167 research outputs found
Bimodality in the transverse fluctuations of a grafted semiflexible polymer and the diffusion-convection analogue: An effective-medium approach
Recent Monte Carlo simulations of a grafted semiflexible polymer in 1+1 dimensions have revealed a pronounced bimodal structure in the probability distribution of the transverse (bending) fluctuations of the free end, when the total contour length is of the order of the persistence length G. Lattanzi , Phys. Rev E 69, 021801 (2004)]. In this paper, we show that the emergence of bimodality is related to a similar behavior observed when a random walker is driven in the transverse direction by a certain type of shear flow. We adapt an effective-medium argument, which was first introduced in the context of the sheared random-walk problem E. Ben-Naim , Phys. Rev. A 45, 7207 (1992)], in order to obtain a simple analytic approximation of the probability distribution of the free-end fluctuations. We show that this approximation captures the bimodality and most of the qualitative features of the free-end fluctuations. We also predict that relaxing the local inextensibility constraint of the wormlike chain could lead to the disappearence of bimodality
Bundle formation in parallel aligned polymers with competing interactions
Aggregation of like-charged polymers is widely observed in biological and
soft matter systems. In many systems, bundles are formed when a short-range
attraction of diverse physical origin like charge-bridging, hydrogen-bonding or
hydrophobic interaction, overcomes the longer- range charge repulsion. In this
Letter, we present a general mechanism of bundle formation in these systems as
the breaking of the translational invariance in parallel aligned polymers with
competing interactions of this type. We derive a criterion for finite-sized
bundle formation as well as for macroscopic phase separation (formation of
infinite bundles).Comment: accepted for publication in Europhys Let
Linear response of a grafted semiflexible polymer to a uniform force field
We use the worm-like chain model to analytically calculate the linear
response of a grafted semiflexible polymer to a uniform force field. The result
is a function of the bending stiffness, the temperature, the total contour
length, and the orientation of the field with respect to that of the grafted
end. We also study the linear response of a worm-like chain with a periodic
alternating sequence of positive and negative charges. This can be considered
as a model for a polyampholyte with intrinsic bending siffness and negligible
intramolecular interactions. We show how the finite intrinsic persistence
length affects the linear response to the external field.Comment: 6 pages, 3 figure
Force-extension relation of cross-linked anisotropic polymer networks
Cross-linked polymer networks with orientational order constitute a wide
class of soft materials and are relevant to biological systems (e.g., F-actin
bundles). We analytically study the nonlinear force-extension relation of an
array of parallel-aligned, strongly stretched semiflexible polymers with random
cross-links. In the strong stretching limit, the effect of the cross-links is
purely entropic, independent of the bending rigidity of the chains. Cross-links
enhance the differential stretching stiffness of the bundle. For hard
cross-links, the cross-link contribution to the force-extension relation scales
inversely proportional to the force. Its dependence on the cross-link density,
close to the gelation transition, is the same as that of the shear modulus. The
qualitative behavior is captured by a toy model of two chains with a single
cross-link in the middle.Comment: 7 pages, 4 figure
Hydrodynamics of liquids of arbitrarily curved flux-lines and vortex loops
We derive a hydrodynamic model for a liquid of arbitrarily curved flux-lines
and vortex loops using the mapping of the vortex liquid onto a liquid of
relativistic charged quantum bosons in 2+1 dimensions recently suggested by
Tesanovic and by Sudbo and collaborators. The loops in the flux-line system
correspond to particle-antiparticle fluctuations in the bosons. We explicitly
incorporate the externally applied magnetic field which in the boson model
corresponds to a chemical potential associated with the conserved charge
density of the bosons. We propose this model as a convenient and physically
appealing starting point for studying the properties of the vortex liquid
Weak point disorder in strongly fluctuating flux-line liquids
We consider the effect of weak uncorrelated quenched disorder (point defects)
on a strongly fluctuating flux-line liquid. We use a hydrodynamic model which
is based on mapping the flux-line system onto a quantum liquid of relativistic
charged bosons in 2+1 dimensions [P. Benetatos and M. C. Marchetti, Phys. Rev.
B 64, 054518, (2001)]. In this model, flux lines are allowed to be arbitrarily
curved and can even form closed loops. Point defects can be scalar or polar. In
the latter case, the direction of their dipole moments can be random or
correlated. Within the Gaussian approximation of our hydrodynamic model, we
calculate disorder-induced corrections to the correlation functions of the
flux-line fields and the elastic moduli of the flux-line liquid. We find that
scalar disorder enhances loop nucleation, and polar (magnetic) defects decrease
the tilt modulus.Comment: 15 pages, submitted to Pramana-Journal of Physics for the special
volume on Vortex State Studie
Orientational order and glassy states in networks of semiflexible polymers
Motivated by the structure of networks of cross-linked cytoskeletal
biopolymers, we study the 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 semi-microscopic 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 crosslink concentration and the stiffness of the polymers. A crossing angle
leads to long range -fold orientational order, e.g.,
"hexatic" or "tetratic" for or , respectively.
The transition is discontinuous and the critical cross-link density depends on
the bending stiffness of the polymers and the cross-link geometry: the higher
the stiffness and the lower , the lower the critical number of cross-links.
In between the sol and the long range ordered state, we always observe a gel
which is a statistically isotropic amorphous solid (SIAS) with random
positional and random orientational localization of the participating polymers.Comment: 20 pages, added references, minor changes, final version as published
in PR
Variational theory of flux-line liquids
We formulate a variational (Hartree like) description of flux line liquids
which improves on the theory we developed in an earlier paper [A.M. Ettouhami,
Phys. Rev. B 65, 134504 (2002)]. We derive, in particular, how the massive term
confining the fluctuations of flux lines varies with temperature and show that
this term vanishes at high enough temperatures where the vortices behave as
freely fluctuating elastic lines.Comment: 10 pages, 1 postscript figur
Transverse fluctuations of grafted polymers
We study the statistical mechanics of grafted polymers of arbitrary stiffness
in a two-dimensional embedding space with Monte Carlo simulations. The
probability distribution function of the free end is found to be highly
anisotropic and non-Gaussian for typical semiflexible polymers. The reduced
distribution in the transverse direction, a Gaussian in the stiff and flexible
limits, shows a double peak structure at intermediate stiffnesses. We also
explore the response to a transverse force applied at the polymer free end. We
identify F-Actin as an ideal benchmark for the effects discussed.Comment: 10 pages, 4 figures, submitted to Physical Review
Tilt Modulus and Angle-Dependent Flux Lattice Melting in the Lowest Landau Level Approximation
For a clean high-T superconductor, we analyze the Lawrence-Doniach free
energy in a tilted magnetic field within the lowest Landau level (LLL)
approximation. The free energy maps onto that of a strictly -axis field, but
with a reduced interlayer coupling. We use this result to calculate the tilt
modulus of a vortex lattice and vortex liquid. The vortex contribution
to can be expressed in terms of the squared -axis Josephson plasmon
frequency . The transverse component of the field has very
little effect on the position of the melting curve.Comment: 8 pages, 2 figures, accepted for publication in Physical Review B
(Rapid Communications
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