26 research outputs found
Non-extensivity of the chemical potential of polymer melts
Following Flory's ideality hypothesis the chemical potential of a test chain
of length immersed into a dense solution of chemically identical polymers
of length distribution P(N) is extensive in . We argue that an additional
contribution arises ( being the
monomer density) for all if which can be traced back to the
overall incompressibility of the solution leading to a long-range repulsion
between monomers. Focusing on Flory distributed melts we obtain for , hence,
if is similar to the typical
length of the bath . Similar results are obtained for monodisperse
solutions. Our perturbation calculations are checked numerically by analyzing
the annealed length distribution P(N) of linear equilibrium polymers generated
by Monte Carlo simulation of the bond-fluctuation model. As predicted we find,
e.g., the non-exponentiality parameter to decay
as for all moments of the distribution.Comment: 14 pages, 6 figures, submitted to EPJ
Why polymer chains in a melt are not random walks
A cornerstone of modern polymer physics is the `Flory ideality hypothesis'
which states that a chain in a polymer melt adopts `ideal' random-walk-like
conformations. Here we revisit theoretically and numerically this pivotal
assumption and demonstrate that there are noticeable deviations from ideality.
The deviations come from the interplay of chain connectivity and the
incompressibility of the melt, leading to an effective repulsion between chain
segments of all sizes . The amplitude of this repulsion increases with
decreasing where chain segments become more and more swollen. We illustrate
this swelling by an analysis of the form factor , i.e. the scattered
intensity at wavevector resulting from intramolecular interferences of a
chain. A `Kratky plot' of {\em vs.} does not exhibit the plateau
for intermediate wavevectors characteristic of ideal chains. One rather finds a
conspicuous depression of the plateau, ,
which increases with and only depends on the monomer density .Comment: 4 pages, 4 figures, EPL, accepted January 200
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
Are polymer melts "ideal"?
It is commonly accepted that in concentrated solutions or melts
high-molecular weight polymers display random-walk conformational properties
without long-range correlations between subsequent bonds. This absence of
memory means, for instance, that the bond-bond correlation function, , of
two bonds separated by monomers along the chain should exponentially decay
with . Presenting numerical results and theoretical arguments for both
monodisperse chains and self-assembled (essentially Flory size-distributed)
equilibrium polymers we demonstrate that some long-range correlations remain
due to self-interactions of the chains caused by the chain connectivity and the
incompressibility of the melt. Suggesting a profound analogy with the
well-known long-range velocity correlations in liquids we find, for instance,
to decay algebraically as . Our study suggests a precise
method for obtaining the statistical segment length \bstar in a computer
experiment.Comment: 4 pages, 3 figure
Compression modulus of macroscopic fiber bundles
We study dense, disordered stacks of elastic macroscopic fibers. These stacks
often exhibit non-linear elasticity, due to the coupling between the applied
stress and the internal distribution of fiber contacts. We propose a
theoretical model for the compression modulus of such systems, and illustrate
our method by studying the conical shapes frequently observed at the
extremities of ropes and other fiber structures. studying the conical shapes
frequently observed at theextremities of ropes and other fiber structures
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
Single chain structure in thin polymer films: Corrections to Flory's and Silberberg's hypotheses
Conformational properties of polymer melts confined between two hard
structureless walls are investigated by Monte Carlo simulation of the
bond-fluctuation model. Parallel and perpendicular components of chain
extension, bond-bond correlation function and structure factor are computed and
compared with recent theoretical approaches attempting to go beyond Flory's and
Silberberg's hypotheses. We demonstrate that for ultrathin films where the
thickness, , is smaller than the excluded volume screening length (blob
size), , the chain size parallel to the walls diverges logarithmically,
with . The corresponding bond-bond
correlation function decreases like a power law, with
being the curvilinear distance between bonds and . % Upon increasing
the film thickness, , we find -- in contrast to Flory's hypothesis -- the
bulk exponent and, more importantly, an {\em decreasing}
that gives direct evidence for an {\em enhanced} self-interaction of chain
segments reflected at the walls. Systematic deviations from the Kratky plateau
as a function of are found for the single chain form factor parallel to the
walls in agreement with the {\em non-monotonous} behaviour predicted by theory.
This structure in the Kratky plateau might give rise to an erroneous estimation
of the chain extension from scattering experiments. For large the
deviations are linear with the wave vector, , but are very weak. In
contrast, for ultrathin films, , very strong corrections are found
(albeit logarithmic in ) suggesting a possible experimental verification of
our results.Comment: 16 pages, 7 figures. Dedicated to L. Sch\"afer on the occasion of his
60th birthda
Effective Soft-Core Potentials and Mesoscopic Simulations of Binary Polymer Mixtures
Mesoscopic molecular dynamics simulations are used to determine the large
scale structure of several binary polymer mixtures of various chemical
architecture, concentration, and thermodynamic conditions. By implementing an
analytical formalism, which is based on the solution to the Ornstein-Zernike
equation, each polymer chain is mapped onto the level of a single soft colloid.
From the appropriate closure relation, the effective, soft-core potential
between coarse-grained units is obtained and used as input to our mesoscale
simulations. The potential derived in this manner is analytical and explicitly
parameter dependent, making it general and transferable to numerous systems of
interest. From computer simulations performed under various thermodynamic
conditions the structure of the polymer mixture, through pair correlation
functions, is determined over the entire miscible region of the phase diagram.
In the athermal regime mesoscale simulations exhibit quantitative agreement
with united atom simulations. Furthermore, they also provide information at
larger scales than can be attained by united atom simulations and in the
thermal regime approaching the phase transition.Comment: 19 pages, 11 figures, 3 table
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