451 research outputs found
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
Elementary simulation of tethered Brownian motion
We describe a simple numerical simulation, suitable for an undergraduate
project (or graduate problem set), of the Brownian motion of a particle in a
Hooke-law potential well. Understanding this physical situation is a practical
necessity in many experimental contexts, for instance in single molecule
biophysics; and its simulation helps the student to appreciate the dynamical
character of thermal equilibrium. We show that the simulation succeeds in
capturing behavior seen in experimental data on tethered particle motion.Comment: Submitted to American Journal of Physic
Fluctuation-dissipation theorem in an aging colloidal glass
We provide a direct experimental test of the Stokes-Einstein relation as a
special case of the fluctuation-dissipation theorem (FDT) in an aging colloidal
glass. The use of combined active and passive microrheology allows us to
independently measure both the correlation and response functions in this
non-equilibrium situation. Contrary to previous reports, we find no deviations
from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging
times. In addition, we find two distinct viscoelastic contributions in the
aging glass, including a nearly elastic response at low frequencies that grows
during aging. This is the clearest change in material properties of the system
with aging.Comment: 5 pages,4 figure
Two-point microrheology and the electrostatic analogy
The recent experiments of Crocker et al. suggest that microrheological
measurements obtained from the correlated fluctuations of widely-separatedprobe
particles determine the rheological properties of soft, complex materials more
accurately than do the more traditional particle autocorrelations. This
presents an interesting problem in viscoelastic dynamics. We develop an
important, simplifing analogy between the present viscoelastic problem and
classical electrostatics. Using this analogy and direct calculation we analyze
both the one and two particle correlations in a viscoelastic medium in order to
explain this observation
One- and two-particle microrheology
We study the dynamics of rigid spheres embedded in viscoelastic media and
address two questions of importance to microrheology. First we calculate the
complete response to an external force of a single bead in a homogeneous
elastic network viscously coupled to an incompressible fluid. From this
response function we find the frequency range where the standard assumptions of
microrheology are valid. Second we study fluctuations when embedded spheres
perturb the media around them and show that mutual fluctuations of two
separated spheres provide a more accurate determination of the complex shear
modulus than do the fluctuations of a single sphere.Comment: 4 pages, 1 figur
Active Microrheology of Networks Composed of Semiflexible Polymers. II. Theory and comparison with simulations
Building on the results of our computer simulation (ArXiv cond-mat/0503573)we
develop a theoretical description of the motion of a bead, embedded in a
network of semiflexible polymers, and responding to an applied force. The
theory reveals the existence of an osmotic restoring force, generated by the
piling up of filaments in front of the moving bead and first deduced through
computer simulations. The theory predicts that the bead displacement scales
like x ~ t^alfa with time, with alfa=0.5 in an intermediate- and alfa=1 in a
long-time regime. It also predicts that the compliance varies with
concentration like c^(-4/3) in agreement with experiment.Comment: 18 pages and 2 figure
The response function of a sphere in a viscoelastic two-fluid medium
In order to address basic questions of importance to microrheology, we study
the dynamics of a rigid sphere embedded in a model viscoelastic medium
consisting of an elastic network permeated by a viscous fluid. We calculate the
complete response of a single bead in this medium to an external force and
compare the result to the commonly-accepted, generalized Stokes-Einstein
relation (GSER). We find that our response function is well approximated by the
GSER only within a particular frequency range determined by the material
parameters of both the bead and the network. We then discuss the relevance of
this result to recent experiments. Finally we discuss the approximations made
in our solution of the response function by comparing our results to the exact
solution for the response function of a bead in a viscous (Newtonian) fluid.Comment: 12 pages, 2 figure
Nonlinear Elasticity in Biological Gels
Unlike most synthetic materials, biological materials often stiffen as they
are deformed. This nonlinear elastic response, critical for the physiological
function of some tissues, has been documented since at least the 19th century,
but the molecular structure and the design principles responsible for it are
unknown. Current models for this response require geometrically complex ordered
structures unique to each material. In this Article we show that a much simpler
molecular theory accounts for strain stiffening in a wide range of molecularly
distinct biopolymer gels formed from purified cytoskeletal and extracellular
proteins. This theory shows that systems of semi-flexible chains such as
filamentous proteins arranged in an open crosslinked meshwork invariably
stiffen at low strains without the need for a specific architecture or multiple
elements with different intrinsic stiffnesses.Comment: 23 pages, 5 figures, submitted to Natur
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