Slip-spring simulations of different constraint release environments for linear polymer chains

The constraint release (CR) mechanism has important effects on polymer relaxation and the chains will show different relaxation behaviour in conditions of monodisperse, bidisperse and other topological environments. By comparing relaxation data of linear polyisoprene (PI) chains dissolved in very long matrix and monodisperse melts, Matsumiya et al. showed that CR mechanism accelerates both dielectric and viscoelastic relaxation (Matsumiya et al. 2013 Macromolecules 46, 6067. (doi:10.1021/ma400606n)). In this work, the experimental data reported by Matsumiya et al. are reproduced using the single slip-spring (SSp) model and the CR accelerating effects on both dielectric and viscoelastic relaxation are validated by simulations. This effect on viscoelastic relaxation is more pronounced. The coincidence for end-to-end relaxation and the viscoelastic relaxation has also been checked using probe version SSp model. A variant of SSp with each entanglement assigning a characteristic lifetime is also proposed to simulate various CR environment flexibly. Using this lifetime version SSp model, the correct relaxation function can be obtained with equal numbers of entanglement destructions by CR and reptation/contour length fluctuation (CLF) for monodisperse melts. Good agreement with published experiment data is also obtained for bidisperse melts, which validates the ability to correctly describe the CR environment of the lifetime version model.


Comments to the Author(s)
The manuscript presents computer simulation studies of the dielectric loss and linear viscoelasticity of polymer melts from coarse-grained models. The authors demonstrate that the model parameters of the slip-spring model can be chosen to obtain reasonably good fits to literature data of experimental results on monodisperse, linear polyisoprene. The more original contribution made here is the investigation of a variant of the slip-spring model, where pairing of constraints is replaced by a lifetime probability, very similar to corresponding slip-link model by Schieber et al. The authors show that this variant of the model can be fitted to reasonably reproduce experimental results on mono-and bi-disperse melts. I consider the lifetime-version of the slip-spring model an interesting approach that could inspire future work due to its flexibility.
I have just few technical comments: Table 3: I guess these parameters correspond to 21K in Fig. 9, but the authors should make this clear in the manuscript. Furthermore, "eqn (3)" does not exist, probably (4.1) is meant ?   Fig 7, 8: How did the authors determine the lifetime distribution? How are they able to numerically calculate this quantity with an accuracy better than 10^-7? page 11: "simulations are in quantitative agreement ..." seems an overstatement, since the loss plateau for 60% (green) in Fig. 11 is about a factor of 2 off. Table 4: Is the exponent alpha really that sensitive that -0.603 and -0.599 give different results from -0.6? A number of typos and awkward wordings should be corrected, such as "mels" -> melts, "simpleness" -> simplicity, etc.
contribution to the literature. Derivative work will not be considered." I am concerned that this paper might fall into the last category.
Here are the facts: -the authors have recreated a previously published simulation algorithm (the "slip-spring model", a type of slip-link model) -they have used it to match some previously published experimental data. So far as I know, the algorithm has not been used for specifically these data before, but it has been used on fairly similar data.
-they have then modified the slip-spring algorithm to include an idea that other authors (ref [31]) used on a slightly different slip-link model, the discrete slip-link model. But the idea is essentially the same and the two models are not so different (both slip-link models).
I admit this is a marginal judgement. There are two (fairly minor) things in the paper which arguably have not been done before: using an algorithm on a set of data it wasn't used for before, and incorporating the idea of ref [31] into specifically this set of data. but I feel the work is still quite derivative in nature, it does not break new ground.
Here are some more detailed comments about further aspects of the paper. 1) On the topic of orientational cross correlations (OCC) I feel the authors have a misunderstanding of the issue, throughout the paper. OCC in the (multi-chain) Masubuchi work, and in the single chain "slip spring" simulations are quite different things, and cannot be compared one against the other. In the Masubuchi work, the OCC is between different stresscarrying chains in the simulation and arise as a result of force balance at entanglement points between those chains. Since those simulation chains are supposed to represent real chains in a polymer melt, the question is whether real chains also have the orientational cross correlations, and that is a meaningful question (but not one that is answered by the work of the present paper).
On the other hand, the present simulations are all "single chain" simulations in that one chain does not directly exchange forces with others -there can be no OCC between different chains. The OCC are between chains and the virtual springs which hold the chains. The virtual springs are not considered to "really" carry stress. However, the OCC must be included in the Green-Kubo formula to calculate G(t), even though it is considered that the real stress is only carried by the chains. So, this is an entirely different situation from the Masubuchi simulations, and not comparable at all.
2) The list of parameters in Table 1 should include Ne_ss.
3) The version of Reptate referred to is no longer available, and the web address no longer works. I believe there is a new Reptate available. 4) Page 6: The authors write "It's fair to note that the simulated dielectric relaxation time of probe chains is underestimated systematically". Potentially the problem is the other way around... the authors should fix the timescale of simulations using the "simpler" probe data (where CR is suppressed) and then model the more complicated CR environment of pure melt. Perhaps the pure melt predictions are actually the things that are wrong? 5) Page 8, the authors write, "The concrete expression of f(t) can be found in ref. 31.". I think the present paper should be self contained and all necessary equations written here. 6) Page 9 onwards discusses the exponential form for CR events used by Shivokhin. It is worth noting that the exponential distribution was used as a test "theoretical" case to explore the effects of a single dominant CR timescale, without necessarily expecting it to be an accurate model for real chains. Further more (figure 9) the exponential distribution is bound to be worst for the shortest chains with fewest entanglements, since such chains have a greater effect of contour length fluctuation. Longer chains should show less discrepancy. 7) For the binary blend case (figure 11) it would be strongly advisable to iterate the procedure for finding f(t), not just take the first iteration. The presence of short chains can greatly accelerate the relaxation of longer chains, so the entanglement lifetime distribution is quite different from the pure melts of the two components in some (but not all) cases.
8) The magenta line in figure 11 shows a spurious relaxation near omega =10s^-1. What is the source of this? 9) Page 11, the following two sentences need to be either removed or elaborated on (how would one do this?) " For example, it may be extended to study the partially dilated tube diameters to check partially DTD." "Further refinement is necessary and the effects of the parameters of the lifetime distributions should be well understand to achieve more complex CR environment such as nanocomposites with rod-like filler" (neither seem obviously do-able to me) Decision letter (RSOS-191046.R0) 29-Jul-2019 Dear Dr Ma, The editors assigned to your paper ("Slip-spring simulations of different constraint release environments for linear polymer chains") have now received comments from reviewers. We would like you to revise your paper in accordance with the referee and Associate Editor suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance.
Please submit a copy of your revised paper before 21-Aug-2019. Please note that the revision deadline will expire at 00.00am on this date. If we do not hear from you within this time then it will be assumed that the paper has been withdrawn. In exceptional circumstances, extensions may be possible if agreed with the Editorial Office in advance. We do not allow multiple rounds of revision so we urge you to make every effort to fully address all of the comments at this stage. If deemed necessary by the Editors, your manuscript will be sent back to one or more of the original reviewers for assessment. If the original reviewers are not available, we may invite new reviewers.
To revise your manuscript, log into http://mc.manuscriptcentral.com/rsos and enter your Author Centre, where you will find your manuscript title listed under "Manuscripts with Decisions." Under "Actions," click on "Create a Revision." Your manuscript number has been appended to denote a revision. Revise your manuscript and upload a new version through your Author Centre.
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• Authors' contributions All submissions, other than those with a single author, must include an Authors' Contributions section which individually lists the specific contribution of each author. The list of Authors should meet all of the following criteria; 1) substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it critically for important intellectual content; and 3) final approval of the version to be published.
All contributors who do not meet all of these criteria should be included in the acknowledgements.
We suggest the following format: AB carried out the molecular lab work, participated in data analysis, carried out sequence alignments, participated in the design of the study and drafted the manuscript; CD carried out the statistical analyses; EF collected field data; GH conceived of the study, designed the study, coordinated the study and helped draft the manuscript. All authors gave final approval for publication.
• Acknowledgements Please acknowledge anyone who contributed to the study but did not meet the authorship criteria.
• Funding statement Please list the source of funding for each author. One of the reviewers has recommend rejection of this manuscript. If you wish to submit an amended version of the manuscript, it would require major revision, addressing each of the points raised by the reviewers, but also specifically outlining the novelty of the work, how it is not simply derivative of the previous work you cite, and the significance of the contribution of the work.

Comments to Author:
Reviewers' Comments to Author: Reviewer: 1 Comments to the Author(s) The manuscript presents computer simulation studies of the dielectric loss and linear viscoelasticity of polymer melts from coarse-grained models. The authors demonstrate that the model parameters of the slip-spring model can be chosen to obtain reasonably good fits to literature data of experimental results on monodisperse, linear polyisoprene. The more original contribution made here is the investigation of a variant of the slip-spring model, where pairing of constraints is replaced by a lifetime probability, very similar to corresponding slip-link model by Schieber et al. The authors show that this variant of the model can be fitted to reasonably reproduce experimental results on mono-and bi-disperse melts. I consider the lifetime-version of the slip-spring model an interesting approach that could inspire future work due to its flexibility.
I have just few technical comments: Table 3: I guess these parameters correspond to 21K in Fig. 9, but the authors should make this clear in the manuscript. Furthermore, "eqn (3)" does not exist, probably (4.1) is meant? Fig 7, 8: How did the authors determine the lifetime distribution? How are they able to numerically calculate this quantity with an accuracy better than 10^-7? page 11: "simulations are in quantitative agreement ..." seems an overstatement, since the loss plateau for 60% (green) in Fig. 11 is about a factor of 2 off. A number of typos and awkward wordings should be corrected, such as "mels" -> melts, "simpleness" -> simplicity, etc.

Reviewer: 2
Comments to the Author(s) The question I am trying to answer in my mind is "is this simply derivative work?" I note from the referee guidelines it says: "Submissions should sufficiently advance scientific knowledge. Negative findings, meta-analyses and studies testing reproducibility of significant work are also encouraged. Repeated experiments will only be considered if they provide a meaningful contribution to the literature. Derivative work will not be considered." I am concerned that this paper might fall into the last category.
Here are the facts: -the authors have recreated a previously published simulation algorithm (the "slip-spring model", a type of slip-link model) -they have used it to match some previously published experimental data. So far as I know, the algorithm has not been used for specifically these data before, but it has been used on fairly similar data.
-they have then modified the slip-spring algorithm to include an idea that other authors (ref [31]) used on a slightly different slip-link model, the discrete slip-link model. But the idea is essentially the same and the two models are not so different (both slip-link models).
I admit this is a marginal judgement. There are two (fairly minor) things in the paper which arguably have not been done before: using an algorithm on a set of data it wasn't used for before, and incorporating the idea of ref [31] into specifically this set of data. but I feel the work is still quite derivative in nature, it does not break new ground.
Here are some more detailed comments about further aspects of the paper. 1) On the topic of orientational cross correlations (OCC) I feel the authors have a misunderstanding of the issue, throughout the paper. OCC in the (multi-chain) Masubuchi work, and in the single chain "slip spring" simulations are quite different things, and cannot be compared one against the other. In the Masubuchi work, the OCC is between different stresscarrying chains in the simulation and arise as a result of force balance at entanglement points between those chains. Since those simulation chains are supposed to represent real chains in a polymer melt, the question is whether real chains also have the orientational cross correlations, and that is a meaningful question (but not one that is answered by the work of the present paper).
On the other hand, the present simulations are all "single chain" simulations in that one chain does not directly exchange forces with others -there can be no OCC between different chains. The OCC are between chains and the virtual springs which hold the chains. The virtual springs are not considered to "really" carry stress. However, the OCC must be included in the Green-Kubo formula to calculate G(t), even though it is considered that the real stress is only carried by the chains. So, this is an entirely different situation from the Masubuchi simulations, and not comparable at all.
2) The list of parameters in Table 1 should include Ne_ss.
3) The version of Reptate referred to is no longer available, and the web address no longer works. I believe there is a new Reptate available. 4) Page 6: The authors write "It's fair to note that the simulated dielectric relaxation time of probe chains is underestimated systematically". Potentially the problem is the other way around... the authors should fix the timescale of simulations using the "simpler" probe data (where CR is suppressed) and then model the more complicated CR environment of pure melt. Perhaps the pure melt predictions are actually the things that are wrong? 5) Page 8, the authors write, "The concrete expression of f(t) can be found in ref. 31.". I think the present paper should be self contained and all necessary equations written here. 6) Page 9 onwards discusses the exponential form for CR events used by Shivokhin. It is worth noting that the exponential distribution was used as a test "theoretical" case to explore the effects of a single dominant CR timescale, without necessarily expecting it to be an accurate model for real chains. Further more (figure 9) the exponential distribution is bound to be worst for the shortest chains with fewest entanglements, since such chains have a greater effect of contour length fluctuation. Longer chains should show less discrepancy. 7) For the binary blend case (figure 11) it would be strongly advisable to iterate the procedure for finding f(t), not just take the first iteration. The presence of short chains can greatly accelerate the relaxation of longer chains, so the entanglement lifetime distribution is quite different from the pure melts of the two components in some (but not all) cases.
8) The magenta line in figure 11 shows a spurious relaxation near omega =10s^-1. What is the source of this? 9) Page 11, the following two sentences need to be either removed or elaborated on (how would one do this?) " For example, it may be extended to study the partially dilated tube diameters to check partially DTD." "Further refinement is necessary and the effects of the parameters of the lifetime distributions should be well understand to achieve more complex CR environment such as nanocomposites with rod-like filler" (neither seem obviously do-able to me) Author's Response to Decision Letter for (RSOS-191046

Are the interpretations and conclusions justified by the results? Yes
Is the language acceptable? Yes Do you have any ethical concerns with this paper? No

Recommendation? Accept as is
Comments to the Author(s) I am happy with the authors response.

Review form: Reviewer 3
Is the manuscript scientifically sound in its present form? Yes

Recommendation?
Major revision is needed (please make suggestions in comments)

Comments to the Author(s)
The results look as expected, so they probably calculated everything correctly. However, there are not sufficient details given. Also, they have not cited our prior work in the area, but appear to have done significantly less. The idea of modifying the slip-spring simulations in this way is actually taken over from our ongoing work, and it seems that proper credit is missing. Moreover, we have looked at this question before, using our slip link model [Pilyugina, E.; Schieber, J. D. & Andreev, M. Dielectric relaxation as an independent examination of relaxation mechanisms in entangled polymers using the discrete slip-link model Macromolecules, 2012, 45, 5728-5743]. There are other papers from our work that are relevant and should also be cited. We have analytic expression for f_d(t) which might be compared to those found here, for example. We also have a more fine-grained version of our model that should be very similar.
In principle, I like that they are working to make the slip-spring simulations more rigorous, but am disappointed that they are largely ignoring our contributions that have largely solved all of these problems. Have they found any new conclusions? Finally, I have a number of important technical issues.
1) Why are the authors treating the modulus as an adjustable parameter? It should be determined completely from other known quantities, like temperature, density and Ne.
2) How many beads were used per slip-spring? How was that value chosen or determined?
3) there should be at least two frictions in the model: between the bead and background, and a friction associated with the hopping rate of the slip-spring. That latter does not appear to be specified anywhere. How do the results depend on these values? How were they chosen? 4) Do the slip-springs hop or slide? The latter is problematic from a thermodynamic point of view. 5) How do they calculate stress? Do the virtual springs contribute? If so, then do they violate stress-optic rule? If not, then the model presumably violates thermodynamics. 6) How do they calculate the dielectric relaxation?

13-Nov-2019
Dear Dr Ma: Manuscript ID RSOS-191046.R1 entitled "Slip-spring simulations of different constraint release environments for linear polymer chains" which you submitted to Royal Society Open Science, has been reviewed. The comments of the reviewer(s) are included at the bottom of this letter.
Please note that multiple rounds of revision are not generally permitted and no further rounds will be acceptable if your manuscript is not ready for publication following this revision.
Please submit a copy of your revised paper before 06-Dec-2019. Please note that the revision deadline will expire at 00.00am on this date. If we do not hear from you within this time then it will be assumed that the paper has been withdrawn. In exceptional circumstances, extensions may be possible if agreed with the Editorial Office in advance. We do not allow multiple rounds of revision so we urge you to make every effort to fully address all of the comments at this stage. If deemed necessary by the Editors, your manuscript will be sent back to one or more of the original reviewers for assessment. If the original reviewers are not available we may invite new reviewers.
To revise your manuscript, log into http://mc.manuscriptcentral.com/rsos and enter your Author Centre, where you will find your manuscript title listed under "Manuscripts with Decisions." Under "Actions," click on "Create a Revision." Your manuscript number has been appended to denote a revision. Revise your manuscript and upload a new version through your Author Centre.
When submitting your revised manuscript, you must respond to the comments made by the referees and upload a file "Response to Referees" in "Section 6 -File Upload". Please use this to document how you have responded to the comments, and the adjustments you have made. In order to expedite the processing of the revised manuscript, please be as specific as possible in your response.
In addition to addressing all of the reviewers' and editor's comments please also ensure that your revised manuscript contains the following sections before the reference list: • Ethics statement If your study uses humans or animals please include details of the ethical approval received, including the name of the committee that granted approval. For human studies please also detail whether informed consent was obtained. For field studies on animals please include details of all permissions, licences and/or approvals granted to carry out the fieldwork.
• Data accessibility It is a condition of publication that all supporting data are made available either as supplementary information or preferably in a suitable permanent repository. The data accessibility section should state where the article's supporting data can be accessed. This section should also include details, where possible of where to access other relevant research materials such as statistical tools, protocols, software etc can be accessed. If the data have been deposited in an external repository this section should list the database, accession number and link to the DOI for all data from the article that have been made publicly available. Data sets that have been deposited in an external repository and have a DOI should also be appropriately cited in the manuscript and included in the reference list.
• Competing interests Please declare any financial or non-financial competing interests, or state that you have no competing interests.
• Authors' contributions All submissions, other than those with a single author, must include an Authors' Contributions section which individually lists the specific contribution of each author. The list of Authors should meet all of the following criteria; 1) substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it critically for important intellectual content; and 3) final approval of the version to be published.
All contributors who do not meet all of these criteria should be included in the acknowledgements.
We suggest the following format: AB carried out the molecular lab work, participated in data analysis, carried out sequence alignments, participated in the design of the study and drafted the manuscript; CD carried out the statistical analyses; EF collected field data; GH conceived of the study, designed the study, coordinated the study and helped draft the manuscript. All authors gave final approval for publication.
• Acknowledgements Please acknowledge anyone who contributed to the study but did not meet the authorship criteria.
• Funding statement Please list the source of funding for each author.
Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Comments to the Author(s) The results look as expected, so they probably calculated everything correctly. However, there are not sufficient details given. Also, they have not cited our prior work in the area, but appear to have done significantly less. The idea of modifying the slip-spring simulations in this way is actually taken over from our ongoing work, and it seems that proper credit is missing. Moreover, we have looked at this question before, using our slip link model [Pilyugina, E.; Schieber, J. D. & Andreev, M. Dielectric relaxation as an independent examination of relaxation mechanisms in entangled polymers using the discrete slip-link model Macromolecules, 2012, 45, 5728-5743]. There are other papers from our work that are relevant and should also be cited. We have analytic expression for f_d(t) which might be compared to those found here, for example. We also have a more fine-grained version of our model that should be very similar.
In principle, I like that they are working to make the slip-spring simulations more rigorous, but am disappointed that they are largely ignoring our contributions that have largely solved all of these problems. Have they found any new conclusions? Finally, I have a number of important technical issues. 1) Why are the authors treating the modulus as an adjustable parameter? It should be determined completely from other known quantities, like temperature, density and Ne.
2) How many beads were used per slip-spring? How was that value chosen or determined?
3) there should be at least two frictions in the model: between the bead and background, and a friction associated with the hopping rate of the slip-spring. That latter does not appear to be specified anywhere. How do the results depend on these values? How were they chosen? 4) Do the slip-springs hop or slide? The latter is problematic from a thermodynamic point of view.

RSOS-191046.R2 (Revision) Review form: Reviewer 3
Is the manuscript scientifically sound in its present form? Yes

Comments to the Author(s)
The authors have largely answered my questions. I do not agree completely with the approach, but they have now given sufficient details to make the results reproducible, and what the conclusions are based on.

10-Feb-2020
Dear Dr Ma, It is a pleasure to accept your manuscript entitled "Slip-spring simulations of different constraint release environments for linear polymer chains" in its current form for publication in Royal Society Open Science. The comments of the reviewer(s) who reviewed your manuscript are included at the foot of this letter.
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Thank you for your fine contribution. On behalf of the Editors of Royal Society Open Science, we look forward to your continued contributions to the Journal. Thanks for your comments and suggestions for our manuscript entitled with " Slip-spring simulations of different constraint release environments for linear polymer chains" (ID: RSOS-191046). The manuscript has been carefully revised according to your comments. Any details of the revised portions highlighted in red are kept in the marked copy of the revised manuscript. We appreciate Editors/Reviewers' warm work earnestly, and hope that the corrections will meet your expectation.
We are looking forward to your acceptance of this paper to be published in Royal Society Open Science . Responses to the reviewers' comments are presented as follows:

Responses to the reviewers' comments
Reviewer 1 Quesetion 1: Table 3: I guess these parameters correspond to 21K in Fig. 9, but the authors should make this clear in the manuscript. Furthermore, "eqn (3)" does not exist, probably (4.1) is meant?
Answer: Yes. These parameters correspond to 21K in Fig.9 and the table head has been changed to "Fitted parameters used in lifetime version SSp for PI21K". The statements of " eqn(3) in this work " were corrected as "eqn (4.2) in this work" . We are sorry for that these parts were not clear in the original manuscript.
Quesetion 2: Fig. 7, 8: How did the authors determine the lifetime distribution? How are they able to numerically calculate this quantity with an accuracy better than 10^-7? Answer: Fig. 7,8 give the curve, from which we divide the relaxation spectrum into power-law region and a single exponential region. Thus we assume the normalized lifetime distribution probability has the following form： The form can be divided into two parts and ，which correspond to CLF mechanism and repation mechanism respectively.
The parameters , , , , are constants and should be obtained by fitting the curve using the function form below.
We first simulate 100 PI21K chains for 1e5 timesteps using the probe version SSp, in which the CR mechanism has been turned off. During the dynamics, each entanglement's lifetime from its birth to its disentanglement was recorded and the normalized curve was shown in Fig. 7 and 8, then we fit the curve using the expression above by nonlinear leastsquares method.
To make this procedure clear, we rewrite this part as below.
In Page 8, the first line of Section 4, we add " " We have revised the contents of this part in the revised manuscript.
Because the sampling points were based on entanglements of 100 chains for 1e5 timesteps, which is a large number and 1e-7 occurred during normalization by it. In fact we cannot achieve the accuracy better than 1e-7.
Quesetion 3: page 11: "simulations are in quantitative agreement ..." seems an overstatement, since the loss plateau for 60% (green) in Fig. 11 is about a factor of 2 off.
Answer: Sorry. The statement was indeed overstated. So the original sentence " Fig.11 gives the simulation results of both monodisperse and bidisperse melts and it can be seen that the results from simulations are in quantitative agreement with experimental measurements from ref . 41. " has been changed to " Fig.11 gives  We also show the probability density function of for different alpha in the figure below, which gives almost same distribution. Quesetion 5: A number of typos and awkward wordings should be corrected, such as "mels" -> melts, "simpleness" -> simplicity, etc.

Answer:
We are sorry that we have made such mistakes in our manuscript. The whole document has been checked carefully. Thank you for your careful reading and illuminating comments.

Reviewer 2
Quesetion 1: On the topic of orientational cross correlations (OCC) I feel the authors have a misunderstanding of the issue, throughout the paper. OCC in the (multi-chain) Masubuchi work, and in the single chain "slip spring" simulations are quite different things, and cannot be compared one against the other. In the Masubuchi work, the OCC is between different stress-carrying chains in the simulation and arise as a result of force balance at entanglement points between those chains. Since those simulation chains are supposed to represent real chains in a polymer melt, the question is whether real chains also have the orientational cross correlations, and that is a meaningful question (but not one that is answered by the work of the present paper).
On the other hand, the present simulations are all "single chain" simulations in that one chain does not directly exchange forces with others -there can be no OCC between different chains. The OCC are between chains and the virtual springs which hold the chains.
The virtual springs are not considered to "really" carry stress. However, the OCC must be included in the Green-Kubo formula to calculate G(t), even though it is considered that the real stress is only carried by the chains. So, this is an entirely different situation from the Masubuchi simulations, and not comparable at all.   Table 4.

Answer
For the cost of computation, we also use the parameters for PS60&177%40. " Quesetion 8: The magenta line in figure 11 shows a spurious relaxation near omega =10s^-1. What is the source of this?
Answer: We are sorry that it seems a fitting error. We repeat the fitting process many times and the new fitting results are shown below with also the raw simulation results (Schwarzl G' G'' from Reptate). The corresponding curves in Fig. 11 in original manuscript have updated using the new fitting results. Figure S4 Fitted viscoelastic storage(broken lines) and loss modulus(solid lines) for PS177(magenta). The magenta symbols are experiment data reproduced from ref. 41 and green symbols are raw simulation results (Schwarzl G' G'' from Reptate).
Quesetion 9: Page 11, the following two sentences need to be either removed or elaborated on (how would one do this?) " For example, it may be extended to study the partially dilated tube diameters to check partially DTD." "Further refinement is necessary and the effects of the parameters of the lifetime distributions should be well understand to achieve more complex CR environment such as nanocomposites with rod-like filler" Answer: We have removed the first sentences. We think they are interesting directions and we have not thought them over yet.
The sentences of "Further refinement is necessary and the effects of the parameters of the lifetime distributions should be well understand to achieve more complex CR environment such as nanocomposites with rod-like filler" are changed to "Further refinement is necessary and the effects of the parameters of the lifetime distributions should be well understand to achieve more complex CR environment." "It may have applicability to complex materials such as nanocomposites and be used as an efficient verification tool for some theory model such as DTD and partially DTD. " has also been removed from the conclusion section.

Response to Associate Editor's comments (Professor Hazel Assender):
We thank for the precious comments from the reviewers and the editor. We have revise the manuscript according to comments by the reviewers. We believe the work in this manuscript has two major innovative points. First, we use single slip-spring model to check So we believe our work is not a simple derivative of the previous work. We appreciate Editors/Reviewers' warm work earnestly again and we are looking forward to your acceptance of this paper to be published in Royal Society Open Science.
Dear Editor, Thank you very much for your reply and help. Thanks a lot for the reviewers' comments and their kind suggestions of our manuscript (ID RSOS-191046.R1) entitled "Slip-spring simulations of different constraint release environments for linear polymer chains". We provide this cover letter to explain, point by point, the details of our revisions in the manuscript and our responses to the reviewers' comments as follows. In order to make the changes easily viewable for you and the reviewers, in the revised paper, we marked the revision with red color. We appreciate Editors/Reviewers' warm work earnestly, and hope that the corrections will meet your expectation.
We appreciate Editors/Reviewers' warm work earnestly again and we are looking forward to your acceptance of this paper to be published in Royal Society Open Science.
Kind Regards,

Teng Ma
Responds to the reviewer's comments: # Reviewer 1 Comment 1: I am happy with the authors response.

Response:
Thank you for your review very much.

Comments to the Author(s)
The results look as expected, so they probably calculated everything correctly. However, there are not sufficient details given. Also, they have not cited our prior work in the area, but appear to have done significantly less. The idea of modifying the slip-spring simulations in this way is actually taken over from our ongoing work, and it seems that proper credit is missing. Moreover, we have looked at this question before, using our slip link model [Pilyugina, E.; Schieber, J. D. & Andreev, M. Dielectric relaxation as an independent examination of relaxation mechanisms in entangled polymers using the discrete sliplink model Macromolecules, 2012, 45, 5728-5743]. There are other papers from our work that are relevant and should also be cited.
We have analytic expression for f_d(t) which might be compared to those found here, for example. We also have a more fine-grained version of our model that should be very similar.