The Statistical Mechanical Theory of Stiff Chains

Saitô, Nobuhiko; Takahashi, Kyoko; Yunoki, Yasuo

doi:10.1143/jpsj.22.219

Cited by 417 publications

(381 citation statements)

References 5 publications

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“…To proceed further we introduce the Rouse-like decay time of the mode of wavelength 2L 11) which is immediately read off by dimensional analysis from Eq. (2.6) as the characteristic time scale.…”

Section: (210)mentioning

confidence: 99%

Dynamic scattering from solutions of semiflexible polymers

Kroy¹,

Frey²

1997

Phys. Rev. E

120

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The dynamic structure factor of semiflexible polymers in solution is derived from the wormlike chain model. Special attention is paid to the rigid constraint of an inextensible contour and to the hydrodynamic interactions. For the cases of dilute and semidilute solutions exact expressions for the initial slope are obtained. When the hydrodynamic interaction is treated on the level of a renormalized friction coefficient, the decay of the structure factor due to the structural relaxation obeys a stretched exponential law in agreement with experiments on actin. We show how the characteristic parameters of the system (the persistence length ℓp, the lateral diameter a of the molecules, and the mesh size ξm of the network) are readily determined by a single scattering experiment with scattering wavelength λ obeying a ≪ λ ≪ ℓp and λ < ξm. We also find an exact explicit expression for the effective (wave-vector-dependent) dynamic exponent z(k) < 3 for semiflexible polymers and thus an enlightening explanation for a longstanding puzzle in polymer physics.

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Section: (210)mentioning

confidence: 99%

Dynamic scattering from solutions of semiflexible polymers

Kroy¹,

Frey²

1997

Phys. Rev. E

120

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“…A different model of semiflexible polymers is the wormlike-chain model 58,59) . In the discrete version we have: 8) where k 1 is the bending elastic constant, which is the energy penalty for the change of angle between the nearests monomers.…”

Section: A Bond Configurationmentioning

confidence: 99%

“…In the discrete version we have: 8) where k 1 is the bending elastic constant, which is the energy penalty for the change of angle between the nearests monomers. The continuous version of this model 58) is defined as follows: 9) subject to the constraint |u| 2 = 1. The next step in the definition of the model is the specification of the interactions between the monomers.…”

Section: A Bond Configurationmentioning

confidence: 99%

The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

Hołyst

Vilgis

1996

Macro Theory & Simulations

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The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers.The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chain close to critical points, fluctuations induced shift of phase boundaries. In particular

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“…In particular we find that as we change the stiffness parameter, t = L/λ, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.PACS numbers: 87.15.-v, 05.20.-y, 36.20.-r, 05.40.-a The simplest model for describing semiflexible polymers without self-avoidance is the so called Worm-LikeChain (WLC) model [1][2][3]. In this model the polymer is modeled as a continuous curve that can be specified by a d−dimensional (d > 1) vectorx(s), s being the distance, measured along the length of the curve, from one fixed end.…”

mentioning

confidence: 99%

“…PACS numbers: 87.15.-v, 05.20.-y, 36.20.-r, 05.40.-a The simplest model for describing semiflexible polymers without self-avoidance is the so called Worm-LikeChain (WLC) model [1][2][3]. In this model the polymer is modeled as a continuous curve that can be specified by a d−dimensional (d > 1) vectorx(s), s being the distance, measured along the length of the curve, from one fixed end.…”

mentioning

confidence: 99%

Triple Minima in the Free Energy of Semiflexible Polymers

Dhar

Chaudhuri

2002

Phys. Rev. Lett.

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We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness λ for finite chains of length L. We find that the polymer properties obtained in this ensemble are qualitatively different from those obtained using constant-force ensembles. In particular we find that as we change the stiffness parameter, t = L/λ, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.PACS numbers: 87.15.-v, 05.20.-y, 36.20.-r, 05.40.-a The simplest model for describing semiflexible polymers without self-avoidance is the so called Worm-LikeChain (WLC) model [1][2][3]. In this model the polymer is modeled as a continuous curve that can be specified by a d−dimensional (d > 1) vectorx(s), s being the distance, measured along the length of the curve, from one fixed end. The energy of the WLC model is just the energy due to curvature and is given bywhereû(s) = ∂x/∂s is the tangent vector and satisfieŝ u 2 = 1. The parameter κ specifies the stiffness of the chain and is related to the persistence length λ defined through û(s).û(s ′ ) = e −|s−s ′ |/λ . It can be shown thatThe thermodynamic properties of such a chain can be obtained from the free energy which can be either the Helmholtz's (F ) free energy or the Gibb's (G) energy. In the former case one considers a polymer whose ends are kept at a fixed distance r [one end fixed at the origin and the other end atr = (0, ...0, r)] by an average force f = ∂F (r, L)/∂r, while in the latter case one fixes the force and the average extension is given by r = −∂G(f, L)/∂f . It can be shown that in the thermodynamic limit L → ∞ the two ensembles are equivalent and related by the usual Legendre transform G = F −f r. For a system with finite L/λ, the equivalence of the two ensembles is not guaranteed, especially when fluctuations become large. We note that real polymers come with a wide range of values of the parameter t = L/λ [e.g. λ ≈ 0.1µm for DNA while λ ≈ 1µm for Actin and their lengths can be varied] and fluctuations in r (or f ) can be very large. Then the choice of the ensemble depends on the experimental conditions. Experiments on stretching polymers are usually performed by fixing one end of the polymer and attaching the other end to a bead which is then pulled by various means (magnetic, optical, mechanical, etc.). In such experiments one can either fix the force on the bead and measure the average polymer extension, or, one could constrain the bead's position and look at the average force on the polymer. In the former case, the Gibb's free energy is relevant while it is the Helmholtz in the second case. This point has been carefully analyzed by Kreuzer and Payne in the context of atomic force microscope experiments [4]. Theoretically, the constant-force ensemble is easier to treat, and infact an exact numerical solution has been o...

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The Statistical Mechanical Theory of Stiff Chains

Cited by 417 publications

References 5 publications

Dynamic scattering from solutions of semiflexible polymers

Dynamic scattering from solutions of semiflexible polymers

The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

Triple Minima in the Free Energy of Semiflexible Polymers

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