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

Stress Propagation and Arching in Static Sandpiles

We present a new approach to the modelling of stress propagation in static granular media, focussing on the conical sandpile constructed from a point source. We view the medium as consisting of cohesionless hard particles held up by static frictional forces; these are subject to microscopic indeterminacy which corresponds macroscopically to the fact that the equations of stress continuity are incomplete -- no strain variable can be defined. We propose that in general the continuity equations should be closed by means of a constitutive relation (or relations) between different components of the (mesoscopically averaged) stress tensor. The primary constitutive relation relates radial and vertical shear and normal stresses (in two dimensions, this is all one needs). We argue that the constitutive relation(s) should be local, and should encode the construction history of the pile: this history determines the organization of the grains at a mesoscopic scale, and thereby the local relationship between stresses. To the accuracy of published experiments, the pattern of stresses beneath a pile shows a scaling between piles of different heights (RSF scaling) which severely limits the form the constitutive relation can take ...Comment: 38 pages, 24 Postscript figures, LATEX, minor misspellings corrected, Journal de Physique I, Ref. Nr. 6.1125, accepte

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

Dynamical Monte Carlo Study of Equilibrium Polymers : Static Properties

We report results of extensive Dynamical Monte Carlo investigations on self-assembled Equilibrium Polymers (EP) without loops in good solvent. (This is thought to provide a good model of giant surfactant micelles.) Using a novel algorithm we are able to describe efficiently both static and dynamic properties of systems in which the mean chain length \Lav is effectively comparable to that of laboratory experiments (up to 5000 monomers, even at high polymer densities). We sample up to scission energies of $E/k_BT=15$ over nearly three orders of magnitude in monomer density $\phi$, and present a detailed crossover study ranging from swollen EP chains in the dilute regime up to dense molten systems. Confirming recent theoretical predictions, the mean-chain length is found to scale as \Lav \propto \phi^\alpha \exp(\delta E) where the exponents approach $\alpha_d=\delta_d=1/(1+\gamma) \approx 0.46$ and $\alpha_s = 1/2 [1+(\gamma-1)/(\nu d -1)] \approx 0.6, \delta_s=1/2$ in the dilute and semidilute limits respectively. The chain length distribution is qualitatively well described in the dilute limit by the Schulz-Zimm distribution \cN(s)\approx s^{\gamma-1} \exp(-s) where the scaling variable is s=\gamma L/\Lav. The very large size of these simulations allows also an accurate determination of the self-avoiding walk susceptibility exponent $\gamma \approx 1.165 \pm 0.01$. ....... Finite-size effects are discussed in detail.Comment: 15 pages, 14 figures, LATE

Note: Scale-free center-of-mass displacement correlations in polymer films without topological constraints and momentum conservation

We present here computational work on the center-of-mass displacements in thin polymer films of finite width without topological constraints and without momentum conservation obtained using a well-known lattice Monte Carlo algorithm with chain lengths ranging up to N=8192. Computing directly the center-of-mass displacement correlation function C_N(t) allows to make manifest the existence of scale-free colored forces acting on a reference chain. As suggested by the scaling arguments put forward in a recent work on three-dimensional melts, we obtain a negative algebraic decay C_N(t) \sim -1/(Nt) for times t << T_N with T_N being the chain relaxation time. This implies a logarithmic correction to the related center-of-mass mean square-displacement h_N(t) as has been checked directly

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

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