Low Frequency Vibrations and Diffusion in Disordered Polymers Bearing an Intrinsic Microporosity as Revealed by Neutron Scattering

Round 1

Reviewer 1 Report

The author studied the low energy excitation and diffusion of amorphous polymers having intrinsic microporosity by INS and QENS methods. Their experimental approaches are quite interesting and the careful data analysis supports the validity of presented data. In principle, the reviewer recommends the publication of this manuscript to crystals. To improve the quality of this manuscript, following points should be considered in the revised manuscript.

1. At materials and methods section, it is better to prepare the table that summarizes BET surface values of polymers used in present study.  
2. In Fig.3, it is better to include error-bars. Since the peak position of boson peak is slightly obscure, including the error bars are quite helpful for supporting the quality of data.
3. For curve fits of Fig. 3a, it is better to adopt log-normal distribution function.
4. The unit of horizontal axis should be ps^-1 not ps.
5. To highlight the anomalous behavior of PIM-EA-TB in Fig.3 (a), the symbols of two polymers should be modified to color (orange and blue, respectively).
6. The authors only focused on the relationship between BET surface area and the peak position of Boson peak. It will be interesting to discuss the relationship between BET surface area and the intensity of Boson peak.
7. In relation to the comment 6, it will be interesting to discuss the relationship between boson peak and fragility of present polymers.
8. It is better to evaluate the backbone stiffness of PIM-EA-TBs to stress the difference compared to those of PIM-1 and polynorbornenes.
9. It is better to include the reason for adopting the value of 1.779A for a jump length of methyl group.

Author Response

1. At materials and methods section, it is better to prepare the table that summarizes BET surface values of polymers used in present study.  

                The requested table is added to the manuscript.

2. In Fig.3, it is better to include error-bars. Since the peak position of boson peak is slightly obscure, including the error bars are quite helpful for supporting the quality of data.

            We agree with reviewer. Error bars are added to Figure 3b.

3. For curve fits of Fig. 3a, it is better to adopt log-normal distribution function.

This is a misunderstanding. The lines given in Figure 3a are just guides to the eyes. The application of log-normal distribution would indicate that there is a physical reason for it, which is not the case. We wish to avoid confusing a possible reader of the manuscript.

4. The unit of horizontal axis should be ps^-1 not ps.

            We are grateful to the reviewer. The typo is corrected

5. To highlight the anomalous behavior of PIM-EA-TB in Fig.3 (a), the symbols of two polymers should be modified to color (orange and blue, respectively).

The data points for the different polymers are already colored in Figure 3a (PIM-EA-TB(CH3) – red, PIM-EA-TB(H2) -blue). It might be that the reviewer has got a black and white copy for review.

6. The authors only focused on the relationship between BET surface area and the peak position of Boson peak. It will be interesting to discuss the relationship between BET surface area and the intensity of Boson peak

This is an interesting question. Unfortunately, in the moment there is no approved model or theory available for the intensity of the Boson peak. A comment is made in the manuscript.

It is further interesting to note that the Boson peak for PIM-EA-TB(CH3) has a higher intensity than that of PIM-EA-TB(H2). Currently the intensity of a Boson peak is under controversial discussion and no convincing approach is available. Therefore, this point needs further experimental and theoretical investigations.

7. In relation to the comment 6, it will be interesting to discuss the relationship between boson peak and fragility of present polymers.

We are grateful to the reviewer for this comment. The fragility is estimated from the temperature dependence of the viscosity or the relaxation times of glassy dynamics close to the thermal glass transition temperature. As discussed in the manuscript for all investigated polymers no glass transition could be measured before the chemical decomposition of the materials. A comment is made in the manuscript.

In the literature also a relationship is discussed between the position of the Boson peak and the fragility of the material.^73,41 The fragility is estimated from the temperature dependence of the viscosity, or the relaxation rates of glassy dynamics close to the thermal glass transition temperature. As discussed above no glass transition temperature could be measured by conventional calorimetry before the thermal decomposition of the polymers. Therefore, also no temperature of the viscosity or the glassy dynamics could be estimated, and the fragility values remains unknown, and this correlation could not be evaluated here.

8. It is better to evaluate the backbone stiffness of PIM-EA-TBs to stress the difference compared to those of PIM-1 and polynorbornenes.

In principle this is a good idea. For conventional polymers the chain stiffness is characterized by the characteristic ratio. Due to the ladder-type chain structure this property cannot be defined for PIMs in a senseful manner. Also, for the polynorbornenes values of the characteristic ratio are not known. A comment is made in the manuscript.

A correlation of the maximum position of the Boson peak and the microscopic stiffness was discussed in the literature.^70-73 For conventional polymers the chain stiffness is characterized by the characteristic ratio. Due to the ladder-type chain structure this property cannot be defined for PIMs in a senseful manner. Also, for the polynorbornenes values of the characteristic ratio are not known. Therefore, a more quantitative comparison could not be established here.

9. It is better to include the reason for adopting the value of 1.779A for a jump length of methyl group.

This is a misunderstanding. This value is not adopted. It follows simply from the from the geometry (bond lengths and angles) of the methyl group. This made clearer in the manuscript.

….which is derived from the geometry of the methyl group

Reviewer 2 Report

In this paper, the Authors study low-frequency vibrations and the microscopic diffusion in microporous polymers by neutron scattering. Two polymers of intrinsic microporosity were measured: PIM-EA-TB(CH3) and the demethylated counterpart PIM-EA-TB(H2). The data obtained supplement the obtained dependencies of the vibrational properties on the BET (Brunauer-Emmett-Teller) area. It was shown that the boson peak frequency decreases with the increase of the BET area. However, the boson peak frequency is higher than for previously studied polymers. It was explained by a more rigid backbone of PIM-EA-TB(CH3) and PIM-EA-TB(H2).

The microscopic diffusion was studied by the analysis of the mean squared displacement measured by elastic fixed window scans. The additional contribution found for PIM-EA-TB(CH3) is assigned to the methyl group rotation, which is possible in PIM-EA-TB(CH3).

This paper is clearly written and contains interesting results, which improves the understanding of the microscopic nature of vibrations in polymers. However, there are some comments, which can improve the paper:

1. It would be fruitful to include some data for the backbone stiffness or the macroscopic stiffness of the studied polymers. It can reveal the overall dependence of the boson peak frequency on the BET area and the stiffness as well. It correlates with the results obtained by the effective medium approximation for jammed solids [E. DeGiuli, A. Laversanne-Finot, G. Diring, E. Lernera, and M. Wyart, Soft Matter 10, 5628 (2014)] and the random matrix theory for amorphous solids [Y. M. Beltukov, D. A. Parshin. Boson peak in various random-matrix models. JETP letters 104, 552 (2016); D. A. Conyuh, Y. M. Beltukov. Physical Review B, 103, 104204 (2021)]. In these theories both the boson peak frequency and the macroscopic stiffness depend on the typical microscopic stiffness (similar to backbone stiffness) and the disorder/connectivity (similar to porosity) of the system as well.

2. At the top of page 7 there is “By measuring spectra of the sample at two different temperatures …”. It would be helpful to add here the values of these two temperatures for clarity.

3. The dash-dotted guide in Figure 3b has a smaller slope than the slope between the two dots.

4. The manuscript requires additional proofreading. Here are some of the typos:

a) Figure 3a: frequency has units ps, but ps^-1 is expected

b) Page 7: PIM-EA-TB(CH3) und PIM-EA-TB(H2)

c) Page 9: the calculated the calculated one

d) Ref 37: Parshin, A. D. → Parshin, D. A.

Also, the text has different font sizes in different places and the references have two different misaligned numerations (see e.g. Ref. 45).

Author Response

1. It would be fruitful to include some data for the backbone stiffness or the macroscopic stiffness of the studied polymers. It can reveal the overall dependence of the boson peak frequency on the BET area and the stiffness as well. …..

In principle this is a good idea. For conventional polymers the chain stiffness is characterized by the characteristic ratio. Due to the ladder-type chain structure this property cannot be defined for PIMs in a senseful manner. Also, for the polynorbornenes values of the characteristic ratio are not known. The suggested literature is cited. A comment is made in the manuscript.

A correlation of the maximum position of the Boson peak and the microscopic stiffness was discussed in the literature^70-72 For conventional polymers the chain stiffness is characterized by the characteristic ratio. Due to ladder-type chain structure this property cannot be defined for PIMs in a senseful manner. Also, for the polynorbornenes values of the characteristic ration are not known. Therefore, a more quantitative comparison could not be established here.

2. At the top of page 7 there is “By measuring spectra of the sample at two different temperatures …”. It would be helpful to add here the values of these two temperatures for clarity.

            The temperatures are added.

3. The dash-dotted guide in Figure 3b has a smaller slope than the slope between the two dots.

            The data are subject to some errors. Error bars are added to Figure 3b.

4. The manuscript requires additional proofreading. Here are some of the typos.

The manuscript is carefully proofread also by native speaking coauthors. The typos are corrected.