3,669 research outputs found
Distance dependence of angular correlations in dense polymer solutions
Angular correlations in dense solutions and melts of flexible polymer chains
are investigated with respect to the distance between the bonds by
comparing quantitative predictions of perturbation calculations with numerical
data obtained by Monte Carlo simulation of the bond-fluctuation model. We
consider both monodisperse systems and grand-canonical (Flory-distributed)
equilibrium polymers. Density effects are discussed as well as finite chain
length corrections. The intrachain bond-bond correlation function is
shown to decay as for \xi \ll r \ll \r^* with being
the screening length of the density fluctuations and a novel
length scale increasing slowly with (mean) chain length .Comment: 17 pages, 5 figures, accepted for publication at Macromolecule
Stress Propagation and Arching in Static Sandpiles
We present a new approach to the modelling of stress propagation in static
granular media, focussing on the conical sandpile constructed from a point
source. We view the medium as consisting of cohesionless hard particles held up
by static frictional forces; these are subject to microscopic indeterminacy
which corresponds macroscopically to the fact that the equations of stress
continuity are incomplete -- no strain variable can be defined. We propose that
in general the continuity equations should be closed by means of a constitutive
relation (or relations) between different components of the (mesoscopically
averaged) stress tensor. The primary constitutive relation relates radial and
vertical shear and normal stresses (in two dimensions, this is all one needs).
We argue that the constitutive relation(s) should be local, and should encode
the construction history of the pile: this history determines the organization
of the grains at a mesoscopic scale, and thereby the local relationship between
stresses. To the accuracy of published experiments, the pattern of stresses
beneath a pile shows a scaling between piles of different heights (RSF scaling)
which severely limits the form the constitutive relation can take ...Comment: 38 pages, 24 Postscript figures, LATEX, minor misspellings corrected,
Journal de Physique I, Ref. Nr. 6.1125, accepte
Computational confirmation of scaling predictions for equilibrium polymers
We report the results of extensive Dynamic Monte Carlo simulations of systems
of self-assembled Equilibrium Polymers without rings in good solvent.
Confirming recent theoretical predictions, the mean-chain length is found to
scale as \Lav = \Lstar (\phi/\phistar)^\alpha \propto \phi^\alpha \exp(\delta
E) with exponents and in the dilute and
semi-dilute limits respectively. The average size of the micelles, as measured
by the end-to-end distance and the radius of gyration, follows a very similar
crossover scaling to that of conventional quenched polymer chains. In the
semi-dilute regime, the chain size distribution is found to be exponential,
crossing over to a Schultz-Zimm type distribution in the dilute limit. The very
large size of our simulations (which involve mean chain lengths up to 5000,
even at high polymer densities) allows also an accurate determination of the
self-avoiding walk susceptibility exponent .Comment: 6 pages, 4 figures, LATE
Dynamical Monte Carlo Study of Equilibrium Polymers : Static Properties
We report results of extensive Dynamical Monte Carlo investigations on
self-assembled Equilibrium Polymers (EP) without loops in good solvent. (This
is thought to provide a good model of giant surfactant micelles.) Using a novel
algorithm we are able to describe efficiently both static and dynamic
properties of systems in which the mean chain length \Lav is effectively
comparable to that of laboratory experiments (up to 5000 monomers, even at high
polymer densities). We sample up to scission energies of over
nearly three orders of magnitude in monomer density , and present a
detailed crossover study ranging from swollen EP chains in the dilute regime up
to dense molten systems. Confirming recent theoretical predictions, the
mean-chain length is found to scale as \Lav \propto \phi^\alpha \exp(\delta
E) where the exponents approach
and in the
dilute and semidilute limits respectively. The chain length distribution is
qualitatively well described in the dilute limit by the Schulz-Zimm
distribution \cN(s)\approx s^{\gamma-1} \exp(-s) where the scaling variable
is s=\gamma L/\Lav. The very large size of these simulations allows also an
accurate determination of the self-avoiding walk susceptibility exponent
. ....... Finite-size effects are discussed in
detail.Comment: 15 pages, 14 figures, LATE
Note: Scale-free center-of-mass displacement correlations in polymer films without topological constraints and momentum conservation
We present here computational work on the center-of-mass displacements in
thin polymer films of finite width without topological constraints and without
momentum conservation obtained using a well-known lattice Monte Carlo algorithm
with chain lengths ranging up to N=8192. Computing directly the center-of-mass
displacement correlation function C_N(t) allows to make manifest the existence
of scale-free colored forces acting on a reference chain. As suggested by the
scaling arguments put forward in a recent work on three-dimensional melts, we
obtain a negative algebraic decay C_N(t) \sim -1/(Nt) for times t << T_N with
T_N being the chain relaxation time. This implies a logarithmic correction to
the related center-of-mass mean square-displacement h_N(t) as has been checked
directly
Characterization of local dynamics and mobilities in polymer melts - a simulation study
The local dynamical features of a PEO melt studied by MD simulations are
compared to two model chain systems, namely the well-known Rouse model as well
as the semiflexible chain model (SFCM) that additionally incorporates chain
stiffness. Apart from the analysis of rather general quantities such as the
mean square displacement (MSD), we present a new statistical method to extract
the local bead mobility from the simulation data on the basis of the Langevin
equation, thus providing a complementary approach to the classical Rouse-mode
analysis. This allows us to check the validity of the Langevin equation and, as
a consequence, the Rouse model. Moreover, the new method has a broad range of
applications for the analysis of the dynamics of more complex polymeric systems
like comb-branched polymers or polymer blends.Comment: 6 pages, 5 figure
On two intrinsic length scales in polymer physics: topological constraints vs. entanglement length
The interplay of topological constraints, excluded volume interactions,
persistence length and dynamical entanglement length in solutions and melts of
linear chains and ring polymers is investigated by means of kinetic Monte Carlo
simulations of a three dimensional lattice model. In unknotted and
unconcatenated rings, topological constraints manifest themselves in the static
properties above a typical length scale ( being
the volume fraction, the mean bond length).
Although one might expect that the same topological length will play a role
in the dynamics of entangled polymers, we show that this is not the case.
Instead, a different intrinsic length de, which scales like excluded volume
blob size , governs the scaling of the dynamical properties of both linear
chains and rings.Comment: 7 pages. 4 figure
Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies
It has been assumed until very recently that all long-range correlations are
screened in three-dimensional melts of linear homopolymers on distances beyond
the correlation length characterizing the decay of the density
fluctuations. Summarizing simulation results obtained by means of a variant of
the bond-fluctuation model with finite monomer excluded volume interactions and
topology violating local and global Monte Carlo moves, we show that due to an
interplay of the chain connectivity and the incompressibility constraint, both
static and dynamical correlations arise on distances . These
correlations are scale-free and, surprisingly, do not depend explicitly on the
compressibility of the solution. Both monodisperse and (essentially)
Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure
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