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 $N$. 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 $\tau$ that scales as $N^2$, 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 $d=1$ and 2), and self-avoiding (in $d=2$) chains. The results indicate that for large $N$, 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 $N$.Comment: 9 pages, 9 figures. Submitted to Physical Review

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

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

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, $H$, is smaller than the excluded volume screening length (blob size), $\xi$, the chain size parallel to the walls diverges logarithmically, $R^2/2N \approx b^2 + c \log(N)$ with $c \sim 1/H$. The corresponding bond-bond correlation function decreases like a power law, $C(s) = d/s^{\omega}$ with $s$ being the curvilinear distance between bonds and $\omega=1$. % Upon increasing the film thickness, $H$, we find -- in contrast to Flory's hypothesis -- the bulk exponent $\omega=3/2$ and, more importantly, an {\em decreasing} $d(H)$ 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 $H$ 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 $H$ the deviations are linear with the wave vector, $q$, but are very weak. In contrast, for ultrathin films, $H<\xi$, very strong corrections are found (albeit logarithmic in $q$) 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

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 ($R_{gz}$) scales with $\chi$, the interfacial selectivity strength, as $R_{gz}=N^{\nu}f(\sqrt{N}\chi)$ where $\nu$ is the usual Flory exponent and $N$ is the copolymer's length; furthermore the monomer density at the interface scales as $\chi^{2\nu}$ for small $\chi$. 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

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 $\rho_0 R_g^3=0.163 ... 0.0406$. 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 $\sqrt{t}$-law is observed in the intermediate stage.Comment: to appear in 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.

Self-Diffusion of a Polymer Chain in a Melt

Self-diffusion of a polymer chain in a melt is studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Polymer chains, each of which consists of $N$ segments, are located on an $L \times L \times L$ simple cubic lattice under periodic boundary conditions, where each segment occupies $2 \times 2 \times 2$ unit cells. The results for $N=32, 48, 64, 96, 128, 192, 256, 384$ and 512 at the volume fraction $\phi \simeq 0.5$ are reported, where $L = 128$ for $N \leq 256$ and L=192 for $N \geq 384$. The $N$-dependence of the self-diffusion constant $D$ is examined. Here, $D$ is estimated from the mean square displacements of the center of mass of a single polymer chain at the times larger than the longest relaxation time. From the data for $N = 256$, 384 and 512, the apparent exponent $x_{\rm d}$, which describes the apparent power law dependence of $D$ on $N$ as $D \propto N^{- x_{\rm d}}$, is estimated as $x_{\rm d} \simeq 2.4$. The ratio $D \tau /$ seems to be a constant for $N = 192, 256, 384$ and 512, where $\tau$ and $$ denote the longest relaxation time and the mean square end-to-end distance, respectively.Comment: 4 pages, 3 figures, submitted to J. Phys. Soc. Jp

Stretched Polymers in a Poor Solvent

Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first and last monomers. We show that both in $d=2$ and $d=3$ a phase transition occurs as this force is increased beyond a critical value, where the polymer changes from a collapsed globule to a stretched configuration. This transition is second order in $d=2$ and first order in $d=3$. For $d=2$ we predict the transition point quantitatively from properties of the unstretched polymer. This is not possible in $d=3$, but even there we can estimate the transition point precisely, and we can study the scaling at temperatures slightly below the collapse temperature of the unstretched polymer. We find very large finite size corrections which would make very difficult the estimate of the transition point from straightforward simulations.Comment: 10 pages, 16 figure

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