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Abstract
A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson–Boltzmann and Maier–Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity to a charged planar wall. The nematic order parameter profile, the counterion density profile and the electrostatic potential profile are interpreted within the framework of a nematic–isotropic wetting phase with a Donnan potential difference.
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Tom AM, Rajesh R, Vemparala S. Aggregation of flexible polyelectrolytes: Phase diagram and dynamics. J Chem Phys 2017; 147:144903. [DOI: 10.1063/1.4993684] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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Tom AM, Rajesh R, Vemparala S. Aggregation dynamics of rigid polyelectrolytes. J Chem Phys 2016; 144:034904. [DOI: 10.1063/1.4939870] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
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Varghese A, Rajesh R, Vemparala S. Aggregation of rod-like polyelectrolyte chains in the presence of monovalent counterions. J Chem Phys 2012; 137:234901. [DOI: 10.1063/1.4771920] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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Kiemes M, Benetatos P, Zippelius A. Orientational order and glassy states in networks of semiflexible polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:021905. [PMID: 21405861 DOI: 10.1103/physreve.83.021905] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2010] [Indexed: 05/30/2023]
Abstract
Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semimicroscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long-range orientational order or are frozen in random directions depending on the value of the crossing angle, the cross-link concentration, and the stiffness of the polymers. A crossing angle θ~2π/M leads to long-range M-fold orientational order, for example, "hexatic" or "tetratic" for θ=60° or 90°, respectively. The transition to the orientationally ordered state is discontinuous and the critical cross-link density, which is higher than that of the gelation transition, depends on the bending stiffness of the polymers and the cross-link angle: The higher the stiffness and the lower the M, the lower is the critical number of cross-links. In between the sol and the long-range ordered state, we always expect a gel which is a statistically isotropic amorphous solid with random positional and random orientational localization of the participating polymers.
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Affiliation(s)
- Martin Kiemes
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
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Wong GCL, Pollack L. Electrostatics of strongly charged biological polymers: ion-mediated interactions and self-organization in nucleic acids and proteins. Annu Rev Phys Chem 2010; 61:171-89. [PMID: 20055668 DOI: 10.1146/annurev.physchem.58.032806.104436] [Citation(s) in RCA: 171] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Charges on biological polymers in physiologically relevant solution conditions are strongly screened by water and salt solutions containing counter-ions. However, the entropy of these counterions can result in surprisingly strong interactions between charged objects in water despite short screening lengths, via coupling between osmotic and electrostatic interactions. Widespread work in theory, experiment, and computation has been carried out to gain a fundamental understanding of the rich, yet sometimes counterintuitive, behavior of these polyelectrolyte systems. Examples of polyelectrolyte association in biology include DNA packaging and RNA folding, as well as aggregation and self-organization phenomena in different disease states.
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Affiliation(s)
- Gerard C L Wong
- Materials Science and Engineering Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
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Franco-Melgar M, Haslam AJ, Jackson G. A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state. Mol Phys 2008. [DOI: 10.1080/00268970801926958] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Komarov PV, Zherenkova LV, Khalatur PG, Reineker P. The formation of planar ribbonlike aggregates from stiff polyanions in the presence of anisotropic cations. J Chem Phys 2007; 125:154906. [PMID: 17059292 DOI: 10.1063/1.2353057] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A dilute salt-free solution of rodlike polyanions in the presence of anisotropic (chain) cations consisting of neutral tails and charged heads is studied. Using Monte Carlo simulation within the framework of the primitive model, different Coulomb coupling regimes were considered. While aggregation in the strong coupling limit is expected, we report new morphology, namely, the formation of ribbonlike nanostructures. At strong electrostatic interaction, the system is found to undergo the self-organization resulting in the formation of planar aggregates that look like a "ladder" of polyanions sandwiched between cationic chains. We investigate the stability of different morphologies and find that these aggregates are thermodynamically stable. Focus has been made on how the chemical structure of anisotropic cations affects the morphology of the aggregates.
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Affiliation(s)
- Pavel V Komarov
- Department of Theoretical Physics, Tver State University, Tver 170002, Russia
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Kindt JT. Simulation and theory of self-assembly and network formation in reversibly cross-linked equilibrium polymers. J Chem Phys 2007; 123:144901. [PMID: 16238418 DOI: 10.1063/1.2046629] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
A simulation model of hard spheres capable of reversible assembly into chains, which then may reversibly cross-link into networks, has been studied through grand canonical Monte Carlo simulation. Effects of varying intra- and interchain bond strengths, chain flexibilities, and restrictions on cross-linking angle were investigated. Observations including chain-length distributions and phase separation could be captured in most cases using a simple model theory. The coupling of chain growth to cross-linking was shown to be highly sensitive to the treatment of cross-linking by chain ends. In some systems, ladderlike domains of several cross-links joining two chains were common, resulting from cooperativity in the cross-linking. Extended to account for this phenomenon, the model theory predicts that such cooperativity will suppress phase separation in weakly polymerizing chains and at high cross-link concentration. In the present model, cross-linking stabilizes the isotropic phase with respect to the nematic phase, causing a shift in the isotropic-nematic transition to higher monomer concentration than in simple equilibrium polymers.
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Affiliation(s)
- James T Kindt
- Department of Chemistry, Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA.
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Liao B, He B, Chen S, Huang Y. The EB-DNA Liquid Crystalline Complex with High Concentration of Mg2+. Polym J 2006. [DOI: 10.1295/polymj.pj2005210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Stilck JF, Levin * Y. Potential of mean force and the charge reversal of rodlike polyions. Mol Phys 2005. [DOI: 10.1080/00268970500185930] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Borukhov I, Bruinsma RF, Gelbart WM, Liu AJ. Structural polymorphism of the cytoskeleton: a model of linker-assisted filament aggregation. Proc Natl Acad Sci U S A 2005; 102:3673-8. [PMID: 15731355 PMCID: PMC553289 DOI: 10.1073/pnas.0404140102] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The phase behavior of charged rods in the presence of interrod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of linkers in the solution modifies the effective interrod interaction and can lead to interfilament attraction. Depending on the composition and physical properties of the system, such as linker-binding energies, filaments will orient either perpendicular or parallel to each other, leading to network-like or bundled structures. We show that such a system can have one of three generic phase diagrams, one dominated by bundles, another by networks, and the third containing both bundle and network-like phases. The first two diagrams can be found over a wide range of interaction energies, whereas the third diagram occurs only for a narrow range. These results provide theoretical understanding of the classification of linker proteins as bundling proteins or crosslinking proteins. In addition, they suggest possible mechanisms by which the cell may control cytoskeletal morphology.
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Affiliation(s)
- Itamar Borukhov
- Department of Chemistry, University of California-Los Angeles, Los Angeles, CA 90095, USA
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Sokolovska TG, Cates ME, Sokolovskii RO. Possible new phase of antagonistic nematogens in a disorienting field. PHYSICAL REVIEW LETTERS 2003; 90:235701. [PMID: 12857272 DOI: 10.1103/physrevlett.90.235701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2002] [Indexed: 05/24/2023]
Abstract
A simple model is proposed for nematogenic molecules that favor perpendicular orientations as well as parallel ones. (Charged rods, for example, show this antagonistic tendency.) When a small disorienting field is applied along z, a low-density phase N- of nematic order parameter S(z)<0 coexists with a dense biaxial nematic N(b). (At zero field, N- becomes isotropic and N(b) uniaxial.) But at stronger fields, a new phase N+4, invariant under pi/2 rotations around the field axis, appears in between N- and N(b). Prospects for finding the N+4 phase experimentally are briefly discussed.
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Affiliation(s)
- T G Sokolovska
- School of Physics, JCMB King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
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Wojciechowski KW, Tretiakov KV, Kowalik M. Elastic properties of dense solid phases of hard cyclic pentamers and heptamers in two dimensions. PHYSICAL REVIEW E 2003; 67:036121. [PMID: 12689146 DOI: 10.1103/physreve.67.036121] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2002] [Indexed: 11/07/2022]
Abstract
Systems of model planar, nonconvex, hard-body "molecules" of fivefold and sevenfold symmetry axes are studied by constant pressure Monte Carlo simulations with variable shape of the periodic box. The molecules, referred to as pentamers (heptamers), are composed of five (seven) identical hard disks "atoms" with centers forming regular pentagons (heptagons) of sides equal to the disk diameter. The elastic compliances of defect-free solid phases are computed by analysis of strain fluctuations and the reference (equilibrium) state is determined within the same run in which the elastic properties are computed. Results obtained by using pseudorandom number generators based on the idea proposed by Holian and co-workers [Holian et al., Phys. Rev. E 50, 1607 (1994)] are in good agreement with the results generated by DRAND48. It is shown that singular behavior of the elastic constants near close packing is in agreement with the free volume approximation; the coefficients of the leading singularities are estimated. The simulations prove that the highest density structures of heptamers (in which the molecules cannot rotate) are auxetic, i.e., show negative Poisson ratios.
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Affiliation(s)
- K W Wojciechowski
- Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznań, Poland.
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