647 research outputs found
Topological versus rheological entanglement length in primitive path analysis protocols
Primitive path analysis algorithms are now routinely employed to analyze
entanglements in computer simulations of polymeric systems, but different
analysis protocols result in different estimates of the entanglement length,
N_e. Here we argue that standard PPA measures the rheological entanglement
length, typically employed by tube models and relevant to quantitative
comparisons with experiment, while codes like Z or CReTA also determine the
topological entanglement length. For loosely entangled systems, a simple
analogy between between phantom networks and the mesh of entangled primitive
paths suggests a factor of two between the two numbers. This result is in
excellent agreement with reported values for poly-ethylene, poly-butadiene and
bead-spring polymer melts.Comment: 3 pages, no figure
Viscoplasticity and large-scale chain relaxation in glassy-polymeric strain hardening
A simple theory for glassy polymeric mechanical response which accounts for
large scale chain relaxation is presented. It captures the crossover from
perfect-plastic response to strong strain hardening as the degree of
polymerization increases, without invoking entanglements. By relating
hardening to interactions on the scale of monomers and chain segments, we
correctly predict its magnitude. Strain activated relaxation arising from the
need to maintain constant chain contour length reduces the dependence of
the characteristic relaxation time by a factor during
active deformation at strain rate . This prediction is consistent
with results from recent experiments and simulations, and we suggest how it may
be further tested experimentally.Comment: The theoretical treatment of the mechanical response has been
significantly revised, and the arguments for coherent relaxation during
active deformation made more transparen
Strain Hardening in Polymer Glasses: Limitations of Network Models
Simulations are used to examine the microscopic origins of strain hardening
in polymer glasses. While traditional entropic network models can be fit to the
total stress, their underlying assumptions are inconsistent with simulation
results. There is a substantial energetic contribution to the stress that rises
rapidly as segments between entanglements are pulled taut. The thermal
component of stress is less sensitive to entanglements, mostly irreversible,
and directly related to the rate of local plastic arrangements. Entangled and
unentangled chains show the same strain hardening when plotted against the
microscopic chain orientation rather than the macroscopic strain.Comment: 4 pages, 3 figure
Thermal Fluctuations and Rubber Elasticity
The effects of thermal elastic fluctuations in rubber materials are examined.
It is shown that, due to an interplay with the incompressibility constraint,
these fluctuations qualitatively modify the large-deformation stress-strain
relation, compared to that of classical rubber elasticity. To leading order,
this mechanism provides a simple and generic explanation for the peak structure
of Mooney-Rivlin stress-strain relation, and shows a good agreement with
experiments. It also leads to the prediction of a phonon correlation function
that depends on the external deformation.Comment: 4 RevTeX pages, 1 figure, submitted to PR
Supersymmetry solution for finitely extensible dumbbell model
Exact relaxation times and eigenfunctions for a simple mechanical model of
polymer dynamics are obtained using supersymmetry methods of quantum mechanics.
The model includes the finite extensibility of the molecule and does not make
use of the self-consistently averaging approximation. The finite extensibility
reduces the relaxation times when compared to a linear force. The linear
viscoelastic behaviour is obtained in the form of the ``generalized Maxwell
model''. Using these results, a numerical integration scheme is proposed in the
presence of a given flow kinematics.Comment: 5 pages, 2 figure
Direct optical observations of surface thermal motions at sub-shot noise levels
We measure spectral properties of surface thermal fluctuations of liquids,
solids, complex fluids and biological matter using light scattering methods.
The random thermal fluctuations are delineated from random noise at sub-shot
noise levels. The principle behind this extraction, which is quite general and
is not limited to surface measurements, is explained. An optical lever is used
to measure the spectrum of fluctuations in the inclinations of surfaces down to
at W optical intensity, corresponding
to in the vertical displacement, in the
frequency range . The dynamical evolution of the
surface properties is also investigated. The measurement requires only a short
amount of time and is essentially passive, so that it can be applied to a wide
variety of surfaces.Comment: 5pp, 5 figure
Strain-dependent localization, microscopic deformations, and macroscopic normal tensions in model polymer networks
We use molecular dynamics simulations to investigate the microscopic and
macroscopic response of model polymer networks to uniaxial elongations. By
studying networks with strands lengths ranging from to 200 we cover
the full crossover from cross-link to entanglement dominated behavior. Our
results support a recent version of the tube model which accounts for the
different strain dependence of chain localization due to chemical cross-links
and entanglements
Scaling of Entropic Shear Rigidity
The scaling of the shear modulus near the gelation/vulcanization transition
is explored heuristically and analytically. It is found that in a dense melt
the effective chains of the infinite cluster have sizes that scale sub-linearly
with their contour length. Consequently, each contributes k_B T to the
rigidity, which leads to a shear modulus exponent d\nu. In contrast, in phantom
elastic networks the scaling is linear in the contour length, yielding an
exponent identical to that of the random resistor network conductivity, as
predicted by de Gennes'. For non-dense systems, the exponent should cross over
to d\nu when the percolation length becomes much larger than the
density-fluctuation length.Comment: 4 pages, 2 eps figure
Smectic-C tilt under shear in Smectic-A elastomers
Stenull and Lubensky [Phys. Rev. E {\bf 76}, 011706 (2007)] have argued that
shear strain and tilt of the director relative to the layer normal are coupled
in smectic elastomers and that the imposition of one necessarily leads to the
development of the other. This means, in particular, that a Smectic-A elastomer
subjected to a simple shear will develop Smectic-C-like tilt of the director.
Recently, Kramer and Finkelmann [arXiv:0708.2024, Phys. Rev. E {\bf 78}, 021704
(2008)] performed shear experiments on Smectic-A elastomers using two different
shear geometries. One of the experiments, which implements simple shear,
produces clear evidence for the development of Smectic-C-like tilt. Here, we
generalize a model for smectic elastomers introduced by Adams and Warner [Phys.
Rev. E {\bf 71}, 021708 (2005)] and use it to study the magnitude of
Smectic-C-like tilt under shear for the two geometries investigated by Kramer
and Finkelmann. Using reasonable estimates of model parameters, we estimate the
tilt angle for both geometries, and we compare our estimates to the
experimental results. The other shear geometry is problematic since it
introduces additional in-plane compressions in a sheet-like sample, thus
inducing instabilities that we discuss.Comment: 8 pages, 5 figure
History Memorized and Recalled upon Glass Transition
The memory effect upon glassification is studied in the glass to rubber
transition of vulcanized rubber with the strain as a controlling parameter. A
phenomenological model is proposed taking the history of the temperature and
the strain into account, by which the experimental results are interpreted. The
data and the model demonstrate that the glassy state memorizes the time-course
of strain upon glassification, not as a single parameter but as the history
itself. The data also show that the effect of irreversible deformation in the
glassy state is beyond the scope of the present model.
Authors' remark: The title of the paper in the accepted version is above. The
title appeared in PRL is the one changed by a Senior Assistant Editor after
acceptance of the paper. The recovery of the title was rejected in the
correction process.Comment: 4 pages, 4 figure
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