Topological Constraints in Directed Polymer Melts
Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simu...
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/100232 https://orcid.org/0000-0002-3488-4532 https://orcid.org/0000-0002-3074-4217 |
| _version_ | 1826194337797505024 |
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| author | Serna, Pablo Bunin, Guy Nahum, Adam |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Serna, Pablo Bunin, Guy Nahum, Adam |
| author_sort | Serna, Pablo |
| collection | MIT |
| description | Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be trivial changes the polymer conformations drastically. Polymers of length L wander in the transverse direction only by a distance of order (lnL)[superscript ζ] with ζ≃1.5. This is strongly suppressed in comparison with the Brownian L[superscript 1/2] scaling which holds in the absence of the topological constraint. It is also much smaller than the predictions of standard heuristic approaches—in particular the L[superscript 1/4] of a mean-field-like “array of obstacles” model—so our results present a sharp challenge to theory. Dynamics are also strongly affected by the constraints, and a tagged monomer in an infinite system performs logarithmically slow subdiffusion in the transverse direction. To cast light on the suppression of the strands’ wandering, we analyze the topological complexity of subregions of the melt: the complexity is also logarithmically small, and is related to the wandering by a power law. We comment on insights the results give for 3D melts, directed and nondirected. |
| first_indexed | 2024-09-23T09:54:28Z |
| format | Article |
| id | mit-1721.1/100232 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:54:28Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1002322022-09-30T17:38:08Z Topological Constraints in Directed Polymer Melts Serna, Pablo Bunin, Guy Nahum, Adam Massachusetts Institute of Technology. Department of Physics Bunin, Guy Nahum, Adam Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be trivial changes the polymer conformations drastically. Polymers of length L wander in the transverse direction only by a distance of order (lnL)[superscript ζ] with ζ≃1.5. This is strongly suppressed in comparison with the Brownian L[superscript 1/2] scaling which holds in the absence of the topological constraint. It is also much smaller than the predictions of standard heuristic approaches—in particular the L[superscript 1/4] of a mean-field-like “array of obstacles” model—so our results present a sharp challenge to theory. Dynamics are also strongly affected by the constraints, and a tagged monomer in an infinite system performs logarithmically slow subdiffusion in the transverse direction. To cast light on the suppression of the strands’ wandering, we analyze the topological complexity of subregions of the melt: the complexity is also logarithmically small, and is related to the wandering by a power law. We comment on insights the results give for 3D melts, directed and nondirected. Spain. Ministerio de Economia y Competitividad (European Union FEDER Grant FIS2012-38206) Spain. Ministerio de Educacion, Cultura y Deporte. Formacion de Profesorado Universitario (Grant AP2009-0668) MIT Department of Physics Pappalardo Program Gordon and Betty Moore Foundation. EPiQS Initiative (Grant GBMF4303) 2015-12-14T03:03:47Z 2015-12-14T03:03:47Z 2015-11 2015-07 2015-11-25T23:00:10Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/100232 Serna, Pablo, Guy Bunin, and Adam Nahum. “Topological Constraints in Directed Polymer Melts.” Physical Review Letters 115, no. 22 (November 2015). © 2015 American Physical Society https://orcid.org/0000-0002-3488-4532 https://orcid.org/0000-0002-3074-4217 en http://dx.doi.org/10.1103/PhysRevLett.115.228303 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Serna, Pablo Bunin, Guy Nahum, Adam Topological Constraints in Directed Polymer Melts |
| title | Topological Constraints in Directed Polymer Melts |
| title_full | Topological Constraints in Directed Polymer Melts |
| title_fullStr | Topological Constraints in Directed Polymer Melts |
| title_full_unstemmed | Topological Constraints in Directed Polymer Melts |
| title_short | Topological Constraints in Directed Polymer Melts |
| title_sort | topological constraints in directed polymer melts |
| url | http://hdl.handle.net/1721.1/100232 https://orcid.org/0000-0002-3488-4532 https://orcid.org/0000-0002-3074-4217 |
| work_keys_str_mv | AT sernapablo topologicalconstraintsindirectedpolymermelts AT buninguy topologicalconstraintsindirectedpolymermelts AT nahumadam topologicalconstraintsindirectedpolymermelts |