Experimental Study of Electrical Properties of Pharmaceutical Materials by Electrical Impedance Spectroscopy
, Wuqiang Yang 2, Marco-A. Rodriguez-Frias 2, Juan-Carlos Olivares-Rojas 1 and Daniel Lorias-Espinoza 3Round 1
Reviewer 1 Report
The manuscript submitted by Vasquez et al. is well written and illustrated.
The concept of the study is interesting. However, the authors have to mention that any equivalent electrical circuits (EEC) should be explained by physical-chemical reactions and are the consequence of the (electro)chemical kinetics of the system studied. As written, it looks like these EEC are chosen a posteriori to fit the data. Such an approach can lead to many misunderstanding or error in the assignement of the different relaxation frequencies observed.
Thus, it is not clear which process(es) is occuring in such systems (conductivity of the solution, diffusion of the species, electrochemical reactions ?) since 2 R//C elements are used to fit the data. What do they stand for ? C1 can vary from 10-2 to 10-8 F (unit should be mentionned in table 7) and R2 can vary from 1012 to 4 Ω ... Are these values consistent with the dieletric permittivity or resistivity of the medium ? Which capacitance stands for the electrochemical double layer ? If it is C1 then what is C2 and reversely ? Same for R0, R1 and R2.
The choice of the EEC is it consistent with the inflection points observed in Bode-phase plot ?
These points should be discussed and detailed in the text in order to avoid any confusion in the interpretation of the data, and the use of EIS to check the electrical properties of drugs.
Author Response
1) “The authors have to mention that any equivalent electrical circuits (EEC) should be explained by physical-chemical reactions and are the consequence of the (electro) chemical kinetics of the system studied”.
We have edited the manuscript to add section 2.3, which correlates basic models to electrochemical processes.
2) It is not clear which process(es) is occurring in such systems 1(conductivity of the solution, diffusion of the species, electrochemical reactions ?)
The properties of capacity and resistance are two parameters that must be measured in the test liquid since some physical properties depend on the ions or electrons that the material has as carrier charge carrier, so the involved process can be mass transfer and charge. The text has been edited in section 2.3.
3) Unit should be mentioned in table 7.
The units for resistance and capacitance have been included in table 7 according to the recommendation.
4) Since 2 R//C elements are used to fit the data. What do they stand for?
We added section 3.1 to explain the correspondence of each parameter to the processes involved, mainly bulk resistance, interfacial layer, charge transfer and double layer capacitance
5) Are these values consistent with the dielectric permittivity or resistivity of the medium?
The values of R0, is related to the resistivity in the test condition and was mentioned in the text, section 3.1
6) What are C1 then what is C2 and reversely? Same for R0, R1 and R2.
In section 3.1, we present the identification of each parameter and a graphical representation as well as a comparison of the resulting Bode and Nyquist diagram to correlate the effect of the EEC components.
7) The choice of the EEC is it consistent with the inflection points observed in Bode-phase plot?
Also, in section 3.1, we present an example of the manner in which the magnitude and phase components of the EEC model form the frequency response, as well of the resulting frequency response of the overall model (Figure 9).
Author Response File: 
Author Response.docx
Reviewer 2 Report
Please, read the comments in the attached PDF.
Comments for author File: 
Comments.pdf
Author Response
The introduction is too short. Usually the introduction is used to discuss the problem of the investigation (characterization and discrimination of different drug formulations in this case), to introduce the reference methods (as well as innovative techniques presented in literature) used to make such measurements and to discuss how the technique proposed by the authors solves the problems of these other techniques and thus improves the state of the art. Please, revise the introduction by discussing these points.
The manuscript has been edited to support the work in terms of current trends in real-time analysis of electrochemical processes; the text further correlates with the beginning of section 3.1 prior to explaining the identification of EEC components.
2) At lines 56-60 there is the sentence “For instance, Grossi et al. developed a low-cost portable measurement system based on an AD5933 impedance analyzer (Analog Devices) to obtain an EIS spectrum of four saline solutions (NaCl, Na2CO3, K2HPO4 and CuSO4) in a frequency range from 1 kHz up to 100 kHz [4]. The excitation signal (i.e. a sinewave) frequency is varied from a few mHz up
to a few MHz so that the frequency response measurement can be approximated to the test solution”. There are some errors in the sentence: the measurement system is not based on an AD5933 impedance analyzer but the sinewave signal is generated by an AD5932 function generator
and all the signals acquisition and analysis are carried out by the microcontroller (STM32F303); the
frequency range (line 58) is not from 1 kHz to 100 kHz but from 10 Hz to 100 kHz and the spectrum
from 10 Hz to 10 kHz has been used to characterize the solutions; thus (line 59) frequency is not varied from a few mHz up to a few MHz since the frequency range is 10 Hz – 100 kHz.
Thank you for your review. The text has been changed according to the review.
3) In paragraphs 2.4 – 2.5 the state space modelling in the frequency domain is presented and a set of equations have been derived to extract the parameters of the equivalent circuit (array of Voigt elements). I think there is an error in equations 10, 11, 12 (sI+A should be sI-A). Moreover what software has been used to estimate the model parameters? Different software exist (both free and
commercial) that can fit the measured data to an equivalent circuit and thus estimate the parameters without the need for the users to manage the equations of paragraphs 2.4 – 2.5 (for example the free software MEISP).
Thank you for pointing out such mistake. The error in equations 10, 11 and 12 have been corrected. The software used was Matlab for modelling and Excel for graphs. This information has been disclosed at the beginning of section 3. In addition, section 3.1 now acknowledges other methods including software, in particular EIS analyser. We do not mention MEISP, since it appears that it is no longer available.
4) In paragraph 2.6 the measurement setup is presented. The EIS measurements are carried out using a liquid test fixture. Since in paragraph 2.2 the authors discuss how the electrodes geometry plays an important role in the measured spectrum, can the authors provide more information on this liquid test fixture (for example the electrode material, electrode geometry and so on)?
The electrodes geometry is important for the potential distribution in the sample as affects the measurement of the impedance parameters. The information was included in section 2.3.
5) Table 7 presents the extracted parameters for the equivalent electrical circuit for the four different drug formulations. I think the error (or standard deviation) for each parameter must be provided in addition to the average value. Moreover, the authors say that from these values the four drug formulations can be discriminated. What algorithm is used to discriminate the drug formulations? What parameters plays a major role in the discrimination?
Since the %fit is obtained from Akaike Information Criterion, the error figures derived from this analysis are the Mean Squared Error (MSE) and the Final Prediction Error (FPE). Tables 3-7 were edited to include both values (MSE and FPE) for each particular model. In order to determine if the model corresponds to a minimal state-space representation, there must be cero unobservable and uncontrollable states as well as finite Hankel singular value. The manuscript has been edited (after table 6) to explain the procedure giving two examples.
6) I think that the title for section 4 should be “Conclusions” and not “Discussion”.
We agree with reviewer#2, the title for section 4 should be conclusions. The title has been edited according to the recommendation.
7) Please check the manuscript for typos and correct them. For example: at line 179 “spate-space”
should be “state-space”; at line 186 “α=1..φ where φ is the number of poles” but according to equation 21 the parameter α range is from 1 to n; In reference [3] the authors names are “M. Grossi and B. Riccò” and not “M G Riccò and B.”.
The manuscript has been re-edited according to recommendation and the typos have been corrected.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The revised version is suitable for publication.
Author Response
A) Reviewer#2
1) A linear approximation of the Warburg Element (Figure 2C) can also account for the interfacial layer capacitance (CI)”. I do not understand very well this sentence. According to my knowledge, Warburg impedance models the mass transport at low frequency, while the non-ideal characteristics of the interface capacitance are often modelled using a Constant Phase Element (CPE).
We apologise for the misunderstanding. The sentence was part of a paragraph that was omitted by mistake in the previous revision and was intended to reference an example of modelling using only passive components. The manuscript has been corrected to include the missing part of the paragraph which is intended to justify modelling of the CPE and Warburg models using passive components.
2) Lines 79-82: “For instance, Grossi et al. developed a low-cost portable measurement system based on an AD5933 impedance analyser (Analog Devices) to obtain an EIS spectrum of four saline solutions (NaCl, Na2CO3, K2HPO4 and CuSO4) in a frequency range from 10 Hz up to 10 kHz”. The system is not based on AD5933 but the impedance measurements are made by the microcontroller internal ADC. I think it should be better to write “For instance, Grossi et al. developed a low-cost portable measurement system based on a microcontroller to obtain an EIS spectrum of four saline solutions (NaCl, Na2CO3, K2HPO4 and CuSO4) in a frequency range from 10 Hz up to 10 kHz”.
Thank you, the manuscript has been edited according to your recommendation.
3) Fig 5 is present two times.
We edited the manuscript to remove the duplicate reference to Figure 5.
4) In equation 19 the character “=” is present two times.
Thank you for your review. The duplicate equal sign has been deleted
On behalf of the authors I would like to take this opportunity to thank the reviewers for their insightful comments and suggestions, spot-on observations and thorough review of the manuscript.
Author Response File: Author Response.docx
Reviewer 2 Report
The authors have revised the paper according to the reviewers’ comments. I think it can be accepted once the authors make the following minor revisions:
- Lines 144-146: “A linear approximation of the Warburg Element (Figure 2C) can also account for the interfacial layer capacitance (CI)”. I do not understand very well this sentence. According to my knowledge, Warburg impedance models the mass transport at low frequency, while the non-ideal characteristics of the interface capacitance are often modeled using a Constant Phase Element (CPE).
- Lines 79-82: “For instance, Grossi et al. developed a low-cost portable measurement system based on an AD5933 impedance analyser (Analog Devices) to obtain an EIS spectrum of four saline solutions (NaCl, Na2CO3, K2HPO4 and CuSO4) in a frequency range from 10 Hz up to 10 kHz”. The system is not based on AD5933 but the impedance measurements are made by the microcontroller internal ADC. I think it should be better to write “For instance, Grossi et al. developed a low-cost portable measurement system based on a microcontroller to obtain an EIS spectrum of four saline solutions (NaCl, Na2CO3, K2HPO4 and CuSO4) in a frequency range from 10 Hz up to 10 kHz”.
- Fig 5 is present two times.
- In equation 19 the character “=” is present two times.
Author Response
A) Reviewer#2
1) A linear approximation of the Warburg Element (Figure 2C) can also account for the interfacial layer capacitance (CI)”. I do not understand very well this sentence. According to my knowledge, Warburg impedance models the mass transport at low frequency, while the non-ideal characteristics of the interface capacitance are often modelled using a Constant Phase Element (CPE).
We apologise for the misunderstanding. The sentence was part of a paragraph that was omitted by mistake in the previous revision and was intended to reference an example of modelling using only passive components. The manuscript has been corrected to include the missing part of the paragraph which is intended to justify modelling of the CPE and Warburg models using passive components.
2) Lines 79-82: “For instance, Grossi et al. developed a low-cost portable measurement system based on an AD5933 impedance analyser (Analog Devices) to obtain an EIS spectrum of four saline solutions (NaCl, Na2CO3, K2HPO4 and CuSO4) in a frequency range from 10 Hz up to 10 kHz”. The system is not based on AD5933 but the impedance measurements are made by the microcontroller internal ADC. I think it should be better to write “For instance, Grossi et al. developed a low-cost portable measurement system based on a microcontroller to obtain an EIS spectrum of four saline solutions (NaCl, Na2CO3, K2HPO4 and CuSO4) in a frequency range from 10 Hz up to 10 kHz”.
Thank you, the manuscript has been edited according to your recommendation.
3) Fig 5 is present two times.
We edited the manuscript to remove the duplicate reference to Figure 5.
4) In equation 19 the character “=” is present two times.
Thank you for your review. The duplicate equal sign has been deleted
On behalf of the authors I would like to take this opportunity to thank the reviewers for their insightful comments and suggestions, spot-on observations and thorough review of the manuscript.
Author Response File: Author Response.docx
