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, $P(s)$, of two bonds separated by $s$ monomers along the chain should exponentially decay with $s$. 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, $P(s)$ to decay algebraically as $s^{-3/2}$. Our study suggests a precise method for obtaining the statistical segment length \bstar in a computer experiment.Comment: 4 pages, 3 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 $r$ 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 $P(r)$ is shown to decay as $P(r) \sim 1/r^3$ for \xi \ll r \ll \r^* with $\xi$ being the screening length of the density fluctuations and $r^* \sim N^{1/3}$ a novel length scale increasing slowly with (mean) chain length $N$.Comment: 17 pages, 5 figures, accepted for publication at Macromolecule

Computational confirmation of scaling predictions for equilibrium polymers

We report the results of extensive Dynamic Monte Carlo simulations of systems of self-assembled Equilibrium Polymers without rings in good solvent. Confirming recent theoretical predictions, the mean-chain length is found to scale as \Lav = \Lstar (\phi/\phistar)^\alpha \propto \phi^\alpha \exp(\delta E) with exponents $\alpha_d=\delta_d=1/(1+\gamma) \approx 0.46$ and $\alpha_s = [1+(\gamma-1)/(\nu d -1)]/2 \approx 0.60, \delta_s=1/2$ in the dilute and semi-dilute limits respectively. The average size of the micelles, as measured by the end-to-end distance and the radius of gyration, follows a very similar crossover scaling to that of conventional quenched polymer chains. In the semi-dilute regime, the chain size distribution is found to be exponential, crossing over to a Schultz-Zimm type distribution in the dilute limit. The very large size of our simulations (which involve mean chain lengths up to 5000, even at high polymer densities) allows also an accurate determination of the self-avoiding walk susceptibility exponent $\gamma = 1.165 \pm 0.01$.Comment: 6 pages, 4 figures, LATE

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

On two intrinsic length scales in polymer physics: topological constraints vs. entanglement length

The interplay of topological constraints, excluded volume interactions, persistence length and dynamical entanglement length in solutions and melts of linear chains and ring polymers is investigated by means of kinetic Monte Carlo simulations of a three dimensional lattice model. In unknotted and unconcatenated rings, topological constraints manifest themselves in the static properties above a typical length scale $dt \sim 1/\sqrt{l\phi}$ ($\phi$ being the volume fraction, $l$ the mean bond length). Although one might expect that the same topological length will play a role in the dynamics of entangled polymers, we show that this is not the case. Instead, a different intrinsic length de, which scales like excluded volume blob size $\xi$, governs the scaling of the dynamical properties of both linear chains and rings.Comment: 7 pages. 4 figure

A common NYX mutation in Flemish patients with X linked CSNB

Aims: The Schubert-Bornschein type of complete congenital stationary night blindness (CSNB) is a genetically heterogeneous retinal disorder. It is characterised by a non-progressive disease course, often associated with high myopia and nystagmus. So far, mutations in two genes, NYX (nyctalopin) and GRM6 (metabotropic glutamate receptor 6) have been associated with this form of CSNB. The purpose of this study was to identify the genetic defect in affected male patients from Flemish families with complete CSNB. Methods: Probands with CSNB from three large Flemish families underwent ophthalmological examination. DNA was extracted from peripheral blood, and the coding region of NYX along with parts of the 5'UTR and 3'UTR and intronic regions covering the splice sites were PCR amplified and sequenced. Results: In the affected individuals of three Flemish families with the complete form of CSNB a novel NYX mutation, c.855delG was identified. This deletion is predicted to lead to a frameshift mutation, p. Asp286ThrfsX62 causing a premature stop codon. Conclusion: Previously, both single families with different mutations in NYX as well as different families with an identical mutation, suggestive of a founder mutation, have been described. The c.855delG deletion in NYX seems to be a common mutation associated with CSNB in the Flemish population from Belgium. Thus, we suggest performing diagnostic testing for CSNB in the Flemish population initially directed towards the identification of this mutation. Subsequent screening for other mutations in NYX or GRM6 could be performed as a second step

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 $\xi$ 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 $r \gg \xi$. 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

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

Osmotic Pressure of Solutions Containing Flexible Polymers Subject to an Annealed Molecular Weight Distribution

The osmotic pressure $P$ in equilibrium polymers (EP) in good solvent is investigated by means of a three dimensional off-lattice Monte Carlo simulation. Our results compare well with real space renormalisation group theory and the osmotic compressibility K \propto \phi \upd \phi/\upd P from recent light scattering study of systems of long worm-like micelles. We confirm the scaling predictions for EP based on traditional physics of quenched monodisperse polymers in the dilute and semidilute limit. Specifically, we find $P\propto \phi^{2.3}$ and, hence, $K \propto \phi^{-0.3}$ in the semidilute regime --- in agreement with both theory and experiment. At higher concentrations where the semidilute blobs become too small and hard-core interactions and packing effects become dominant, a much stronger increase % \log(P/\phi)\approx \log(\Nav^2/\phi) \propto \phi is evidenced and, consequently, the compressibility decreases much more rapidly with $\phi$ than predicted from semidilute polymer theory, but again in agreement with experiment.Comment: 7 pages, 4 figures, LATE

Stresses in silos: Comparison between theoretical models and new experiments

We present precise and reproducible mean pressure measurements at the bottom of a cylindrical granular column. If a constant overload is added, the pressure is linear in overload and nonmonotonic in the column height. The results are {\em quantitatively} consistent with a local, linear relation between stress components, as was recently proposed by some of us. They contradict the simplest classical (Janssen) approximation, and may pose a rather severe test of competing models.Comment: 4 pages, 2 figures, final version to appear in Phys. Rev. Let