the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Nov 2024
Pseudo Rotary Resonance Relaxation Dispersion Effects in Isotropic Samples
Abstract. Enhanced transverse relaxation near rotary-resonance conditions is a well-documented effect for anisotropic solid samples undergoing magic-angle spinning (MAS). It is a surprising behavior for rotating liquids, in which first-order anisotropic interactions are averaged at a much faster timescale as compared with the spinning frequency. Here we report measurements of 13C transverse relaxation under spin lock for spinning samples of both polybutadiene rubber and polyethylene glycol solution. Maxima in the relaxation rates are observed when the spin-lock frequency matches one or two times the MAS rate. Through simulations, we qualitatively describe the appearance of this effect, which can be explained by time dependence caused by sample rotation and an inhomogeneous rf-field distribution. Consideration of this effect is important for MAS experiments based on rotary-resonance conditions, and motivates the design of new MAS coils with improved rf-field homogeneity.
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CC1: 'Comment on mr-2024-21', Tom Barbara, 21 Nov 2024
The authors may find the paper by Kupce, Keifer and Delepierre of some interest: JMR 148,115-120 (2001). These reported on rotary resonance effects in MAS and TOCSY.
Citation: https://doi.org/10.5194/mr-2024-21-CC1 -
AC1: 'Reply on CC1', Evgeny Nimerovsky, 20 Dec 2024
Thanks for pointing out this literature. We will be sure to include this citation in the final version of the article.
Citation: https://doi.org/10.5194/mr-2024-21-AC1
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AC1: 'Reply on CC1', Evgeny Nimerovsky, 20 Dec 2024
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RC1: 'Comment on mr-2024-21', Anonymous Referee #1, 28 Nov 2024
The comment was uploaded in the form of a supplement: https://mr.copernicus.org/preprints/mr-2024-21/mr-2024-21-RC1-supplement.pdf
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RC2: 'Comment on mr-2024-21', Zdeněk Tošner, 05 Dec 2024
This contribution reports about a surprising observation that T1rho of liquid-like samples shows enhanced relaxation at rotary resonance conditions known from rotating solids. It is not expected for samples where dipolar interactions are completely averaged by fast motions. It is argued that this phenomenon arises when liquid-like samples are rotated in a spatially inhomogeneous radiofrequency field of solenoid coils. Consequently, similar effect could be expected for solids, changing thus interpretation of rotary resonance relaxation dispersion experiments.
While I understand urgency of this report, I would appreciate a more thorough study. Here are my concerns:
- Rubber and polymer samples are liquid-like, but not quite typical liquids. There still might be nonzero residual dipolar couplings. MAS imposes centrifugal forces and polymer particles may become “solidified” on the rotor walls – can it be excluded?
- If the explanation is solely time-variable rf field, it can be modelled in liquid state probes without sample spinning by applying shaped pulses. These experiments would then be very convincing experimental proof of the phenomenon.
- Quality of the supporting material is not sufficient to reproduce the simulations. There are many typos and unclear nomenclature. For example, what is integral of “df dg f(x) g(B1)” (what is the “df” element?) The time-variable rf Hamiltonians are defined using a sum over n (n=1, 2) of cos(\omega_R t) – there is no “n” under the sum. A graph of these Hamiltonians would help. No reasoning is given for f(\nu_1) being biquadrate exponential distribution function, etc…
- I miss more detailed simulation study on the extent of rf modulations introducing enhanced relaxation. I mean some assessment what the amplitude of rf modulations must be, perhaps in relation to the nominal rf amplitude, to observe the phenomenon? RF field modulations within an MAS rotor are of different amplitude, depending on the position along the coil axis as well as on the radial distance… In simulations, 10% amplitude modulations are assumed regardless of the position.
- Our detailed calculation of rf field in solenoids show MAS induced variations on the frequency of \omega_R. Where exactly is the origin of the second recoupling condition at two times \omega_R? It comes naturally from MAS modulations of the residual dipolar couplings (rank-2 tensors) but rf field is modulated at just a single frequency…
I think these issues should be clarified before the report comes out from the discussion forum here, prior the final publication.
Citation: https://doi.org/10.5194/mr-2024-21-RC2 -
AC2: 'Response to all reviewer comments', Evgeny Nimerovsky, 20 Dec 2024
The comment was uploaded in the form of a supplement: https://mr.copernicus.org/preprints/mr-2024-21/mr-2024-21-AC2-supplement.pdf
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RC3: 'Comment on mr-2024-21', Anonymous Referee #3, 07 Dec 2024
This study observes enhanced magnetization decay at rotary-resonance conditions in a "liquid-like" sample similar to that observed in magic-angle spinning (MAS) solids. This behavior should not be typically observed for molecules when molecular tumbling averages out the dipolar interactions. The authors rationalize this behavior to spatially inhomogeneous rf field interfering with sample spinning, causing a rapid magnetization decay. This is an experimental observation; however, it is necessary to rationalize the samples, simulations and the conclusions drawn from the study before the manuscript can be accepted.
- Would one expect such behavior for water or generally for molecules tumbling in the picosecond time scale, true "liquid-like," for example, glycine in water? Is there any specific reason for restricting the study to PEG and rubber? The molecular weight of the PEG used in the study is unclear. One would also expect high molecular weight PEGs to show anisotropic molecular tumbling or sediment on the rotor wall. Perhaps data on molecules showing averaging of dipolar interactions would be comprehensive proof.
- Perhaps it might be helpful to measure the rotation correlation timescale of the PEG sample instead of making a hand-waving argument.
- The decay of magnetization appears (not sure) to indicate minima/oscillations. Is this a feature of incoherent effects?
- Is there any special reason for using different decoupling schemes at different MAS frequencies, especially if the claim is that the samples are "solution-like"? It's probably not a relevant point, but it's just curiosity.
- Comparing Figure 2 and Figure 4, despite using smaller rf inhomogeneity in simulations compared to typically reported on MAS probes, the magnetization decays substantially faster in simulations. What is the experimental rf inhomogeneity of the rf field?
- The simulation details are sketchy, especially the terms in Eq S2.
- By naively looking at Equations S3A and S3B, it's not so apparent why the simulations differ except for the weighting factors, which have a different slope and magnitude. In Eq S3, "n is missing" in the cosine term. Is there a justification for summing over n=1,2, or is it motivated by experimental observations?
- Is it sufficient to consider inhomogeneity distribution along one axis in both scenarios? Why should that be the case?
Minor points
- Page 3, line 9 chose
- Different figures have different labels for the rf axis.
Citation: https://doi.org/10.5194/mr-2024-21-RC3 -
AC2: 'Response to all reviewer comments', Evgeny Nimerovsky, 20 Dec 2024
The comment was uploaded in the form of a supplement: https://mr.copernicus.org/preprints/mr-2024-21/mr-2024-21-AC2-supplement.pdf
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