Anomalous Humidity Dependence in Photoacoustic Spectroscopy of CO Explained by Kinetic Cooling

Round 1

Reviewer 1 Report

In this manuscript, the authors reported on a study of the influnce of water vapour on carbon oxide relaxation rate. This arguments is surely of interestefor the applide Scinece community readers and should be accpeted for publication once few minor revisions/suggestions taht follow have been considered.  

Page 1, Line 30: recently it has been shown that oxygen can act as a quencher for the non-radiative relaxation of certain molecules, therefore I would suggest rephrasing the sentence or eliminate the reference to oxygen. Page 1, Line 38: authors should include a recent reference on CO detection with QEPAS where dry and wet mixtures have been investigated ( S. Li, et al. Anal. Chem. 91, 5834-5840 (2019)). Page 1, Line 40: “was observed previously”, please add any references. Page 2, Line 77: the authors claim to have used a laser that emits 45 mW (Page 2, Line 64), assuming that the transmittivity of windows and lenses is about 95%, how is it possible that the power has almost halved? Please explain Page 3, Line 107: for the normalization of the QEPAS signal to be physically consistent it is necessary to be sure that there is a linear dependence of the signal on the target gas concentration. It is therefore appropriate to show a calibration curve or insert information about linearity in the text. Page 4, Line 141; Is it possible to quantify the Q-factor variation from the water concentration? The dependence of the quality factor on pressure is well known in the literature, instead it would be appropriate to spend few words on the dependence of the quality factor on the water concentration. Page 6, Equation 5: the meaning of the symbols ↑ and ↓ is not explained in the text, please provide. In case the symbol ↑ represents the excitation of a molecule and its passage from ground state to excited state there is a problem with the signs in the formula: the promotion of a molecule from ground state to excited state makes the terms and positive, therefore these two terms must agree in the rate equation. Page 6, Equation 7a: see comments on Equation 5. Page 6, Equation 8a: see comments on Equation 5. Page 8, Line 249: How was the phase calculated from the knowledge of H? Please add the explicit form of or rephrase to make the concept clearer. Page 8, Line 252. Please add references. Page 8, Line 261, Ref. 25 refer to standard photoacoustic technique, here a reference related to the influence of pressure on the QTF Q-factor should be used (see e.g., P. Patimisco et al., App. Phys. Rev. 5, 011106 (2018)). Page 9, Line 296: The kinetic cooling effect is typical of non-radiative de-excitations, the photothermal detection is based on the variation of power incident on the detector following direct absorption. The two physical phenomena are different. Please explain how the model could be used for photothermal detection or delete the comment.

Author Response

The authors would like to thank the reviewer for his/her review of our submission and gratefully acknowledge the positive and constructive remarks. Please find our point-to-point replies to your comments below. All changes to the original text are clearly marked in the revised manuscript and in this document.

 

 

Page 1, Line 30: recently it has been shown that oxygen can act as a quencher for the non-radiative relaxation of certain molecules, therefore I would suggest rephrasing the sentence or eliminate the reference to oxygen.

 

We agree that the statement in Line 30 did not account for exceptions to this generally true argument. In fact, the near resonant V-V transfer between CO and N₂ is one of these exceptions. We therefore slightly changed the sentence to clearly indicate that what is described is only the more common situation:

 

“Water is an efficient quencher that facilitates the conversion of vibrational energy of other molecules into heat much more rapidly than other collision partners, such as N₂ or O₂, typically would.”

 

We want to point out, however, the important difference between the non-radiative relaxation of a molecule (here CO), which is what the reviewer’s comment refers to, and the release of heat, which is discussed in line 30. Resonant V-V transfer, e.g. to O₂ or N₂, will lead to the relaxation of a molecule (here CO), but the vibrational energy will not be released as heat in the process. The transfer from the second molecule’s vibration to translational degrees of freedom may take a long time, as is the case in this manuscript for N₂.

 

Page 1, Line 38: authors should include a recent reference on CO detection with QEPAS where dry and wet mixtures have been investigated ( S. Li, et al. Anal. Chem. 91, 5834-5840 (2019)).

 

Although one spectrum of a dry sample and one of a wet sample are shown in the reference suggested by the reviewer, no continuous trend of QEPAS signal versus humidity is provided. Therefore, the reference does not support the statement made in line 38 and we did not include it. Also, the relevant Figure 4 in the suggested reference might be misleading to the readership since, according to the data and results we discuss in our manuscript, the sign of the two spectra (dry and wet CO in N2) should be inverted, in contrast to Figure 4 in the reference. Although it is not discussed in the reference, we assume the phase of the lock-in detection was changed between the two measurements in the reference.

However, we found that references [3,4] in line 38 were not listed in the references section and we included the correct references that clearly show the discussed trend of QEPAS signal with humidity. We apologize for this flaw!

 

Page 1, Line 40: “was observed previously”, please add any references.

 

References [3,4] provide the necessary data, we included them in line 40.

 

Page 2, Line 77: the authors claim to have used a laser that emits 45 mW (Page 2, Line 64), assuming that the transmittivity of windows and lenses is about 95%, how is it possible that the power has almost halved?

 

The high losses originate from additional optical elements in the beam path (lenses, mirrors, half-wave plate and polarizer) that were used for another experiment (see Ref [26]) and left in place for convenience. These elements neither affected the experiments shown in this manuscript in any way nor served any function in the context of this work.

To avoid confusion and since the power originally emitted by the QCL is irrelevant, we removed the statement about the laser emitting 45 mW in line 64:

“A distributed feedback quantum cascade laser (DFB-QCL, Adtech Optics) was operated in continuous wave mode at a wavenumber of 2179.77 cm^‑1.”

 

Please explain Page 3, Line 107: for the normalization of the QEPAS signal to be physically consistent it is necessary to be sure that there is a linear dependence of the signal on the target gas concentration. It is therefore appropriate to show a calibration curve or insert information about linearity in the text.

 

The absorbance from CO for the experimental conditions is approximately 5x10^-3 for a pathlength of 5 cm through the gas volume. At this low absorbance, both 2f-WMS and QEPAS signals scale linearly with absorbance and sample concentration. While no calibration was performed together with the experiments for this manuscript, it was shown previously, using the same t-shaped tuning fork and acoustic detection module used in this study, that QEPAS signals scale linearly with concentration [1]. The reference [1] was added in line 78. Also, the optical intensity during experiments puts them in a linear regime without optical saturation. We appreciate the concerns of the reviewer about normalization and linearity, but consider the linearity of QEPAS signals with concentration, within the given concentration range, certain and common place and hence decided not to add further comments on this topic to the manuscript.

[1] Giglio, M.; Elefante, A.; Patimisco, P.; Sampaolo, A.; Sgobba, F.; Rossmadl, H.; Mackowiak, V.; Wu, H.; Tittel, F.K.; Dong, L.; et al. Quartz-enhanced photoacoustic sensor for ethylene detection implementing optimized custom tuning fork-based spectrophone. Opt. Express 2019, 27, 4271.

 

Page 4, Line 141; Is it possible to quantify the Q-factor variation from the water concentration? The dependence of the quality factor on pressure is well known in the literature, instead it would be appropriate to spend few words on the dependence of the quality factor on the water concentration.

 

As suggested by reviewer 3, we included a graph showing the quality factor and resonance tuning fork plotted versus humidity in the supplementary information and referenced to this data in the main text.

 

Page 6, Equation 5: the meaning of the symbols ↑ and ↓ is not explained in the text, please provide. In case the symbol ↑ represents the excitation of a molecule and its passage from ground state to excited state there is a problem with the signs in the formula: the promotion of a molecule from ground state to excited state makes the terms and positive, therefore these two terms must agree in the rate equation.

 

A clear explanation of the symbols in equation 5 was added to line 193.

The signs in front of the summands in equation 5 only account for the fact that the rates for CO and CO* must have opposite sign. The excitation of CO makes the rate for CO (first summand in equation 5) negative (see also equation 10). The additional negative sign in equation 5 yields a positive contribution to the rate for CO*. On the contrary, the second summand in equation 5 represents a rate of CO* and must hence be of equal sign as the left hand side that is also a rate for CO*.

 

Page 6, Equation 7a: see comments on Equation 5.

 

See previous answer. In equations 7a, the first and last summand refer to rates of N*, which is the same species as on the left hand side of the equation, hence positive sign, while the second summand refers to a rate for the number density of CO*, therefore the negative sign.

 

Page 6, Equation 8a: see comments on Equation 5.

 

See previous answer. In equations 8a, the last summand refers to a rate of H₂O*, which is the same species as on the left hand side of the equation, hence positive sign, while the first two summands refers to rates for the number densities of CO* and N₂*, therefore the negative sign.

 

Page 8, Line 249: How was the phase calculated from the knowledge of H? Please add the explicit form of or rephrase to make the concept clearer.

 

Equation 12, together with equation 10, describes the excitation of CO vs time, which, together with the kinetic model and equation 9, yields H(t). The Fourier transform of H(t) at 2f_mod yields a complex value, and the phase of this complex number is plotted in Figure 4. In this way, the phase is calculated with respect to the excitation given by equations 12 and 10.

In line 248, the term “complex amplitude” might have been misleading towards an amplitude only (without a phase). Therefore we rephrased this term to “complex valued heat”.

 

Page 8, Line 252. Please add references.

 

In Line 252, we included a reference to Table 1.

 

Page 8, Line 261, Ref. 25 refer to standard photoacoustic technique, here a reference related to the influence of pressure on the QTF Q-factor should be used (see e.g., P. Patimisco et al., App. Phys. Rev. 5, 011106 (2018)).

 

In line 261, the acoustic quality factor of the resonator tubes, rather than the Q-factor of the tuning fork, is discussed. Unfortunately, we are not aware of a report on the acoustic quality factor of resonator tubes as used in QEPAS, and therefore included a reference that discusses this issue for the standard photoacoustic technique.

Note that, based on a suggestion of reviewer 3, we added the measured Q-factor of the tuning fork versus pressure in the electronic supporting material.

 

Page 9, Line 296: The kinetic cooling effect is typical of non-radiative de-excitations, the photothermal detection is based on the variation of power incident on the detector following direct absorption. The two physical phenomena are different. Please explain how the model could be used for photothermal detection or delete the comment.

 

We disagree with the reviewer’s description of the principal of photothermal detection. As the name suggests, photothermal detection senses changes in the temperature of a sample in response to optical absorption and consecutive thermal dissipation of the absorbed energy (i.e., it detects H(t), divided by the heat capacity of the sample). To clarify this, we added a reference to a paper on “Fabry-Perot photothermal interferometry. To us, the definition given by the reviewer rather seems to fit direct absorption, such as TLAS.

 

Reviewer 2 Report

PAS has been successfully applied in detection of trace gas concentrations and monitoring of a wide variety of applications, such as environmental monitoring, industrial process control, combustion processes and detection of toxic and flammable gases.

Since generation of a photoacoustic waves involves the energy transfer from internal to translational molecular degrees of freedom the subject of the paper is timely and should be of interest for a broad audience of researchers and practitioners.

The paper develops the kinetic model for collisional relaxation of CO in N2 and H2O that quantitatively explains the humidity dependence of photoacoustic signals from CO as measured in PAS and QEPAS experiments. The comparison of simulations with experimental data validates the model.  The model can be adapted to include other collision partners in ambient measurements. The presented model provides better understanding of the relaxation dynamics of CO and may be used to further improve photoacoustic trace gas sensors.

Paper is well written and properly referenced. It should be published as it stands.

Author Response

The authors kindly thank the reviewer for the positive assessment and her/his appreciation of the relevance and scope of the manuscript.

Reviewer 3 Report

The topic and work presented in this paper is sound and worth publishing after minor revisions.

The reviewer advises the authors adding one or two additional references to support the statements of line 40 and 41. Only references where the PAS signal minimum at low humidity’s for CO were presented.

Reference 11 may describe the gas mixing system in all details but it is quite complicated to access, and therefore the reviewer was unable to check this fact within the given deadline for the review process. From the reviewers point of view details about the specifications of the used MFC’s like maximum flux and uncertainties are mandatory information that have to be included in the paper. The authors may consider providing a detailed description of their setup within the electronic support material.

From line 107 to 113 the authors described their CO concentration correction procedure. The reviewer wants to know why an inline CO concentration check was not performed, as changes in humidity caused changes in the CO concentration? Measurements with and without correction may be interesting for the scientific community and may be provided in the supplementary files.

Figure 2 shows the main experimental result in this work, unfortunately the authors lack to provide the temperature during the measurement, please add this in the text as well in the figure caption. 2 vol. % water in air is extremely closed to the maximum relative humidity @ 20°C and my cause those s-shapes at high humidity’s. As the resonant frequency f_QTF and the Q factor are effected by the humidity the authors may consider to include two additional graphs showing those values over humidity. The reviewer strongly recommends including those graphs in the supplementary files.

Author Response

The authors would like to thank the reviewer for his/her review of our submission and gratefully acknowledge the positive and constructive remarks. Please find our point-to-point replies to your comments below. All changes to the original text are clearly marked in the revised manuscript and in this document.

 

The reviewer advises the authors adding one or two additional references to support the statements of line 40 and 41. Only references where the PAS signal minimum at low humidity’s for CO were presented.

Looking at the references given, we found that references [3,4] in line 38 were not listed in the references section and we included the correct references that clearly show the discussed trend of QEPAS signal with humidity. We apologize for this flaw! Also, these two references are cited again in line 40.

Reference 11 may describe the gas mixing system in all details but it is quite complicated to access, and therefore the reviewer was unable to check this fact within the given deadline for the review process. From the reviewers point of view details about the specifications of the used MFC’s like maximum flux and uncertainties are mandatory information that have to be included in the paper. The authors may consider providing a detailed description of their setup within the electronic support material.

We included more details on the used MFCs and gas mixing rig to the electronic supporting information and referenced to the ESI in line 96 of the manuscript.

From line 107 to 113 the authors described their CO concentration correction procedure. The reviewer wants to know why an inline CO concentration check was not performed, as changes in humidity caused changes in the CO concentration? Measurements with and without correction may be interesting for the scientific community and may be provided in the supplementary files.

An inline concentration measurement might have been feasible using a standard FTIR spectrometer or 2f-WMS. Since measurement runs (i.e. stepped humidity profiles) were, however, highly reproducible (less than 2 % relative deviation between repeated measurement runs), there would have been no significant difference between an inline measurement and sequential measurements with repeated humidity profiles. For convenience, we therefore chose sequential measurements and corrected for changes in CO concentration with humidity this way.

Figure 2 shows the main experimental result in this work, unfortunately the authors lack to provide the temperature during the measurement, please add this in the text as well in the figure caption. 2 vol. % water in air is extremely closed to the maximum relative humidity @ 20°C and my cause those s-shapes at high humidity’s.

We included the gas temperature of 23 °C in the caption of Figure 2. At this temperature, the saturation concentration is 2.7 %_V. As described in the experimental section, the actual humidity that was applied to the acoustic detection module was measured by transmission FTIR spectroscopy to prevent errors on the x-axis of Figure 2 that might originate from partial condensation.

As the resonant frequency f_QTF and the Q factor are effected by the humidity the authors may consider to include two additional graphs showing those values over humidity. The reviewer strongly recommends including those graphs in the supplementary files.

We included the data in the electronic supporting information and referenced to this data in line 143 of the main text.