3,433 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
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
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
Development of Stresses in Cohesionless Poured Sand
The pressure distribution beneath a conical sandpile, created by pouring sand
from a point source onto a rough rigid support, shows a pronounced minimum
below the apex (`the dip'). Recent work of the authors has attempted to explain
this phenomenon by invoking local rules for stress propagation that depend on
the local geometry, and hence on the construction history, of the medium. We
discuss the fundamental difference between such approaches, which lead to
hyperbolic differential equations, and elastoplastic models, for which the
equations are elliptic within any elastic zones present .... This displacement
field appears to be either ill-defined, or defined relative to a reference
state whose physical existence is in doubt. Insofar as their predictions depend
on physical factors unknown and outside experimental control, such
elastoplastic models predict that the observations should be intrinsically
irreproducible .... Our hyperbolic models are based instead on a physical
picture of the material, in which (a) the load is supported by a skeletal
network of force chains ("stress paths") whose geometry depends on construction
history; (b) this network is `fragile' or marginally stable, in a sense that we
define. .... We point out that our hyperbolic models can nonetheless be
reconciled with elastoplastic ideas by taking the limit of an extremely
anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps.
Philosophical Transactions A, Royal Society, submitted 02/9
Copper flows in buildings, infrastructure and mobiles: a dynamic model and its application to Switzerland
During the last century, the consumption of materials for human needs increased by several orders of magnitude, even for non-renewable materials such as metals. Some data on annual consumption (input) and recycling/waste (output) can often be found in the federal statistics, but a clear picture of the main flows is missing. A dynamic material flow model is developed for the example of copper in Switzerland in order to simulate the relevant copper flows and stocks over the last 150years. The model is calibrated using data from statistical and published sources as well as from interviews and measurements. A simulation of the current state (2000) is compared with data from other studies. The results show that Swiss consumption and losses are both high, at a level of about 8 and 2kg/(capyear), respectively, or about three times higher than the world average. The model gives an understanding of the flows and stocks and their interdependencies as a function of time. This is crucial for materials whose consumption dynamics are characterised by long lifetimes and hence for relating the current output to the input of the whole past. The model allows a comprehensive discussion of possible measures to reduce resource use and losses to the environment. While increasing the recycling reduces losses to landfill, only copper substitution can reduce the different losses to the environment, although with a time delay of the order of a lifetim
Continuum limit of amorphous elastic bodies (III): Three dimensional systems
Extending recent numerical studies on two dimensional amorphous bodies, we
characterize the approach of elastic continuum limit in three dimensional
(weakly polydisperse) Lennard-Jones systems. While performing a systematic
finite-size analysis (for two different quench protocols) we investigate the
non-affine displacement field under external strain, the linear response to an
external delta force and the low-frequency harmonic eigenmodes and their
density distribution. Qualitatively similar behavior is found as in two
dimensions. We demonstrate that the classical elasticity description breaks
down below an intermediate length scale , which in our system is
approximately 23 molecular sizes. This length characterizes the correlations of
the non-affine displacement field, the self-averaging of external noise with
distance from the source and gives the lower wave length bound for the
applicability of the classical eigenfrequency calculations. We trace back the
"Boson-peak" of the density of eigenfrequencies (obtained from the velocity
auto-correlation function) to the inhomogeneities on wave lengths smaller than
.Comment: 27 pages, 11 figures, submitted to Phys. Rev.
Statistical Mechanics of Stress Transmission in Disordered Granular Arrays
We give a statistical-mechanical theory of stress transmission in disordered
arrays of rigid grains with perfect friction. Starting from the equations of
microscopic force and torque balance we derive the fundamental equations of
stress equilibrium. We illustrate the validity of our approach by solving the
stress distribution of a homogeneous and isotropic array.Comment: 4 pages, to be published in PR
Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential
The truncation of a pair potential at a distance r_cut is well-known to imply
in general an impulsive correction to the pressure and other moments of the
first derivatives of the potential. That depending on r_cut the truncation may
also be of relevance to higher derivatives is shown theoretically for the Born
contributions to the elastic moduli obtained using the stress-fluctuation
formalism in d dimensions. Focusing on isotropic liquids for which the shear
modulus G must vanish by construction, the predicted corrections are tested
numerically for binary mixtures and polydisperse Lennard-Jones beads in,
respectively, d=3 and d=2 dimensions
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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