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Chubak I, Likos CN, Smrek J. Topological and threading effects in polydisperse ring polymer solutions. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1883140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Iurii Chubak
- Faculty of Physics, University of Vienna, Vienna, Austria
| | | | - Jan Smrek
- Faculty of Physics, University of Vienna, Vienna, Austria
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Chubak I, Likos CN, Egorov SA. Multiscale Approaches for Confined Ring Polymer Solutions. J Phys Chem B 2021; 125:4910-4923. [PMID: 33938750 PMCID: PMC8279562 DOI: 10.1021/acs.jpcb.1c01953] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 04/18/2021] [Indexed: 11/29/2022]
Abstract
We apply a hierarchy of multiscale modeling approaches to investigate the structure of ring polymer solutions under planar confinement. In particular, we employ both monomer-resolved (MR-DFT) and a coarse-grained (CG-DFT) density functional theories for fully flexible ring polymers, with the former based on a flexible tangent hard-sphere model and the latter based on an effective soft-colloid representation, to elucidate the ring polymer organization within slits of variable width in different concentration regimes. The predicted monomer and polymer center-of-mass densities in confinement, as well as the surface tension at the solution-wall interface, are compared to explicit molecular dynamics (MD) simulations. The approaches yield quantitative (MR-DFT) or semiquantitative (CG-DFT) agreement with MD. In addition, we provide a systematic comparison between confined linear and ring polymer solutions. When compared to their linear counterparts, the rings are found to feature a higher propensity to structure in confinement that translates into a distinct shape of the depletion potentials between two walls immersed into a polymer solution. The depletion potentials that we extract from CG-DFT and MR-DFT are in semiquantitative agreement with each other. Overall, we find consistency among all approaches as regards the shapes, trends, and qualitative characteristics of density profiles and depletion potentials induced on hard walls by linear and cyclic polymers.
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Affiliation(s)
- Iurii Chubak
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
- Sorbonne
Université CNRS, Physico-Chimie des
Électrolytes et Nanosystèmes Interfaciaux, F-75005 Paris, France
| | - Christos N. Likos
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Sergei A. Egorov
- Department
of Chemistry, University of Virginia, Charlottesville, Virginia 22901, United States
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Guo F, Li K, Wu J, He L, Zhang L. Effects of Topological Constraints on Penetration Structures of Semi-Flexible Ring Polymers. Polymers (Basel) 2020; 12:E2659. [PMID: 33187232 PMCID: PMC7696204 DOI: 10.3390/polym12112659] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Revised: 11/03/2020] [Accepted: 11/08/2020] [Indexed: 11/24/2022] Open
Abstract
The effects of topological constraints on penetration structures of semi-flexible ring polymers in a melt are investigated using molecular dynamics simulations, considering simultaneously the effects of the chain stiffness. Three topology types of rings are considered: 01-knot (the unknotted), 31-knot and 61-knot ring polymers, respectively. With the improved algorithm to detect and quantify the inter-ring penetration (or inter-ring threading), the degree of ring threading does not increase monotonously with the chain stiffness, existing a peak value at the intermediate stiffness. It indicates that rings interpenetrate most at intermediate stiffness where there is a balance between coil expansion (favoring penetrations) and stiffness (inhibiting penetrations). Meanwhile, the inter-ring penetration would be suppressed with the knot complexity of the rings. The analysis of effective potential between the rings provides a better understanding for this non-monotonous behavior in inter-ring penetration.
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Affiliation(s)
- Fuchen Guo
- Department of Physics, Zhejiang University, Hangzhou 310027, China; (F.G.); (K.L.); (J.W.)
| | - Ke Li
- Department of Physics, Zhejiang University, Hangzhou 310027, China; (F.G.); (K.L.); (J.W.)
| | - Jiaxin Wu
- Department of Physics, Zhejiang University, Hangzhou 310027, China; (F.G.); (K.L.); (J.W.)
| | - Linli He
- Department of Physics, Wenzhou University, Wenzhou 325035, China
| | - Linxi Zhang
- Department of Physics, Zhejiang University, Hangzhou 310027, China; (F.G.); (K.L.); (J.W.)
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Pachong SM, Chubak I, Kremer K, Smrek J. Melts of nonconcatenated rings in spherical confinement. J Chem Phys 2020; 153:064903. [DOI: 10.1063/5.0013929] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
| | - Iurii Chubak
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
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Ahmadian Dehaghani Z, Chubak I, Likos CN, Ejtehadi MR. Effects of topological constraints on linked ring polymers in solvents of varying quality. SOFT MATTER 2020; 16:3029-3038. [PMID: 32129365 DOI: 10.1039/c9sm02374g] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their θ-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. Using molecular dynamics simulations, we study the scaling of the poly[n]catenane's radius of gyration in a good solvent, assuming in general that Rg∼mμnν and we find that μ = 0.65 ± 0.02 and ν = 0.60 ± 0.01 for the range of n and m considered. These findings are further rationalized with the help of a mean-field Flory-like theory yielding the values of μ = 16/25 and ν = 3/5, consistent with the numerical results. We show that individual rings within catenanes feature a surplus swelling due to the presence of NL topological links. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its θ-temperature in comparison to isolated linear and ring chains with the following ordering: T > T > T. Finally, we show that the presence of links similarly raises the θ-temperature of a single linked ring in comparison to an unlinked one, bringing its θ-temperature close to the one of a poly[n]catenane.
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Affiliation(s)
- Iurii Chubak
- Faculty of Physics, University of Vienna, Vienna, Austria
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Narros A, Likos CN, Moreno AJ, Capone B. Multi-blob coarse graining for ring polymer solutions. SOFT MATTER 2014; 10:9601-9614. [PMID: 25356818 DOI: 10.1039/c4sm01904k] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a multi-scale molecular modeling of concentrated solutions of unknotted and non-concatenated ring polymers under good solvent conditions. The approach is based on a multi-blob representation of each ring polymer, which is capable of overcoming the shortcomings of single-blob approaches that lose their validity at concentrations exceeding the overlap density of the solution [A. Narros, A. J. Moreno, and C. N. Likos, Soft Matter, 2010, 6, 2435]. By means of a first principles coarse-graining strategy based on analytically determined effective pair potentials between the blobs, computed at zero density, we quantitatively reproduce the single molecule and solution properties of a system with well-defined topological constraints. Detailed comparisons with the underlying, monomer-resolved model demonstrate the validity of our approach, which employs fully transferable pair potentials between connected and unconnected blobs. We demonstrate that the pair structure between the centers of mass of the rings is accurately reproduced by the multi-blob approach, thus opening the way for simulation of arbitrarily long polymers. Finally, we show the importance of the topological constraint of non-concatenation on the structure of the concentrated solution and in particular on the size of the correlation hole and the shrinkage of the rings as melt concentrations are approached.
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Affiliation(s)
- Arturo Narros
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria.
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Narros A, Moreno AJ, Likos CN. Effects of Knots on Ring Polymers in Solvents of Varying Quality. Macromolecules 2013; 46:3654-3668. [PMID: 23729865 PMCID: PMC3667624 DOI: 10.1021/ma400308x] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2013] [Revised: 04/03/2013] [Indexed: 11/30/2022]
Abstract
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We employ extensive computer simulations to investigate the conformations
and the interactions of ring polymers under conditions of worsening
solvent quality, in comparison with those for linear polymers. We
determine the dependence of the Θ-temperature on knotedness
by considering ring polymers of different topologies. We establish
a clear decrease of the former upon changing the topology of the polymer
from linear to an unknotted ring and a further decrease of the same
upon introducing trefoil- or 5-fold knots but we find no difference
in the Θ-point between the two knotted molecules. Our results
are based on two independent methods: one considering the scaling
of the gyration radius with molecular weight and one based on the
dependence of the effective interaction on solvent quality. In addition,
we calculate several shape-parameters of the polymers to characterize
linear, unknotted, and knotted topologies in good solvents and in
the proximity of the Θ-point. The shape parameters of the knotted
molecules show an interesting crossover at a degree of polymerization
that depends on the degree of knottedness of the molecule.
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Affiliation(s)
- Arturo Narros
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, A- 1090 Vienna, Austria
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Abstract
The Topological Aspects of DNA Function and Protein Folding international meeting provided an interdisciplinary forum for biological scientists, physicists and mathematicians to discuss recent developments in the application of topology to the study of DNA and protein structure. It had 111 invited participants, 48 talks and 21 posters. The present article discusses the importance of topology and introduces the articles from the meeting's speakers.
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