144 research outputs found
Anomalous Dynamics of Translocation
We study the dynamics of the passage of a polymer through a membrane pore
(translocation), focusing on the scaling properties with the number of monomers
. The natural coordinate for translocation is the number of monomers on one
side of the hole at a given time. Commonly used models which assume Brownian
dynamics for this variable predict a mean (unforced) passage time that
scales as , even in the presence of an entropic barrier. However, the time
it takes for a free polymer to diffuse a distance of the order of its radius by
Rouse dynamics scales with an exponent larger than 2, and this should provide a
lower bound to the translocation time. To resolve this discrepancy, we perform
numerical simulations with Rouse dynamics for both phantom (in space dimensions
and 2), and self-avoiding (in ) chains. The results indicate that
for large , translocation times scale in the same manner as diffusion times,
but with a larger prefactor that depends on the size of the hole. Such scaling
implies anomalous dynamics for the translocation process. In particular, the
fluctuations in the monomer number at the hole are predicted to be
non-diffusive at short times, while the average pulling velocity of the polymer
in the presence of a chemical potential difference is predicted to depend on
.Comment: 9 pages, 9 figures. Submitted to Physical Review
Monte Carlo simulations of random copolymers at a selective interface
We investigate numerically using the bond--fluctuation model the adsorption
of a random AB--copolymer at the interface between two solvents. From our
results we infer several scaling relations: the radius of gyration of the
copolymer in the direction perpendicular to the interface () scales
with , the interfacial selectivity strength, as
where is the usual Flory exponent and
is the copolymer's length; furthermore the monomer density at the interface
scales as for small . We also determine numerically the
monomer densities in the two solvents and discuss their dependence on the
distance from the interface.Comment: Latex text file appended with figures.tar.g
A Dynamical Mean Field Theory for the Study of Surface Diffusion Constants
We present a combined analytical and numerical approach based on the Mori
projection operator formalism and Monte Carlo simulations to study surface
diffusion within the lattice-gas model. In the present theory, the average jump
rate and the susceptibility factor appearing are evaluated through Monte Carlo
simulations, while the memory functions are approximated by the known results
for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for
collective diffusion, while approximate correlation effects beyond DMF are
included for tracer diffusion. We apply our formalism to three very different
strongly interacting systems and compare the results of the new approach with
those of usual Monte Carlo simulations. We find that the combined approach
works very well for collective diffusion, whereas for tracer diffusion the
influence of interactions on the memory effects is more prominent.Comment: 13 pages LaTeX and 6 PostScript figures, style files included. To
appear in Surface Science Letter
Small-Angle Excess Scattering: Glassy Freezing or Local Orientational Ordering?
We present Monte Carlo simulations of a dense polymer melt which shows
glass-transition-like slowing-down upon cooling, as well as a build up of
nematic order. At small wave vectors q this model system shows excess
scattering similar to that recently reported for light-scattering experiments
on some polymeric and molecular glass-forming liquids. For our model system we
can provide clear evidence that this excess scattering is due to the onset of
short-range nematic order and not directly related to the glass transition.Comment: 3 Pages of Latex + 4 Figure
Diffusive Spreading of Chainlike Molecules on Surfaces
We study the diffusion and submonolayer spreading of chainlike molecules on
surfaces. Using the fluctuating bond model we extract the collective and tracer
diffusion coefficients D_c and D_t with a variety of methods. We show that
D_c(theta) has unusual behavior as a function of the coverage theta. It first
increases but after a maximum goes to zero as theta go to one. We show that the
increase is due to entropic repulsion that leads to steep density profiles for
spreading droplets seen in experiments. We also develop an analytic model for
D_c(theta) which agrees well with the simulations.Comment: 3 pages, RevTeX, 4 postscript figures, to appear in Phys. Rev.
Letters (1996
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
A new bond fluctuation method for a polymer undergoing gel electrophoresis
We present a new computational methodology for the investigation of gel
electrophoresis of polyelectrolytes. We have developed the method initially to
incorporate sliding motion of tight parts of a polymer pulled by an electric
field into the bond fluctuation method (BFM). Such motion due to tensile force
over distances much larger than the persistent length is realized by non-local
movement of a slack monomer at an either end of the tight part. The latter
movement is introduced stochastically. This new BFM overcomes the well-known
difficulty in the conventional BFM that polymers are trapped by gel fibers in
relatively large fields. At the same time it also reproduces properly
equilibrium properties of a polymer in a vanishing filed limit. The new BFM
thus turns out an efficient computational method to study gel electrophoresis
in a wide range of the electric field strength.Comment: 15 pages, 11 figure
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
Intrinsic profiles and capillary waves at homopolymer interfaces: a Monte Carlo study
A popular concept which describes the structure of polymer interfaces by
``intrinsic profiles'' centered around a two dimensional surface, the ``local
interface position'', is tested by extensive Monte Carlo simulations of
interfaces between demixed homopolymer phases in symmetric binary (AB)
homopolymer blends, using the bond fluctuation model. The simulations are done
in an LxLxD geometry. The interface is forced to run parallel to the LxL planes
by imposing periodic boundary conditions in these directions and fixed boundary
conditions in the D direction, with one side favoring A and the other side
favoring B. Intrinsic profiles are calculated as a function of the ``coarse
graining length'' B by splitting the system into columns of size BxBxD and
averaging in each column over profiles relative to the local interface
position. The results are compared to predictions of the self-consistent field
theory. It is shown that the coarse graining length can be chosen such that the
interfacial width matches that of the self-consistent field profiles, and that
for this choice of B the ``intrinsic'' profiles compare well with the
theoretical predictions.Comment: to appear in Phys. Rev.
Reactions at polymer interfaces: A Monte Carlo Simulation
Reactions at a strongly segregated interface of a symmetric binary polymer
blend are investigated via Monte Carlo simulations. End functionalized
homopolymers of different species interact at the interface instantaneously and
irreversibly to form diblock copolymers. The simulations, in the framework of
the bond fluctuation model, determine the time dependence of the copolymer
production in the initial and intermediate time regime for small reactant
concentration . The results are compared to
recent theories and simulation data of a simple reaction diffusion model. For
the reactant concentration accessible in the simulation, no linear growth of
the copolymer density is found in the initial regime, and a -law is
observed in the intermediate stage.Comment: to appear in Macromolecule
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