1
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Girard M, de la Cruz MO, Marko JF, Erbaş A. Heterogeneous flexibility can contribute to chromatin segregation in the cell nucleus. Phys Rev E 2024; 110:014403. [PMID: 39160964 PMCID: PMC11371272 DOI: 10.1103/physreve.110.014403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 05/29/2024] [Indexed: 08/21/2024]
Abstract
The highly and slightly condensed forms of chromatin, heterochromatin and euchromatin, respectively, segregate in the cell nucleus. Heterochromatin is more abundant in the nucleus periphery. Here we study the mechanism of heterochromatin segregation by modeling interphase chromosomes as diblock ring copolymers confined in a rigid spherical shell using molecular dynamics simulations. In our model, heterochromatin and euchromatin are distinguished by their bending stiffnesses only, while an interaction potential between the spherical shell and chromatin is used to model lamin-associated proteins. Our simulations indicate that in the absence of attractive interactions between the nuclear shell and the chromatin, most heterochromatin segregates towards the nuclear interior due to the depletion of less flexible heterochromatin segments from the nuclear periphery. This inverted chromatin distribution,which is opposite to the conventional case with heterochromatin dominating at the periphery, is in accord with experimental observations in rod cells. This "inversion" is also found to be independent of the heterochromatin concentration and chromosome number. The chromatin distribution at the periphery found in vivo can be recovered by further increasing the bending stiffness of heterochromatin segments or by turning on attractive interactions between the nuclear shell and heterochromatin. Our results indicate that the bending stiffness of chromatin could be a contributor to chromosome organization along with differential effects of HP1α-driven phase segregation and of loop extruders and interactions with the nuclear envelope and topological constraints.
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Affiliation(s)
| | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Department of Chemistry, Department of Chemical and Biological Engineering, and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | | | - Aykut Erbaş
- UNAM-National Nanotechnology Research Center and Institute of Materials Science & Nanotechnology, Bilkent University, Ankara 06800, Turkey
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2
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Grossman D, Katzav E. Effects of self-avoidance on the packing of stiff rods on ellipsoids. Phys Rev E 2024; 109:054111. [PMID: 38907449 DOI: 10.1103/physreve.109.054111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Accepted: 02/27/2024] [Indexed: 06/24/2024]
Abstract
Using a statistical-mechanics approach, we study the effects of geometry and self-avoidance on the ordering of slender filaments inside nonisotropic containers, considering cortical microtubules in plant cells, and packing of genetic material inside viral capsids as concrete examples. Within a mean-field approximation, we show analytically how the shape of the container, together with self-avoidance, affects the ordering of the stiff rods. We find that the strength of the self-avoiding interaction plays a significant role in the preferred packing orientation, leading to a first-order transition for oblate cells, where the preferred orientation changes from azimuthal, along the equator, to a polar one, when self-avoidance is strong enough. While for prolate spheroids the ground state is always a polar-like order, strong self-avoidance results with a deep metastable state along the equator. We compute the critical surface describing the transition between azimuthal and polar ordering in the three-dimensional parameter space (persistence length, eccentricity, and self-avoidance) and show that the critical behavior of this system is in fact related to the butterfly catastrophe model. We calculate the pressure and shear stress applied by the filament on the surface, and the injection force needed to be applied on the filament in order to insert it into the volume. We compare these results to the pure mechanical study where self-avoidance is ignored, and discuss similarities and differences.
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Affiliation(s)
- Doron Grossman
- LadHyX, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
| | - Eytan Katzav
- Racah Institute of Physics, Hebrew University, Jerusalem 9190401, Israel
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3
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Chandrasekaran A, Graham K, Stachowiak JC, Rangamani P. Kinetic trapping organizes actin filaments within liquid-like protein droplets. Nat Commun 2024; 15:3139. [PMID: 38605007 PMCID: PMC11009352 DOI: 10.1038/s41467-024-46726-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Accepted: 03/07/2024] [Indexed: 04/13/2024] Open
Abstract
Several actin-binding proteins (ABPs) phase separate to form condensates capable of curating the actin network shapes. Here, we use computational modeling to understand the principles of actin network organization within VASP condensate droplets. Our simulations reveal that the different actin shapes, namely shells, rings, and mixture states are highly dependent on the kinetics of VASP-actin interactions, suggesting that they arise from kinetic trapping. Specifically, we show that reducing the residence time of VASP on actin filaments reduces degree of bundling, thereby promoting assembly of shells rather than rings. We validate the model predictions experimentally using a VASP-mutant with decreased bundling capability. Finally, we investigate the ring opening within deformed droplets and found that the sphere-to-ellipsoid transition is favored under a wide range of filament lengths while the ellipsoid-to-rod transition is only permitted when filaments have a specific range of lengths. Our findings highlight key mechanisms of actin organization within phase-separated ABPs.
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Affiliation(s)
- Aravind Chandrasekaran
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, 92093-0411, USA
| | - Kristin Graham
- Department of Biomedical Engineering, University of Texas at Austin, Austin, TX, 78712, USA
| | - Jeanne C Stachowiak
- Department of Biomedical Engineering, University of Texas at Austin, Austin, TX, 78712, USA.
- Department of Chemical Engineering, University of Texas at Austin, Austin, TX, 78712, USA.
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, 92093-0411, USA.
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4
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Zhu G, Gao L, Wang Y, Tlusty T, Yan LT. Programmable Potentials Choreograph Defects in a Colloidal Crystal Shell. PHYSICAL REVIEW LETTERS 2024; 132:048201. [PMID: 38335345 DOI: 10.1103/physrevlett.132.048201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Revised: 11/06/2023] [Accepted: 12/19/2023] [Indexed: 02/12/2024]
Abstract
Crystallization on spherical surfaces is obliged by topology to induce lattice defects. But controlling the organization of such defects remains a great challenge due to the long-range constraints of the curved geometry. Here, we report on DNA-coated colloids whose programmable interaction potentials can be used to regulate the arrangement of defects and even achieve perfect icosahedral order on a sphere. Combined simulations and theoretical analysis show how the potential can be tuned by changing the temperature, thereby controlling the number of defects. An explicit expression for the effective potential is derived, allowing us to distinguish the effects of entropic repulsion and enthalpic attraction. Altogether, the present findings provide insights into the physics of crystallization on curved spaces and may be used for designing desired crystal geometries.
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Affiliation(s)
- Guolong Zhu
- School of Physics and Electronics, Hunan University, Changsha 410082, China
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 44919, South Korea
| | - Lijuan Gao
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
| | - Yuming Wang
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
| | - Tsvi Tlusty
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 44919, South Korea
- Departments of Physics and Chemistry, Ulsan National Institute of Science and Technology, Ulsan 44919, South Korea
| | - Li-Tang Yan
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
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5
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Zeng L, Reisner WW. Mixing and demixing arising from compression of two semiflexible polymer chains in nanochannels. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:88. [PMID: 37755600 DOI: 10.1140/epje/s10189-023-00346-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2023] [Accepted: 09/03/2023] [Indexed: 09/28/2023]
Abstract
We use molecular dynamics simulation to probe the non-equilibrium physics of two nanochannel-confined semiflexible polymers in a homogeneous flow field. We find that for sufficiently stiff chains the internal organization of the two chains takes the form of interwoven folds and circular coils. This organization can lead to mixing or demixing depending on chain stiffness and flow speed. At low and intermediate flow, the two chains adopt a folded configuration, which favours mixing. At high flow, the two chains adopt a predominantly coiled configuration. The coiled configuration results in demixing when the chains are compressed from an initially demixed condition and mixing when the chains are compressed from an initially mixed condition. We find that the mixing/demixing behaviour is governed by the ratio of the number of folded segments of one chain relative to the other at low flow and by the degree of coiling in both chains at high flow. For decreasing stiffness, the chains start to aggregate locally instead of mixing smoothly at low and intermediate flow. In the limit of completely flexible chains, the two chains either completely segregate at low flow, or adopt a locally demixed configuration consisting of large aggregates of one chain relative to the other that undergo complex stochastic dynamics, diffusing, disintegrating, and reforming at intermediate flow. The transition from complete segregation to the aggregate-dominated configuration occurs when the linear intra-chain ordering breaks down.
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Affiliation(s)
- Lili Zeng
- Department of Physics, McGill University, 3600 University Street, Montreal, QC, H3A 2T8, Canada.
| | - Walter W Reisner
- Department of Physics, McGill University, 3600 University Street, Montreal, QC, H3A 2T8, Canada
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6
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Tortora MMC, Jost D. Orientational Wetting and Topological Transitions in Confined Solutions of Semiflexible Polymers. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c02350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023]
Affiliation(s)
- Maxime M. C. Tortora
- Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Biologie et Modélisation de la Cellule, 69364 Lyon CEDEX 07, France
| | - Daniel Jost
- Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Biologie et Modélisation de la Cellule, 69364 Lyon CEDEX 07, France
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7
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Adherent Moving of Polymers in Spherical Confined Binary Semiflexible Ring Polymer Mixtures. BIOPHYSICA 2022. [DOI: 10.3390/biophysica2040044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
Based on the coarse-grained model, we used molecular dynamics methods to calculate and simulate a semiflexible long ring–semiflexible short ring blended polymer system confined in a hard sphere. We systematically studied the distribution and motion characteristics of the long ring chain. The results show that when the short ring is short enough (Lshort < 20), the long ring (Llong = 50) is separated from the blend system and then distributed against the inner wall. As the length of the short ring increases (Lshort ≥ 20), the long ring can no longer be separated from the blending system. Moreover, we found that the long ring demonstrates a random direction of adherent walking behavior on the inner surface of the hard sphere. The velocity of the long ring decreases with the increase in the short ring length Lshort. Specifically for Lshort ≥ 20, the system does not undergo phase separation and the speed of the long ring decreases sharply along with the long ring distributed inside the confined bulk. This is related to the inner wall layer moving faster than the inside bulk of the restricted system. Our simulation results can help us to understand the distribution of macromolecules in biological systems in confined systems, including the restricted chromosome partitioning distribution and packing structure of circular DNA molecules.
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8
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Hou C, Gao L, Wang Y, Yan LT. Entropic control of nanoparticle self-assembly through confinement. NANOSCALE HORIZONS 2022; 7:1016-1028. [PMID: 35762392 DOI: 10.1039/d2nh00156j] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Entropy can be the sole driving force for the construction and regulation of ordered structures of soft matter systems. Specifically, under confinement, the entropic penalty could induce enhanced entropic effects which potentially generate visually ordered structures. Therefore, spatial confinement or a crowding environment offers an important approach to control entropy effects in these systems. Here, we review how spatial confinement-mediated entropic effects accurately and even dynamically control the self-assembly of nanoscale objects into ordered structures, focusing on our efforts towards computer simulations and theoretical analysis. First, we introduce the basic principle of entropic ordering through confinement. We then introduce the applications of this concept to various systems containing nanoparticles, including polymer nanocomposites, biological macromolecular systems and macromolecular colloids. Finally, the future directions and challenges for tailoring nanoparticle organization through spatial confinement-mediated entropic effects are detailed. We expect that this review could stimulate further efforts in the fundamental research on the relationship between confinement and entropy and in the applications of this concept for designer nanomaterials.
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Affiliation(s)
- Cuiling Hou
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. China.
| | - Lijuan Gao
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. China.
| | - Yuming Wang
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. China.
| | - Li-Tang Yan
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, P. R. China.
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9
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Poblete S, Božič A, Kanduč M, Podgornik R, Guzman HV. RNA Secondary Structures Regulate Adsorption of Fragments onto Flat Substrates. ACS OMEGA 2021; 6:32823-32831. [PMID: 34901632 PMCID: PMC8655909 DOI: 10.1021/acsomega.1c04774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 11/04/2021] [Indexed: 06/14/2023]
Abstract
RNA is a functionally rich molecule with multilevel, hierarchical structures whose role in the adsorption to molecular substrates is only beginning to be elucidated. Here, we introduce a multiscale simulation approach that combines a tractable coarse-grained RNA structural model with an interaction potential of a structureless flat adsorbing substrate. Within this approach, we study the specific role of stem-hairpin and multibranch RNA secondary structure motifs on its adsorption phenomenology. Our findings identify a dual regime of adsorption for short RNA fragments with and without the secondary structure and underline the adsorption efficiency in both cases as a function of the surface interaction strength. The observed behavior results from an interplay between the number of contacts formed at the surface and the conformational entropy of the RNA molecule. The adsorption phenomenology of RNA seems to persist also for much longer RNAs as qualitatively observed by comparing the trends of our simulations with a theoretical approach based on an ideal semiflexible polymer chain.
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Affiliation(s)
- Simón Poblete
- Instituto
de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia 5091000, Chile
- Computational
Biology Lab, Fundación Ciencia &
Vida, Santiago 7780272, Chile
| | - Anže Božič
- Department
of Theoretical Physics, Jožef Stefan
Institute, SI-1000 Ljubljana, Slovenia
| | - Matej Kanduč
- Department
of Theoretical Physics, Jožef Stefan
Institute, SI-1000 Ljubljana, Slovenia
| | - Rudolf Podgornik
- School
of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Institute
of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Wenzhou
Institute of the University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
- Department
of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Horacio V. Guzman
- Department
of Theoretical Physics, Jožef Stefan
Institute, SI-1000 Ljubljana, Slovenia
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10
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Zhu G, Gao L, Xu Z, Dai X, Zhang X, Yan LT. Entropy-Driven Unconventional Crystallization of Spherical Colloidal Nanocrystals Confined in Wide Cylinders. NANO LETTERS 2021; 21:8439-8446. [PMID: 34591482 DOI: 10.1021/acs.nanolett.1c03127] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The densest packings of identical spherical colloidal nanocrystals in a thin cylinder generally give rise to confinement-induced chiral ordering. Here, we demonstrate that entropy can invalidate Pauling's packing rules for the nanocrystals confined in wide cylinders and novel ordered phases, where chiral ordering is broken, emerge. The nucleation and growth of spherical colloidal nanocrystals in the wide cylinders exhibit unique mechanisms which are distinctly different from that of thin ones. Furthermore, theoretical models which capture the essential physics of the ordering transitions are developed to reproduce the achiral ordering and reveal that the ordered phases are thermodynamically stable and stabilized through confinement-mediated entropic effect. These findings demonstrate that entropy arising from thermal motion can invalidate Pauling's packing rules of spherical colloidal nanocrystals confined in cylinders, which provides new insights into confinement physics of colloidal particles and might inspire nonintuitive design rules for the fabrication of novel ordered phases through confinement.
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Affiliation(s)
- Guolong Zhu
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Lijuan Gao
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Ziyang Xu
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Xiaobin Dai
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Xuanyu Zhang
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Li-Tang Yan
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
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11
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Milchev A, Egorov SA, Binder K. Phase Separation in a Binary Mixture of Semiflexible Polymers Confined in a Repulsive Sphere. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00785] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Andrey Milchev
- Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
| | - Sergei A. Egorov
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901, United States
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
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12
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Milchev A, Binder K. Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation. SOFT MATTER 2021; 17:3443-3454. [PMID: 33646224 DOI: 10.1039/d1sm00172h] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.
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Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113, Sofia, Bulgaria.
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13
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Xu Z, Dai X, Bu X, Yang Y, Zhang X, Man X, Zhang X, Doi M, Yan LT. Enhanced Heterogeneous Diffusion of Nanoparticles in Semiflexible Networks. ACS NANO 2021; 15:4608-4616. [PMID: 33625839 DOI: 10.1021/acsnano.0c08877] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The transport of nanoparticles in semiflexible networks, which form diverse principal structural components throughout living systems, is important in biology and biomedical applications. By combining large-scale molecular simulations as well as theoretical analysis, we demonstrate here that nanoparticles in polymer networks with semiflexible strands possess enhanced heterogeneous diffusion characterized by more evident hopping dynamics. Particularly, the hopping energy barrier approximates to linear dependence on confinement parameters in the regime of moderate rigidity, in contrast to the quadratic dependence of both its soft and hard counterparts. This nonmonotonic feature can be attributed to the competition between the conformation entropy and the bending energy regulated by the chain rigidity, captured by developing an analytical model of a hopping energy barrier. Moreover, these theoretical results agree reasonably well with previous experiments. The findings bear significance in unraveling the fundamental physics of substance transport confined in network-topological environments and would provide an explanation for the dynamics diversity of nanoparticles within various networks, biological or synthetic.
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Affiliation(s)
- Ziyang Xu
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China
| | - Xiaobin Dai
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China
| | - Xiangyu Bu
- School of Science, Beijing Jiaotong University, Beijing, 100044, China
| | - Ye Yang
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China
| | - Xuanyu Zhang
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China
| | - Xingkun Man
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing, 100191, China
- School of Physics, Beihang University, Beijing, 100191, China
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing, 100044, China
| | - Masao Doi
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing, 100191, China
- School of Physics, Beihang University, Beijing, 100191, China
| | - Li-Tang Yan
- State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China
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14
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Nikoubashman A. Ordering, phase behavior, and correlations of semiflexible polymers in confinement. J Chem Phys 2021; 154:090901. [DOI: 10.1063/5.0038052] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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15
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Jangizehi A, Schmid F, Besenius P, Kremer K, Seiffert S. Defects and defect engineering in Soft Matter. SOFT MATTER 2020; 16:10809-10859. [PMID: 33306078 DOI: 10.1039/d0sm01371d] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Soft matter covers a wide range of materials based on linear or branched polymers, gels and rubbers, amphiphilic (macro)molecules, colloids, and self-assembled structures. These materials have applications in various industries, all highly important for our daily life, and they control all biological functions; therefore, controlling and tailoring their properties is crucial. One way to approach this target is defect engineering, which aims to control defects in the material's structure, and/or to purposely add defects into it to trigger specific functions. While this approach has been a striking success story in crystalline inorganic hard matter, both for mechanical and electronic properties, and has also been applied to organic hard materials, defect engineering is rarely used in soft matter design. In this review, we present a survey on investigations on defects and/or defect engineering in nine classes of soft matter composed of liquid crystals, colloids, linear polymers with moderate degree of branching, hyperbranched polymers and dendrimers, conjugated polymers, polymeric networks, self-assembled amphiphiles and proteins, block copolymers and supramolecular polymers. This overview proposes a promising role of this approach for tuning the properties of soft matter.
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Affiliation(s)
- Amir Jangizehi
- Johannes Gutenberg University Mainz, Department of Chemistry, Duesbergweg 10-14, D-55128 Mainz, Germany
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16
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Ishii Y, Zhou Y, He K, Takanishi Y, Yamamoto J, de Pablo J, Lopez-Leon T. Structural transformations in tetravalent nematic shells induced by a magnetic field. SOFT MATTER 2020; 16:8169-8178. [PMID: 32555908 DOI: 10.1039/d0sm00340a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The role of applied fields on the structure of liquid crystals confined to shell geometries has been studied in past theoretical work, providing strategies to produce liquid crystal shells with controlled defect structure or valence. However, the predictions of such studies have not been experimentally explored yet. In this work, we study the structural transformations undergone by tetravalent nematic liquid crystal shells under a strong uniform magnetic field, using both experiments and simulations. We consider two different cases in terms of shell geometry and initial defect symmetry: (i) homogeneous shells with four s = +1/2 defects in a tetrahedral arrangement, and (ii) inhomogeneous shells with four s = +1/2 defects localized in their thinner parts. Consistently with previous theoretical results, we observe that the initial defect structure evolves into a bipolar one, in a process where the defects migrate towards the poles. Interestingly, we find that the defect trajectories and dynamics are controlled by curvature walls that connect the defects by pairs. Based on the angle between Bs, the local projection of the magnetic field on the shell surface, and n+½, a vector describing the defect orientations, we are able to predict the nature and shape of those inversion walls, and therefore, the trajectory and dynamics of the defects. This rule, based on symmetry arguments, is consistent with both experiments and simulations and applies for shells that are either homogeneous or inhomogeneous in thickness. By modifying the angle between Bs and n+½, we are able to induce, in controlled way, complex routes towards the final bipolar state. In the case of inhomogeneous shells, the specific symmetry of the shell allowed us to observe a hybrid splay-bend Helfrich wall for the first time.
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Affiliation(s)
- Yoko Ishii
- Department of Physics, Graduate School of Science, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto, 606-8562, Japan
| | - Ye Zhou
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA.
| | - Kunyun He
- UMR No. 7083, CNRS, Gulliver, ESPCI Paris, PSL Research University, 10 Rue Vauquelin, 75005 Paris, France.
| | - Yoichi Takanishi
- Department of Physics, Graduate School of Science, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto, 606-8562, Japan
| | - Jun Yamamoto
- Department of Physics, Graduate School of Science, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto, 606-8562, Japan
| | - Juan de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA.
| | - Teresa Lopez-Leon
- UMR No. 7083, CNRS, Gulliver, ESPCI Paris, PSL Research University, 10 Rue Vauquelin, 75005 Paris, France.
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17
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Yao X, Chen JZY. Rodlike molecules in extreme confinement. Phys Rev E 2020; 101:062706. [PMID: 32688519 DOI: 10.1103/physreve.101.062706] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 06/15/2020] [Indexed: 11/07/2022]
Abstract
A unique feature of colloid particles and biopolymers is the molecule's intrinsic rigidity characterized by a molecular-level length scale. Under extreme confinement conditions at cellular scales or in nanodevices, these molecules can display orientational ordering accompanied by severe density depletion. Conventional liquid-crystal theories, such as the Oseen-Frank or Landau-de Gennes theories, cannot capture the essential molecular-level properties: the boundary effects, which extend to a distance of the rigidity length scale, and the drastic variations of the inhomogeneous molecular density. Here we show, based on a simple interpretation of the Onsager model, that rodlike molecules in extreme annular confinement produce unusual liquid-crystal defect structures that are independent phases from the patterns usually seen in a weaker confinement environment.
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Affiliation(s)
- Xiaomei Yao
- School of Chemistry, Beihang University, Beijing 100191, People's Republic of China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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18
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Zhou X, Wu J, Zhang L. Ordered aggregation of semiflexible ring-linear blends in ellipsoidal confinement. POLYMER 2020. [DOI: 10.1016/j.polymer.2020.122494] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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19
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Das S, Cacciuto A. Dynamics of an active semi-flexible filament in a spherical cavity. J Chem Phys 2019; 151:244904. [DOI: 10.1063/1.5132757] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- S. Das
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - A. Cacciuto
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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20
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Zhou X, Guo F, Li K, He L, Zhang L. Entropy-induced Separation of Binary Semiflexible Ring Polymer Mixtures in Spherical Confinement. Polymers (Basel) 2019; 11:E1992. [PMID: 31810347 PMCID: PMC6960585 DOI: 10.3390/polym11121992] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 11/24/2019] [Accepted: 11/27/2019] [Indexed: 11/25/2022] Open
Abstract
Coarse-grained molecular dynamics simulations are used to investigate the conformations of binary semiflexible ring polymers (SRPs) of two different lengths confined in a hard sphere. Segregated structures of SRPs in binary mixtures are strongly dependent upon the number density of system (ρ), the bending energy of long SRPs (Kb, long), and the chain length ratio of long to short SRPs (α). With a low ρ or a weak Kb, long at a small ratio α, long SRPs are immersed randomly in the matrix of short SRPs. As ρ and bending energy of long SRPs (Kb, long) are increased up to a certain value for a large ratio α, a nearly complete segregation between long and short SRPs is observed, which can be further characterized by the ratio of tangential and radial components of long SRPs velocity. These explicit segregated structures of the two components in spherical confinement are induced by a delicate competition between the entropic excluded volume (depletion) effects and bending contributions.
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Affiliation(s)
- Xiaolin Zhou
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Fuchen Guo
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Ke Li
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
| | - Linli He
- Department of Physics, Wenzhou University, Wenzhou 325035, Zhejiang, China
| | - Linxi Zhang
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China; (X.Z.); (F.G.); (K.L.)
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21
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Liang Q, Jiang Y, Chen JZY. Orientationally ordered states of a wormlike chain in spherical confinement. Phys Rev E 2019; 100:032502. [PMID: 31640076 DOI: 10.1103/physreve.100.032502] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2019] [Indexed: 06/10/2023]
Abstract
One of the basic characteristics of a linear dsDNA molecule is its persistence length, typically of order 50 nm. The DNA chain inflicts a large energy penalty if it is bent sharply at that length scale. Viruses of bacteria, known as bacteriophages, typically have a dimension of a few tens of nanometers. Yet, it is known that a bacteriophage actively packages viral DNA inside the capsid and ejects it afterwards. Here, adopting a commonly used polymer model known as the wormlike chain, we answer an idealized question: Placing a linear DNA molecule inside a spherical cavity, what ordered states can we derive from known tools in statistical physics? Solving the model in a rigorous field-theory framework, we report a universal phase diagram for four orientationally ordered and disordered states, in terms of two relevant physical parameters.
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Affiliation(s)
- Qin Liang
- Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
- School of Chemistry, Beihang University, Beijing 100191, China
| | - Ying Jiang
- School of Chemistry, Beihang University, Beijing 100191, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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22
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Wang X, Procházka K, Limpouchová Z. Pore size effect on the separation of polymers by interaction chromatography. A Monte Carlo study. Anal Chim Acta 2019; 1064:126-137. [DOI: 10.1016/j.aca.2019.03.017] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Revised: 03/02/2019] [Accepted: 03/09/2019] [Indexed: 12/16/2022]
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23
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Soik SM, Sharp TA. Effects of spherical confinement and backbone stiffness on flexible polymer jamming. Phys Rev E 2019; 99:052505. [PMID: 31212486 DOI: 10.1103/physreve.99.052505] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Indexed: 11/07/2022]
Abstract
We use molecular simulations to study jamming of a crumpled bead-spring model polymer in a finite container and compare to jamming of repulsive spheres. After proper constraint counting, the onset of rigidity is seen to occur isostatically as in the case of repulsive spheres. Despite this commonality, the presence of the curved container wall and polymer backbone bonds introduce new mechanical properties. Notably, these include additional bands in the vibrational density of states that reflect the material structure as well as oscillations in local contact number and density near the wall but with lower amplitude for polymers. Polymers have fewer boundary contacts, and this low-density surface layer strongly reduces the global bulk modulus. We further show that bulk-modulus dependence on backbone stiffness can be described by a model of stiffnesses in series and discuss potential experimental and biological applications.
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Affiliation(s)
- Samuel M Soik
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Tristan A Sharp
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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24
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Affiliation(s)
- Michael P. Allen
- Department of Physics, University of Warwick, Coventry, UK
- H. H. Wills Physics Laboratory, Royal Fort, Bristol, UK
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25
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Azote S, Müller-Nedebock KK. Density fields for branching, stiff networks in rigid confining regions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:23. [PMID: 30788631 DOI: 10.1140/epje/i2019-11784-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Accepted: 01/23/2019] [Indexed: 06/09/2023]
Abstract
We develop a formalism to describe the equilibrium distributions for segments of confined branched networks consisting of stiff filaments. This is applicable to certain situations of cytoskeleton in cells, such as for example actin filaments with branching due to the Arp2/3 complex. We develop a grand ensemble formalism that enables the computation of segment density and polarisation profiles within the confines of the cell. This is expressed in terms of the solution to nonlinear integral equations for auxiliary functions. We find three specific classes of behaviour depending on filament length, degree of branching and the ratio of persistence length to the dimensions of the geometry. Our method allows a numerical approach for semi-flexible filaments that are networked.
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Affiliation(s)
- Somiéalo Azote
- Institute of Theoretical Physics, Department of Physics, Stellenbosch University, Stellenbosch, South Africa.
| | - Kristian K Müller-Nedebock
- Institute of Theoretical Physics, Department of Physics, Stellenbosch University, Stellenbosch, South Africa
- National Institute for Theoretical Physics, Stellenbosch, South Africa
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26
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Manna RK, Kumar PBS. Emergent topological phenomena in active polymeric fluids. SOFT MATTER 2019; 15:477-486. [PMID: 30575844 DOI: 10.1039/c8sm01981a] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Polymeric fluids show a wealth of topological phenomena, from entanglement and reptation at microscales to orientational ordering and defect production at macroscales, which can be explained by statistical-mechanical theories. In the presence of activity, the latter must be augmented by forces that cause spontaneous chain motion and fluid flow. Here, using such augmented Langevin equations, we study active polymeric solutions and melts composed of chains of hydrodynamically interacting stresslets. In a spherical volume, contractile chains are unstable and self-knot into entangled melts at both low and high densities. Extensile chains in the same geometry form an unentangled reptating state at low densities and an entangled, coherently moving, non-reptating state at high densities. On a spherical surface, contractile chains show transitions, with increasing areal density, between isotropic, orientationally ordered and micro-phase separated states. Extensile chains in the same geometry show a transition between isotropic and nematic states. In both cases, defects in orientationally ordered states are produced athermally and without conserving topological charge. Our work reproduces the phenomenology of several recent experiments, highlights the importance of hydrodynamic interactions in active polymer fluids, and suggests non-equilibrium kinetic routes to topological structures that are otherwise difficult to obtain in equilibrium.
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Affiliation(s)
- Raj Kumar Manna
- Department of Physics, Indian Institute of Technology Madras, Chennai, India.
| | - P B Sunil Kumar
- Department of Physics, Indian Institute of Technology Madras, Chennai, India. and Department of Physics, Indian Institute of Technology Palakkad, Palakkad 678557, India.
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27
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Khadilkar MR, Nikoubashman A. Self-assembly of semiflexible polymers confined to thin spherical shells. SOFT MATTER 2018; 14:6903-6911. [PMID: 30091775 DOI: 10.1039/c8sm01170b] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Confinement effects are critical for stiff macromolecules in biological cells, vesicles, and other systems in soft matter. For these molecules, the competition between the packing entropy and the enthalpic cost of bending is further shaped by strong confinement effects. Through coarse-grained molecular dynamics simulations, we explore the self-assembly of semiflexible polymers confined in thin spherical shells for various chain lengths, chain stiffnesses, and shell thicknesses. Here, we focus on the case where the contour and persistence length of the polymers are comparable to the radius of the confining cavity. The range of ordered structures is analyzed using several order parameters to elucidate the nature of orientational ordering in different parameter regimes. Previous simulations have revealed the emergence of bipolar and quadrupolar topological defects on the surface when the entire cavity was filled with a concentrated polymer solution [Phys. Rev. Lett., 2017, 118, 217803]. In contrast, spherical shell confinement restricts the appearance of a bipolar order. Instead, only the extent of the quadrupolar order changes with chain stiffness, as evidenced by the relative motion of topological defects. In the case of monolayers, we observe a nematic to smectic transition accompanied by a change in the nematic grain-size distribution as the contour length was decreased.
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Affiliation(s)
- Mihir R Khadilkar
- Johannes Gutenberg University Mainz, Staudinger Weg 7, Mainz 55128, Germany.
| | - Arash Nikoubashman
- Johannes Gutenberg University Mainz, Staudinger Weg 7, Mainz 55128, Germany.
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28
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29
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Milchev A, Egorov SA, Vega DA, Binder K, Nikoubashman A. Densely Packed Semiflexible Macromolecules in a Rigid Spherical Capsule. Macromolecules 2018. [DOI: 10.1021/acs.macromol.7b02643] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113 Sofia, Bulgaria
| | - Sergei A. Egorov
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901, United States
| | - Daniel A. Vega
- Department of Physics, Universidad Nacional del Sur-IFISUR-CONICET, 8000 Bahía Blanca, Argentina
| | - Kurt Binder
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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30
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Sentker K, Zantop AW, Lippmann M, Hofmann T, Seeck OH, Kityk AV, Yildirim A, Schönhals A, Mazza MG, Huber P. Quantized Self-Assembly of Discotic Rings in a Liquid Crystal Confined in Nanopores. PHYSICAL REVIEW LETTERS 2018; 120:067801. [PMID: 29481274 DOI: 10.1103/physrevlett.120.067801] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Revised: 11/21/2017] [Indexed: 05/16/2023]
Abstract
Disklike molecules with aromatic cores spontaneously stack up in linear columns with high, one-dimensional charge carrier mobilities along the columnar axes, making them prominent model systems for functional, self-organized matter. We show by high-resolution optical birefringence and synchrotron-based x-ray diffraction that confining a thermotropic discotic liquid crystal in cylindrical nanopores induces a quantized formation of annular layers consisting of concentric circular bent columns, unknown in the bulk state. Starting from the walls this ring self-assembly propagates layer by layer towards the pore center in the supercooled domain of the bulk isotropic-columnar transition and thus allows one to switch on and off reversibly single, nanosized rings through small temperature variations. By establishing a Gibbs free energy phase diagram we trace the phase transition quantization to the discreteness of the layers' excess bend deformation energies in comparison to the thermal energy, even for this near room-temperature system. Monte Carlo simulations yielding spatially resolved nematic order parameters, density maps, and bond-orientational order parameters corroborate the universality and robustness of the confinement-induced columnar ring formation as well as its quantized nature.
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Affiliation(s)
- Kathrin Sentker
- Institut für Materialphysik und -technologie, Technische Universität Hamburg (TUHH), Eißendorferstr. 42, D-21073 Hamburg, Germany
| | - Arne W Zantop
- Max-Planck-Institut für Dynamik und Selbstorganisation, Am Faßberg 17, D-37077 Göttingen, Germany
| | - Milena Lippmann
- Deutsches Elektronen Synchrotron (DESY), Notkestraße 85, D-22607 Hamburg, Germany
| | - Tommy Hofmann
- Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
| | - Oliver H Seeck
- Deutsches Elektronen Synchrotron (DESY), Notkestraße 85, D-22607 Hamburg, Germany
| | - Andriy V Kityk
- Faculty of Electrical Engineering, Czestochowa University of Technology, Al. Armii Krajowej 17, P-42-200 Czestochowa, Poland
| | - Arda Yildirim
- Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, D-12205 Berlin, Germany
| | - Andreas Schönhals
- Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, D-12205 Berlin, Germany
| | - Marco G Mazza
- Max-Planck-Institut für Dynamik und Selbstorganisation, Am Faßberg 17, D-37077 Göttingen, Germany
| | - Patrick Huber
- Institut für Materialphysik und -technologie, Technische Universität Hamburg (TUHH), Eißendorferstr. 42, D-21073 Hamburg, Germany
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31
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Milchev A, Egorov SA, Nikoubashman A, Binder K. Conformations and orientational ordering of semiflexible polymers in spherical confinement. J Chem Phys 2017; 146:194907. [PMID: 28527445 PMCID: PMC5438305 DOI: 10.1063/1.4983131] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2017] [Accepted: 04/25/2017] [Indexed: 12/28/2022] Open
Abstract
Semiflexible polymers in lyotropic solution confined inside spherical nanoscopic "containers" with repulsive walls are studied by molecular dynamics simulations and density functional theory, as a first step to model confinement effects on stiff polymers inside of miniemulsions, vesicles, and cells. It is shown that the depletion effects caused by the monomer-wall repulsion depend distinctly on the radius R of the sphere. Further, nontrivial orientational effects occur when R, the persistence length ℓp, and the contour length L of the polymers are of similar magnitude. At intermediate densities, a "shell" of wall-attached chains is forming, such that the monomers belonging to those chains are in a layer at about the distance of one monomer from the container wall. At the same time, the density of the centers of mass of these chains is peaked somewhat further inside, but still near the wall. However, the arrangement of chains is such that the total monomer density is almost uniform in the sphere, apart from a small layering peak at the wall. It is shown that excluded volume effects among the monomers are crucial to account for this behavior, although they are negligible for comparable isolated single semiflexible chains of the same length.
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Affiliation(s)
- Andrey Milchev
- Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113 Sofia, Bulgaria
| | - Sergei A Egorov
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Kurt Binder
- Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
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