References
- 1Gusev AA. Numerical Estimates of the Topological Effects in the Elasticity of Gaussian Polymer Networks and Their Exact Theoretical Description. Macromolecules. May 2019;52(9):3244–3251.
issn : 0024-9297, 1520-5835. DOI: 10.1021/acs.macromol.9b00262 - 2Gusev AA, Schwarz F. Molecular Dynamics Validation and Applications of the Maximum Entropy Homogenization Procedure for Predicting the Elastic Properties of Gaussian Polymer Networks. Macromolecules. Dec. 2019;52(24):9445–9455.
issn : 0024-9297, 1520-5835. DOI: 10.1021/acs.macromol.9b01766 - 3Komarov PV, Yu-Tsung C, Shih-Ming C, Khalatur PG, Reineker P. Highly Cross-Linked Epoxy Resins: An Atomistic Molecular Dynamics Simulation Combined with a Mapping/Reverse Mapping Procedure. Macromolecules. Oct. 2007;40(22):8104–8113.
issn : 0024-9297. DOI: 10.1021/ma070702 - 4Zhang G, Moreira LA, Stuehn T, Daoulas KC, Kremer K. Equilibration of High Molecular Weight Polymer Melts: A Hierarchical Strategy. ACS Macro Letters. Feb. 2014;3(2):198–203. DOI: 10.1021/mz5000015
- 5Svaneborg C, Everaers R, Grest GS, Curro JG. Connectivity and Entanglement Stress Contributions in Strained Polymer Networks. Macromolecules. July 2008;41(13):4920–4928.
issn : 0024-9297. DOI: 10.1021/ma800018f - 6Gusev AA, Schwarz F. Molecular Dynamics Study on the Validity of Miller–Macosko Theory for Entanglement and Crosslink Contributions to the Elastic Modulus of End-Linked Polymer Networks. Macromolecules. Sept. 2022;55(18):8372–8383.
issn : 0024-9297. DOI: 10.1021/acs.macromol.2c00814 - 7Gula IA, Karimi-Varzaneh HA, Svaneborg C. Computational Study of Cross-Link and Entanglement Contributions to the Elastic Properties of Model PDMS Networks. Macromolecules. Aug. 2020;53(16):6907–6927.
issn : 0024-9297. DOI: 10.1021/acs.macromol.0c00682 - 8Grest GS, Kremer K. Molecular dynamics simulation for polymers in the presence of a heat bath. Physical Review A. May 1986;33(5):3628–3631.
issn : 0556-2791. DOI: 10.1103/PhysRevA.33.3628 - 9Grest GS, Dünweg B, Kremer K. Vectorized link cell Fortran code for molecular dynamics simulations for a large number of particles. Computer Physics Communications. Oct. 1989;55(3):269–285.
issn : 00104655. DOI: 10.1016/0010-4655(89)90125-2 - 10Kremer K, Grest GS. Dynamics of entangled linear polymer melts: A molecular-dynamics simulation. The Journal of Chemical Physics. Apr. 1990;92(8):5057–5086.
issn : 0021-9606, 1089-7690. DOI: 10.1063/1.458541 - 11Thompson AP, et al. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comp Phys Comm. 2022;271:
10817 . DOI: 10.1016/j.cpc.2021.108171 - 12Abraham M, et al. GROMACS 2025.0 source code. Feb. 2025. URL:
https://gitlab.com/gromacs/gromacs . - 13COGNAC – OCTA.jp. URL:
https://octa.jp/components/cognac/ (visited on 03/04/2025). - 14OCTA – Integrated Simulation System for Soft Materials, Free and open software of Multi-Scale Simulation for Materials Design. URL:
https://octa.jp/ (visited on 03/04/2025). - 15Kühne TD, et al. CP2K: An electronic structure and molecular dynamics software package – Quickstep: Efficient and accurate electronic structure calculations. The Journal of Chemical Physics. May 2020;152(19):
194103 .issn : 0021-9606. DOI: 10.1063/5.0007045 - 16Van Rossum G, Drake FL. Python 3 Reference Manual. Scotts Valley, CA: CreateSpace; 2009.
isbn : 1-4414-1269-7. - 17Michaud-Agrawal N, Denning EJ, Woolf TB, Beckstein O. MDAnalysis: A toolkit for the analysis of molecular dynamics simulations. Journal of Computational Chemistry. 2011;32(10):2319–2327.
issn : 1096-987X. DOI: 10.1002/jcc.21787 - 18Gowers RJ, et al. MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations. scipy; June 2016. DOI: 10.25080/Majora-629e541a-00e
- 19Stefko M, Douglass K, Manley S. PolymerCpp. July 2020. DOI: 10.5281/zenodo.3928659
- 20Ramprasad-Group/PSP. original-date: 2020-05-17T03:11:56Z. Feb. 2025. URL:
https://github.com/Ramprasad-Group/PSP (visited on 03/04/2025). - 21Barrett T. Tj-Barrett/Polymer-Toolbox. original-date: 2022-07-28T16:11:09Z. Jan. 2024. URL:
https://github.com/Tj-Barrett/Polymer-Toolbox (visited on 03/04/2025). - 22Bernhard T. GenieTim/polymer-graph-sketcher. original-date: 2025-02-19T13:29:53Z. Oct. 2025. URL:
https://github.com/GenieTim/polymer-graph-sketcher (visited on 10/30/2025). - 23Intro — pybind11 documentation. URL:
https://pybind11.readthedocs.io/en/stable/ (visited on 03/31/2022). - 24Csardi G, Nepusz T. The igraph software package for complex network research. InterJournal Complex Systems. 2006;
1695 . URL:https://igraph.org . - 25Tsimouri IC, Caseri WR, Gusev AA. Monte Carlo Evidence on Simple Conventional Means to Characterize the Final Extent of Reaction of Cured End-Linked Polymer Networks through the Miller–Macosko Nonlinear Polymerization Theory. Macromolecules. Feb. 2021;54(4):1589–1598.
issn : 0024-9297. DOI: 10.1021/acs.macromol.0c02251 - 26Tsimouri IC, Caseri W, Hine PJ, Gusev AA. Lightweight silicon and glass composites with submicron viscoelastic interlayers and unconventional combinations of stiffness and damping. Composites Part B: Engineering. Sept. 2024;284:
111717 .issn : 1359-8368. DOI: 10.1016/j.compositesb.2024.111717 - 27Mansuy R, Yor M, editors. Aspects of Brownian Motion. en. Universitext. Berlin Heidelberg: Springer; 2008.
isbn : 978-3-540-22347-4. DOI: 10.1007/978-3-540-49966-4 - 28Ibe OC.
Brownian Motion . In: Ibe OC, editor. Markov Processes for Stochastic Modeling (Second Edition). Oxford: Elsevier; Jan. 2013. pp. 263–293.isbn : 978-0-12-407795-9. DOI: 10.1016/B978-0-12-407795-9.00009-8 - 29Chow WC. Brownian bridge. WIREs Computational Statistics. 2009;1(3):325–332.
issn : 1939-0068. DOI: 10.1002/wics.38 - 30Martínez S, Petritis D. Thermodynamics of a Brownian bridge polymer model in a random environment. Journal of Physics A: Mathematical and General. Mar. 1996;29(6):1267–1279.
issn : 0305-4470, 1361-6447. DOI: 10.1088/0305-4470/29/6/013 - 31Wang S, Ramkrishna D, Narsimhan V. Exact sampling of polymer conformations using Brownian bridges. The Journal of Chemical Physics. July 2020;153(3):
034901 .issn : 0021-9606. DOI: 10.1063/5.0010368 - 32Bernhard T, Gusev AA. Phantom Force Balance Procedure for Predicting the Modulus of Entangled Polymer Networks. ACS Polymers Au. Aug. 2025;5(5):500–513. DOI: 10.1021/acspolymersau.5c00036
- 33Langeloth M, Masubuchi Y, Böhm MC, Müller-Plathe F. Recovering the reptation dynamics of polymer melts in dissipative particle dynamics simulations via slip-springs. The Journal of Chemical Physics. Mar. 2013;138(10):
104907 .issn : 0021-9606. DOI: 10.1063/1.4794156 - 34Schneider L, de Pablo J. Entanglements via Slip-Springs with Soft, Coarse-Grained Models for Systems Having Explicit Liquid-Vapor Interfaces. arXiv:2211.05161 [cond-mat, physics:physics]. Nov. 2022. DOI: 10.48550/arXiv.2211.05161
- 35Gusev AA, Bernhard T. Molecular Model for Linear Viscoelastic Properties of Entangled Polymer Networks. Macromolecules. Nov. 2024;57(21):10152–10163.
issn : 0024-9297. DOI: 10.1021/acs.macromol.4c01429 - 36Anderson E, et al. LAPACK users’ guide. 3rd ed. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1999.
isbn : 0-89871-447-8 (paperback). - 37Johnson DB. Finding All the Elementary Circuits of a Directed Graph. SIAM Journal on Computing. Mar. 1975;4(1):77–84.
issn : 0097-5397, 1095-7111. DOI: 10.1137/0204007 - 38Pint: makes units easy — pint 0.23rc3.dev1+g52ac9f5 documentation. URL:
https://pint.readthedocs.io/en/stable/index.html (visited on 02/06/2024). - 39units command — LAMMPS documentation. URL:
https://lammps.sandia.gov/doc/units.html (visited on 12/09/2020). - 40Everaers R, Karimi-Varzaneh HA, Fleck F, Hojdis N, Svaneborg C. Kremer–Grest Models for Commodity Polymer Melts: Linking Theory, Experiment, and Simulation at the Kuhn Scale. Macromolecules. Mar. 2020;53(6):1901–1916.
issn : 0024-9297. DOI: 10.1021/acs.macromol.9b02428 - 41Miller DR, Macosko CW. A New Derivation of Post Gel Properties of Network Polymers. Macromolecules. Mar. 1976;9(2):206–211.
issn : 0024-9297. DOI: 10.1021/ma60050a004 - 42Macosko CW, Miller DR. A New Derivation of Average Molecular Weights of Nonlinear Polymers. Macromolecules. Mar. 1976;9(2):199–206.
issn : 0024-9297. DOI: 10.1021/ma60050a003 - 43Urayama K, Miki T, Takigawa T, Kohjiya S. Damping Elastomer Based on Model Irregular Networks of End-Linked Poly(Dimethylsiloxane). Chemistry of Materials. Jan. 2004;16(1):173–178.
issn : 0897-4756. DOI: 10.1021/cm0343507 - 44Patel SK, Malone S, Cohen C, Gillmor JR, Colby RH. Elastic modulus and equilibrium swelling of poly(dimethylsiloxane) networks. Macromolecules. Sept. 1992;25(20):5241–5251.
issn : 0024-9297, 1520-5835. DOI: 10.1021/ma00046a021 - 45McKinney W. Data Structures for Statistical Computing in Python. In: van der Walt S, Millman J, editors. Proceedings of the 9th Python in Science Conference; 2010. pp. 56–61. DOI: 10.25080/Majora-92bf1922-00a
- 46The pandas development team. pandas-dev/pandas: Pandas. Feb. 2020. DOI: 10.5281/zenodo.3509134
- 47Harris CR, et al. Array programming with NumPy. Nature. Sept. 2020;585(7825):357–362. DOI: 10.1038/s41586-020-2649-2
- 48Guennebaud G, Jacob B, et al. Eigen v3. 2010. URL:
http://eigen.tuxfamily.org . - 49Johnson SG. stevengj/nlopt. original-date: 2013-08-27T16:59:11Z. July 2022. URL:
https://github.com/stevengj/nlopt (visited on 07/06/2022). - 50Qiu Y. Spectra: C++ library for large scale eigenvalue problems; 2015. URL:
https://spectralib.org . - 51Ramírez J, Sukumaran SK, Vorselaars B, Likhtman AE. Efficient on the fly calculation of time correlation functions in computer simulations. The Journal of Chemical Physics. Oct. 2010;133(15):
154103 .issn : 0021-9606. DOI: 10.1063/1.3491098 - 52Rubinstein M, Colby RH.
Polymer Physics . English. 1st edition. Oxford; New York: Oxford University Press, June 2003.isbn : 978-0-19-852059-7.