Marginally compact fractal trees with semiflexibility

We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness the self-contact density gets drastically reduced.Comment: 16 pages, 12 figures, accepted for publication in PR

Dynamical Monte Carlo Study of Equilibrium Polymers (II): The Role of Rings

We investigate by means of a number of different dynamical Monte Carlo simulation methods the self-assembly of equilibrium polymers in dilute, semidilute and concentrated solutions under good-solvent conditions. In our simulations, both linear chains and closed loops compete for the monomers, expanding on earlier work in which loop formation was disallowed. Our findings show that the conformational properties of the linear chains, as well as the shape of their size distribution function, are not altered by the formation of rings. Rings only seem to deplete material from the solution available to the linear chains. In agreement with scaling theory, the rings obey an algebraic size distribution, whereas the linear chains conform to a Schultz--Zimm type of distribution in dilute solution, and to an exponentional distribution in semidilute and concentrated solution. A diagram presenting different states of aggregation, including monomer-, ring- and chain-dominated regimes, is given

Continuum limit of amorphous elastic bodies (III): Three dimensional systems

Extending recent numerical studies on two dimensional amorphous bodies, we characterize the approach of elastic continuum limit in three dimensional (weakly polydisperse) Lennard-Jones systems. While performing a systematic finite-size analysis (for two different quench protocols) we investigate the non-affine displacement field under external strain, the linear response to an external delta force and the low-frequency harmonic eigenmodes and their density distribution. Qualitatively similar behavior is found as in two dimensions. We demonstrate that the classical elasticity description breaks down below an intermediate length scale $\xi$, which in our system is approximately 23 molecular sizes. This length characterizes the correlations of the non-affine displacement field, the self-averaging of external noise with distance from the source and gives the lower wave length bound for the applicability of the classical eigenfrequency calculations. We trace back the "Boson-peak" of the density of eigenfrequencies (obtained from the velocity auto-correlation function) to the inhomogeneities on wave lengths smaller than $\xi$.Comment: 27 pages, 11 figures, submitted to Phys. Rev.

Vibrations of amorphous, nanometric structures: When does continuum theory apply?

Structures involving solid particles of nanometric dimensions play an increasingly important role in material sciences. These structures are often characterized through the vibrational properties of their constituent particles, which can be probed by spectroscopic methods. Interpretation of such experimental data requires an extension of continuum elasticity theory down to increasingly small scales. Using numerical simulation and exact diagonalization for simple models, we show that continuum elasticity, applied to disordered system, actually breaks down below a length scale of typically 30 to 50 molecular sizes. This length scale is likely related to the one which is generally invoked to explain the peculiar vibrational properties of glassy systems.Comment: 4 pages, 5 figures, LATEX, Europhysics Letters accepte

Dynamical Properties of the Slithering Snake Algorithm: A numerical test of the activated reptation hypothesis

The correlations in the motion of reptating polymers in their melt are investigated by means of kinetic Monte Carlo simulations of the three dimensional slithering snake version of the bond-fluctuation model. Surprisingly, the slithering snake dynamics becomes inconsistent with classical reptation predictions at high chain overlap (either chain length $N$ or volume fraction $\phi$) where the relaxation times increase much faster than expected. This is due to the anomalous curvilinear diffusion in a finite time window whose upper bound $\tau_+$ is set by the chain end density $\phi/N$. Density fluctuations created by passing chain ends allow a reference polymer to break out of the local cage of immobile obstacles created by neighboring chains. The dynamics of dense solutions of snakes at $t \ll \tau_+$ is identical to that of a benchmark system where all but one chain are frozen. We demonstrate that it is the slow creeping of a chain out of its correlation hole which causes the subdiffusive dynamical regime. Our results are in good qualitative agreement with the activated reptation scheme proposed recently by Semenov and Rubinstein [Eur. Phys. J. B, {\bf 1} (1998) 87]. Additionally, we briefly comment on the relevance of local relaxation pathways within a slithering snake scheme. Our preliminary results suggest that a judicious choice of the ratio of local to slithering snake moves is crucial to equilibrate a melt of long chains efficiently.Comment: 24 pages, 18 figures, submitted to EPJ

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

Models of stress fluctuations in granular media

We investigate in detail two models describing how stresses propagate and fluctuate in granular media. The first one is a scalar model where only the vertical component of the stress tensor is considered. In the continuum limit, this model is equivalent to a diffusion equation (where the r\^ole of time is played by the vertical coordinate) plus a randomly varying convection term. We calculate the response and correlation function of this model, and discuss several properties, in particular related to the stress distribution function. We then turn to the tensorial model, where the basic starting point is a wave equation which, in the absence of disorder, leads to a ray-like propagation of stress. In the presence of disorder, the rays acquire a diffusive width and the angle of propagation is shifted. A striking feature is that the response function becomes negative, which suggests that the contact network is mechanically unstable to very weak perturbations. The stress correlation function reveals characteristic features related to the ray-like propagation, which are absent in the scalar description. Our analytical calculations are confirmed and extended by a numerical analysis of the stochastic wave equation.Comment: 32 pages, latex, 18 figures and 6 diagram

Inhomogeneous elastic response of silica glass

Using large scale molecular dynamics simulations we investigate the properties of the {\em non-affine} displacement field induced by macroscopic uniaxial deformation of amorphous silica,a strong glass according to Angell's classification. We demonstrate the existence of a length scale $\xi$ characterizing the correlations of this field (corresponding to a volume of about 1000 atoms), and compare its structure to the one observed in a standard fragile model glass. The "Boson-peak'' anomaly of the density of states can be traced back in both cases to elastic inhomogeneities on wavelengths smaller than $\xi$, where classical continuum elasticity becomes simply unapplicable

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