the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Nov 2025
Static-Gradient NMR imaging for Depth-Resolved Molecular Diffusion in Amorphous Regions in Semicrystalline PTFE Film
Abstract. Understanding spatially heterogeneous molecular diffusion in semicrystalline polymers is critical for elucidating interfacial dynamics in soft materials. This study employs static-gradient nuclear magnetic resonance (NMR) imaging to capture depth-resolved translational motion of polymer chains in a polytetrafluoroethylene (PTFE) film. By focusing on spin–spin relaxation behavior in amorphous regions near crystalline lamellae, we identify multiple diffusion regimes consistent with Bloch–Torrey analysis. The results reveal that molecular mobility at the substrate interface is significantly constrained, likely due to interfacial pinning, while the air-side surface shows signs of enhanced mobility. Our findings highlight the utility of static-field-gradient NMR for probing nanoscale dynamical heterogeneity in semicrystalline systems.
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RC1: 'Comment on mr-2025-14', Anonymous Referee #1, 16 Nov 2025
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AC1: 'Reply on RC1', Naoki Asakawa, 17 Nov 2025
We would like to thank Referee 1 for their review and for their positive feedback regarding the publication of our manuscript.
Citation: https://doi.org/10.5194/mr-2025-14-AC1
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AC1: 'Reply on RC1', Naoki Asakawa, 17 Nov 2025
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RC2: 'Comment on mr-2025-14', Anonymous Referee #2, 17 Nov 2025
In this manuscript the motion of molecules constituting a PTFE film attached to a supporting substrate is analyzed with depth resolution across the film thickness by an intriguing unilateral NMR relaxometry technique. I am intrigued by the authors’ approach and like to see that work being published. Yet I do have questions and suggestions:
- Upon reading the manuscript while unfamiliar with the authors’ prior work, it took quite a bit of reading to understand what is meant by “substrate interface”. Perhaps the authors could mention in the abstract (or early in the introduction) “…. of a poytetrafluoroethylene (PTFE) film immobilized on a glass substrate.”
- P 1, line 20. What about a reference to P.T. Callaghan, Translational Motion and Magnetic Resonance, Oxford University Press, Oxford, 2011?
- What is the number-averaged degree of polymerization? I have trouble visualizing the translational motion of the molecules. Is it reptation of linear polymer chains? What distances do the chain segments cover? How does the diffusive distance compare to the average size of the amorphous domains? Does the film have a lamellar morphology or is its morphology better described by the para-crystallinity model? Can you relate your findings to the chain motion in solid polyethylene (K. Schmidt-Rohr, H.W. Spiess, Chain diffusion between crystalline and amorphous regions in polyethylene detected by 2D exchange carbon-13 NMR, Macromolecules 1991) or to the free volume in the amorphous domains? How has the film been prepared?
- P 3, lines 79–83. These sentences are difficult to understand: “The interplay between static magnetic field gradient and external static field effectively compensates for the insufficient magnetic field strength to generate NMR signals. Consequently, a spatial region at which the magnetic field intensity reaches the required threshold for the onset of nuclear magnetic resonance (NMR), referred to as the excited volume, is established (see Fig. 1(a)).” My understanding is that the nuclear spins are exited in a way similar to slice-selective excitation in MRI within a volume defined by orthogonal components of the B1 field and the B0 field resulting from the superposition of the fields from the ferromagnet and the electromagnet with a flip angle depending on the resonance off-set.
- Figure 1. It would help to identify BNd and Be in the figure. In the caption the second sentence could be rewritten as “The shape of the excited volume, determined by the …..”.
- P 4, Experimental setup and Fig. 1. I seem to understand that the angle between B1 and the effective B0 varies with depth into the film. Is that variation negligible or does it require readjustment of the nominal flip angle at each depth?
- Figure 2. The labels b) and c) do not match the caption.
- P 6, line 125. “Based on the experimental findings presented above, we hypothesize that the variation in the dependence of R2 on increasing tau arises from differences in the translational diffusion effects.“ Can you exclude, that the tau dependence is not due to the spin-lock effect and you are not probing relaxation in the rotating frame? How does the pulse width compare to t?
- P 7, line 132. Reference is made to the z-axis of a two-dimensional xy plot in Fig. 4a. Would it not be simpler to write “The contribution of diffusion to the spin-spin relaxation rate R2 is color coded”?
- Figure 4b. Would it be possible to support the interpretation of the echo attenuation with realistic numbers for the diffusion coefficient and diffusion distances?
- P 7, line 143. “This behavior of R2 arises from its intrinsic modification instead of the diffusion process.” What do you mean by intrinsic modification of the polymer film? Do you mean differences in polymer morphology between surface and film interior?
- P 9, line 171. “This behavior can be attributed to the system transitioning between the localization and motional averaging regimes, triggered by the change in tau as shown in Fig. 4(a).“: How can the system (I assume you mean the polymer film) react to a pulse-sequence parameter like tau? A better way of writing may be “The observed behavior can be attributed to a transition of the observable from the localization regime to the averaging regime with increasing tau“.
- P 9, line 84. Reference is made to Fig. 4c. I cannot find Fig. 4c.
- P 10, line 216. “the regime transition occurs at a smaller ˜D near the diffusion barrier where the magnetic field gradient is substantial“: Are the diffusion barriers the surface and the substrate interface of the film or the crystalline regions embedding the amorphous regions in the polymer? Why is the magnetic field gradient substantial near the diffusion barrier as opposed to regions away from it? How big is the gradient?
Citation: https://doi.org/10.5194/mr-2025-14-RC2 -
AC2: 'Reply on RC2', Naoki Asakawa, 19 Nov 2025
First of all, we would like to express our sincere gratitude for reviewing our manuscript(mr-2025-14)).
We sincerely appreciate Reviewer #2's thorough reading of our manuscript and their positive assessment of its potential contribution to Magnetic Resonance. Below we provide point-by-point responses to all comments raised.
Reviewer comment:
Upon reading the manuscript while unfamiliar with the authors's prior work, it took quite a bit of reading to understand what is meant by ``substrate interface". Perhaps the authors could mention in the abstract (or early in the introduction) ``.... of a poytetrafluoroethylene (PTFE) film immobilized on a glass substrate."Response:
We thank Reviewer #2 for highlighting the ambiguity in the term ``substrate interface." In the present study, the PTFE film is affixed to a glass substrate using an epoxy resin layer; therefore, ``substrate interface" specifically denotes the PTFE/epoxy-resin interface.
Reviewer comment:
P 1, line 20. What about a reference to P.T. Callaghan, Translational Motion and Magnetic Resonance, Oxford University Press, Oxford, 2011?Response:
We appreciate Reviewer #2's suggestion. The previously cited 1984 article by P. T. Callaghan has been replaced with a citation to the recommended monograph.
Reviewer comment:
What is the number-averaged degree of polymerization? I have trouble visualizing the translational motion of the molecules. Is it reptation of linear polymer chains? What distances do the chain segments cover? How does the diffusive distance compare to the average size of the amorphous domains? Does the film have a lamellar morphology or is its morphology better described by the para-crystallinity model? Can you relate your findings to the chain motion in solid polyethylene (K. Schmidt-Rohr, H.W. Spiess, Macromolecules 1991) or to the free volume in the amorphous domains? How has the film been prepared?Response:
Because PTFE exhibits an ultrahigh melt viscosity, conventional methods for molecular-weight determination such as melt rheology or gel-permeation chromatography are not applicable. Consequently, we did not measure the molecular weight of our samples and used the commercial PTFE film as received. Industrial PTFE is generally known to possess molecular weights on the order of several million. Although the surface morphology of semicrystalline PTFE is not yet fully established, AFM studies (e.g., V. Korolkov, NANOscientific Magazine, 21 (2021)) report a multiscale hierarchical surface structure. At the ~100 um scale, large domains (~20 um) interconnected by rope-like features are observed. At higher spatial resolution (~100 nm), highly oriented crystalline regions presumably lamellae on the order of ~100 nm are separated by amorphous regions of several tens of nanometers. In our study, the characteristic distance between diffusion barriers, L_s, is therefore presumed to be on the order of several tens of nanometers. However, our technique does not allow direct determination of L_s or the effective spin packet length L_g, because the effective magnetic-field gradient contains a significant but unknown local component arising from the intrinsic magnetic-susceptibility variations of the PTFE sample.We appreciate Reviewer #2's suggestion regarding comparisons with polyethylene; however, for brevity and clarity, we restrict the discussion to PTFE.
From above discussion, we added the following sentences in Appendix C in the revised manuscript.
Revised text:
``Although the surface morphology of semicrystalline PTFE is not yet fully established, AFM study has reported a multiscale hierarchical surface structure. At the ~100 um scale, large domains (~20 um) interconnected by rope-like features are observed. At higher spatial resolution (~100 nm), highly oriented crystalline regions presumably lamellae on the order of ~100\ nm are separated by amorphous regions of several tens of nanometers. In our study, the characteristic distance between diffusion barriers, L_s, is therefore presumed to be on the order of several tens of nanometers. However, our technique does not allow direct determination of L_s or the effective spin packet length L_g, because the effective magnetic-field gradient contains a significant but unknown local component arising from the intrinsic magnetic-susceptibility variations of the PTFE sample."
Reviewer comment:
P 3, lines 79-83. These sentences are difficult to understand: ``The interplay between static magnetic field gradient and external static field effectively compensates for the insufficient magnetic field strength to generate NMR signals. Consequently, a spatial region at which the magnetic field intensity reaches the required threshold for the onset of nuclear magnetic resonance (NMR), referred to as the excited volume, is established (see Fig. 1(a))." My understanding is that the nuclear spins are exited in a way similar to slice-selective excitation in MRI within a volume defined by orthogonal components of the $B_1$ field and the $B_0$ field resulting from the superposition of the fields from the ferromagnet and the electromagnet with a flip angle depending on the resonance off-set.
Response:
We sincerely thank the reviewer for identifying this ambiguity and welcome the opportunity to clarify the underlying concept. The reviewer interpreted the ``excited volume" as being generated by a slice-selective RF excitation mechanism analogous to conventional MRI, where orthogonal components of B_0 and B_1 determine the spatial excitation profile. However, our intended meaning differs fundamentally, and we acknowledge that our original phrasing did not adequately convey this distinction. In our experimental configuration (Fig. 1(a)), the static magnetic field B_0 exhibits a strong spatial dependence due to the superposition of the fields from the needle-like ferromagnet and the electromagnet. This leads to a pronounced magnetic-field gradient along the sample. Although the electromagnet alone does not produce a uniform field of sufficient magnitude for NMR detection, the combined field distribution yields a narrow spatial region in which the local field strength satisfies the resonance condition corresponding to the fixed excitation frequency employed in the experiment. Crucially, this region is not produced by RF slice-selection. Rather, it represents the locus of points at which the static resonance condition\gamma B_0 r = 2 \pi \nu_0
is fulfilled. Only nuclear spins within this resonant field contour contribute to the detected signal. Our use of the term "excited volume" therefore refers solely to a region defined by the static-field topology, independent of the spatial characteristics of the RF field B_1.
To prevent further misunderstanding, we have revised the manuscript text as follows:Revised text:
``In the proposed geometry, the static magnetic field is highly inhomogeneous owing to the superposition of the fields from the ferromagnet and the electromagnet (Fig. 1(a)). Although the external electromagnet alone does not supply a sufficiently strong uniform field for NMR detection, the composite field distribution creates a narrow spatial region in which the local magnetic-field magnitude matches the resonance condition for the applied excitation frequency. Only spins within this region contribute to the observed NMR signal. We therefore define this region -- determined exclusively by the static field distribution rather than by RF slice selection as the resonant (or NMR-active) volume."
Reviewer comment:
Figure 1. It would help to identify BNd and Be in the figure. In the caption the second sentence could be rewritten as ``The shape of the excited volume, determined by the ...".Response:
In accordance with Reviewer #2's suggestion, we have revised Figure 1 and its caption to explicitly identify B_Nd and B_e, and updated the second sentence accordingly.
Reviewer comment:
P 4, Experimental setup and Fig. 1. I seem to understand that the angle between B_1 and the effective B_0 varies with depth into the film. Is that variation negligible or does it require readjustment of the nominal flip angle at each depth?Response:
We thank Reviewer #2 for raising this point. At the current proof-of-concept stage of the method, we neglect the depth-dependent variation of the angle between B_1 and the effective B_0. However, future developments may require adjustment of the nominal flip angle as a function of depth, potentially enabling a novel form of ``quantization-axis imaging."
Reviewer comment:
Figure 2. The labels b) and c) do not match the caption.Response:
We thank Reviewer #2 for pointing this out. The labels for panels (b) and (c) in Figure 2 have been corrected.Reviewer comment:
P 6, line 125. ``Based on the experimental findings presented above, we hypothesize that the variation in the dependence of R2 on increasing tau arises from differences in the translational diffusion effects." Can you exclude, that the tau dependence is not due to the spin-lock effect and you are not probing relaxation in the rotating frame? How does the pulse width compare to t?Response:
In our CPMG measurements, we employed nominal 90 pulses with tau = 20-50 us. As demonstrated in Fig. A1, CPMG echoes up to at most 10th order, and in some cases higher were detected, and the pulse width is sufficiently short relative to t. We therefore consider spin-locking effects to be negligible under our experimental conditions.
Reviewer comment:
P 7, line 132. Reference is made to the z-axis of a two-dimensional xy plot in Fig. 4a. Would it not be simpler to write ``The contribution of diffusion to the spin-spin relaxation rate R_2 is color coded?"Response:
We appreciate the reviewer's suggestion and have revised the caption accordingly:
``The contribution of diffusion to the spin-spin relaxation rate R_2 is color-coded (Panel (a)), where the relaxation exponent of the CPMG echo intensity M(2n\tau) (for n=1) is plotted as a function of the dimensionless diffusion coefficient (or dimensionless echo time) and position within the sample."
Reviewer comment:
Figure 4b. Would it be possible to support the interpretation of the echo attenuation with realistic numbers for the diffusion coefficient and diffusion distances?Response:
This is an important question. Unfortunately, the diffusion coefficient D, the effective magnetic-field gradient G, and the characteristic distance between diffusion barriers L_s are interdependent. Knowledge of any one parameter is required to determine the remaining two. Consequently, we cannot presently assign realistic numerical values for both the diffusion coefficient and diffusion distance simultaneously. Nonetheless, the method allows qualitative probing of diffusive behavior.
Reviewer comment:
P 7, line 143. ``This behavior of R_2 arises from its intrinsic modification instead of the diffusion process." What do you mean by intrinsic modification of the polymer film? Do you mean differences in polymer morphology between surface and film interior?Response:
We apologize for the ambiguous wording in the original manuscript. The reviewer's interpretation is correct: the observed difference in R_2 between the surface and the interior of the film originates from intrinsic variations in the local polymer morphology rather than from differences in diffusion.We added the following sentence at the related paragraph.
Revised Text:
``The observed difference in R_2 between the surface and the interior of the film originates from intrinsic variations in the local polymer morphology rather than from differences in diffusion."
Reviewer comment:
P 9, line 171. ``This behavior can be attributed to the system transitioning between the localization and motional averaging regimes, triggered by the change in tau as shown in Fig. 4(a).": How can the system (I assume you mean the polymer film) react to a pulse-sequence parameter like tau? A better way of writing may be ``The observed behavior can be attributed to a transition of the observable from the localization regime to the averaging regime with increasing tau".Response:
We are grateful for this suggestion and have revised the manuscript accordingly.Reviewer comment:
P 9, line 84. Reference is made to Fig. 4c. I cannot find Fig. 4c.Response:
We thank Reviewer #2 for noting this inconsistency. The reference to Fig. 4c corresponds to the inset of the tau = 20 us data in Fig. 3.
Reviewer comment:
P 10, line 216. ``the regime transition occurs at a smaller tilde{D} near the diffusion barrier where the magnetic field gradient is substantial": Are the diffusion barriers the surface and the substrate interface of the film or the crystalline regions embedding the amorphous regions in the polymer? Why is the magnetic field gradient substantial near the diffusion barrier as opposed to regions away from it? How big is the gradient?Response:
We appreciate Reviewer #2's insightful question. Diffusion barriers may correspond either to the film surfaces and the substrate interface or to crystalline regions surrounding the amorphous domains. In such regions, magnetic-susceptibility contrast is generally larger than in the homogeneous interior of the film. Larger susceptibility contrasts are known to generate stronger local magnetic-field gradients. However, quantifying the magnitude of these gradients is challenging, because determining R_2 in regions with very large gradients is difficult due to rapid signal attenuation that hampers echo detection.Citation: https://doi.org/10.5194/mr-2025-14-AC2 -
RC3: 'Reply on AC2', Anonymous Referee #2, 19 Nov 2025
Thank you for your explanations and answering my questions.
- Concerning the CPMG parameters, it would be helpful to state not only the values of tau (is that the echo time of half the echo time?) in the manuscript but also the pulse width.
- To my understanding your description of the excited volume, or the volume, where the signal comes from is incomplete. As far as I see, the resultant static magnetic field of your setup is highly inhomogeneous, i. e., it is so inhomogeneous, that every finite-length rf pulse, is a selective pulse. Hürlimann calls such fields ‘grossly inhomogeneous’ (Hürlimann & Griffin, JMR 143 (2000) 120; Zielinski & Sen, JMR 164 (2003) 145) as opposed to weakly inhomogeneous fields, in which the rf pulse excites all spins in the sample. In the resonance condition, which defines the extent of that volume, only the components of B0 and B1 enter which are orthogonal to each other. Moreover, the magnetization is rotated around the effective field with a flip angle which depends on the resonance offset. This is the concept of slice selection in MRI, which to my understanding equally well applies to your setup. Only the spins within this volume can contribute to the detected signal. Do I misunderstand your setup? How else would you get the spatial resolution other than by locally selective excitation and detection?
Citation: https://doi.org/10.5194/mr-2025-14-RC3 -
AC3: 'Reply on RC3', Naoki Asakawa, 21 Nov 2025
We appreciate Reviewer #2's constructive and insightful comments.
Below, we provide our detailed responses to the questions raised by the reviewer.Reviewer comment:
"Concerning the CPMG parameters, it would be helpful to state not only the values of tau (is that the echo time or half the echo time?) in the manuscript but also the pulse width."Response:
We thank the reviewer for this helpful suggestion. We have revised the second paragraph of Results and Discussion section to clearly state that tau denotes the delay between the 90 degree pulse and the subsequent 180 degree pulse, i.e., half of the echo time in the standard CPMG sequence. We have also added the RF intensity of the nominal 90 degree pulses used in our measurements.Reviewer comment (summary):
"The manuscript seems to understate the influence of the RF field on selective excitation. In a grossly inhomogeneous field, every finite-length RF pulse is selective. How does your method obtain spatial resolution if not through selective excitation and detection?"Response:
We appreciate the reviewer's insightful remarks. Our original explanation--that the RF field does not influence the formation of the NMR-active slice--as indeed not entirely accurate. As the reviewer correctly notes, in a grossly inhomogeneous static field, any finite-length RF pulse inevitably produces frequency-selective excitation, and thus the RF field contributes to the excitation profile to some extent.
But, when the magnetic field from electromagnet is stepped, spins that newly satisfy resonant condition become strongly excited and produce the majority of the detected echo peak. In contrast, spins that remain far off-resonance after the field step contribute only negligibly, because their transverse magnetization is strongly suppressed by the large resonance offset.
Thus, while RF-induced slice selectivity does exist in principle, its contribution is minor compared with the overwhelming effect of the movement of the static on-resonance region. We have revised the manuscript to clearly reflect this corrected understanding and to provide a more accurate explanation of how spatial selectivity arises in our method.
We added the following sentences in the revised manuscript:In the proposed geometry, the static magnetic field is highly inhomogeneous owing to the superposition of the fields from the ferromagnet and the electromagnet (Fig. 1(a)). Although the external electromagnet alone does not supply a sufficiently strong uniform field for NMR detection, the composite field distribution creates a narrow spatial region in which the local magnetic-field magnitude matches the resonance condition for the applied excitation frequency. Only spins within this region contribute to the observed NMR signal. We therefore define this region--determined dominantly by the static field distribution rather than by RF slice selection as the resonant (or NMR-active) volume. Of course, in a grossly inhomogeneous static field(Huerlimann and Griffin (2000)), any finite-length RF pulse inevitably produces frequency-selective excitation, and thus the RF field contributes to the excitation profile to some extent. But, when the magnetic field from electromagnet is stepped, spins that newly satisfy resonant condition become strongly excited and produce the majority of the detected echo peak. In contrast, spins that remain far off-resonance after the field step contribute only negligibly, because their transverse magnetization is strongly suppressed by the large resonance offset. Thus, while RF-induced slice selectivity does exist in principle, its contribution is minor compared with the overwhelming effect of the movement of the static on-resonance region.
Citation: https://doi.org/10.5194/mr-2025-14-AC3 -
RC4: 'Reply on AC3', Anonymous Referee #2, 21 Nov 2025
Essentially you are moving a selective volume along an extended object. The same situation is in encountered in well-logging NMR albeit on different scales. This type of 1D imaging works because of the inherent combination of selectivity and movement of the selective volume, and one is not more important than the other. I think your revised paragraph does not get to the point.
Citation: https://doi.org/10.5194/mr-2025-14-RC4 -
AC4: 'Reply on RC4', Naoki Asakawa, 21 Nov 2025
We would like to thank Reviewer #2 for the helpful comment.
We think that we now understand the reviewer's point.Reviewer comment:
``Essentially you are moving a selective volume along an extended object. The same situation is encountered in well-logging NMR albeit on different scales. This type of 1D imaging works because of the inherent combination of selectivity and movement of the selective volume, and one is not more important than the other. I think your revised paragraph does not get to the point."
Response:
We thank the reviewer for this insightful comment. We agree that our one-dimensional MRI method relies on the combined effects of (i) spatially selective excitation and (ii) controlled displacement of the selective excitation volume, both of which are essential for obtaining depth-resolved information from the film sample. Following the reviewer's suggestion, we have substantially revised the relevant paragraph in the manuscript to clearly articulate this point.
In our method, the carrier frequency of the RF pulse is fixed, and a spatially selective excitation is generated using an RF amplitude of nominal 50 kHz under a static magnetic-field gradient. Because the excitation frequency is constant, the spatial position of the NMR-active slice is uniquely determined by the local magnetic field. By incrementally varying the static magnetic field, we modify the effective magnetic-field gradient experienced by the sample. This results in a shift of the spatial position that corresponds to the fixed excitation frequency, so that the NMR-active slice is translated along the film-thickness direction. Repeating this process allows us to sweep the selective volume across the entire film thickness and reconstruct a one-dimensional MRI profile.
We have clarified in the revised manuscript (the first paragraph in Section 2.1 Principle of depth profiling) that this mechanism indeed parallels the principle used in well-logging NMR, where the sensitive volume is translated through the medium by altering the magnetic-field configuration. We believe this revision directly addresses the reviewer's concern and makes the imaging principle more transparent to readers.
Revised text:
``In our one-dimensional MRI approach, we fix the resonance frequency and apply a spatially selective RF pulse with an RF field strength of nominal 50 kHz. This pulse excites nuclear spins only within a narrow slice (the NMR-active slice), whose spatial position is defined by the static field gradient at the chosen resonance frequency. By incrementally varying the static magnetic field, the effective field gradient experienced by the sample changes, and consequently, the position of the NMR-active slice is shifted along the thickness direction of the membrane. This procedure enables one-dimensional imaging along the sample depth without the need for frequency-swept selective excitation or gradient switching during RF irradiation.A similar principle--distance encoding realized by the translation of a spatially selective sensitive volume--has long been employed in well-logging NMR(¥cite{hurlimann2000spin}). Our method shares the same fundamental mechanism: the imaging contrast arises from the interplay between a localized excitation region and its systematic displacement through the sample. This conceptual parallel underscores the validity of our approach and places it within the broader class of 1D imaging methods that rely on spatial selectivity and controlled volume movement."
Citation: https://doi.org/10.5194/mr-2025-14-AC4 -
RC5: 'Reply on AC4', Anonymous Referee #2, 21 Nov 2025
Thank you. Now we are on the same page, and I have no further comments.
Citation: https://doi.org/10.5194/mr-2025-14-RC5
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RC5: 'Reply on AC4', Anonymous Referee #2, 21 Nov 2025
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AC4: 'Reply on RC4', Naoki Asakawa, 21 Nov 2025
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RC4: 'Reply on AC3', Anonymous Referee #2, 21 Nov 2025
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RC3: 'Reply on AC2', Anonymous Referee #2, 19 Nov 2025
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RC6: 'Comment on mr-2025-14', Anonymous Referee #2, 23 Nov 2025
Dear Authors,
Another review of your manuscript has been received, which I forward to you here:
General Comments
This is an interesting manuscript that ultimately deserves publication but there are number of issues that need correcting or rectified.
Specific Comments
Although years ago many authors, including myself, used the abbreviation PFG NMR for NMR diffusion measurements, it should be noted that pulsed field gradients could be merely being used for coherence selection. Consequently, it is better to use the expression pulsed gradient spin echo (PGSE) NMR, since a spin echo is necessarily sensitive to diffusion.
The last paragraph on page 1 talks about the issues with using PFG (i.e., PGSE) NMR to study solids and the first paragraph on page 2 discusses the various static field gradient (SFG) methodologies available. Then somewhat out of place, the next paragraph starts by stating that despite the advances in PFG methods they are still not suited for solid-state applications. The contents of these chapters need to be reordered.
Page 2, line 40. “Additionally, the abrupt shifts … can lead to prolonged dead times in the magnetic resonance signal …”. This seems confused – at least in how it is written. It is not that there is no signal, it is that the signal is scrambled by eddy currents and other effects and so one needs to wait a sufficient amount of time for these to decay before you can acquire a useful signal.
Page 2, line 44. I am not sure that there are too many logistical burdens. Few would attempt to move a superconducting magnet on field.
Page 2, line 47. I assume that the authors are referring to SFG systems when they mention “independently controllable”?
Page 2, line 69. CPMG should have been defined here (i.e., the first occurrence) and not on Page 5 line 105 or Page 14 line 282 with the references (move these to page 2 as well).
Page 3, line 81. I am a little mystified by comment “reaches the required threshold for the onset of nuclear magnetic resonance”. My point is that everywhere is resonating to some degree (e.g., the Earth’s Magnetic field is about 50 μT). Do the authors mean resonating in a particular frequency range?
Page 4, Fig. 1. Please define “NAS”.
Page 7, line 132. “…diffusion is not in progress…”? Do you mean “diffusion is not measurable because of the short τ”? But diffusion is always occurring.
Page 11, line 232. Please give a reference for the “Landweber iteration method”.
1
Typographical CorrecƟons
The manuscript has many typographical errors that detract from the manuscript.
Many references run against the previous word (e.g., page 1, line 11”viscoelasticity(Keddie et al.”)). This type of error is throughout the manuscript.
There is a mysterious “8” in the middle of the text on line 34 on page 2.
“NMR” was defined on page 1, there is no need to redefine it on page 3 line 83. Indeed, given the journal that this manuscript has been submitted to it is doubtful that NMR needs to be defined at all.
Page 6, line 177. “… no variations present in R2 near …” sounds odd. How about “… no variations in R2 are present near …”
Page 8, Fig. 4. Some of the variables in the axes labels should be italicised.
Page 9, line 3. Instead of “when τ = 20 μs was held constant”, did the authors mean “when τ was set to 20 μs”?
Page 10, line 194. It is a small point and I know that “rotational motion” is in common usage (so there is no need to change), but “rotational” implies rotating about one axis, whereas the molecules are tumbling and so to me “reorientational” seems more appropriate.
Page 13, line 247. Boembergen → Bloembergen
Citation: https://doi.org/10.5194/mr-2025-14-RC6 -
AC5: 'Reply on RC6', Naoki Asakawa, 01 Dec 2025
Dear Editor,
we would like to express our sincere gratitude for reviewing our manuscript(mr-2025-14)).
We sincerely appreciate Reviewer's thorough reading of our manuscript and their positive assessment of its potential contribution to Magnetic Resonance. Below we provide point-by-point responses to all comments raised.Reviewer comment:
Although years ago many authors, including myself, used the abbreviation PFG NMR for NMR diffusion measurements, it should be noted that pulsed field gradients could be merely being used for coherence selection. Consequently, it is better to use the expression pulsed gradient spin echo (PGSE) NMR, since a spin echo is necessarily sensitive to diffusion.Response:
We would like to thank the reviewer for the comment. We revised our manuscript in line with the comment.Reviewer comment:
The last paragraph on page 1 talks about the issues with using PFG (i.e., PGSE) NMR to study solids and the first paragraph on page 2 discusses the various static field gradient (SFG) methodologies available. Then somewhat out of place, the next paragraph starts by stating that despite the advances in PFG methods they are still not suited for solid-state applications. The contents of these chapters need to be reordered.Response:
We appreciate the reviewer's comment on the readability of Introduction. We rewrote the Introduction part to gain the readability.Reviewer comment:
Page 2, line 40. “Additionally, the abrupt shifts … can lead to prolonged dead times in the magnetic resonance signal …”. This seems confused – at least in how it is written. It is not that there is no signal, it is that the signal is scrambled by eddy currents and other effects and so one needs to wait a sufficient amount of time for these to decay before you can acquire a useful signal.Response:
We thank the reviewer again for their comment. We replace the sentence in original manuscript to the following.Revised text:
"Because eddy currents distort the NMR signal, it is necessary to wait an adequate period for their decay prior to acquiring a reliable measurement."Reviewer comment:
Page 2, line 44. I am not sure that there are too many logistical burdens. Few would attempt to move a superconducting magnet on field.Response:
The reviewer's point is valid once a superconducting magnet has been installed. However, we believe that the effort required up to the point of installation is far from negligible, and our comment refers to the burdens associated with the installation and decommissioning processes.Reviewer comment:
Page 2, line 47. I assume that the authors are referring to SFG systems when they mention “independently controllable”?Response:
We are afraid that the reviewer’s assumption is not correct. Even in SFG-based methods, such as the SFF technique, changing the resonance frequency requires repositioning the detector coil or the sample, and at the same time the magnitude of the field gradient inevitably changes. In the case of the STRAFI method, the resonance frequency is essentially fixed; however, altering the static magnetic field strength would require redesigning the geometry of the GarFIELD magnet. Therefore, variable-frequency measurements under a constant magnetic-field gradient—i.e., with identical spatial resolution—are not feasible.
The ability to independently vary the static field strength and the field-gradient strength is essential for imaging spectral density functions, and the development of such techniques is highly desired. We consider the method presented in this study to be one such approach.Reviewer comment:
Page 2, line 69. CPMG should have been defined here (i.e., the first occurrence) and not on Page 5 line 105 or Page 14 line 282 with the references (move these to page 2 as well).Response:
We would like to thank the reviewer again. We revised our manuscript in line with the comment.Reviewer comment:
Page 3, line 81. I am a little mystified by comment “reaches the required threshold for the onset of nuclear magnetic resonance”. My point is that everywhere is resonating to some degree (e.g., the Earth’s Magnetic field is about 50 μT). Do the authors mean resonating in a particular frequency range?Response:
Thank you for drawing our attention to this important point. Our intention was to refer specifically to a particular range of resonance frequencies. We have completely rewritten the relevant paragraph, and we believe this revision resolves the reviewer’s concerns.
Reviewer comment:
Page 4, Fig. 1. Please define “NAS”.Response:
We would like to thank the reviewer for their comment. We have completely rewritten the caption of Fig. 1. In doing so, we explicitly clarified the original term behind the abbreviation “NAS,” namely “NMR-active slice.”Revised Text:
The revised figure caption is the following:"Figure 1. In our one-dimensional MRI approach, the resonance frequency was fixed and a spatially selective RF pulse with an RF field strength of nominal 50 kHz were applied. This pulse excites nuclear spins only within a narrow slice (the NMR-active slice;NAS), whose spatial position is defined by the static field gradient at the chosen resonance frequency. By incrementally varying the static magnetic field, the effective field gradient experienced by the sample changes, and consequently, the position of the NAS is shifted along the thickness direction of the membrane. The combined effect of the magnetic field generated by the needle-like ferromagnet, BNd, and the static magnetic field from the electromagnet, Be gives rise to tha mechanism of movement of NMR active slice."
Reviewer comment:
Page 7, line 132. “…diffusion is not in progress…”? Do you mean “diffusion is not measurable because of the short τ”? But diffusion is always occurring.Response:
We did not mean to suggest that diffusion cannot be measured because τ is short; rather, our intention was to indicate that when τ is short, the spins have not yet reached the diffusion barrier and therefore undergo free diffusion.Revised text:
"When the echo time τ is short, and the spins have not yet reached the diffusion barrier and therefore undergo free diffusion. Therefore, spins remain within the short-time regime."Revier comment:
Page 11, line 232. Please give a reference for the “Landweber iteration method”.Response:
We added four references for the Landweber iteration method.Typographical Corrections
Reviewer comment:
Many references run against the previous word (e.g., page 1, line 11”viscoelasticity(Keddie et al.”)). This type of error is throughout the manuscript.Response:
We revised our manuscript in line with the comment.Reviewer comment:
There is a mysterious “8” in the middle of the text on line 34 on page 2.Response:
We omitted the mysterious "8".Reviewer comment:
“NMR” was defined on page 1, there is no need to redefine it on page 3 line 83. Indeed, given the journal that this manuscript has been submitted to it is doubtful that NMR needs to be defined at all.Response:
We revised our manuscript in accordance with the comment, except for the first occurrence of the term “NMR.”Reviewer comment:
Page 6, line 177. “… no variations present in R2 near …” sounds odd. How about “… no variations in R2 are present near …”Response:
We revised our manuscript in line with the reviewer's suggestion.
Reviewer comment:
Page 8, Fig. 4. Some of the variables in the axes labels should be italicised.Response:
We redrew Fig.4 in line with the reviewer's suggestion.Reviewer comment:
Page 9, line 3. Instead of “when τ = 20 μs was held constant”, did the authors mean “when τ was set to 20 μs”?Response:
The reviewer's comment is correct. We revised our manuscript in line with the reviewer's suggestion.
Reviewer comment:
Page 10, line 194. It is a small point and I know that “rotational motion” is in common usage (so there is no need to change), but “rotational” implies rotating about one axis, whereas the molecules are tumbling and so to me “reorientational” seems more appropriate.Response:
We would like to thank the reviewer for their helpful comment. We have revised the text by adding “reorientation” alongside “rotational.”Reviewer comment:
Page 13, line 247. Boembergen → BloembergenResponse:
We would like to thank again for the comment. We corrected the missspelling of "Bloembergen."Citation: https://doi.org/10.5194/mr-2025-14-AC5 -
EC1: 'Reply on AC5', Geoffrey Bodenhausen, 02 Dec 2025
The paper is now ready to go into production.
Many thanks to authors and reviewers
Geoffrey Bodenhausen
Citation: https://doi.org/10.5194/mr-2025-14-EC1
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EC1: 'Reply on AC5', Geoffrey Bodenhausen, 02 Dec 2025
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AC5: 'Reply on RC6', Naoki Asakawa, 01 Dec 2025
Status: closed
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RC1: 'Comment on mr-2025-14', Anonymous Referee #1, 16 Nov 2025
This is very nice work showing an innovative way of assessing (measuring?) diffusion in solid films, by generating a strong magnetic field gradient with a ferromagnetic needle in a one-sided surface NMR measurement. The excited valume is shifted by sweeping the field. The effective spin–spin relaxation rate is mapped vs. depth. The tau-dependence can help isolating diffusion from relaxation and a qualitative linkage to three diffusional regimes is reported. Simulations support the conclusions that these regimes could be separated. This appears to be a fine paper and I support publication in its current form.
Citation: https://doi.org/10.5194/mr-2025-14-RC1 -
AC1: 'Reply on RC1', Naoki Asakawa, 17 Nov 2025
We would like to thank Referee 1 for their review and for their positive feedback regarding the publication of our manuscript.
Citation: https://doi.org/10.5194/mr-2025-14-AC1
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AC1: 'Reply on RC1', Naoki Asakawa, 17 Nov 2025
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RC2: 'Comment on mr-2025-14', Anonymous Referee #2, 17 Nov 2025
In this manuscript the motion of molecules constituting a PTFE film attached to a supporting substrate is analyzed with depth resolution across the film thickness by an intriguing unilateral NMR relaxometry technique. I am intrigued by the authors’ approach and like to see that work being published. Yet I do have questions and suggestions:
- Upon reading the manuscript while unfamiliar with the authors’ prior work, it took quite a bit of reading to understand what is meant by “substrate interface”. Perhaps the authors could mention in the abstract (or early in the introduction) “…. of a poytetrafluoroethylene (PTFE) film immobilized on a glass substrate.”
- P 1, line 20. What about a reference to P.T. Callaghan, Translational Motion and Magnetic Resonance, Oxford University Press, Oxford, 2011?
- What is the number-averaged degree of polymerization? I have trouble visualizing the translational motion of the molecules. Is it reptation of linear polymer chains? What distances do the chain segments cover? How does the diffusive distance compare to the average size of the amorphous domains? Does the film have a lamellar morphology or is its morphology better described by the para-crystallinity model? Can you relate your findings to the chain motion in solid polyethylene (K. Schmidt-Rohr, H.W. Spiess, Chain diffusion between crystalline and amorphous regions in polyethylene detected by 2D exchange carbon-13 NMR, Macromolecules 1991) or to the free volume in the amorphous domains? How has the film been prepared?
- P 3, lines 79–83. These sentences are difficult to understand: “The interplay between static magnetic field gradient and external static field effectively compensates for the insufficient magnetic field strength to generate NMR signals. Consequently, a spatial region at which the magnetic field intensity reaches the required threshold for the onset of nuclear magnetic resonance (NMR), referred to as the excited volume, is established (see Fig. 1(a)).” My understanding is that the nuclear spins are exited in a way similar to slice-selective excitation in MRI within a volume defined by orthogonal components of the B1 field and the B0 field resulting from the superposition of the fields from the ferromagnet and the electromagnet with a flip angle depending on the resonance off-set.
- Figure 1. It would help to identify BNd and Be in the figure. In the caption the second sentence could be rewritten as “The shape of the excited volume, determined by the …..”.
- P 4, Experimental setup and Fig. 1. I seem to understand that the angle between B1 and the effective B0 varies with depth into the film. Is that variation negligible or does it require readjustment of the nominal flip angle at each depth?
- Figure 2. The labels b) and c) do not match the caption.
- P 6, line 125. “Based on the experimental findings presented above, we hypothesize that the variation in the dependence of R2 on increasing tau arises from differences in the translational diffusion effects.“ Can you exclude, that the tau dependence is not due to the spin-lock effect and you are not probing relaxation in the rotating frame? How does the pulse width compare to t?
- P 7, line 132. Reference is made to the z-axis of a two-dimensional xy plot in Fig. 4a. Would it not be simpler to write “The contribution of diffusion to the spin-spin relaxation rate R2 is color coded”?
- Figure 4b. Would it be possible to support the interpretation of the echo attenuation with realistic numbers for the diffusion coefficient and diffusion distances?
- P 7, line 143. “This behavior of R2 arises from its intrinsic modification instead of the diffusion process.” What do you mean by intrinsic modification of the polymer film? Do you mean differences in polymer morphology between surface and film interior?
- P 9, line 171. “This behavior can be attributed to the system transitioning between the localization and motional averaging regimes, triggered by the change in tau as shown in Fig. 4(a).“: How can the system (I assume you mean the polymer film) react to a pulse-sequence parameter like tau? A better way of writing may be “The observed behavior can be attributed to a transition of the observable from the localization regime to the averaging regime with increasing tau“.
- P 9, line 84. Reference is made to Fig. 4c. I cannot find Fig. 4c.
- P 10, line 216. “the regime transition occurs at a smaller ˜D near the diffusion barrier where the magnetic field gradient is substantial“: Are the diffusion barriers the surface and the substrate interface of the film or the crystalline regions embedding the amorphous regions in the polymer? Why is the magnetic field gradient substantial near the diffusion barrier as opposed to regions away from it? How big is the gradient?
Citation: https://doi.org/10.5194/mr-2025-14-RC2 -
AC2: 'Reply on RC2', Naoki Asakawa, 19 Nov 2025
First of all, we would like to express our sincere gratitude for reviewing our manuscript(mr-2025-14)).
We sincerely appreciate Reviewer #2's thorough reading of our manuscript and their positive assessment of its potential contribution to Magnetic Resonance. Below we provide point-by-point responses to all comments raised.
Reviewer comment:
Upon reading the manuscript while unfamiliar with the authors's prior work, it took quite a bit of reading to understand what is meant by ``substrate interface". Perhaps the authors could mention in the abstract (or early in the introduction) ``.... of a poytetrafluoroethylene (PTFE) film immobilized on a glass substrate."Response:
We thank Reviewer #2 for highlighting the ambiguity in the term ``substrate interface." In the present study, the PTFE film is affixed to a glass substrate using an epoxy resin layer; therefore, ``substrate interface" specifically denotes the PTFE/epoxy-resin interface.
Reviewer comment:
P 1, line 20. What about a reference to P.T. Callaghan, Translational Motion and Magnetic Resonance, Oxford University Press, Oxford, 2011?Response:
We appreciate Reviewer #2's suggestion. The previously cited 1984 article by P. T. Callaghan has been replaced with a citation to the recommended monograph.
Reviewer comment:
What is the number-averaged degree of polymerization? I have trouble visualizing the translational motion of the molecules. Is it reptation of linear polymer chains? What distances do the chain segments cover? How does the diffusive distance compare to the average size of the amorphous domains? Does the film have a lamellar morphology or is its morphology better described by the para-crystallinity model? Can you relate your findings to the chain motion in solid polyethylene (K. Schmidt-Rohr, H.W. Spiess, Macromolecules 1991) or to the free volume in the amorphous domains? How has the film been prepared?Response:
Because PTFE exhibits an ultrahigh melt viscosity, conventional methods for molecular-weight determination such as melt rheology or gel-permeation chromatography are not applicable. Consequently, we did not measure the molecular weight of our samples and used the commercial PTFE film as received. Industrial PTFE is generally known to possess molecular weights on the order of several million. Although the surface morphology of semicrystalline PTFE is not yet fully established, AFM studies (e.g., V. Korolkov, NANOscientific Magazine, 21 (2021)) report a multiscale hierarchical surface structure. At the ~100 um scale, large domains (~20 um) interconnected by rope-like features are observed. At higher spatial resolution (~100 nm), highly oriented crystalline regions presumably lamellae on the order of ~100 nm are separated by amorphous regions of several tens of nanometers. In our study, the characteristic distance between diffusion barriers, L_s, is therefore presumed to be on the order of several tens of nanometers. However, our technique does not allow direct determination of L_s or the effective spin packet length L_g, because the effective magnetic-field gradient contains a significant but unknown local component arising from the intrinsic magnetic-susceptibility variations of the PTFE sample.We appreciate Reviewer #2's suggestion regarding comparisons with polyethylene; however, for brevity and clarity, we restrict the discussion to PTFE.
From above discussion, we added the following sentences in Appendix C in the revised manuscript.
Revised text:
``Although the surface morphology of semicrystalline PTFE is not yet fully established, AFM study has reported a multiscale hierarchical surface structure. At the ~100 um scale, large domains (~20 um) interconnected by rope-like features are observed. At higher spatial resolution (~100 nm), highly oriented crystalline regions presumably lamellae on the order of ~100\ nm are separated by amorphous regions of several tens of nanometers. In our study, the characteristic distance between diffusion barriers, L_s, is therefore presumed to be on the order of several tens of nanometers. However, our technique does not allow direct determination of L_s or the effective spin packet length L_g, because the effective magnetic-field gradient contains a significant but unknown local component arising from the intrinsic magnetic-susceptibility variations of the PTFE sample."
Reviewer comment:
P 3, lines 79-83. These sentences are difficult to understand: ``The interplay between static magnetic field gradient and external static field effectively compensates for the insufficient magnetic field strength to generate NMR signals. Consequently, a spatial region at which the magnetic field intensity reaches the required threshold for the onset of nuclear magnetic resonance (NMR), referred to as the excited volume, is established (see Fig. 1(a))." My understanding is that the nuclear spins are exited in a way similar to slice-selective excitation in MRI within a volume defined by orthogonal components of the $B_1$ field and the $B_0$ field resulting from the superposition of the fields from the ferromagnet and the electromagnet with a flip angle depending on the resonance off-set.
Response:
We sincerely thank the reviewer for identifying this ambiguity and welcome the opportunity to clarify the underlying concept. The reviewer interpreted the ``excited volume" as being generated by a slice-selective RF excitation mechanism analogous to conventional MRI, where orthogonal components of B_0 and B_1 determine the spatial excitation profile. However, our intended meaning differs fundamentally, and we acknowledge that our original phrasing did not adequately convey this distinction. In our experimental configuration (Fig. 1(a)), the static magnetic field B_0 exhibits a strong spatial dependence due to the superposition of the fields from the needle-like ferromagnet and the electromagnet. This leads to a pronounced magnetic-field gradient along the sample. Although the electromagnet alone does not produce a uniform field of sufficient magnitude for NMR detection, the combined field distribution yields a narrow spatial region in which the local field strength satisfies the resonance condition corresponding to the fixed excitation frequency employed in the experiment. Crucially, this region is not produced by RF slice-selection. Rather, it represents the locus of points at which the static resonance condition\gamma B_0 r = 2 \pi \nu_0
is fulfilled. Only nuclear spins within this resonant field contour contribute to the detected signal. Our use of the term "excited volume" therefore refers solely to a region defined by the static-field topology, independent of the spatial characteristics of the RF field B_1.
To prevent further misunderstanding, we have revised the manuscript text as follows:Revised text:
``In the proposed geometry, the static magnetic field is highly inhomogeneous owing to the superposition of the fields from the ferromagnet and the electromagnet (Fig. 1(a)). Although the external electromagnet alone does not supply a sufficiently strong uniform field for NMR detection, the composite field distribution creates a narrow spatial region in which the local magnetic-field magnitude matches the resonance condition for the applied excitation frequency. Only spins within this region contribute to the observed NMR signal. We therefore define this region -- determined exclusively by the static field distribution rather than by RF slice selection as the resonant (or NMR-active) volume."
Reviewer comment:
Figure 1. It would help to identify BNd and Be in the figure. In the caption the second sentence could be rewritten as ``The shape of the excited volume, determined by the ...".Response:
In accordance with Reviewer #2's suggestion, we have revised Figure 1 and its caption to explicitly identify B_Nd and B_e, and updated the second sentence accordingly.
Reviewer comment:
P 4, Experimental setup and Fig. 1. I seem to understand that the angle between B_1 and the effective B_0 varies with depth into the film. Is that variation negligible or does it require readjustment of the nominal flip angle at each depth?Response:
We thank Reviewer #2 for raising this point. At the current proof-of-concept stage of the method, we neglect the depth-dependent variation of the angle between B_1 and the effective B_0. However, future developments may require adjustment of the nominal flip angle as a function of depth, potentially enabling a novel form of ``quantization-axis imaging."
Reviewer comment:
Figure 2. The labels b) and c) do not match the caption.Response:
We thank Reviewer #2 for pointing this out. The labels for panels (b) and (c) in Figure 2 have been corrected.Reviewer comment:
P 6, line 125. ``Based on the experimental findings presented above, we hypothesize that the variation in the dependence of R2 on increasing tau arises from differences in the translational diffusion effects." Can you exclude, that the tau dependence is not due to the spin-lock effect and you are not probing relaxation in the rotating frame? How does the pulse width compare to t?Response:
In our CPMG measurements, we employed nominal 90 pulses with tau = 20-50 us. As demonstrated in Fig. A1, CPMG echoes up to at most 10th order, and in some cases higher were detected, and the pulse width is sufficiently short relative to t. We therefore consider spin-locking effects to be negligible under our experimental conditions.
Reviewer comment:
P 7, line 132. Reference is made to the z-axis of a two-dimensional xy plot in Fig. 4a. Would it not be simpler to write ``The contribution of diffusion to the spin-spin relaxation rate R_2 is color coded?"Response:
We appreciate the reviewer's suggestion and have revised the caption accordingly:
``The contribution of diffusion to the spin-spin relaxation rate R_2 is color-coded (Panel (a)), where the relaxation exponent of the CPMG echo intensity M(2n\tau) (for n=1) is plotted as a function of the dimensionless diffusion coefficient (or dimensionless echo time) and position within the sample."
Reviewer comment:
Figure 4b. Would it be possible to support the interpretation of the echo attenuation with realistic numbers for the diffusion coefficient and diffusion distances?Response:
This is an important question. Unfortunately, the diffusion coefficient D, the effective magnetic-field gradient G, and the characteristic distance between diffusion barriers L_s are interdependent. Knowledge of any one parameter is required to determine the remaining two. Consequently, we cannot presently assign realistic numerical values for both the diffusion coefficient and diffusion distance simultaneously. Nonetheless, the method allows qualitative probing of diffusive behavior.
Reviewer comment:
P 7, line 143. ``This behavior of R_2 arises from its intrinsic modification instead of the diffusion process." What do you mean by intrinsic modification of the polymer film? Do you mean differences in polymer morphology between surface and film interior?Response:
We apologize for the ambiguous wording in the original manuscript. The reviewer's interpretation is correct: the observed difference in R_2 between the surface and the interior of the film originates from intrinsic variations in the local polymer morphology rather than from differences in diffusion.We added the following sentence at the related paragraph.
Revised Text:
``The observed difference in R_2 between the surface and the interior of the film originates from intrinsic variations in the local polymer morphology rather than from differences in diffusion."
Reviewer comment:
P 9, line 171. ``This behavior can be attributed to the system transitioning between the localization and motional averaging regimes, triggered by the change in tau as shown in Fig. 4(a).": How can the system (I assume you mean the polymer film) react to a pulse-sequence parameter like tau? A better way of writing may be ``The observed behavior can be attributed to a transition of the observable from the localization regime to the averaging regime with increasing tau".Response:
We are grateful for this suggestion and have revised the manuscript accordingly.Reviewer comment:
P 9, line 84. Reference is made to Fig. 4c. I cannot find Fig. 4c.Response:
We thank Reviewer #2 for noting this inconsistency. The reference to Fig. 4c corresponds to the inset of the tau = 20 us data in Fig. 3.
Reviewer comment:
P 10, line 216. ``the regime transition occurs at a smaller tilde{D} near the diffusion barrier where the magnetic field gradient is substantial": Are the diffusion barriers the surface and the substrate interface of the film or the crystalline regions embedding the amorphous regions in the polymer? Why is the magnetic field gradient substantial near the diffusion barrier as opposed to regions away from it? How big is the gradient?Response:
We appreciate Reviewer #2's insightful question. Diffusion barriers may correspond either to the film surfaces and the substrate interface or to crystalline regions surrounding the amorphous domains. In such regions, magnetic-susceptibility contrast is generally larger than in the homogeneous interior of the film. Larger susceptibility contrasts are known to generate stronger local magnetic-field gradients. However, quantifying the magnitude of these gradients is challenging, because determining R_2 in regions with very large gradients is difficult due to rapid signal attenuation that hampers echo detection.Citation: https://doi.org/10.5194/mr-2025-14-AC2 -
RC3: 'Reply on AC2', Anonymous Referee #2, 19 Nov 2025
Thank you for your explanations and answering my questions.
- Concerning the CPMG parameters, it would be helpful to state not only the values of tau (is that the echo time of half the echo time?) in the manuscript but also the pulse width.
- To my understanding your description of the excited volume, or the volume, where the signal comes from is incomplete. As far as I see, the resultant static magnetic field of your setup is highly inhomogeneous, i. e., it is so inhomogeneous, that every finite-length rf pulse, is a selective pulse. Hürlimann calls such fields ‘grossly inhomogeneous’ (Hürlimann & Griffin, JMR 143 (2000) 120; Zielinski & Sen, JMR 164 (2003) 145) as opposed to weakly inhomogeneous fields, in which the rf pulse excites all spins in the sample. In the resonance condition, which defines the extent of that volume, only the components of B0 and B1 enter which are orthogonal to each other. Moreover, the magnetization is rotated around the effective field with a flip angle which depends on the resonance offset. This is the concept of slice selection in MRI, which to my understanding equally well applies to your setup. Only the spins within this volume can contribute to the detected signal. Do I misunderstand your setup? How else would you get the spatial resolution other than by locally selective excitation and detection?
Citation: https://doi.org/10.5194/mr-2025-14-RC3 -
AC3: 'Reply on RC3', Naoki Asakawa, 21 Nov 2025
We appreciate Reviewer #2's constructive and insightful comments.
Below, we provide our detailed responses to the questions raised by the reviewer.Reviewer comment:
"Concerning the CPMG parameters, it would be helpful to state not only the values of tau (is that the echo time or half the echo time?) in the manuscript but also the pulse width."Response:
We thank the reviewer for this helpful suggestion. We have revised the second paragraph of Results and Discussion section to clearly state that tau denotes the delay between the 90 degree pulse and the subsequent 180 degree pulse, i.e., half of the echo time in the standard CPMG sequence. We have also added the RF intensity of the nominal 90 degree pulses used in our measurements.Reviewer comment (summary):
"The manuscript seems to understate the influence of the RF field on selective excitation. In a grossly inhomogeneous field, every finite-length RF pulse is selective. How does your method obtain spatial resolution if not through selective excitation and detection?"Response:
We appreciate the reviewer's insightful remarks. Our original explanation--that the RF field does not influence the formation of the NMR-active slice--as indeed not entirely accurate. As the reviewer correctly notes, in a grossly inhomogeneous static field, any finite-length RF pulse inevitably produces frequency-selective excitation, and thus the RF field contributes to the excitation profile to some extent.
But, when the magnetic field from electromagnet is stepped, spins that newly satisfy resonant condition become strongly excited and produce the majority of the detected echo peak. In contrast, spins that remain far off-resonance after the field step contribute only negligibly, because their transverse magnetization is strongly suppressed by the large resonance offset.
Thus, while RF-induced slice selectivity does exist in principle, its contribution is minor compared with the overwhelming effect of the movement of the static on-resonance region. We have revised the manuscript to clearly reflect this corrected understanding and to provide a more accurate explanation of how spatial selectivity arises in our method.
We added the following sentences in the revised manuscript:In the proposed geometry, the static magnetic field is highly inhomogeneous owing to the superposition of the fields from the ferromagnet and the electromagnet (Fig. 1(a)). Although the external electromagnet alone does not supply a sufficiently strong uniform field for NMR detection, the composite field distribution creates a narrow spatial region in which the local magnetic-field magnitude matches the resonance condition for the applied excitation frequency. Only spins within this region contribute to the observed NMR signal. We therefore define this region--determined dominantly by the static field distribution rather than by RF slice selection as the resonant (or NMR-active) volume. Of course, in a grossly inhomogeneous static field(Huerlimann and Griffin (2000)), any finite-length RF pulse inevitably produces frequency-selective excitation, and thus the RF field contributes to the excitation profile to some extent. But, when the magnetic field from electromagnet is stepped, spins that newly satisfy resonant condition become strongly excited and produce the majority of the detected echo peak. In contrast, spins that remain far off-resonance after the field step contribute only negligibly, because their transverse magnetization is strongly suppressed by the large resonance offset. Thus, while RF-induced slice selectivity does exist in principle, its contribution is minor compared with the overwhelming effect of the movement of the static on-resonance region.
Citation: https://doi.org/10.5194/mr-2025-14-AC3 -
RC4: 'Reply on AC3', Anonymous Referee #2, 21 Nov 2025
Essentially you are moving a selective volume along an extended object. The same situation is in encountered in well-logging NMR albeit on different scales. This type of 1D imaging works because of the inherent combination of selectivity and movement of the selective volume, and one is not more important than the other. I think your revised paragraph does not get to the point.
Citation: https://doi.org/10.5194/mr-2025-14-RC4 -
AC4: 'Reply on RC4', Naoki Asakawa, 21 Nov 2025
We would like to thank Reviewer #2 for the helpful comment.
We think that we now understand the reviewer's point.Reviewer comment:
``Essentially you are moving a selective volume along an extended object. The same situation is encountered in well-logging NMR albeit on different scales. This type of 1D imaging works because of the inherent combination of selectivity and movement of the selective volume, and one is not more important than the other. I think your revised paragraph does not get to the point."
Response:
We thank the reviewer for this insightful comment. We agree that our one-dimensional MRI method relies on the combined effects of (i) spatially selective excitation and (ii) controlled displacement of the selective excitation volume, both of which are essential for obtaining depth-resolved information from the film sample. Following the reviewer's suggestion, we have substantially revised the relevant paragraph in the manuscript to clearly articulate this point.
In our method, the carrier frequency of the RF pulse is fixed, and a spatially selective excitation is generated using an RF amplitude of nominal 50 kHz under a static magnetic-field gradient. Because the excitation frequency is constant, the spatial position of the NMR-active slice is uniquely determined by the local magnetic field. By incrementally varying the static magnetic field, we modify the effective magnetic-field gradient experienced by the sample. This results in a shift of the spatial position that corresponds to the fixed excitation frequency, so that the NMR-active slice is translated along the film-thickness direction. Repeating this process allows us to sweep the selective volume across the entire film thickness and reconstruct a one-dimensional MRI profile.
We have clarified in the revised manuscript (the first paragraph in Section 2.1 Principle of depth profiling) that this mechanism indeed parallels the principle used in well-logging NMR, where the sensitive volume is translated through the medium by altering the magnetic-field configuration. We believe this revision directly addresses the reviewer's concern and makes the imaging principle more transparent to readers.
Revised text:
``In our one-dimensional MRI approach, we fix the resonance frequency and apply a spatially selective RF pulse with an RF field strength of nominal 50 kHz. This pulse excites nuclear spins only within a narrow slice (the NMR-active slice), whose spatial position is defined by the static field gradient at the chosen resonance frequency. By incrementally varying the static magnetic field, the effective field gradient experienced by the sample changes, and consequently, the position of the NMR-active slice is shifted along the thickness direction of the membrane. This procedure enables one-dimensional imaging along the sample depth without the need for frequency-swept selective excitation or gradient switching during RF irradiation.A similar principle--distance encoding realized by the translation of a spatially selective sensitive volume--has long been employed in well-logging NMR(¥cite{hurlimann2000spin}). Our method shares the same fundamental mechanism: the imaging contrast arises from the interplay between a localized excitation region and its systematic displacement through the sample. This conceptual parallel underscores the validity of our approach and places it within the broader class of 1D imaging methods that rely on spatial selectivity and controlled volume movement."
Citation: https://doi.org/10.5194/mr-2025-14-AC4 -
RC5: 'Reply on AC4', Anonymous Referee #2, 21 Nov 2025
Thank you. Now we are on the same page, and I have no further comments.
Citation: https://doi.org/10.5194/mr-2025-14-RC5
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RC5: 'Reply on AC4', Anonymous Referee #2, 21 Nov 2025
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AC4: 'Reply on RC4', Naoki Asakawa, 21 Nov 2025
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RC4: 'Reply on AC3', Anonymous Referee #2, 21 Nov 2025
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RC3: 'Reply on AC2', Anonymous Referee #2, 19 Nov 2025
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RC6: 'Comment on mr-2025-14', Anonymous Referee #2, 23 Nov 2025
Dear Authors,
Another review of your manuscript has been received, which I forward to you here:
General Comments
This is an interesting manuscript that ultimately deserves publication but there are number of issues that need correcting or rectified.
Specific Comments
Although years ago many authors, including myself, used the abbreviation PFG NMR for NMR diffusion measurements, it should be noted that pulsed field gradients could be merely being used for coherence selection. Consequently, it is better to use the expression pulsed gradient spin echo (PGSE) NMR, since a spin echo is necessarily sensitive to diffusion.
The last paragraph on page 1 talks about the issues with using PFG (i.e., PGSE) NMR to study solids and the first paragraph on page 2 discusses the various static field gradient (SFG) methodologies available. Then somewhat out of place, the next paragraph starts by stating that despite the advances in PFG methods they are still not suited for solid-state applications. The contents of these chapters need to be reordered.
Page 2, line 40. “Additionally, the abrupt shifts … can lead to prolonged dead times in the magnetic resonance signal …”. This seems confused – at least in how it is written. It is not that there is no signal, it is that the signal is scrambled by eddy currents and other effects and so one needs to wait a sufficient amount of time for these to decay before you can acquire a useful signal.
Page 2, line 44. I am not sure that there are too many logistical burdens. Few would attempt to move a superconducting magnet on field.
Page 2, line 47. I assume that the authors are referring to SFG systems when they mention “independently controllable”?
Page 2, line 69. CPMG should have been defined here (i.e., the first occurrence) and not on Page 5 line 105 or Page 14 line 282 with the references (move these to page 2 as well).
Page 3, line 81. I am a little mystified by comment “reaches the required threshold for the onset of nuclear magnetic resonance”. My point is that everywhere is resonating to some degree (e.g., the Earth’s Magnetic field is about 50 μT). Do the authors mean resonating in a particular frequency range?
Page 4, Fig. 1. Please define “NAS”.
Page 7, line 132. “…diffusion is not in progress…”? Do you mean “diffusion is not measurable because of the short τ”? But diffusion is always occurring.
Page 11, line 232. Please give a reference for the “Landweber iteration method”.
1
Typographical CorrecƟons
The manuscript has many typographical errors that detract from the manuscript.
Many references run against the previous word (e.g., page 1, line 11”viscoelasticity(Keddie et al.”)). This type of error is throughout the manuscript.
There is a mysterious “8” in the middle of the text on line 34 on page 2.
“NMR” was defined on page 1, there is no need to redefine it on page 3 line 83. Indeed, given the journal that this manuscript has been submitted to it is doubtful that NMR needs to be defined at all.
Page 6, line 177. “… no variations present in R2 near …” sounds odd. How about “… no variations in R2 are present near …”
Page 8, Fig. 4. Some of the variables in the axes labels should be italicised.
Page 9, line 3. Instead of “when τ = 20 μs was held constant”, did the authors mean “when τ was set to 20 μs”?
Page 10, line 194. It is a small point and I know that “rotational motion” is in common usage (so there is no need to change), but “rotational” implies rotating about one axis, whereas the molecules are tumbling and so to me “reorientational” seems more appropriate.
Page 13, line 247. Boembergen → Bloembergen
Citation: https://doi.org/10.5194/mr-2025-14-RC6 -
AC5: 'Reply on RC6', Naoki Asakawa, 01 Dec 2025
Dear Editor,
we would like to express our sincere gratitude for reviewing our manuscript(mr-2025-14)).
We sincerely appreciate Reviewer's thorough reading of our manuscript and their positive assessment of its potential contribution to Magnetic Resonance. Below we provide point-by-point responses to all comments raised.Reviewer comment:
Although years ago many authors, including myself, used the abbreviation PFG NMR for NMR diffusion measurements, it should be noted that pulsed field gradients could be merely being used for coherence selection. Consequently, it is better to use the expression pulsed gradient spin echo (PGSE) NMR, since a spin echo is necessarily sensitive to diffusion.Response:
We would like to thank the reviewer for the comment. We revised our manuscript in line with the comment.Reviewer comment:
The last paragraph on page 1 talks about the issues with using PFG (i.e., PGSE) NMR to study solids and the first paragraph on page 2 discusses the various static field gradient (SFG) methodologies available. Then somewhat out of place, the next paragraph starts by stating that despite the advances in PFG methods they are still not suited for solid-state applications. The contents of these chapters need to be reordered.Response:
We appreciate the reviewer's comment on the readability of Introduction. We rewrote the Introduction part to gain the readability.Reviewer comment:
Page 2, line 40. “Additionally, the abrupt shifts … can lead to prolonged dead times in the magnetic resonance signal …”. This seems confused – at least in how it is written. It is not that there is no signal, it is that the signal is scrambled by eddy currents and other effects and so one needs to wait a sufficient amount of time for these to decay before you can acquire a useful signal.Response:
We thank the reviewer again for their comment. We replace the sentence in original manuscript to the following.Revised text:
"Because eddy currents distort the NMR signal, it is necessary to wait an adequate period for their decay prior to acquiring a reliable measurement."Reviewer comment:
Page 2, line 44. I am not sure that there are too many logistical burdens. Few would attempt to move a superconducting magnet on field.Response:
The reviewer's point is valid once a superconducting magnet has been installed. However, we believe that the effort required up to the point of installation is far from negligible, and our comment refers to the burdens associated with the installation and decommissioning processes.Reviewer comment:
Page 2, line 47. I assume that the authors are referring to SFG systems when they mention “independently controllable”?Response:
We are afraid that the reviewer’s assumption is not correct. Even in SFG-based methods, such as the SFF technique, changing the resonance frequency requires repositioning the detector coil or the sample, and at the same time the magnitude of the field gradient inevitably changes. In the case of the STRAFI method, the resonance frequency is essentially fixed; however, altering the static magnetic field strength would require redesigning the geometry of the GarFIELD magnet. Therefore, variable-frequency measurements under a constant magnetic-field gradient—i.e., with identical spatial resolution—are not feasible.
The ability to independently vary the static field strength and the field-gradient strength is essential for imaging spectral density functions, and the development of such techniques is highly desired. We consider the method presented in this study to be one such approach.Reviewer comment:
Page 2, line 69. CPMG should have been defined here (i.e., the first occurrence) and not on Page 5 line 105 or Page 14 line 282 with the references (move these to page 2 as well).Response:
We would like to thank the reviewer again. We revised our manuscript in line with the comment.Reviewer comment:
Page 3, line 81. I am a little mystified by comment “reaches the required threshold for the onset of nuclear magnetic resonance”. My point is that everywhere is resonating to some degree (e.g., the Earth’s Magnetic field is about 50 μT). Do the authors mean resonating in a particular frequency range?Response:
Thank you for drawing our attention to this important point. Our intention was to refer specifically to a particular range of resonance frequencies. We have completely rewritten the relevant paragraph, and we believe this revision resolves the reviewer’s concerns.
Reviewer comment:
Page 4, Fig. 1. Please define “NAS”.Response:
We would like to thank the reviewer for their comment. We have completely rewritten the caption of Fig. 1. In doing so, we explicitly clarified the original term behind the abbreviation “NAS,” namely “NMR-active slice.”Revised Text:
The revised figure caption is the following:"Figure 1. In our one-dimensional MRI approach, the resonance frequency was fixed and a spatially selective RF pulse with an RF field strength of nominal 50 kHz were applied. This pulse excites nuclear spins only within a narrow slice (the NMR-active slice;NAS), whose spatial position is defined by the static field gradient at the chosen resonance frequency. By incrementally varying the static magnetic field, the effective field gradient experienced by the sample changes, and consequently, the position of the NAS is shifted along the thickness direction of the membrane. The combined effect of the magnetic field generated by the needle-like ferromagnet, BNd, and the static magnetic field from the electromagnet, Be gives rise to tha mechanism of movement of NMR active slice."
Reviewer comment:
Page 7, line 132. “…diffusion is not in progress…”? Do you mean “diffusion is not measurable because of the short τ”? But diffusion is always occurring.Response:
We did not mean to suggest that diffusion cannot be measured because τ is short; rather, our intention was to indicate that when τ is short, the spins have not yet reached the diffusion barrier and therefore undergo free diffusion.Revised text:
"When the echo time τ is short, and the spins have not yet reached the diffusion barrier and therefore undergo free diffusion. Therefore, spins remain within the short-time regime."Revier comment:
Page 11, line 232. Please give a reference for the “Landweber iteration method”.Response:
We added four references for the Landweber iteration method.Typographical Corrections
Reviewer comment:
Many references run against the previous word (e.g., page 1, line 11”viscoelasticity(Keddie et al.”)). This type of error is throughout the manuscript.Response:
We revised our manuscript in line with the comment.Reviewer comment:
There is a mysterious “8” in the middle of the text on line 34 on page 2.Response:
We omitted the mysterious "8".Reviewer comment:
“NMR” was defined on page 1, there is no need to redefine it on page 3 line 83. Indeed, given the journal that this manuscript has been submitted to it is doubtful that NMR needs to be defined at all.Response:
We revised our manuscript in accordance with the comment, except for the first occurrence of the term “NMR.”Reviewer comment:
Page 6, line 177. “… no variations present in R2 near …” sounds odd. How about “… no variations in R2 are present near …”Response:
We revised our manuscript in line with the reviewer's suggestion.
Reviewer comment:
Page 8, Fig. 4. Some of the variables in the axes labels should be italicised.Response:
We redrew Fig.4 in line with the reviewer's suggestion.Reviewer comment:
Page 9, line 3. Instead of “when τ = 20 μs was held constant”, did the authors mean “when τ was set to 20 μs”?Response:
The reviewer's comment is correct. We revised our manuscript in line with the reviewer's suggestion.
Reviewer comment:
Page 10, line 194. It is a small point and I know that “rotational motion” is in common usage (so there is no need to change), but “rotational” implies rotating about one axis, whereas the molecules are tumbling and so to me “reorientational” seems more appropriate.Response:
We would like to thank the reviewer for their helpful comment. We have revised the text by adding “reorientation” alongside “rotational.”Reviewer comment:
Page 13, line 247. Boembergen → BloembergenResponse:
We would like to thank again for the comment. We corrected the missspelling of "Bloembergen."Citation: https://doi.org/10.5194/mr-2025-14-AC5 -
EC1: 'Reply on AC5', Geoffrey Bodenhausen, 02 Dec 2025
The paper is now ready to go into production.
Many thanks to authors and reviewers
Geoffrey Bodenhausen
Citation: https://doi.org/10.5194/mr-2025-14-EC1
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EC1: 'Reply on AC5', Geoffrey Bodenhausen, 02 Dec 2025
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AC5: 'Reply on RC6', Naoki Asakawa, 01 Dec 2025
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This is very nice work showing an innovative way of assessing (measuring?) diffusion in solid films, by generating a strong magnetic field gradient with a ferromagnetic needle in a one-sided surface NMR measurement. The excited valume is shifted by sweeping the field. The effective spin–spin relaxation rate is mapped vs. depth. The tau-dependence can help isolating diffusion from relaxation and a qualitative linkage to three diffusional regimes is reported. Simulations support the conclusions that these regimes could be separated. This appears to be a fine paper and I support publication in its current form.