2,746 research outputs found
Effective medium approach for stiff polymer networks with flexible cross-links
Recent experiments have demonstrated that the nonlinear elasticity of in
vitro networks of the biopolymer actin is dramatically altered in the presence
of a flexible cross-linker such as the abundant cytoskeletal protein filamin.
The basic principles of such networks remain poorly understood. Here we
describe an effective medium theory of flexibly cross-linked stiff polymer
networks. We argue that the response of the cross-links can be fully attributed
to entropic stiffening, while softening due to domain unfolding can be ignored.
The network is modeled as a collection of randomly oriented rods connected by
flexible cross-links to an elastic continuum. This effective medium is treated
in a linear elastic limit as well as in a more general framework, in which the
medium self-consistently represents the nonlinear network behavior. This model
predicts that the nonlinear elastic response sets in at strains proportional to
cross-linker length and inversely proportional to filament length. Furthermore,
we find that the differential modulus scales linearly with the stress in the
stiffening regime. These results are in excellent agreement with bulk rheology
data.Comment: 12 pages, 8 figure
Instability and front propagation in laser-tweezed lipid bilayer tubules
We study the mechanism of the `pearling' instability seen recently in
experiments on lipid tubules under a local applied laser intensity. We argue
that the correct boundary conditions are fixed chemical potentials, or surface
tensions \Sigma, at the laser spot and the reservoir in contact with the
tubule. We support this with a microscopic picture which includes the intensity
profile of the laser beam, and show how this leads to a steady-state flow of
lipid along the surface and gradients in the local lipid concentration and
surface tension (or chemical potential). This leads to a natural explanation
for front propagation and makes several predictions based on the tubule length.
While most of the qualitative conclusions of previous studies remain the same,
the `ramped' control parameter (surface tension) implies several new
qualitative results. We also explore some of the consequences of front
propagation into a noisy (due to pre-existing thermal fluctuations) unstable
medium.Comment: 12 page latex + figures using epsf.sty to be published in Journal de
Physique II, January 199
Breakup coupling effects on near-barrier <sup>6</sup>Li, <sup>7</sup>Be and <sup>8</sup>B + <sup>58</sup>Ni elastic scattering compared
New data for near-barrier 6Li, 7Be and 8B + 58Ni elastic scattering enable a comparison of breakup coupling effects for these loosely-bound projectiles. Coupled Discretised Continuum Channels (CDCC) calculations suggest that the large total reaction cross sections for 8B + 58Ni are dominated by breakup at near-barrier energies, unlike 6Li and 7Be where breakup makes a small contribution. In spite of this, the CDCC calculations show a small coupling influence due to breakup for 8B, in contrast to the situation for 6Li and 7Be. An examination of the S matrices gives a clue to this counter-intuitive behaviour
Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations
We have developed a new technique to measure viscoelasticity in soft
materials such as polymer solutions, by monitoring thermal fluctuations of
embedded probe particles using laser interferometry in a microscope.
Interferometry allows us to obtain power spectra of fluctuating beads from 0.1
Hz to 20 kHz, and with sub-nanometer spatial resolution. Using linear response
theory, we determined the frequency-dependent loss and storage shear moduli up
to frequencies on the order of a kHz. Our technique measures local values of
the viscoelastic response, without actively straining the system, and is
especially suited to soft biopolymer networks. We studied semiflexible F-actin
solutions and, as a control, flexible polyacrylamide (PAAm) gels, the latter
close to their gelation threshold. With small particles, we could probe the
transition from macroscopic viscoelasticity to more complex microscopic
dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G'=0.11
+/- 0.03 Pa and 0.17 +/- 0.07 Pa for 1 and 2 mg/ml actin solutions, close to
the onset of the elastic plateau, and scaling behavior consistent with G(omega)
as omega^(3/4) at higher frequencies. For polyacrylamide we measured plateau
moduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5%
concentration (weight/volume) respectively, in agreement to within a factor of
two with values obtained from conventional rheology. We also found evidence for
scaling of G(omega) as \omega^(1/2), consistent with the predictions of the
Rouse model for flexible polymers.Comment: 16 pages, with 15 PostScript figures (to be published in
Macromolecules
Origin of slow stress relaxation in the cytoskeleton
Dynamically crosslinked semiflexible biopolymers such as the actin
cytoskeleton govern the mechanical behavior of living cells. Semiflexible
biopolymers nonlinearly stiffen in response to mechanical loads, whereas the
crosslinker dynamics allow for stress relaxation over time. Here we show,
through rheology and theoretical modeling, that the combined nonlinearity in
time and stress leads to an unexpectedly slow stress relaxation, similar to the
dynamics of disordered systems close to the glass transition. Our work suggests
that transient crosslinking combined with internal stress can explain prior
reports of soft glassy rheology of cells, in which the shear modulus increases
weakly with frequency.Comment: 6 pages, 4 figure
Normal stress anisotropy and marginal stability in athermal elastic networks
Hydrogels of semiflexible biopolymers such as collagen have been shown to
contract axially under shear strain, in contrast to the axial dilation observed
for most elastic materials. Recent work has shown that this behavior can be
understood in terms of the porous, two-component nature and consequent
time-dependent compressibility of hydrogels. The apparent normal stress
measured by a torsional rheometer reflects only the tensile contribution of the
axial component on long (compressible) timescales, crossing over
to the first normal stress difference, at short
(incompressible) times. While the behavior of is well understood for
isotropic viscoelastic materials undergoing affine shear deformation,
biopolymer networks are often anisotropic and deform nonaffinely. Here, we
numerically study the normal stresses that arise under shear in subisostatic,
athermal semiflexible polymer networks. We show that such systems exhibit
strong deviations from affine behavior and that these anomalies are controlled
by a rigidity transition as a function of strain
Budding and Domain Shape Transformations in Mixed Lipid Films and Bilayer Membranes
We study the stability and shapes of domains with spontaneous curvature in
fluid films and membranes, embedded in a surrounding membrane with zero
spontaneous curvature. These domains can result from the inclusion of an
impurity in a fluid membrane, or from phase separation within the membrane. We
show that for small but finite line and surface tensions and for finite
spontaneous curvatures, an equilibrium phase of protruding circular domains is
obtained at low impurity concentrations. At higher concentrations, we predict a
transition from circular domains, or "caplets", to stripes. In both cases, we
calculate the shapes of these domains within the Monge representation for the
membrane shape. With increasing line tension, we show numerically that there is
a budding transformation from stable protruding circular domains to spherical
buds. We calculate the full phase diagram, and demonstrate a two triple points,
of respectively bud-flat-caplet and flat-stripe-caplet coexistence.Comment: 14 pages, to appear in Phys Rev
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