34 research outputs found
Anisotropic Random Networks of Semiflexible Polymers
Motivated by the organization of crosslinked cytoskeletal biopolymers, we
present a semimicroscopic replica field theory for the formation of anisotropic
random networks of semiflexible polymers. The networks are formed by
introducing random permanent crosslinks which fix the orientations of the
corresponding polymer segments to align with one another. Upon increasing the
crosslink density, we obtain a continuous gelation transition from a fluid
phase to a gel where a finite fraction of the system gets localized at random
positions. For sufficiently stiff polymers, this positional localization is
accompanied by a {\em continuous} isotropic-to-nematic (IN) transition occuring
at the same crosslink density. As the polymer stiffness decreases, the IN
transition becomes first order, shifts to a higher crosslink density, and is
preceeded by an orientational glass (statistically isotropic amorphous solid)
where the average polymer orientations freeze in random directions.Comment: 5 pages, 2 figures; final version with expanded discussion to appear
in PR
Random networks of cross-linked directed polymers
We explore the effect of random permanent cross-links on a system of directed
polymers confined between two planes with their end-points free to slide on
them. We treat the cross-links as quenched disorder and we use a
semimicroscopic replica field theory to study the structure and elasticity of
this system. Upon increasing the cross-link density, we get a continuous
gelation transition signaled by the emergence of a finite in-plane localization
length. The distribution of localization length turns out to depend on the
height along the preferred direction of the directed polymers. The gelation
transition also gives rise to a finite in-plane shear modulus which we
calculate and turns out to be universal, i.e., independent of the energy and
length scales of the polymers and the cross-links. Using a symmetry argument,
we show that cross-links of negligible extent along the preferred axis of the
directed polymers do not cause any renormalization to the tilt modulus of the
uncross-linked system.Comment: 7 pages, 3 figure
Bundling in brushes of directed and semiflexible polymers
We explore the effect of an attractive interaction between parallel-aligned
polymers, which are perpendicularly grafted on a substrate. Such an attractive
interaction could be due to, e.g., reversible cross-links. The competition
between permanent grafting favoring a homogeneous state of the polymer brush
and the attraction, which tends to induce in-plane collapse of the aligned
polymers, gives rise to an instability of the homogeneous phase to a bundled
state. In this latter state the in-plane translational symmetry is
spontaneously broken and the density is modulated with a finite wavelength,
which is set by the length scale of transverse fluctuations of the grafted
polymers. We analyze the instability for two models of aligned polymers:
directed polymers with a line tension and weakly bending chains with a bending
stiffness.Comment: 7 pages, 5 figures, final version as published in PR
Mechanical properties of branched actin filaments
Cells moving on a two dimensional substrate generate motion by polymerizing
actin filament networks inside a flat membrane protrusion. New filaments are
generated by branching off existing ones, giving rise to branched network
structures. We investigate the force-extension relation of branched filaments,
grafted on an elastic structure at one end and pushing with the free ends
against the leading edge cell membrane. Single filaments are modeled as
worm-like chains, whose thermal bending fluctuations are restricted by the
leading edge cell membrane, resulting in an effective force. Branching can
increase the stiffness considerably; however the effect depends on branch point
position and filament orientation, being most pronounced for intermediate tilt
angles and intermediate branch point positions. We describe filament networks
without cross-linkers to focus on the effect of branching. We use randomly
positioned branch points, as generated in the process of treadmilling, and
orientation distributions as measured in lamellipodia. These networks reproduce
both the weak and strong force response of lamellipodia as measured in
force-velocity experiments. We compare properties of branched and unbranched
networks. The ratio of the network average of the force per branched filament
to the average force per unbranched filament depends on the orientation
distribution of the filaments. The ratio exhibits compression dependence and
may go up to about 4.5 in networks with a narrow orientation distribution. With
orientation distributions measured in lamellipodia, it is about two and
essentially independent from network compression, graft elasticity and filament
persistence length
Nonlinear Hydrodynamics of Disentangled Flux-Line Liquids
In this paper we use non-Gaussian hydrodynamics to study the magnetic response of a flux-line liquid in the mixed state of a type-II superconductor. Both the derivation of our model, which goes beyond conventional Gaussian flux liquid hydrodynamics, and its relationship to other approaches used in the literature are discussed. We focus on the response to a transverse tilting field which is controlled by the tilt modulus, c44, of the flux array. We show that interaction effects can enhance c44 even in infinitely thick clean materials. This enhancement can be interpreted as the appearance of a disentangled flux-liquid fraction. In contrast to earlier work, our theory incorporates the nonlocality of the intervortex interaction in the field direction. This nonlocality is crucial for obtaining a nonvanishing renormalization of the tilt modulus in the thermodynamic limit of thick samples
Plasticity in Current-Driven Vortex Lattices
We present a theoretical analysis of recent experiments on current-driven vortex dynamics in the Corbino disk geometry. This geometry introduces controlled spatial gradients in the driving force and allows the study of the onset of plasticity and tearing in clean vortex lattices. We describe plastic slip in terms of the stress-driven unbinding of dislocation pairs, which in turn contribute to the relaxation of the shear, yielding a nonlinear response. The steady state density of free dislocations induced by the applied stress is calculated as a function of the applied current and temperature. A criterion for the onset of plasticity at a radial location in the disk yields a temperature-dependent critical current that is in qualitative agreement with experiments
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