercial SOFC stack is determined in this study. The thermal behavior of the SOFC stack under various operating conditions, as well as various synthetic wood gas mixtures classified by their hydrogen-to-carbon (H/C) ratio, was assessed. The decrease in the H/C ratio from 8 to 1, observed during syngas and real wood gas operation, leads to a rightward shift in the Nyquist plots, suggesting an increase in the SOFC stack's impedance. Correlations between variations in the H/C ratio and their effects on anodic electrooxidation, ionic conduction, gas transport, and diffusion were identified using DRT analysis to interpret the EIS results. By incorporating an upstream desulfurization system and ensuring an H/C ratio greater than 2, the coupling of biomass gasification with the SOFC stack was stable to degradation issues.

Lanthanum-Ferrite based cathode: Impedance data interpretation via complex nonlinear least-squares and distribution of relaxation times analyses

Lanthanum Strontium Cobalt Ferrite Oxide (LaSrCoFeO3) has been widely used as cathode material for intermediate-temperature solid oxide fuel cells at the temperature of 500–800 °C. At this temperature range, understanding the electrochemical behavior which is commonly analyzed by complex nonlinear least-squares (CNLS) analysis is very crucial in improving the cathode's performance. However, this analysis shows some limitations in interpreting the electrochemical processes in detail, particularly at the electrode-electrolyte interface. Hence, this study is conducted to compare the electrochemical impedance data analyses by CNLS and the distribution of relaxation times (DRT) of a fabricated LaSrCoFe|BCZY|LaSrCoFe (LaSrCoFeLa0.6Sr0.4Co0.2Fe0.8O3 and BCZY=BaCe0.54Zr0.36Y0.1O2.95) symmetrical cell. Impedance data of the cell is collected at T = 800 °C at two different stabilization times and to further enhance the analysis process, the impedance data of the cell at measurement temperatures of 700 °C and 750 °C are also included. In a Nyquist plot, the cell exhibits depressed semi-circles that represent a few processes occurring at the interface. The DRT analysis is more precise and easily reveals the semi-circles consisting of four different sub-processes (represented by four peaks) than CNLS (represented by four impedance arcs). The extracted responses from both analyses correspond to the oxygen reduction reactions that follow the Adler-Lane-Steele model. The stabilized symmetrical cells for respective 34 h and 17 h show an area-specific resistance (ASR) of (i) 0.22 Ωcm2 and 0.30 Ωcm2 (by CNLS) and (ii) 0.20 Ωcm2 and 0.26 Ωcm2 (by DRT). In addition, the ASR of the cell at T = 700 °C and T = 750 °C after being stabilized for 34 h is (iii) 0.71 Ωcm2 and 0.40 Ωcm2 (by CNLS) and (iv) 0.70 Ωcm2 and 0.44 Ωcm2 (by DRT), accordingly. Conversely, the cell's microstructure is not affected by the applied stabilization periods as observed by a scanning electron microscope.

Durability analysis of polymer electrolyte membrane fuel Cell's gas diffusion layer based on distribution relaxation time analysis: Influence of the presence or absence of a micro-porous layer

The U.S. Department of Energy accelerated stress test carbon protocol emphasizes improving the durability of both the catalyst layer and the micro-porous layer (MPL) carbon support. This underscores the need for research focused solely on the degradation of the Gas Diffusion Layer (GDL). Traditionally, electrochemical impedance spectroscopy impedance data used to analyze resistance due to GDL durability has been interpreted through equivalent circuit models. However, this method simplifies simultaneous response and multiple models for the same data, which reduces the objectivity of the analysis. Therefore, this study analyzed the durability characteristics of GDLs with and without MPLs using distribution of relaxation times, a method less prone to subjectivity. In short, the results showed that substrates without MPL are more susceptible to performance degradation and loss, and highlighted the emergence of Warburg resistance due to limited diffusion under harsh environmental conditions.

Data-driven diagnosis of high temperature PEM fuel cells based on the electrochemical impedance spectroscopy: Robustness improvement and evaluation

Utilizing machine learning techniques for data-driven diagnosis of high temperature PEM fuel cells is beneficial and meaningful to the system durability. Nevertheless, ensuring the robustness of diagnosis remains a critical and challenging task in real application. To enhance the robustness of diagnosis and achieve a more thorough evaluation of diagnostic performance, a robust diagnostic procedure based on electrochemical impedance spectroscopy (EIS) and a new method for evaluation of the diagnosis robustness was proposed and investigated in this work. To improve the diagnosis robustness: (1) the degradation mechanism of different faults in the high temperature PEM fuel cell was first analyzed via the distribution of relaxation time of EIS to determine the equivalent circuit model (ECM) with better interpretability, simplicity and accuracy; (2) the feature extraction was implemented on the identified parameters of the ECM and extra attention was paid to distinguishing between the long-term normal degradation and other faults; (3) a Siamese Network was adopted to get features with higher robustness in a new embedding. The diagnosis was conducted using 6 classic classification algorithms—support vector machine (SVM), K-nearest neighbor (KNN), logistic regression (LR), decision tree (DT), random forest (RF), and Naive Bayes employing a dataset comprising a total of 1935 collected EIS. To evaluate the robustness of trained models: (1) different levels of errors were added to the features for performance evaluation; (2) a robustness coefficient (Roubust_C) was defined for a quantified and explicit evaluation of the diagnosis robustness. The diagnostic models employing the proposed feature extraction method can not only achieve the higher performance of around 100% but also higher robustness for diagnosis models. Despite the initial performance being similar, the KNN demonstrated a superior robustness after feature selection and re-embedding by triplet-loss method, which suggests the necessity of robustness evaluation for the machine learning models and the effectiveness of the defined robustness coefficient. This work hopes to give new insights to the robust diagnosis of high temperature PEM fuel cells and more comprehensive performance evaluation of the data-driven method for diagnostic application.

Optimisation and effect of ionomer loading on porous Fe–N–C-based proton exchange membrane fuel cells probed by emerging electrochemical methods

The next generation of proton exchange membrane fuel cells (PEMFCs) require a substantial reduction or elimination of Pt-based electrocatalyst from the cathode, where O2 reduction takes place. The most promising alternative to Pt is atomic Fe embedded in N-doped C (Fe–N–C). Successful incorporation of Fe–N–C in PEMFCs relies on a thorough understanding of the catalyst layer properties, both ex situ and in situ, with tailored electrode interface engineering. To help resolve this conundrum, we provide a quantitative protocol on the optimisation of I/C for Fe–N–Cs. It is demonstrated that a high pore volume (3.33 cm3 g−1FeNC) Fe–N–C catalyst requires a sufficiently high ionomer to catalyst mass ratio (I/C, 2.8≤I/C ≤ 4.2) for optimum PEMFC activity under H2/O2. Emerging electrochemical techniques (distribution of relaxation times and Fourier transformed alternating current voltammetry) were used to deconvolute for the first time the trade-off between proton and electron resistance and accessible FeNx active site density with increasing ionomer loading. These findings highlight the significant impact of tuning the I/C ratio based on the catalyst layer properties and feature the power of evolving electrochemical tools for optimising performance in PEMFCs and other electrochemical devices.

How do high-voltage cathode and PEO electrolyte get along well? EIS analysis mechanism & potentiometric control strategy

PEO-based all-solid-state electrolytes are extensively utilized and researched owing to their exceptional safety, low-mass-density, and cost-effectiveness. However, the low oxidation potential of PEO makes the interface problem with the high-voltage cathode extremely severe. In this work, the impedance of PEO-based all-solid-state batteries with high-voltage cathode (NCM811) was studied at different potentials. The Nyquist plots displayed a gyrate arc at low-frequencies for NCM811/PEO interface. Based on the kinetic modeling, it was deduced that there is a decomposition reaction of PEO-matrix in addition to de-embedded reaction of NCM811, and the PEO intermediate product (dehydra-PEO) adsorbed on the electrode surface leading to low-frequency inductive arcs. Furthermore, the distribution of relaxation time shows the dehydra-PEO results in the kinetic tardiness of the charge transfer process in the temporal dimension. Hence, an artificial interface layer (CEIx) was modified on the surface of NCM811 to regulate the potential of cathode/electrolyte interface to prevent the high-voltage deterioration of PEO. NCM/CEIx/PEO batteries exhibit capacity retentions of 96.0%, 84.6%, and 76.8% after undergoing 100 cycles at cut-off voltages of 4.1, 4.2, and 4.3 V, respectively. Therefore, here the failure mechanism of high-voltage PEO electrolyte is investigated by EIS and a proposed solving strategy is presented.

Observation and suppression of metallic and metallic-like plating on hard carbon for high-performance sodium-ion batteries

Increasing the lifespan of Na-ion batteries (NIBs) is one of the primary requirements for stationary energy storage. Metallic and metallic-like Na plating on hard carbon (HC) could be one of the main causes for degraded performance during cycling, but the mechanism remains unclear. Here, we systematically investigate the plating phenomenon on HC under various cycling conditions in NIBs. We reveal that underpotential deposition (UPD) could potentially trigger the metallic-like plating on the surface of HC electrodes. In-situ distribution of relaxation times (DRT) analysis provides an effective indictor to identify the occurring of metallic and metallic-like Na plating on HC electrode by probing the time constant for charge transfer process. Based on the understanding, we apply a uniform nano porous coating layer on HC electrode to restrict potential UPD on the HC electrode surface but allow uniform Na+ transport across interface, which greatly suppress the plating phenomenon, leading to significantly improved cycling stability of NIBs.

Humidity impact on polarization dynamics in polymer electrolyte membrane fuel cells through distribution of relaxation times analysis

The interaction among relative humidity, current density, and internal polarization plays a crucial role in optimizing the performance of polymer electrolyte membrane fuel cells (PEMFCs). However, achieving swift analysis and feedback on the internal humidity status of PEMFCs through on-vehicle impedance spectroscopy measurements remains a significant challenge. Conducting a series of impedance spectra under operating conditions of 30 %, 50 %, and 80 % relative humidity sheds light on the impact of humidity on performance. Correlations between specific distribution of relaxation times (DRT) peaks and internal polarization are established. Through DRT analysis, four polarization dynamics related to proton transfer at the proton exchange membrane interface, proton transport in the cathode catalyst layer, charge transfer, and the oxygen diffusion process are effectively identified based on characteristic frequencies and peaks. The rate-determining step of the polarization varies under idling, rated, and overload conditions, providing valuable insights. This study contributes analytical models and strategic guidance for tailoring relative humidity conditions to mitigate polarization, thereby enabling real-time control and enhancement of PEMFC performance.

Mixed polyanionic NaFe1.6V0.4(PO4)(SO4)2@CNT cathode for sodium-ion batteries: Electrochemical diffusion kinetics and distribution of relaxation time analysis at different temperatures

We report the electrochemical sodium-ion kinetics and distribution of relaxation time (DRT) analysis of a newly designed mixed polyanionic NaFe1.6V0.4(PO4)(SO4)2@CNT composite as a cathode. The specific capacity of 104 mAhg−1 is observed at 0.1 C with the average working voltage of ∼3 V. Intriguingly, a remarkable rate capability and reversibility are demonstrated up to very high current rate of 25 C. The long cycling test up to 10 C shows high capacity retention even after 2000 cycles. The detailed analysis of galvanostatic intermittent titration technique (GITT) and cyclic voltammetry (CV) data reveal the diffusion coefficient of 10−8–10−11 cm2s−1. We find excellent stability in the thermal testing between 25–55 °C temperatures and 80% capacity retention up to 100 cycles at 5 C. Further, we analyze the individual electrochemical processes in the time domain using the novel DRT technique at different temperatures. The ex-situ investigation shows the stable and reversible structure, morphology and electronic states of the long cycled cathode material. More importantly, we demonstrate relatively high specific energy of ≈155 Wh kg−1 (considering the total active material loading of both the electrodes) at 0.2 C for full cell battery having excellent rate capability up to 10 C and long cyclic stability at 1 C.

Microstructures and complex impedance analysis of spray pyrolysis-synthesized Ni doped ZnO for optoelectronic applications

This study focuses on the physical exploration, particularly examining the structural and electrical attributes of ZnO thin films produced through spray deposition, with variations in the Ni/Zn ratio (0.25 %, 0.5 %, and 0.75 %). X-ray diffraction (XRD) analysis reveals that both undoped and Ni-doped ZnO films exhibit a hexagonal crystalline structure, with a preferred orientation along the (002) direction perpendicular to the substrate. The semiconductor nature of all prepared compounds is confirmed by the grain boundary resistance. An escalation in Ni concentration corresponds to an increase in grain boundary resistance. The activation energy values, derived from both relaxation time and grain boundary resistances, closely align. Impedance studies indicate the presence of two relaxation processes within the compounds. The Nyquist diagram illustrates the emergence of semicircles, with decreasing radii at higher temperatures, indicating thermally activated semiconductor behavior in these samples, as evidenced by electrical conductance and distribution of relaxation times.

Evaluation of Polymetallic Phosphide Cathodes for Sodium-Air Batteries by Distribution of Relaxation Time.

Sodium-oxygen batteries are emerging as a new energy storage system because of their high energy density and low cost. However, the cycling performance of the battery is not satisfying due to its insulating discharge product. Here, we synthesized metallic phosphides with gradient concentration (g-CoNiFe-P) and their uniform counterpart (CoNiFe-P) as cathode catalysts in a Na-O2 battery. Notably, the distribution of relaxation time (DRT) was utilized to identify the rate-determining step in a Na-O2 battery, evaluate the catalytic performance of the catalysts, and monitor the change of every single electrochemical process along the whole cycling process to study the degradation mechanism. The g-CoNiFe-P catalyst presented better initial capacity and cycling performances. The evolution of the kinetic processes resulting in battery degradation has been investigated by DRT analysis, which assists with characterizations. Our work demonstrates the application of DRT in battery diagnosis to evaluate the catalytic performance of catalysts and monitor the changes in different kinetic processes of new energy systems.

High-precision identification of polarization processes of proton exchange membrane fuel cells through relaxation time analysis: Targeted experimental design and verification

Distribution of relaxation time (DRT) technology can achieve more precise decoupling of polarization process of proton exchange membrane fuel cell (PEMFC). However, except for the two peaks of DRT at low frequency, which are widely acknowledged to the cathode charge transfer impedance and the oxygen mass transfer impedance, there has been ongoing debate regarding the interpretation of other peaks observed at high frequency. In this work, the single-state variable control method is introduced by design of the membrane electrode assembly (MEA) and corresponding working operating conditions to simulate performance degradation factors of PEMFC, enabling accurate identification and verification of each peak in DRT. Based on the previous understanding that peaks P1 and P2 are oxygen mass transfer impedance and cathode charge transfer impedance, peaks P3-P5, ranging from high to low time scales, are determined to correspond to the other three polarization impedances. Specifically, peaks P3 and P4 are influenced by ionomer content in cathode and anode catalyst layers, respectively, and exhibit a decline with increasing humidity. They correspond to proton transfer processes within their respective catalyst layers. And the peak P5 is affected by anode catalyst loading and displays an increase with rising current density at low loading, signifying its involvement in the charge transfer process of anodic hydrogen oxidation reaction. A novel ECM was developed, consisting of five series-connected Randles circuits with polarization significance. The cathode and anode were separated in this design. The results demonstrate the enhanced sensitivity of DRT analysis to the performance degradation of PEMFC caused by oxygen transfer, charge transfer, and proton migration. This perspective provides a clear refinement for prior work of DRT polarization characteristic peaks.

Modeling and health feature extraction method for lithium-ion batteries state of health estimation by distribution of relaxation times

Accurate state of health (SOH) estimation of lithium batteries (LIBs) depends on the accuracy of LIBs modeling and the correlation of extracted health features (HFs). Aiming at the problems of a priori assumptions for existing battery modeling and poor correlation of HFs, this paper proposes a SOH estimation method for LIBs based on distribution of relaxation times (DRT). Firstly, we deduce and establish the developed DRT-based impedance model from battery electrochemical impedance spectroscopy (EIS), and the model parameters are calculated by EIS split-frequency domain method based on the principle of parsimony. Then, we analyze the variation rules of the peak and valley information in the distribution function of relaxation times curve with the capacity decay, and we extract multiple features strongly correlated with SOH as HFs. The extracted HFs are subjected to Weighted Principal Component Analysis (WPCA) to obtain indirect health features (IHFs), which achieve the estimation of SOH for LIBs. Finally, the effectiveness of the proposed modeling and health feature extraction method is validated by SOH estimation using the public dataset from Nature subseries. The results indicated that the EIS fitting accuracy R2 of the developed model is the best and the RMSE of SOH estimation is within 0.873 %.