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

Long Range Bond-Bond Correlations in Dense Polymer Solutions

The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $\rho$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) \sim s^{-\omega}$ with $\omega=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) \approx g^{-\omega_0} (s/g)^{-\omega}$ with $\omega_0=2-2\nu=0.824$ ($\nu=0.588$ being Flory's exponent) is set by the number of monomers $g(\rho)$ contained in an excluded volume blob of size $\xi$. % Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains on distances $s \gg g$ caused by the connectivity of chains and the incompressibility of the melt. %Comment: 4 pages, 4 figure

Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in $L^\infty$ in space and time.Comment: 23 pages, 2 fugure

Diffraction effects on light-atomic ensemble quantum interface

We present a simple method to include the effects of diffraction into the description of a light-atomic ensemble quantum interface in the context of collective variables. Carrying out a scattering calculation we single out the purely geometrical effect. We apply our method to the experimentally relevant case of Gaussian shaped atomic samples stored in single beam optical dipole traps and probed by a Gaussian beam. We derive analytical scaling relations for the effect of the interaction geometry and compare our findings to results from 1-dimensional models of light propagation.Comment: 13 pages, 7 figures, comments welcom

On the experimental determination of the one-way speed of light

In this contribution the question of the isotropy of the one-way speed of light from an experimental perspective is addressed. In particular, we analyze two experimental methods commonly used in its determination. The analysis is aimed at clarifying the view that the one-way speed of light cannot be determined by techniques in which physical entities close paths. The procedure employed here will provide epistemological tools such that physicists understand that a direct measurement of the speed not only of light but of any physical entity is by no means trivial. Our results shed light on the physics behind the experiments which may be of interest for both physicists with an elemental knowledge in special relativity and philosophers of science.Comment: 8 pages, 5 figures. To appear in the European Journal of Physic

Equation of State for Macromolecules of Variable Flexibility in Good Solvents: A Comparison of Techniques for Monte Carlo Simulations of Lattice Models

The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length N=20) we study the influence of various choices for the chain stiffness on the equation of state. Three techniques are applied and compared in order to critically assess their efficiency and accuracy: the repulsive wall method, the thermodynamic integration method (which rests on the feasibility of simulations in the grand canonical ensemble), and the recently advocated sedimentation equilibrium method, which records the density profile in an external (e.g. gravitation-like) field and infers, via a local density approximation, the equation of state from the hydrostatic equilibrium condition. We confirm the conclusion that the latter technique is far more efficient than the repulsive wall method, but we find that the thermodynamic integration method is similarly efficient as the sedimentation equilibrium method. For very stiff chains the onset of nematic order enforces the formation of isotropic-nematic interface in the sedimentation equilibrium method leading to strong rounding effects and deviations from the true equation of state in the transition regime.Comment: 32 pages, 18 figures, submitted to Phys.Rev.E; one paragraph added to conclusions sectio