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Dolgushev M, Hauber AL, Pelagejcev P, Wittmer JP. Marginally compact fractal trees with semiflexibility. Phys Rev E 2018; 96:012501. [PMID: 29347244 DOI: 10.1103/physreve.96.012501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2017] [Indexed: 11/07/2022]
Abstract
We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness, the self-contact density gets drastically reduced.
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Affiliation(s)
- Maxim Dolgushev
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany.,Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France
| | - Adrian L Hauber
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
| | - Philipp Pelagejcev
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
| | - Joachim P Wittmer
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France
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Dolgushev M, Wittmer JP, Johner A, Benzerara O, Meyer H, Baschnagel J. Marginally compact hyperbranched polymer trees. SOFT MATTER 2017; 13:2499-2512. [PMID: 28304066 DOI: 10.1039/c7sm00243b] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution ρpair(r) or the shear-stress relaxation modulus G(t), are investigated theoretically and by means of computer simulations. We emphasize that albeit the self-contact density diverges logarithmically with the total mass N, this effect becomes rapidly irrelevant with increasing spacer length S. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time τp of mode p must scale as τp ∼ (N/p)5/3 rather than the usual square power law for linear chains.
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Affiliation(s)
- M Dolgushev
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany and Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
| | - J P Wittmer
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
| | - A Johner
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
| | - O Benzerara
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
| | - H Meyer
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
| | - J Baschnagel
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
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Dolgushev M, Liu H, Zhang Z. Extended Vicsek fractals: Laplacian spectra and their applications. Phys Rev E 2016; 94:052501. [PMID: 27967151 DOI: 10.1103/physreve.94.052501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Indexed: 06/06/2023]
Abstract
Extended Vicsek fractals (EVF) are the structures constructed by introducing linear spacers into traditional Vicsek fractals. Here we study the Laplacian spectra of the EVF. In particularly, the recurrence relations for the Laplacian spectra allow us to obtain an analytic expression for the sum of all inverse nonvanishing Laplacian eigenvalues. This quantity characterizes the large-scale properties, such as the gyration radius of the polymeric structures, or the global mean-first passage time for the random walk processes. Introduction of the linear spacers leads to local heterogeneities, which reveal themselves, for example, in the dynamics of EVF under external forces.
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Affiliation(s)
- Maxim Dolgushev
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
- Institut Charles Sadron, Université de Strasbourg and CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France
| | - Hongxiao Liu
- School of Computer Science, Fudan University, Shanghai 200433, China
- Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China
| | - Zhongzhi Zhang
- School of Computer Science, Fudan University, Shanghai 200433, China
- Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China
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Dolgushev M, Markelov DA, Fürstenberg F, Guérin T. Local orientational mobility in regular hyperbranched polymers. Phys Rev E 2016; 94:012502. [PMID: 27575171 DOI: 10.1103/physreve.94.012502] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2016] [Indexed: 11/07/2022]
Abstract
We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after structural average. We analyze the most relevant processes of single segment motion and provide an analytic approximation for the corresponding relaxation times. Furthermore, we describe an iterative method to calculate the orientational dynamics in the case of very large macromolecular sizes.
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Affiliation(s)
- Maxim Dolgushev
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany.,Institut Charles Sadron, Université de Strasbourg and CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France
| | - Denis A Markelov
- St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia.,St. Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University), Kronverkskiy pr. 49, St. Petersburg, 197101, Russia
| | - Florian Fürstenberg
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Thomas Guérin
- Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS UMR 5798, Talence, France
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Mielke J, Dolgushev M. Relaxation Dynamics of Semiflexible Fractal Macromolecules. Polymers (Basel) 2016; 8:polym8070263. [PMID: 30974539 PMCID: PMC6432473 DOI: 10.3390/polym8070263] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2016] [Revised: 06/28/2016] [Accepted: 07/01/2016] [Indexed: 11/21/2022] Open
Abstract
We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locally-dendritic structure that is more pronounced for higher stiffness.
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Affiliation(s)
- Jonas Mielke
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
| | - Maxim Dolgushev
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France.
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Rabbel H, Frey H, Schmid F. Statistical properties of linear-hyperbranched graft copolymers prepared via “hypergrafting” of ABm monomers from linear B-functional core chains: A molecular dynamics simulation. J Chem Phys 2015; 143:243125. [DOI: 10.1063/1.4935371] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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