3,479 research outputs found
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
Formation and Equilibrium Properties of Living Polymer Brushes
Polydisperse brushes obtained by reversible radical chain polymerization
reaction onto a solid substrate with surface-attached initiators, are studied
by means of an off-lattice Monte Carlo algorithm of living polymers (LP).
Various properties of such brushes, like the average chain length and the
conformational orientation of the polymers, or the force exerted by the brush
on the opposite container wall, reveal power-law dependence on the relevant
parameters. The observed molecular weight distribution (MWD) of the grafted LP
decays much more slowly than the corresponding LP bulk system due to the
gradient of the monomer density within the dense pseudo-brush which favors
longer chains. Both MWD and the density profiles of grafted polymers and chain
ends are well fitted by effective power laws whereby the different exponents
turn out to be mutually self-consistent for a pseudo-brush in the
strong-stretching regime.Comment: 33 pages, 11 figues, J.Chem. Phys. accepted Oct. 199
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
Effects of compression on the vibrational modes of marginally jammed solids
Glasses have a large excess of low-frequency vibrational modes in comparison
with most crystalline solids. We show that such a feature is a necessary
consequence of the weak connectivity of the solid, and that the frequency of
modes in excess is very sensitive to the pressure. We analyze in particular two
systems whose density D(w) of vibrational modes of angular frequency w display
scaling behaviors with the packing fraction: (i) simulations of jammed packings
of particles interacting through finite-range, purely repulsive potentials,
comprised of weakly compressed spheres at zero temperature and (ii) a system
with the same network of contacts, but where the force between any particles in
contact (and therefore the total pressure) is set to zero. We account in the
two cases for the observed a) convergence of D(w) toward a non-zero constant as
w goes to 0, b) appearance of a low-frequency cutoff w*, and c) power-law
increase of w* with compression. Differences between these two systems occur at
lower frequency. The density of states of the modified system displays an
abrupt plateau that appears at w*, below which we expect the system to behave
as a normal, continuous, elastic body. In the unmodified system, the pressure
lowers the frequency of the modes in excess. The requirement of stability
despite the destabilizing effect of pressure yields a lower bound on the number
of extra contact per particle dz: dz > p^(1/2), which generalizes the Maxwell
criterion for rigidity when pressure is present. This scaling behavior is
observed in the simulations. We finally discuss how the cooling procedure can
affect the microscopic structure and the density of normal modes.Comment: 13 pages, 8 figure
Models of stress fluctuations in granular media
We investigate in detail two models describing how stresses propagate and
fluctuate in granular media. The first one is a scalar model where only the
vertical component of the stress tensor is considered. In the continuum limit,
this model is equivalent to a diffusion equation (where the r\^ole of time is
played by the vertical coordinate) plus a randomly varying convection term. We
calculate the response and correlation function of this model, and discuss
several properties, in particular related to the stress distribution function.
We then turn to the tensorial model, where the basic starting point is a wave
equation which, in the absence of disorder, leads to a ray-like propagation of
stress. In the presence of disorder, the rays acquire a diffusive width and the
angle of propagation is shifted. A striking feature is that the response
function becomes negative, which suggests that the contact network is
mechanically unstable to very weak perturbations. The stress correlation
function reveals characteristic features related to the ray-like propagation,
which are absent in the scalar description. Our analytical calculations are
confirmed and extended by a numerical analysis of the stochastic wave equation.Comment: 32 pages, latex, 18 figures and 6 diagram
Vibrations of amorphous, nanometric structures: When does continuum theory apply?
Structures involving solid particles of nanometric dimensions play an
increasingly important role in material sciences. These structures are often
characterized through the vibrational properties of their constituent
particles, which can be probed by spectroscopic methods. Interpretation of such
experimental data requires an extension of continuum elasticity theory down to
increasingly small scales. Using numerical simulation and exact diagonalization
for simple models, we show that continuum elasticity, applied to disordered
system, actually breaks down below a length scale of typically 30 to 50
molecular sizes. This length scale is likely related to the one which is
generally invoked to explain the peculiar vibrational properties of glassy
systems.Comment: 4 pages, 5 figures, LATEX, Europhysics Letters accepte
Inhomogeneous elastic response of silica glass
Using large scale molecular dynamics simulations we investigate the
properties of the {\em non-affine} displacement field induced by macroscopic
uniaxial deformation of amorphous silica,a strong glass according to Angell's
classification. We demonstrate the existence of a length scale
characterizing the correlations of this field (corresponding to a volume of
about 1000 atoms), and compare its structure to the one observed in a standard
fragile model glass. The "Boson-peak'' anomaly of the density of states can be
traced back in both cases to elastic inhomogeneities on wavelengths smaller
than , where classical continuum elasticity becomes simply unapplicable
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