{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:10:59Z","timestamp":1760148659433,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T00:00:00Z","timestamp":1685059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"SOLVAY"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Mesoscopic simulations of long polymer chains and soft matter systems are conducted routinely in the literature in order to assess the long-lived relaxation processes manifested in these systems. Coarse-grained chains are, however, prone to unphysical intercrossing due to their inherent softness. This issue can be resolved by introducing long intermolecular bonds (the so-called slip-springs) which restore these topological constraints. The separation vector of intermolecular bonds can be determined by enforcing the commonly adopted minimum image convention (MIC). Because these bonds are soft and long (ca 3\u201320 nm), subjecting the samples to extreme deformations can lead to topology violations when enforcing the MIC. We propose the fixed image convention (FIC) for determining the separation vectors of overextended bonds, which is more stable than the MIC and applicable to extreme deformations. The FIC is simple to implement and, in general, more efficient than the MIC. Side-by-side comparisons between the MIC and FIC demonstrate that, when using the FIC, the topology remains intact even in situations with extreme particle displacement and nonaffine deformation. The accuracy of these conventions is the same when applying affine deformation. The article is accompanied by the corresponding code for implementing the FIC.<\/jats:p>","DOI":"10.3390\/computation11060106","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T16:10:53Z","timestamp":1685203853000},"page":"106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Addressing the Folding of Intermolecular Springs in Particle Simulations: Fixed Image Convention"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4183-686X","authenticated-orcid":false,"given":"Aristotelis P.","family":"Sgouros","sequence":"first","affiliation":[{"name":"School of Chemical Engineering, National Technical University of Athens (NTUA), GR-15780 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4763-9739","authenticated-orcid":false,"given":"Doros N.","family":"Theodorou","sequence":"additional","affiliation":[{"name":"School of Chemical Engineering, National Technical University of Athens (NTUA), GR-15780 Athens, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"25004","DOI":"10.1103\/RevModPhys.91.025004","article-title":"Mesoscopic Simulations at the Physics-Chemistry-Biology Interface","volume":"91","author":"Bernaschi","year":"2019","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.progpolymsci.2007.09.002","article-title":"Multiscale Modeling and Simulation of Polymer Nanocomposites","volume":"33","author":"Zeng","year":"2008","journal-title":"Prog. Polym. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5102","DOI":"10.1039\/c2sm07293a","article-title":"Mesoscale Modeling of Block Copolymer Nanocomposites","volume":"8","author":"Langner","year":"2012","journal-title":"Soft Matter"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1134\/S1811238216010082","article-title":"Multiscale Computer Simulation of Polymer Nanocomposites Based on Thermoplastics","volume":"58","author":"Lyulin","year":"2016","journal-title":"Polym. Sci. Ser. C"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7503","DOI":"10.1021\/acs.macromol.9b01379","article-title":"Multiscale Simulations of Graphite-Capped Polyethylene Melts: Brownian Dynamics\/Kinetic Monte Carlo Compared to Atomistic Calculations and Experiment","volume":"52","author":"Sgouros","year":"2019","journal-title":"Macromolecules"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4367","DOI":"10.1039\/b911329k","article-title":"Review of Multi-Scale Particulate Simulation of the Rheology of Wormlike Micellar Fluids","volume":"5","author":"Padding","year":"2009","journal-title":"Soft Matter"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1122\/1.4903498","article-title":"Individual Chain Dynamics of a Polyethylene Melt Undergoing Steady Shear Flow","volume":"59","author":"Edwards","year":"2015","journal-title":"J. Rheol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4524","DOI":"10.1021\/acs.macromol.7b00694","article-title":"Slip-Spring Model for the Linear and Nonlinear Viscoelastic Properties of Molten Polyethylene Derived from Atomistic Simulations","volume":"50","author":"Sgouros","year":"2017","journal-title":"Macromolecules"},{"key":"ref_9","unstructured":"Allen, M.P., and Tildeslay, D.J. (1989). Computer Simulation of Liquids, Clarendon Press."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4423","DOI":"10.1063\/1.474784","article-title":"Dissipative Particle Dynamics: Bridging the Gap between Atomistic and Mesoscopic Simulation","volume":"107","author":"Groot","year":"1997","journal-title":"J. Chem. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"150901","DOI":"10.1063\/1.4979514","article-title":"Perspective: Dissipative Particle Dynamics","volume":"146","author":"Warren","year":"2017","journal-title":"J. Chem. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1063\/1.1481859","article-title":"Time and Length Scales of Polymer Melts Studied by Coarse-Grained Molecular Dynamics Simulations","volume":"117","author":"Padding","year":"2002","journal-title":"J. Chem. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1122\/1.1530155","article-title":"A Full-Chain, Temporary Network Model with Sliplinks, Chain-Length Fluctuations, Chain Connectivity and Chain Stretching","volume":"47","author":"Schieber","year":"2003","journal-title":"J. Rheol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3386","DOI":"10.1021\/ma0519056","article-title":"Linear Viscoelastic Predictions of a Consistently Unconstrained Brownian Slip-Link Model","volume":"39","author":"Nair","year":"2006","journal-title":"Macromolecules"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6128","DOI":"10.1021\/ma050399h","article-title":"Single-Chain Slip-Link Model of Entangled Polymers: Simultaneous Description of Neutron Spin-Echo, Rheology, and Diffusion","volume":"38","author":"Likhtman","year":"2005","journal-title":"Macromolecules"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1146\/annurev-chembioeng-060713-040401","article-title":"Simulating the Flow of Entangled Polymers","volume":"5","author":"Masubuchi","year":"2014","journal-title":"Annu. Rev. Chem. Biomol. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3004","DOI":"10.1021\/acs.macromol.6b01705","article-title":"Equation of State-Based Slip-Spring Model for Entangled Polymer Dynamics","volume":"50","author":"Vogiatzis","year":"2017","journal-title":"Macromolecules"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1088\/0370-1328\/92\/1\/303","article-title":"The Statistical Mechanics of Polymerized Material","volume":"92","author":"Edwards","year":"1967","journal-title":"Proc. Phys. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1063\/1.1675789","article-title":"Reptation of a Polymer Chain in the Presence of Fixed Obstacles","volume":"55","year":"1971","journal-title":"J. Chem. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1002\/pol.1983.180210501","article-title":"Explanation for the 3.4-Power Law for Viscosity of Polymeric Liquids on the Basis of the Tube Model","volume":"21","author":"Doi","year":"1983","journal-title":"J. Polym. Sci. Polym. Phys. Ed."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"014903","DOI":"10.1063\/1.4972582","article-title":"A Multi-Chain Polymer Slip-Spring Model with Fluctuating Number of Entanglements: Density Fluctuations, Confinement, and Phase Separation","volume":"146","author":"Peters","year":"2017","journal-title":"J. Chem. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2930","DOI":"10.1021\/acs.jpcb.2c00697","article-title":"Effects of Slip-Spring Parameters and Rouse Bead Density on Polymer Dynamics in Multichain Slip-Spring Simulations","volume":"126","author":"Masubuchi","year":"2022","journal-title":"J. Phys. Chem. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"10184","DOI":"10.1021\/acs.macromol.8b01739","article-title":"Multi-Chain Slip-Spring Simulations for Branch Polymers","volume":"51","author":"Masubuchi","year":"2018","journal-title":"Macromolecules"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Philippas, A.P., Sgouros, A.P., Megariotis, G., and Theodorou, D.N. (May, January 29). Mesoscopic Simulations of Star Polyethylene Melts at Equilibrium and under Steady Shear Flow. Proceedings of the International Conference of Computational Methods in Sciences and Engineering ICCMSE 2020, Crete, Greece.","DOI":"10.1063\/5.0047757"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Megariotis, G., Vogiatzis, G.G., Sgouros, A.P., and Theodorou, D.N. (2018). Slip Spring-Based Mesoscopic Simulations of Polymer Networks: Methodology and the Corresponding Computational Code. Polymers, 10.","DOI":"10.3390\/polym10101156"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5109","DOI":"10.1039\/C9SM00681H","article-title":"Retardation of the Reaction Kinetics of Polymers Due to Entanglement in the Post-Gel Stage in Multi-Chain Slip-Spring Simulations","volume":"15","author":"Masubuchi","year":"2019","journal-title":"Soft Matter"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5155","DOI":"10.1021\/acs.macromol.1c00567","article-title":"Simulation of Elastomers by Slip-Spring Dissipative Particle Dynamics","volume":"54","author":"Schneider","year":"2021","journal-title":"Macromolecules"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"9798","DOI":"10.1021\/acs.macromol.8b01873","article-title":"Mesoscopic Simulations of Free Surfaces of Molten Polyethylene: Brownian Dynamics\/Kinetic Monte Carlo Coupled with Square Gradient Theory and Compared to Atomistic Calculations and Experiment","volume":"51","author":"Sgouros","year":"2018","journal-title":"Macromolecules"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"148302","DOI":"10.1103\/PhysRevLett.109.148302","article-title":"Translationally Invariant Slip-Spring Model for Entangled Polymer Dynamics","volume":"109","author":"Chappa","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Moghadam, S., Saha Dalal, I., and Larson, R.G. (2019). Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids. Polymers, 11.","DOI":"10.3390\/polym11030465"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1088\/0022-3719\/5\/15\/006","article-title":"The Computer Study of Transport Processes under Extreme Conditions","volume":"5","author":"Lees","year":"1972","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_32","unstructured":"Fetters, L.J., Lohse, D.J., and Colby, R.H. (2006). Physical Properties of Polymers Handbook, Springer."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/BF00396051","article-title":"Extensional Flow\u2014A Mathematical Perspective","volume":"34","author":"Petrie","year":"1995","journal-title":"Rheol. Acta"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jnnfm.2006.01.010","article-title":"One Hundred Years of Extensional Flow","volume":"137","author":"Petrie","year":"2006","journal-title":"J. Nonnewton. Fluid Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1524\/zpch.2013.0311","article-title":"Efficient Coding of the Minimum Image Convention","volume":"227","author":"Deiters","year":"2013","journal-title":"Z. Phys. Chem."},{"key":"ref_36","unstructured":"Sgouros, P.A., and Theodorou, D.N. (2023, May 22). FixImag. Available online: https:\/\/github.com\/ArisSgouros\/FixImag.git."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"108171","DOI":"10.1016\/j.cpc.2021.108171","article-title":"LAMMPS\u2014A Flexible Simulation Tool for Particle-Based Materials Modeling at the Atomic, Meso, and Continuum Scales","volume":"271","author":"Thompson","year":"2022","journal-title":"Comput. Phys. Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1093\/comjnl\/7.2.149","article-title":"Function Minimization by Conjugate Gradients","volume":"7","author":"Fletcher","year":"1964","journal-title":"Comput. J."},{"key":"ref_39","first-page":"35","article-title":"Note sur la convergence de m\u00e9thodes de directions conjugu\u00e9es","volume":"3","author":"Polak","year":"1969","journal-title":"ESAIM Math. Model. Numer. Anal. Mod\u00e9lisation Math\u00e9matique Anal. Num\u00e9rique"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/6\/106\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:42:51Z","timestamp":1760125371000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/6\/106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,26]]},"references-count":39,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["computation11060106"],"URL":"https:\/\/doi.org\/10.3390\/computation11060106","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2023,5,26]]}}}