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Razbin M, Benetatos P. Elasticity of a Grafted Rod-like Filament with Fluctuating Bending Stiffness. Polymers (Basel) 2023; 15:polym15102307. [PMID: 37242882 DOI: 10.3390/polym15102307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Revised: 04/20/2023] [Accepted: 05/10/2023] [Indexed: 05/28/2023] Open
Abstract
Quite often polymers exhibit different elastic behavior depending on the statistical ensemble (Gibbs vs. Helmholtz). This is an effect of strong fluctuations. In particular, two-state polymers, which locally or globally fluctuate between two classes of microstates, can exhibit strong ensemble inequivalence with negative elastic moduli (extensibility or compressibility) in the Helmholtz ensemble. Two-state polymers consisting of flexible beads and springs have been studied extensively. Recently, similar behavior was predicted in a strongly stretched wormlike chain consisting of a sequence of reversible blocks, fluctuating between two values of the bending stiffness (the so called reversible wormlike chain, rWLC). In this article, we theoretically analyse the elasticity of a grafted rod-like semiflexible filament which fluctuates between two states of bending stiffness. We consider the response to a point force at the fluctuating tip in both the Gibbs and the Helmholtz ensemble. We also calculate the entropic force exerted by the filament on a confining wall. This is done in the Helmholtz ensemble and, under certain conditions, it yields negative compressibility. We consider a two-state homopolymer and a two-block copolymer with two-state blocks. Possible physical realizations of such a system would be grafted DNA or carbon nanorods undergoing hybridization, or grafted F-actin bundles undergoing collective reversible unbinding.
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Affiliation(s)
- Mohammadhosein Razbin
- Department of Energy Engineering and Physics, Amirkabir University of Technology, Tehran 14588, Iran
| | - Panayotis Benetatos
- Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea
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2
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Noh G, Benetatos P. Tensile elasticity of a freely jointed chain with reversible hinges. SOFT MATTER 2021; 17:3333-3345. [PMID: 33630011 DOI: 10.1039/d1sm00053e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Many biopolymers exhibit reversible conformational transitions within the chain, which affect their bending stiffness and their response to a stretching force. For example, double stranded DNA may have denatured "bubbles" of unzipped single strands which open and close randomly. In other polymers, the transitions may be due to the reversible attachment and detachment of ligands on ligand-receptor complexes along the backbone. Semiflexible bundles under tension formed by the reversible attachment of cross-linkers, on a coarse-grained level, exhibit similar behaviour. The simplest theoretical model which captures what the above mentioned systems have in common is a freely jointed chain (FJC) with reversible hinges. Each hinge can be open, as in the usual FJC, or closed forcing the adjacent segments to align (stretch). In this article, we analyse it in the Gibbs ensemble. Remarkably, even though the usual FJC in the thermodynamic limit exhibits ensemble equivalence, the reversible FJC exhibits ensemble inequivalence. Even though a mean field treatment suggests a continuous phase transition to a fully hinged state at a certain force, the generating function method ("necklace model") shows that there is no phase transition. However, there is a crossover between the two states with clearly different responses. In the low force (linear response) regime, the reversible FJC has higher tensile compliance than its usual counterpart. In contrast, in the strong force regime, the tensile compliance of the reversible FJC is much lower than that of the usual FJC.
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Affiliation(s)
- Geunho Noh
- Department of Physics, Kyungpook National University, Bukgu, 80 Daehakro, Daegu 41566, Korea.
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3
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Dutta S, Benetatos P. Statistical ensemble inequivalence for flexible polymers under confinement in various geometries. SOFT MATTER 2020; 16:2114-2127. [PMID: 32016271 DOI: 10.1039/c9sm02246e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The problem of statistical ensemble inequivalence for single polymers has been the subject of intense research. In a recent publication, we show that even though the force-extension relation of a free Gaussian chain exhibits ensemble equivalence, confinement to half-space due to tethering to a planar substrate induces significant inequivalence [S. Dutta and P. Benetatos, Soft Matter, 2018, 14, 6857-6866]. In the present article, we extend that work to the conformational response to confining forces distributed over surfaces. We analyze in both the Helmholtz and the Gibbs ensemble the pressure-volume equation of state of a chain in rectangular, spherical, and cylindrical confinement. We especially consider the case of a directed polymer in a cylinder. We also analyze the case of a tethered chain inside a rectangular box, a sphere, and outside a sphere. In general, confinement causes significant ensemble inequivalence. Remarkably, we recover ensemble equivalence in the limit of squashing confinement. We trace the ensemble inequivalence to the persistence of strong fluctuations. Our work may be useful in the interpretation of single molecule experiments and caging phenomena.
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Affiliation(s)
- Sandipan Dutta
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, Korea
| | - Panayotis Benetatos
- Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Korea.
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4
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Klushin LI, Skvortsov AM, Qi S, Schmid F. Polydisperse Brush with the Linear Density Profile. POLYMER SCIENCE SERIES C 2018. [DOI: 10.1134/s1811238218020121] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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5
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Dutta S, Benetatos P. Inequivalence of fixed-force and fixed-extension statistical ensembles for a flexible polymer tethered to a planar substrate. SOFT MATTER 2018; 14:6857-6866. [PMID: 30101250 DOI: 10.1039/c8sm01321g] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Recent advances in single macromolecule experiments have sparked interest in the ensemble dependence of force-extension relations. The thermodynamic limit may not be attainable for such systems, which leads to inequivalence of the fixed-force and the fixed-extension ensembles. We consider an ideal Gaussian chain described by the Edwards Hamiltonian with one end tethered to a rigid planar substrate. We analytically calculate the force-extension relation in the two ensembles and we show their inequivalence, which is caused by the confinement of the polymer to half space. The inequivalence is quite remarkable for strong compressional forces. We also perform Monte-Carlo simulations of a tethered wormlike chain with contour length 20 times its persistence length, which corresponds to experiments measuring the conformations of DNA tethered to a wall. The simulations confirm the ensemble inequivalence and qualitatively agree with the analytical predictions of the Gaussian model. Our analysis shows that confinement due to tethering causes ensemble inequivalence, irrespective of the polymer model.
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Affiliation(s)
- Sandipan Dutta
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, Korea
| | - Panayotis Benetatos
- Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Korea.
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6
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Benedito M, Giordano S. Thermodynamics of small systems with conformational transitions: The case of two-state freely jointed chains with extensible units. J Chem Phys 2018; 149:054901. [DOI: 10.1063/1.5026386] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Manon Benedito
- Institute of Electronics, Microelectronics and Nanotechnology, UMR 8520, University Lille, CNRS, Centrale Lille, ISEN, University Valenciennes, LIA LICS/LEMAC, F-59000 Lille, France
| | - Stefano Giordano
- Institute of Electronics, Microelectronics and Nanotechnology, UMR 8520, University Lille, CNRS, Centrale Lille, ISEN, University Valenciennes, LIA LICS/LEMAC, F-59000 Lille, France
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7
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Zhang S, Qi S, Klushin LI, Skvortsov AM, Yan D, Schmid F. Phase transitions in single macromolecules: Loop-stretch transition versus loop adsorption transition in end-grafted polymer chains. J Chem Phys 2018; 148:044903. [PMID: 29390835 DOI: 10.1063/1.5013346] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter ε and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force F applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static behavior and the dynamic behavior of chains with different length N are very well described by a scaling ansatz with the scaling parameters (ε - ε*)Nϕ (adsorption transition) and (F - F*)Nν (loop-stretch transition), respectively, where ϕ is the crossover exponent of the adsorption transition and ν is the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes. This is attributed to the fact that the surface contact dynamics in a strongly adsorbed chain is governed by local processes, whereas the end height relaxation of a strongly stretched chain involves the full spectrum of Rouse modes.
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Affiliation(s)
| | - Shuanhu Qi
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, D-55099 Mainz, Germany
| | - Leonid I Klushin
- Department of Physics, American University of Beirut, P. O. Box 11-0236, Beirut 1107 2020, Lebanon
| | - Alexander M Skvortsov
- Chemical-Pharmaceutical Academy, Professora Popova 14, 197022 St. Petersburg, Russia
| | - Dadong Yan
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, D-55099 Mainz, Germany
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8
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Kantor Y, Kardar M. Attractive and repulsive polymer-mediated forces between scale-free surfaces. Phys Rev E 2017; 96:022148. [PMID: 28950594 DOI: 10.1103/physreve.96.022148] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2017] [Indexed: 11/07/2022]
Abstract
We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone) when the polymer is repelled by the obstacles or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation h between obstacles is the only relevant macroscopic length scale, and the polymer-mediated force equals Ak_{B}T/h, where T is temperature. The amplitude A is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of A, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find A=0 for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e., at this special point there is no polymer-mediated force between obstacles (scale free or not).
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Affiliation(s)
- Yacov Kantor
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Mehran Kardar
- Massachusetts Institute of Technology, Department of Physics, Cambridge, Massachusetts 02139, USA
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Zhang S, Qi S, Klushin LI, Skvortsov AM, Yan D, Schmid F. Anomalous critical slowdown at a first order phase transition in single polymer chains. J Chem Phys 2017; 147:064902. [PMID: 28810755 DOI: 10.1063/1.4997435] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
Using Brownian dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order (in the infinite chain length limit, the stretching degree of the chain jumps discontinuously), the characteristic relaxation time is found to grow according to a power law as the transition point is approached. We present a dynamic effective interface model which reproduces these observations and provides an excellent quantitative description of the simulation data. The generic nature of the theoretical model suggests that the unconventional mixing of features that are characteristic for first-order transitions (a jump in an order parameter) and features that are characteristic of critical points (an anomalous slowdown) may be a common phenomenon in force-driven phase transitions of macromolecules.
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Affiliation(s)
| | - Shuanhu Qi
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, D-55099 Mainz, Germany
| | - Leonid I Klushin
- Department of Physics, American University of Beirut, P.O. Box 11-0236, Beirut 1107 2020, Lebanon and Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoy 31, 199004 St. Petersburg, Russia
| | - Alexander M Skvortsov
- Chemical-Pharmaceutical Academy, Professora Popova 14, 197022 St. Petersburg, Russia
| | - Dadong Yan
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, D-55099 Mainz, Germany
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Iliev GK, Whittington SG. Polymers undergoing inhomogeneous adsorption: Order parameters for a partially directed walk model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012111. [PMID: 26274129 DOI: 10.1103/physreve.92.012111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Indexed: 06/04/2023]
Abstract
We consider partially directed walk models of polymers undergoing inhomogeneous adsorption. The inhomogeneity can be in the polymer, in the surface, or in both. For the cases where the polymer is either a homopolymer or a strictly alternating copolymer and where the surface is either homogeneous or has stripes of width 1, we calculate detailed order parameters and show that these provide important information about the ways in which the polymer adsorbs.
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Affiliation(s)
- G K Iliev
- Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3H6
| | - S G Whittington
- Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3H6
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11
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Luettmer-Strathmann J, Binder K. Transitions of tethered chain molecules under tension. J Chem Phys 2014; 141:114911. [DOI: 10.1063/1.4895729] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Affiliation(s)
- Jutta Luettmer-Strathmann
- Department of Physics and Department of Chemistry, The University of Akron, Akron, Ohio 44325-4001, USA
| | - Kurt Binder
- Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
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12
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Klushin LI, Skvortsov AM, Polotsky AA, Hsu HP, Binder K. Coil-bridge transition in a single polymer chain as an unconventional phase transition: theory and simulation. J Chem Phys 2014; 140:204908. [PMID: 24880326 DOI: 10.1063/1.4876717] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The coil-bridge transition in a self-avoiding lattice chain with one end fixed at height H above the attractive planar surface is investigated by theory and Monte Carlo simulation. We focus on the details of the first-order phase transition between the coil state at large height H ⩾ Htr and a bridge state at H ⩽ Htr, where Htr corresponds to the coil-bridge transition point. The equilibrium properties of the chain were calculated using the Monte Carlo pruned-enriched Rosenbluth method in the moderate adsorption regime at (H/Na)tr ⩽ 0.27 where N is the number of monomer units of linear size a. An analytical theory of the coil-bridge transition for lattice chains with excluded volume interactions is presented in this regime. The theory provides an excellent quantitative description of numerical results at all heights, 10 ⩽ H/a ⩽ 320 and all chain lengths 40 < N < 2560 without free fitting parameters. A simple theory taking into account the effect of finite extensibility of the lattice chain in the strong adsorption regime at (H/Na)tr ⩾ 0.5 is presented. We discuss some unconventional properties of the coil-bridge transition: the absence of phase coexistence, two micro-phases involved in the bridge state, and abnormal behavior in the microcanonical ensemble.
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Affiliation(s)
- Leonid I Klushin
- Department of Physics, American University of Beirut, P.O. Box 11-0236, Beirut 1107 2020, Lebanon
| | | | - Alexey A Polotsky
- Institute of Macromolecular Compounds of Russian Academy of Sciences, 31 Bolshoy pr., 199004 St. Petersburg, Russia
| | - Hsiao-Ping Hsu
- Institut für Physik, Johannes-Gutenberg Universität Mainz, Staudinger Weg 7, 55099 Mainz, Germany
| | - Kurt Binder
- Institut für Physik, Johannes-Gutenberg Universität Mainz, Staudinger Weg 7, 55099 Mainz, Germany
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13
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Iliev GK, Whittington SG. Pulling alternating copolymers adsorbed on a striped surface. Phys Rev E 2013; 88:052105. [PMID: 24329212 DOI: 10.1103/physreve.88.052105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2013] [Indexed: 11/07/2022]
Abstract
We consider a partially directed walk model of a strictly alternating copolymer adsorbing on a striped surface where the energy is associated with the numbers of the two types of monomers adsorbed on the two types of surface sites. A force is applied to the last monomer and the polymer responds to this force, sometimes by desorbing. The force can be applied at various angles, with the surface component parallel or perpendicular (or at some other angle) to the stripe direction. The desorption behavior is strongly dependent on the force direction and the response gives information about the shape and direction of the polymer adsorbed on the surface, especially at low temperatures. In some cases the ground state is degenerate and this also has an important effect on the temperature dependence of the critical force needed for desorption. We give a complete solution of the problem using generating function techniques and an approximate treatment that is especially useful at low temperatures and helps in our physical understanding of the situation.
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Affiliation(s)
- G K Iliev
- Department of Mathematics and Statistics, York University, Toronto, Canada
| | - S G Whittington
- Department of Chemistry, University of Toronto, Toronto, Canada
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14
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Hsu HP, Paul W, Binder K. Pulling Single Adsorbed Bottle-Brush Polymers off a Flat Surface: A Monte Carlo Simulation. Macromolecules 2013. [DOI: 10.1021/ma401996n] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Hsiao-Ping Hsu
- Institut
für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg
7, D-55099 Mainz, Germany
| | - Wolfgang Paul
- Institut
für Physik, Martin Luther-Universität Halle-Wittenberg, von
Seckendorff Platz 1, 06120 Halle, Germany
| | - Kurt Binder
- Institut
für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg
7, D-55099 Mainz, Germany
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15
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Samanta HS, Thirumalai D. Exact solution of the Zwanzig-Lauritzen model of polymer crystallization under tension. J Chem Phys 2013; 138:104901. [DOI: 10.1063/1.4794154] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Hsu HP, Binder K. Effect of Chain Stiffness on the Adsorption Transition of Polymers. Macromolecules 2013. [DOI: 10.1021/ma400112q] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hsiao-Ping Hsu
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
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