Anis Allagui
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Anis Allagui has a total of 131 co-authors. Here are the top co-authors by number of shared publications:
- Ahmed S. Elwakil
University of Sharjah
53 shared publications - Costas Psychalinos
Physics Department, Electronics Laboratory University of Patras Rio Patras Greece
13 shared publications - Enrique Hernandez-Balaguera
Universidad Rey Juan Carlos
13 shared publications Ahmed S. Elwakil
Department of Electrical Engineering University of Sharjah Sharjah UAE
12 shared publicationsHussain Alawadhi
Department of Basic Sciences, University of Sharjah, Sharjah, United Arab Emirates
11 shared publications- Elena A. Baranova
University of Ottawa
10 shared publications
Latest Publications
- Open Access
- 15 October 2026
- Published by Elsevier in SSRN Electronic Journal
From local $RC$ dynamics to fractional memory in the constant phase elementThe constant phase element (CPE) is commonly emulated in equivalent circuit form using topologies built exclusively from ordinary resistors and capacitors. Each of these elements obeys a local, first-order equation with no memory kernel of its own. Yet the input impedance of the emulator is the fractional power law $Z(s)=1/(C_\alpha s^\alpha)$, whose time-domain current depends on the entire past history of the voltage through a power-law kernel. This raises the question: where does the memory come from if the individual components have local, first-order dynamics? This paper answers this question using two complementary routes. Route~1 starts from a finite $N$ parallel ensemble of series-$RC$ branches and shows that eliminating the internal capacitor states produces a reduced memory kernel, i.e. a finite sum of exponentials for finite $N$, and a power law only when the relaxation spectrum becomes scale free, and effectively continuous. Route~2 examines two spatial distributed $RC$ constructions: the self-similar $RC$ ladder, where scale freedom is imposed on the component values, and the uniform $RC$ transmission line, where scale freedom arises from the absence of a finite boundary. The findings provides a direct physical interpretation of a fitted CPE exponent $\alpha$ in terms of the relaxation time spectrum sampled by the measurement, and redirects the search for the physical origin of the CPE to the processes that generate such a distribution of time constants.- 15 October 2026
- Published by Elsevier in SSRN Electronic Journal
Open AccessFrom local $RC$ dynamics to fractional memory in the constant phase elementThe constant phase element (CPE) is commonly emulated in equivalent circuit form using topologies built exclusively from ordinary resistors and capacitors. Each of these elements obeys a local, first-order equation with no memory kernel of its own. Yet the input impedance of the emulator is the fractional power law $Z(s)=1/(C_\alpha s^\alpha)$, whose time-domain current depends on the entire past history of the voltage through a power-law kernel. This raises the question: where does the memory come from if the individual components have local, first-order dynamics? This paper answers this question using two complementary routes. Route~1 starts from a finite $N$ parallel ensemble of series-$RC$ branches and shows that eliminating the internal capacitor states produces a reduced memory kernel, i.e. a finite sum of exponentials for finite $N$, and a power law only when the relaxation spectrum becomes scale free, and effectively continuous. Route~2 examines two spatial distributed $RC$ constructions: the self-similar $RC$ ladder, where scale freedom is imposed on the component values, and the uniform $RC$ transmission line, where scale freedom arises from the absence of a finite boundary. The findings provides a direct physical interpretation of a fitted CPE exponent $\alpha$ in terms of the relaxation time spectrum sampled by the measurement, and redirects the search for the physical origin of the CPE to the processes that generate such a distribution of time constants. - 8 September 2026
- Published by American Chemical Society (ACS) in The Journal of Physical Chemistry C
Maximizing the Charging Efficiency of a Constant Phase Element via Fractional Calculus of Variations
In this study, we determine the optimal voltage profile for charging a constant phase element (CPE) of order α ∈]0, 1[ that maximizes the ratio of stored to total input energy over a fixed charging interval. Using the frequency-distributed RC network representation of the CPE, the efficiency maximization is reformulated as an isoperimetric variational problem, and solved via the fractional Euler–Lagrange equation. A Mellin transform analysis of the resulting optimality condition identifies the admissible solutions as a one-parameter family of power-law voltage profiles v(t; s0) = V0(t/T)β*, β* = α – s0 > 0. Within the physically relevant class of concave waveforms β* ∈]0, 1[, the optimal charging protocol is the linear ramp, which achieves the maximum energy storage efficiency η* = (4 – 22−α – α)/(2 – α), and produces a power-law current response. Extending to all β* > 0, the efficiency is shown to be monotonically increasing with β*, approaching the supremum α asymptotically as β* → ∞ but never reaching it, establishing α as the theoretical efficiency ceiling for power-law charging of a CPE. This result also provides an energetic interpretation of the CPE order α as the maximum fraction of input energy that can be stored in the capacitive modes of the CPE, over all power-law voltage excitations.
- 8 September 2026
- Published by American Chemical Society (ACS) in The Journal of Physical Chemistry C
Maximizing the Charging Efficiency of a Constant Phase Element via Fractional Calculus of Variations
In this study, we determine the optimal voltage profile for charging a constant phase element (CPE) of order α ∈]0, 1[ that maximizes the ratio of stored to total input energy over a fixed charging interval. Using the frequency-distributed RC network representation of the CPE, the efficiency maximization is reformulated as an isoperimetric variational problem, and solved via the fractional Euler–Lagrange equation. A Mellin transform analysis of the resulting optimality condition identifies the admissible solutions as a one-parameter family of power-law voltage profiles v(t; s0) = V0(t/T)β*, β* = α – s0 > 0. Within the physically relevant class of concave waveforms β* ∈]0, 1[, the optimal charging protocol is the linear ramp, which achieves the maximum energy storage efficiency η* = (4 – 22−α – α)/(2 – α), and produces a power-law current response. Extending to all β* > 0, the efficiency is shown to be monotonically increasing with β*, approaching the supremum α asymptotically as β* → ∞ but never reaching it, establishing α as the theoretical efficiency ceiling for power-law charging of a CPE. This result also provides an energetic interpretation of the CPE order α as the maximum fraction of input energy that can be stored in the capacitive modes of the CPE, over all power-law voltage excitations.
- 1 September 2026
- Published by The Electrochemical Society in Journal of the Electrochemical Society
- Vol. 173 (17) , 170502
Exact Electrochemical Impedance of Heterogeneous Electrodes Modeled as Coupled Finite RC Transmission Lines
A porous electrode interfaced with an electrolyte does not have necessarily uniform electrical properties along its thickness. For instance, the front of the electrode may age at a different rate than that of the back, resulting in different oxidative states of the solid matrix along its thickness and thus a depth-dependent electrical conductivity. Likewise, the electric double-layer capacitance cannot be spatially uniform, given the complex pore geometry and the resulting spatial distribution of ionic species and dielectric properties. In this work, we investigate the electrical response of a heterogeneous porous electrode/electrolyte system, modeled as two R C transmission line (TL) subdomains of different lengths and with distinct electrical properties, coupled through an ideal interface that enforces the continuity of both voltage and current, thus giving rise to a shared flux between the two diffusion problems. This is different combining the impedances of the R C TL segments in series, which implicitly imposes a blocking condition at the interface, and thereby discards any dynamic coupling between the subdomains. We derive the exact input impedance of the overall composite system, and demonstrate that it does not reduce to the sum of two independent Z n = p − 1 coth p ( p = j ω τ ) impedances except in the limit where both subdomains share identical characteristic electrical and propagation properties. We analyze how variations in downstream subdomain’s electrical and geometrical properties affect the overall impedance response, and show that the internal coupling induces characteristic signatures in the impedance spectrum, most pronounced in the low and if regimes. The results provide a simple, yet physically grounded picture for interpreting the impedance spectra of electrochemical energy storage and conversion devices with spatially heterogeneous porous structures.
- 1 September 2026
- Published by The Electrochemical Society in Journal of the Electrochemical Society
- Vol. 173 (17) , 170502
Exact Electrochemical Impedance of Heterogeneous Electrodes Modeled as Coupled Finite RC Transmission Lines
A porous electrode interfaced with an electrolyte does not have necessarily uniform electrical properties along its thickness. For instance, the front of the electrode may age at a different rate than that of the back, resulting in different oxidative states of the solid matrix along its thickness and thus a depth-dependent electrical conductivity. Likewise, the electric double-layer capacitance cannot be spatially uniform, given the complex pore geometry and the resulting spatial distribution of ionic species and dielectric properties. In this work, we investigate the electrical response of a heterogeneous porous electrode/electrolyte system, modeled as two R C transmission line (TL) subdomains of different lengths and with distinct electrical properties, coupled through an ideal interface that enforces the continuity of both voltage and current, thus giving rise to a shared flux between the two diffusion problems. This is different combining the impedances of the R C TL segments in series, which implicitly imposes a blocking condition at the interface, and thereby discards any dynamic coupling between the subdomains. We derive the exact input impedance of the overall composite system, and demonstrate that it does not reduce to the sum of two independent Z n = p − 1 coth p ( p = j ω τ ) impedances except in the limit where both subdomains share identical characteristic electrical and propagation properties. We analyze how variations in downstream subdomain’s electrical and geometrical properties affect the overall impedance response, and show that the internal coupling induces characteristic signatures in the impedance spectrum, most pronounced in the low and if regimes. The results provide a simple, yet physically grounded picture for interpreting the impedance spectra of electrochemical energy storage and conversion devices with spatially heterogeneous porous structures.
- 27 August 2026
- Published by Elsevier in Solid State Ionics
- Vol. 446
Delayed fractional Poisson-Nernst–Planck model for the dispersive impedance of blocking electrodes
- 27 August 2026
- Published by Elsevier in Solid State Ionics
- Vol. 446
Delayed fractional Poisson-Nernst–Planck model for the dispersive impedance of blocking electrodes
- Open Access
- 21 August 2026
- Published by Elsevier in SSRN Electronic Journal
Mellin Centroid as a Transition Frequency Estimator for the Impedance of Blocking Transmission Lines with Distributed Resistors and Constant Phase Elements
Electrochemical impedance spectroscopy of porous or intercalation electrodes is frequently modeled by the impedance function $Z_{\mathrm{n}}= p^{-1} {\coth p} $ ($p = (j\omega\tau)^{\alpha/2}$, $0< \alpha \leqslant 1$). A persistent difficulty is the identification of the characteristic transition frequency $\omega^*$ that separates the high-frequency branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha/2}$) from the low-frequency branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha}$), which is useful for determining the fundamental transport parameters of the system. Here, we propose as an estimator for $\omega^*$ the Mellin centroid, which is the geometric mean of the angular frequency weighted by the absolute second logarithmic derivative of the impedance magnitude. For the classical finite-length Warburg impedance ($\alpha = 1$), the estimator yields $\omega^* \approx 2.40\,\omega_0$. For subdiffusive exponents, for example for $\alpha = 0.8$ and $\alpha = 0.5$, the estimator gives $\omega^* \approx 1.82\,\omega_0$ and $\omega^* \approx 1.26\,\omega_0$, respectively. A sensitivity analysis shows that the window-truncation bias decays rapidly once the measurement band extends to more than two-three decades into each power-law regime, while the noise bias grows with the increase of relative noise level. We illustrate the method on the impedance of a commercial supercapacitor with $\alpha=0.954$, where the centroid estimate of $\omega_0$ agrees with the nonlinear-fit value to within $25\%$.- 21 August 2026
- Published by Elsevier in SSRN Electronic Journal
Open AccessMellin Centroid as a Transition Frequency Estimator for the Impedance of Blocking Transmission Lines with Distributed Resistors and Constant Phase Elements
Electrochemical impedance spectroscopy of porous or intercalation electrodes is frequently modeled by the impedance function $Z_{\mathrm{n}}= p^{-1} {\coth p} $ ($p = (j\omega\tau)^{\alpha/2}$, $0< \alpha \leqslant 1$). A persistent difficulty is the identification of the characteristic transition frequency $\omega^*$ that separates the high-frequency branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha/2}$) from the low-frequency branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha}$), which is useful for determining the fundamental transport parameters of the system. Here, we propose as an estimator for $\omega^*$ the Mellin centroid, which is the geometric mean of the angular frequency weighted by the absolute second logarithmic derivative of the impedance magnitude. For the classical finite-length Warburg impedance ($\alpha = 1$), the estimator yields $\omega^* \approx 2.40\,\omega_0$. For subdiffusive exponents, for example for $\alpha = 0.8$ and $\alpha = 0.5$, the estimator gives $\omega^* \approx 1.82\,\omega_0$ and $\omega^* \approx 1.26\,\omega_0$, respectively. A sensitivity analysis shows that the window-truncation bias decays rapidly once the measurement band extends to more than two-three decades into each power-law regime, while the noise bias grows with the increase of relative noise level. We illustrate the method on the impedance of a commercial supercapacitor with $\alpha=0.954$, where the centroid estimate of $\omega_0$ agrees with the nonlinear-fit value to within $25\%$. - Open Access
- 7 July 2026
- Published by Elsevier in SSRN Electronic Journal
Mellin Centroid as a Transition Frequency Estimator for the Impedance of Blocking Transmission Lines with Distributed Resistors and Constant Phase Elements
Electrochemical impedance spectroscopy of porous or intercalation electrodes is frequently modeled by the (normalized) impedance function $ Z_{\mathrm{n}}= p^{-1} {\coth p} $ ($p = (j\omega\tau)^{\alpha/2}$, $0< \alpha \leqslant 1$), which is derived from the time-fractional, finite-length transmission line equation with blocking boundary. A persistent difficulty with this impedance response is the identification of the characteristic transition frequency $\omega^*$ that separates the high-frequency Warburg-like diffusion branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha/2}$) from the low-frequency pseudocapacitive branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha}$), which is useful for determining the fundamental transport parameters of the system. Here, we propose as an estimator for $\omega^*$ the Mellin centroid, which is the geometric mean of the angular frequency weighted by the absolute second logarithmic derivative of the impedance magnitude (i.e. by $S(\omega)=|d^2\ln|Z_\mathrm{n}|/d(\ln\omega)^2|$). This weight function vanishes on both power law branches and peaks in the transition region, so the centroid is concentrated near $\omega^*$ without requiring prior knowledge of $\alpha$ or $\omega_0=1/\tau$. For the classical finite-length Warburg impedance ($\alpha = 1$), the estimator yields $\omega^* \approx 2.40\,\omega_0$. For subdiffusive exponents, for example for $\alpha = 0.8$ and $\alpha = 0.5$, the estimator gives $\omega^* \approx 1.82\,\omega_0$ and $\omega^* \approx 1.26\,\omega_0$, respectively. A sensitivity analysis shows that the window-truncation bias decays rapidly once the measurement band extends to more than two-three decades into each power-law regime, while the noise bias grows with the increase of relative noise level, which can exceeding $25\%$ at $\sigma_\mathrm{rel}=1\%$. This implies that pre-smoothing of the impedance data is recommended for noisy measurements. We illustrate the method on the impedance spectrum of a commercial supercapacitor with $\alpha=0.954$, where the centroid estimate of $\omega_0$ agrees with the nonlinear-fit value to within $25\%$.- 7 July 2026
- Published by Elsevier in SSRN Electronic Journal
Open AccessMellin Centroid as a Transition Frequency Estimator for the Impedance of Blocking Transmission Lines with Distributed Resistors and Constant Phase Elements
Electrochemical impedance spectroscopy of porous or intercalation electrodes is frequently modeled by the (normalized) impedance function $ Z_{\mathrm{n}}= p^{-1} {\coth p} $ ($p = (j\omega\tau)^{\alpha/2}$, $0< \alpha \leqslant 1$), which is derived from the time-fractional, finite-length transmission line equation with blocking boundary. A persistent difficulty with this impedance response is the identification of the characteristic transition frequency $\omega^*$ that separates the high-frequency Warburg-like diffusion branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha/2}$) from the low-frequency pseudocapacitive branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha}$), which is useful for determining the fundamental transport parameters of the system. Here, we propose as an estimator for $\omega^*$ the Mellin centroid, which is the geometric mean of the angular frequency weighted by the absolute second logarithmic derivative of the impedance magnitude (i.e. by $S(\omega)=|d^2\ln|Z_\mathrm{n}|/d(\ln\omega)^2|$). This weight function vanishes on both power law branches and peaks in the transition region, so the centroid is concentrated near $\omega^*$ without requiring prior knowledge of $\alpha$ or $\omega_0=1/\tau$. For the classical finite-length Warburg impedance ($\alpha = 1$), the estimator yields $\omega^* \approx 2.40\,\omega_0$. For subdiffusive exponents, for example for $\alpha = 0.8$ and $\alpha = 0.5$, the estimator gives $\omega^* \approx 1.82\,\omega_0$ and $\omega^* \approx 1.26\,\omega_0$, respectively. A sensitivity analysis shows that the window-truncation bias decays rapidly once the measurement band extends to more than two-three decades into each power-law regime, while the noise bias grows with the increase of relative noise level, which can exceeding $25\%$ at $\sigma_\mathrm{rel}=1\%$. This implies that pre-smoothing of the impedance data is recommended for noisy measurements. We illustrate the method on the impedance spectrum of a commercial supercapacitor with $\alpha=0.954$, where the centroid estimate of $\omega_0$ agrees with the nonlinear-fit value to within $25\%$. - Open Access
- 29 June 2026
- Published by Elsevier in SSRN Electronic Journal
Mellin Centroid as a Transition Frequency Estimator for the Impedance of Blocking $R$-CPE Transmission Line
Electrochemical impedance spectroscopy of porous or intercalation electrodes is frequently modeled by the (normalized) impedance function $ Z_{\mathrm{n}}= p^{-1} {\coth p} $ ($p = (j\omega\tau)^{\alpha/2}$, $0< \alpha \leqslant 1$), which is derived from the Caputo time-fractional finite-length transmission line equation with blocking boundary. A persistent difficulty with this impedance response is the identification of the characteristic transition frequency $\omega^*$ that separates the high-frequency Warburg-like diffusion branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha/2}$) from the low-frequency pseudocapacitive branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha}$), which is useful for determining the fundamental transport parameters of the system. Here we propose the Mellin centroid as a model-free, numerically stable estimator of $\omega^*$, which is the geometric mean of the angular frequency weighted by the absolute second logarithmic derivative of the impedance magnitude (i.e. by $S(\omega)=|d^2\ln|Z_\mathrm{n}|/d(\ln\omega)^2|$). The estimator is grounded in the Mellin transform framework because the two power-law regimes correspond to poles of the Mellin transform of $|Z_\mathrm{n}|$ at $s=\alpha/2$ and $s=\alpha$, and the centroid locates the frequency at which neither pole dominates. For the classical finite-length Warburg impedance ($\alpha = 1$), the estimator yields $\omega^* \approx 2.40\,\omega_0$, where $\omega_0$ is the intrinsic characteristic frequency of the line. For subdiffusive exponents, for example for $\alpha = 0.8$ and $\alpha = 0.5$, the estimator gives $\omega^* \approx 1.82\,\omega_0$ and $\omega^* \approx 1.26\,\omega_0$, respectively. A sensitivity analysis shows that the window-truncation bias decays rapidly once the measurement band extends to more than two-three decades into each power-law regime, while the noise bias grows with the increase of relative noise level, which can exceeding $25\%$ at $\sigma_\mathrm{rel}=1\%$. This implies that pre-smoothing of the impedance data is recommended for noisy measurements. We illustrate the method to the impedance spectrum of a commercial supercapacitor with $\alpha=0.954$.- 29 June 2026
- Published by Elsevier in SSRN Electronic Journal
Open AccessMellin Centroid as a Transition Frequency Estimator for the Impedance of Blocking $R$-CPE Transmission Line
Electrochemical impedance spectroscopy of porous or intercalation electrodes is frequently modeled by the (normalized) impedance function $ Z_{\mathrm{n}}= p^{-1} {\coth p} $ ($p = (j\omega\tau)^{\alpha/2}$, $0< \alpha \leqslant 1$), which is derived from the Caputo time-fractional finite-length transmission line equation with blocking boundary. A persistent difficulty with this impedance response is the identification of the characteristic transition frequency $\omega^*$ that separates the high-frequency Warburg-like diffusion branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha/2}$) from the low-frequency pseudocapacitive branch ($|Z_{\mathrm{n}}| \propto \omega^{-\alpha}$), which is useful for determining the fundamental transport parameters of the system. Here we propose the Mellin centroid as a model-free, numerically stable estimator of $\omega^*$, which is the geometric mean of the angular frequency weighted by the absolute second logarithmic derivative of the impedance magnitude (i.e. by $S(\omega)=|d^2\ln|Z_\mathrm{n}|/d(\ln\omega)^2|$). The estimator is grounded in the Mellin transform framework because the two power-law regimes correspond to poles of the Mellin transform of $|Z_\mathrm{n}|$ at $s=\alpha/2$ and $s=\alpha$, and the centroid locates the frequency at which neither pole dominates. For the classical finite-length Warburg impedance ($\alpha = 1$), the estimator yields $\omega^* \approx 2.40\,\omega_0$, where $\omega_0$ is the intrinsic characteristic frequency of the line. For subdiffusive exponents, for example for $\alpha = 0.8$ and $\alpha = 0.5$, the estimator gives $\omega^* \approx 1.82\,\omega_0$ and $\omega^* \approx 1.26\,\omega_0$, respectively. A sensitivity analysis shows that the window-truncation bias decays rapidly once the measurement band extends to more than two-three decades into each power-law regime, while the noise bias grows with the increase of relative noise level, which can exceeding $25\%$ at $\sigma_\mathrm{rel}=1\%$. This implies that pre-smoothing of the impedance data is recommended for noisy measurements. We illustrate the method to the impedance spectrum of a commercial supercapacitor with $\alpha=0.954$. - Open Access
- 26 June 2026
- Published by Elsevier in Journal of Energy Storage
- Vol. 175
Influence of the series resistance on the anomalous diffusion transients of mixed ionic-electronic conductors for energy storage applications
- 26 June 2026
- Published by Elsevier in Journal of Energy Storage
- Vol. 175
Open AccessInfluence of the series resistance on the anomalous diffusion transients of mixed ionic-electronic conductors for energy storage applications
- Top Cited Papers
- 2 April 2026
- Published by Elsevier in Journal of Electroanalytical Chemistry
- Vol. 1011
Splitting the stored and dissipated energies in a bounded resistor-constant phase element transmission line network
- 2 April 2026
- Published by Elsevier in Journal of Electroanalytical Chemistry
- Vol. 1011
Top Cited PapersSplitting the stored and dissipated energies in a bounded resistor-constant phase element transmission line network
- 20 March 2026
- Published by The Electrochemical Society in Journal of the Electrochemical Society
- Vol. 173 (6) , 060510
Memory Effects Encoded in Open-Circuit Voltage Recovery of Electrochemical Capacitors
In this study, we show that the specific historical charging/discharging pattern applied on an electrochemical capacitor or supercapacitor effectively acts as an encoded signature of the past. Specifically, we applied a constant-current, constant-voltage charging sequence, followed by a constant-current discharging sequence (to zero volt), and then we let the device relax back to equilibrium at open circuit condition. The non-equilibrium internal charge distribution that developed in the device in response to the latest discharge sequence is shown to be the reason that measurable open-circuit voltage recovery profiles are observed, which are found to be strongly depend on the pre-history. This phenomena, where the transient history drives the subsequent relaxation process, suggests memory effects that are central to draw a general picture of our understanding of such complex electrochemical capacitive systems. We used the R s -CPE transmission line model for quantitatively describing these observations.
- 20 March 2026
- Published by The Electrochemical Society in Journal of the Electrochemical Society
- Vol. 173 (6) , 060510
Memory Effects Encoded in Open-Circuit Voltage Recovery of Electrochemical Capacitors
In this study, we show that the specific historical charging/discharging pattern applied on an electrochemical capacitor or supercapacitor effectively acts as an encoded signature of the past. Specifically, we applied a constant-current, constant-voltage charging sequence, followed by a constant-current discharging sequence (to zero volt), and then we let the device relax back to equilibrium at open circuit condition. The non-equilibrium internal charge distribution that developed in the device in response to the latest discharge sequence is shown to be the reason that measurable open-circuit voltage recovery profiles are observed, which are found to be strongly depend on the pre-history. This phenomena, where the transient history drives the subsequent relaxation process, suggests memory effects that are central to draw a general picture of our understanding of such complex electrochemical capacitive systems. We used the R s -CPE transmission line model for quantitatively describing these observations.