2,867 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
Hyperbranched polymer stars with Gaussian chain statistics revisited
Conformational properties of regular dendrimers and more general
hyperbranched polymer stars with Gaussian statistics for the spacer chains
between branching points are revisited numerically. We investigate the scaling
for asymptotically long chains especially for fractal dimensions
(marginally compact) and (diffusion limited aggregation). Power-law
stars obtained by imposing the number of additional arms per generation are
compared to truly self-similar stars. We discuss effects of weak excluded
volume interactions and sketch the regime where the Gaussian approximation
should hold in dense solutions and melts for sufficiently large spacer chains.Comment: 13 pages, 14 figure
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
Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time
The shear modulus G of two glass-forming colloidal model systems in d=3 and
d=2 dimensions is investigated by means of, respectively, molecular dynamics
and Monte Carlo simulations. Comparing ensembles where either the shear strain
gamma or the conjugated (mean) shear stress tau are imposed, we compute G from
the respective stress and strain fluctuations as a function of temperature T
while keeping a constant normal pressure P. The choice of the ensemble is seen
to be highly relevant for the shear stress fluctuations mu_F(T) which at
constant tau decay monotonously with T following the affine shear elasticity
mu_A(T), i.e. a simple two-point correlation function. At variance,
non-monotonous behavior with a maximum at the glass transition temperature T_g
is demonstrated for mu_F(T) at constant gamma. The increase of G below T_g is
reasonably fitted for both models by a continuous cusp singularity, G(T) is
proportional to (1-T/T_g)^(1/2), in qualitative agreement with some recent
replica calculations. It is argued, however, that longer sampling times may
lead to a sharper transition. The additive jump discontinuity predicted by
mode-coupling theory and other replica calculations thus cannot ultimately be
ruled out
Static Rouse Modes and Related Quantities: Corrections to Chain Ideality in Polymer Melts
Following the Flory ideality hypothesis intrachain and interchain excluded
volume interactions are supposed to compensate each other in dense polymer
systems. Multi-chain effects should thus be neglected and polymer conformations
may be understood from simple phantom chain models. Here we provide evidence
against this phantom chain, mean-field picture. We analyze numerically and
theoretically the static correlation function of the Rouse modes. Our numerical
results are obtained from computer simulations of two coarse-grained polymer
models for which the strength of the monomer repulsion can be varied, from full
excluded volume (`hard monomers') to no excluded volume (`phantom chains'). For
nonvanishing excluded volume we find the simulated correlation function of the
Rouse modes to deviate markedly from the predictions of phantom chain models.
This demonstrates that there are nonnegligible correlations along the chains in
a melt. These correlations can be taken into account by perturbation theory.
Our simulation results are in good agreement with these new theoretical
predictions.Comment: 9 pages, 7 figures, accepted for publication in EPJ
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