I would greatly appreciate it if you could offer a physical explanation for why the boundaries of pores are treated as having an open or infinite impedance, and under what circumstances this assumption holds true. Personally, I would expect that the same electrochemical processes take place at the boundaries of the pores as they do within the pores, which is represented by Y, especially when considering spherical pores.
First of all, the transmission line (TxL) model is not specifically designed to represent spherical pores, so while it may work for such systems (honestly I don't know for sure, I don't have personal experience with it to say for sure or not), it is really more suited for the kind of rectangular shape I show in this video. As far as why the boundaries are infinite, open, short, or really frankly anything dissimilar to 'Y' at all, this is a good question, and one to which I don't know that I have a perfect answer, to be candid. I can only give a little adjacent pontification, if I would call it anything. Mainly, in engineering science and mathematics, it is common to apply known end/boundary conditions (e.g., Dirichlet, Neumann) to differential and partial differential equations as a means to solve the mathematics analytically. The TxL, to my understanding, is something of this nature. So, one (admittedly a bit unsatisfying) reason is that simply put, mathematical solutions to the complex infinite summation included in the TxL requires a set boundary/end condition. Without this, it is somewhat of a non-starter and circuit fitting cannot really be performed at all. The other thing that is somewhat unique to the TxL is that the infinite 'Y' sum is supposed to be representative of an aggregate of charge distribution throughout the pore. In fact, this is the explanation used by Juan Bisquert in the papers from which the TxL originated (to the best of my knowledge). In other words, we observe the phenomenon of charge distribution in a porous electrode, and the TxL is a way to capture that behavior, and doing so also means there is necessarily a difference in the resistive and/or capacitive elements at either end, and throughout the pore. Perhaps in some way, this can help explain why there is a need for different elements at different physical locations in the TxL model.
@@Pineresearch Based on my personal experience, I can confidently assert that the transmission line (TxL) model can effectively fit EIS data of porous materials that possess spherical pores. I am currently working with a material that exhibits such a morphology, and interestingly, its Bode plot bears a striking resemblance to the Bode plot demonstrated in this video. Upon qualitative comparison, the only noticeable difference I observed is that the horizontal lines in my Bode plot appear flatter across the entire high to mid frequency range. This observation leads me to argue that the TxL model can indeed be applied to porous materials with spherical pores. Regarding the boundary conditions of the TxL model, there is one aspect that confuses me. If the mathematical solutions involving complex infinite summations within the TxL model necessitate specific boundary conditions, why is it permissible for the boundary conditions Za and Zb to be similar to Y? Wouldn't this essentially imply the absence of any boundary conditions at all? In fact, when fitting my porous electrode data, I obtained the most satisfactory outcomes when Za and Zb were exactly akin to Y. Perhaps this alignment indicates that I am indeed working with spherical-shaped pores, where the charge distribution is relatively uniform. This could potentially explain why I do not require additional physical locations within the TxL model, apart from Y (and X1). In any case, I recognize the need to delve deeper into the fundamental principles of the TxL model to gain a better understanding.
@@TarikZahzah-ns2bu Having a boundary condition with the same form as 'Y' does not necessarily mean it has the same value as 'Y', so they can still be distinctly different. Additionally, I don't think in general the TxL requires they be different, I was merely using an example I am aware of with engineering mathematics to help explain their presence.
*Summary* *Intro* - *0:02**:* [Music] - *0:08**:* Introduction to the video on EIS transmission line fitting of a coin cell battery under blocking conditions. - *0:27**:* Outline of the video structure covering the electrochemical system, modeling using a transmission line, circuit fitting, and calculating tortuosity. *Description of Coin Cell Battery* - *1:00**:* Description of a coin cell battery, consisting of a metal case, cap, compression spring, gasket, and identical NMC-111 electrodes. - *1:47**:* Details on the electrolyte used and the concept of a blocking condition in the battery setup. - *2:35**:* Explanation of blocking boundaries and their use in studying the microstructure of porous electrodes. - *3:10**:* Discussion on how to fit data using the transmission line model and calculate tortuosity. *EIS Transmission Line Model* - *3:29**:* Microscopic structure of the electrode resembling cracked earth, indicating porous microstructure. - *3:59**:* Simplified model of porous microstructure including electrolyte, electrode, and backing electrode. - *4:26**:* Explanation of the transmission line model, including leading resistor, impedance in electrolyte, boundary conditions, interaction in the pore, and impedance in the electrode. - *6:10**:* The model reflects the distribution of current in the pore, representing non-uniform current distribution. *Transmission Line Circuit Fitting* - *8:30**:* Analysis of EIS data, showing capacitance, 45-degree lagging behavior, and diffusion typical of a transmission line. - *8:57**:* Use of specialized transmission line circuit fit in software and adjustments to the model for fitting. - *9:32**:* Refinement of the circuit fit and analysis of the fit quality. - *10:53**:* Consideration of variations in the model assumptions and the overall fit quality. *How to Calculate Tortuosity* - *11:24**:* Introduction to tortuosity, its representation, and its calculation using the McMullen number. - *13:00**:* Method for calculating tortuosity involving impedance resistance, surface area conductivity, thickness, and porosity. - *14:09**:* Assumptions and calculations for determining tortuosity in the specific coin cell battery setup. - *14:58**:* Interpretation of the calculated tortuosity value and its implications for electrode material and diffusion. *Conclusion* - *15:18**:* Conclusion of the video with an invitation for questions and information on advanced EIS webinars by Dr. Neil Spinner.
I have a question regarding tortuosity. My understanding is that tortuosity primarily provides insight into the transport properties of the electrode material itself. However, I am curious if the electrolyte, specifically the type of cations and anions, also contributes to the tortuosity. If that is the case, I am wondering how the diffusional contribution of the electrolyte ions could be calculated using values obtained from circuit fitting. One idea that comes to mind is introducing a Warburg element in series with resistor x1, which represents the electrolyte resistance inside the pores. The incorporation of a Warburg element would enable the calculation of the diffusion coefficient of ions, particularly in cases involving pure double-layer charging, within the pores. Does such a modification seem reasonable, or are you aware of alternative methods to address this?
"I am curious if the electrolyte, specifically the type of cations and anions, also contributes to the tortuosity" I don't think so. I believe tortuosity is strictly a physical measurement of the material and describes how tortuous, or not direct, the pathway is through it, essentially, regardless of what is moving through it. I do think it possible, and perhaps even likely, that the choice of electrolyte could impact the reproduceability of the experiment and measurement of tortuosity to a certain degree. But I would more attribute that to the normal amount of error and uncertainty associated with all electrochemistry experiments, and not necessarily to the definition of the property itself. I also don't think such Warburg modification of the transmission line model is appropriate, but that may be a bit more of a longer discussion of the transmission line. My other answer to a similar comment you made elsewhere went into a little more depth on this issue as well.
@@Pineresearch I am interested in exploring the diffusion-limited behavior of cations and anions within a particular porous electrode, aiming to capture both qualitative and quantitative trends. Since the TxL model accurately represents the morphology of a porous electrode, I would like to know how to effectively study the diffusion-limited behavior using this model. Specifically, I am keen to understand which electrical circuit elements of the TxL model should be the main focus and if there are any additional elements that need to be incorporated to accurately account for the diffusional-limited behavior. Any suggestions or insights on this matter would be highly appreciated. In literature, I came across an example where a simple Randles circuit (consisting of a Warburg element in series with a resistor) was modified by substituting the conventional Warburg element with the M element from the De Levie model, which is known to account for restrictive diffusion (whether linear or non-linear). However, as we previously discussed, considering that the De Levie model is essentially a variant of the TxL model, it would seem logical to replace the Warburg element with the TxL model. What I find puzzling, though, is why the TxL model does not appear to have an element specifically associated with diffusion.
@@TarikZahzah-ns2bu This is definitely an interesting a worthwhile kind of investigation for you, and likely one that requires more in-depth discussion and research than can be covered in this video's comments. I think there may be some explanation regarding the seeming absence of diffusional characteristics within the TxL model, but again, I think this discussion may be a little beyond this comment section.
Should the transmission line model be the default choice for simulating porous electrode materials, or can a standard Randles circuit also be used for fitting? If the latter is applicable, what are the advantages of using the transmission line model? Additionally, are there specific characteristics in EIS data that indicate the suitability of the transmission line model? For instance, would it be appropriate when the data begins with a 45-degree angle line, similar to the example shown in this video?
1. Yes, you can certainly still use a Randles circuit (or series of Randles circuit) instead of the transmission line. It is just a choice of how you wish to represent and analyze your system. The advantage I suppose to using the transmission line is that, in some sense, it can more accurately represent the reality of an electrode microstructure because the infinite sum is designed to capture the distribution of charge within the pores, which is something a single Randles circuit does not describe on its own. 2. Generally, I recommend the use of a transmission line from a priori knowledge of the electrode microstructure, rather than looking at the data and applying it based on the data appearance. That being said, your suggestion is not necessarily wrong, and perhaps in a situation where you are unsure of your electrode microstructure but suspect it might be porous, the appearance of a high frequency 45° line could help inform the application of a transmission line.
@@Pineresearch I am interested in the transmission line model due to the unique characteristics of one of the electrode types I'm using, specifically a highly porous and amorphous IrOx electrode. However, when conducting a PEIS measurement to evaluate the Ohmic drop, I consistently observe an almost perfect semi-circle (albeit slightly depressed) in the high-frequency range. This makes me question whether employing the transmission line model, as opposed to a Randles circuit, is truly justified in this scenario.
@@TarikZahzah-ns2bu Typically EIS data that displays a small and almost perfect semicircle in the high frequency region, regardless of the other conditions and parameters used, is an indication of one of two different phenomena; either, (1) there is an artifact going on and the semicircle should be largely disregarded, or else a shunt employed to try and clarify this feature, or (2) it represents an underlying substrate-film interaction that is always present in your system no matter what potential you're applying. In fact, if it's #2, you may not really be able to apply the transmission line element very easily because in situations like this the time constant is much faster (i.e. smaller, where it shows at higher frequency) and unless you are able to simply cut out or disregard (just for analysis purposes) that first feature (which is possible, for example, with our AfterMath software), you will probably be forced to use some combination of Randles elements.
@@Pineresearch I don't believe there is any artifact present in my experimental data. Despite not using a shunt in my recent experiments, the same semicircle appeared when I did use a shunt. It's worth noting that this semicircle remained highly reproducible across different electrolytes. Moreover, the semicircle was not of a small magnitude; although I should verify the exact measurements in my data, it encompassed the mid-frequency range. Based on my observations, I'm inclined to attribute this phenomenon to an underlying substrate-film interaction. I am actually utilizing a super thin (20 nm) IrOx film on a Ti substrate. I am particularly interested in the origins of the charge transfer resistance associated with this semicircle. My suspicion is that it may be linked to the oxidation process of the porous IrOx film, i.e. deprotonation of the OH groups via a proton-coupled electron transfer (PCET). I'm measuring at anodic potentials. I am measuring the Ohmic drop at anodic potentials (0.5 V_RHE); however, it is important to acknowledge that IrOx undergoes oxidation at an early stage and over a very broad potential range. What are your thoughts?
@@TarikZahzah-ns2bu That sounds reasonable to me, though of course I am not an expert in this exact field and probably cannot speak with more authority other than to note that your explanation sounds logical. As I mentioned in my last comment, the fact that your semicircle is consistent across a variety of experimental situations, including potentials and even electrolytes, tells me most likely it is intrinsic to your electrode. That means it probably is related to the substrate-film interaction that is constant throughout all those systems, and not related to anything happening between the top film layer and the varying electrolyte or applied conditions, which may be different across tests.
I would greatly appreciate it if you could offer a physical explanation for why the boundaries of pores are treated as having an open or infinite impedance, and under what circumstances this assumption holds true. Personally, I would expect that the same electrochemical processes take place at the boundaries of the pores as they do within the pores, which is represented by Y, especially when considering spherical pores.
First of all, the transmission line (TxL) model is not specifically designed to represent spherical pores, so while it may work for such systems (honestly I don't know for sure, I don't have personal experience with it to say for sure or not), it is really more suited for the kind of rectangular shape I show in this video.
As far as why the boundaries are infinite, open, short, or really frankly anything dissimilar to 'Y' at all, this is a good question, and one to which I don't know that I have a perfect answer, to be candid. I can only give a little adjacent pontification, if I would call it anything. Mainly, in engineering science and mathematics, it is common to apply known end/boundary conditions (e.g., Dirichlet, Neumann) to differential and partial differential equations as a means to solve the mathematics analytically. The TxL, to my understanding, is something of this nature. So, one (admittedly a bit unsatisfying) reason is that simply put, mathematical solutions to the complex infinite summation included in the TxL requires a set boundary/end condition. Without this, it is somewhat of a non-starter and circuit fitting cannot really be performed at all.
The other thing that is somewhat unique to the TxL is that the infinite 'Y' sum is supposed to be representative of an aggregate of charge distribution throughout the pore. In fact, this is the explanation used by Juan Bisquert in the papers from which the TxL originated (to the best of my knowledge). In other words, we observe the phenomenon of charge distribution in a porous electrode, and the TxL is a way to capture that behavior, and doing so also means there is necessarily a difference in the resistive and/or capacitive elements at either end, and throughout the pore. Perhaps in some way, this can help explain why there is a need for different elements at different physical locations in the TxL model.
@@Pineresearch Based on my personal experience, I can confidently assert that the transmission line (TxL) model can effectively fit EIS data of porous materials that possess spherical pores. I am currently working with a material that exhibits such a morphology, and interestingly, its Bode plot bears a striking resemblance to the Bode plot demonstrated in this video. Upon qualitative comparison, the only noticeable difference I observed is that the horizontal lines in my Bode plot appear flatter across the entire high to mid frequency range. This observation leads me to argue that the TxL model can indeed be applied to porous materials with spherical pores.
Regarding the boundary conditions of the TxL model, there is one aspect that confuses me. If the mathematical solutions involving complex infinite summations within the TxL model necessitate specific boundary conditions, why is it permissible for the boundary conditions Za and Zb to be similar to Y? Wouldn't this essentially imply the absence of any boundary conditions at all? In fact, when fitting my porous electrode data, I obtained the most satisfactory outcomes when Za and Zb were exactly akin to Y.
Perhaps this alignment indicates that I am indeed working with spherical-shaped pores, where the charge distribution is relatively uniform. This could potentially explain why I do not require additional physical locations within the TxL model, apart from Y (and X1). In any case, I recognize the need to delve deeper into the fundamental principles of the TxL model to gain a better understanding.
@@TarikZahzah-ns2bu Having a boundary condition with the same form as 'Y' does not necessarily mean it has the same value as 'Y', so they can still be distinctly different. Additionally, I don't think in general the TxL requires they be different, I was merely using an example I am aware of with engineering mathematics to help explain their presence.
*Summary*
*Intro*
- *0:02**:* [Music]
- *0:08**:* Introduction to the video on EIS transmission line fitting of a coin cell battery under blocking conditions.
- *0:27**:* Outline of the video structure covering the electrochemical system, modeling using a transmission line, circuit fitting, and calculating tortuosity.
*Description of Coin Cell Battery*
- *1:00**:* Description of a coin cell battery, consisting of a metal case, cap, compression spring, gasket, and identical NMC-111 electrodes.
- *1:47**:* Details on the electrolyte used and the concept of a blocking condition in the battery setup.
- *2:35**:* Explanation of blocking boundaries and their use in studying the microstructure of porous electrodes.
- *3:10**:* Discussion on how to fit data using the transmission line model and calculate tortuosity.
*EIS Transmission Line Model*
- *3:29**:* Microscopic structure of the electrode resembling cracked earth, indicating porous microstructure.
- *3:59**:* Simplified model of porous microstructure including electrolyte, electrode, and backing electrode.
- *4:26**:* Explanation of the transmission line model, including leading resistor, impedance in electrolyte, boundary conditions, interaction in the pore, and impedance in the electrode.
- *6:10**:* The model reflects the distribution of current in the pore, representing non-uniform current distribution.
*Transmission Line Circuit Fitting*
- *8:30**:* Analysis of EIS data, showing capacitance, 45-degree lagging behavior, and diffusion typical of a transmission line.
- *8:57**:* Use of specialized transmission line circuit fit in software and adjustments to the model for fitting.
- *9:32**:* Refinement of the circuit fit and analysis of the fit quality.
- *10:53**:* Consideration of variations in the model assumptions and the overall fit quality.
*How to Calculate Tortuosity*
- *11:24**:* Introduction to tortuosity, its representation, and its calculation using the McMullen number.
- *13:00**:* Method for calculating tortuosity involving impedance resistance, surface area conductivity, thickness, and porosity.
- *14:09**:* Assumptions and calculations for determining tortuosity in the specific coin cell battery setup.
- *14:58**:* Interpretation of the calculated tortuosity value and its implications for electrode material and diffusion.
*Conclusion*
- *15:18**:* Conclusion of the video with an invitation for questions and information on advanced EIS webinars by Dr. Neil Spinner.
Thanks for the in-depth description
I have a question regarding tortuosity. My understanding is that tortuosity primarily provides insight into the transport properties of the electrode material itself. However, I am curious if the electrolyte, specifically the type of cations and anions, also contributes to the tortuosity. If that is the case, I am wondering how the diffusional contribution of the electrolyte ions could be calculated using values obtained from circuit fitting. One idea that comes to mind is introducing a Warburg element in series with resistor x1, which represents the electrolyte resistance inside the pores. The incorporation of a Warburg element would enable the calculation of the diffusion coefficient of ions, particularly in cases involving pure double-layer charging, within the pores. Does such a modification seem reasonable, or are you aware of alternative methods to address this?
"I am curious if the electrolyte, specifically the type of cations and anions, also contributes to the tortuosity"
I don't think so. I believe tortuosity is strictly a physical measurement of the material and describes how tortuous, or not direct, the pathway is through it, essentially, regardless of what is moving through it. I do think it possible, and perhaps even likely, that the choice of electrolyte could impact the reproduceability of the experiment and measurement of tortuosity to a certain degree. But I would more attribute that to the normal amount of error and uncertainty associated with all electrochemistry experiments, and not necessarily to the definition of the property itself.
I also don't think such Warburg modification of the transmission line model is appropriate, but that may be a bit more of a longer discussion of the transmission line. My other answer to a similar comment you made elsewhere went into a little more depth on this issue as well.
@@Pineresearch I am interested in exploring the diffusion-limited behavior of cations and anions within a particular porous electrode, aiming to capture both qualitative and quantitative trends. Since the TxL model accurately represents the morphology of a porous electrode, I would like to know how to effectively study the diffusion-limited behavior using this model. Specifically, I am keen to understand which electrical circuit elements of the TxL model should be the main focus and if there are any additional elements that need to be incorporated to accurately account for the diffusional-limited behavior. Any suggestions or insights on this matter would be highly appreciated.
In literature, I came across an example where a simple Randles circuit (consisting of a Warburg element in series with a resistor) was modified by substituting the conventional Warburg element with the M element from the De Levie model, which is known to account for restrictive diffusion (whether linear or non-linear). However, as we previously discussed, considering that the De Levie model is essentially a variant of the TxL model, it would seem logical to replace the Warburg element with the TxL model. What I find puzzling, though, is why the TxL model does not appear to have an element specifically associated with diffusion.
@@TarikZahzah-ns2bu This is definitely an interesting a worthwhile kind of investigation for you, and likely one that requires more in-depth discussion and research than can be covered in this video's comments. I think there may be some explanation regarding the seeming absence of diffusional characteristics within the TxL model, but again, I think this discussion may be a little beyond this comment section.
Should the transmission line model be the default choice for simulating porous electrode materials, or can a standard Randles circuit also be used for fitting? If the latter is applicable, what are the advantages of using the transmission line model? Additionally, are there specific characteristics in EIS data that indicate the suitability of the transmission line model? For instance, would it be appropriate when the data begins with a 45-degree angle line, similar to the example shown in this video?
1. Yes, you can certainly still use a Randles circuit (or series of Randles circuit) instead of the transmission line. It is just a choice of how you wish to represent and analyze your system. The advantage I suppose to using the transmission line is that, in some sense, it can more accurately represent the reality of an electrode microstructure because the infinite sum is designed to capture the distribution of charge within the pores, which is something a single Randles circuit does not describe on its own.
2. Generally, I recommend the use of a transmission line from a priori knowledge of the electrode microstructure, rather than looking at the data and applying it based on the data appearance. That being said, your suggestion is not necessarily wrong, and perhaps in a situation where you are unsure of your electrode microstructure but suspect it might be porous, the appearance of a high frequency 45° line could help inform the application of a transmission line.
@@Pineresearch I am interested in the transmission line model due to the unique characteristics of one of the electrode types I'm using, specifically a highly porous and amorphous IrOx electrode. However, when conducting a PEIS measurement to evaluate the Ohmic drop, I consistently observe an almost perfect semi-circle (albeit slightly depressed) in the high-frequency range. This makes me question whether employing the transmission line model, as opposed to a Randles circuit, is truly justified in this scenario.
@@TarikZahzah-ns2bu Typically EIS data that displays a small and almost perfect semicircle in the high frequency region, regardless of the other conditions and parameters used, is an indication of one of two different phenomena; either, (1) there is an artifact going on and the semicircle should be largely disregarded, or else a shunt employed to try and clarify this feature, or (2) it represents an underlying substrate-film interaction that is always present in your system no matter what potential you're applying. In fact, if it's #2, you may not really be able to apply the transmission line element very easily because in situations like this the time constant is much faster (i.e. smaller, where it shows at higher frequency) and unless you are able to simply cut out or disregard (just for analysis purposes) that first feature (which is possible, for example, with our AfterMath software), you will probably be forced to use some combination of Randles elements.
@@Pineresearch I don't believe there is any artifact present in my experimental data. Despite not using a shunt in my recent experiments, the same semicircle appeared when I did use a shunt. It's worth noting that this semicircle remained highly reproducible across different electrolytes. Moreover, the semicircle was not of a small magnitude; although I should verify the exact measurements in my data, it encompassed the mid-frequency range.
Based on my observations, I'm inclined to attribute this phenomenon to an underlying substrate-film interaction. I am actually utilizing a super thin (20 nm) IrOx film on a Ti substrate. I am particularly interested in the origins of the charge transfer resistance associated with this semicircle. My suspicion is that it may be linked to the oxidation process of the porous IrOx film, i.e. deprotonation of the OH groups via a proton-coupled electron transfer (PCET). I'm measuring at anodic potentials. I am measuring the Ohmic drop at anodic potentials (0.5 V_RHE); however, it is important to acknowledge that IrOx undergoes oxidation at an early stage and over a very broad potential range. What are your thoughts?
@@TarikZahzah-ns2bu That sounds reasonable to me, though of course I am not an expert in this exact field and probably cannot speak with more authority other than to note that your explanation sounds logical. As I mentioned in my last comment, the fact that your semicircle is consistent across a variety of experimental situations, including potentials and even electrolytes, tells me most likely it is intrinsic to your electrode. That means it probably is related to the substrate-film interaction that is constant throughout all those systems, and not related to anything happening between the top film layer and the varying electrolyte or applied conditions, which may be different across tests.
Kindly made one vudeo on GCD as well
We definitely have some plans to make a GCD video in the future. Thank you