arXiv subjects

J. Baschnagel

Publications and source records attributed to J. Baschnagel.

At least 37 records · Page 2Linked to original sources

arXiv2013

Pressure fluctuations in isotropic solids and fluids

Comparing isotropic solids and fluids at either imposed volume or pressure we investigate various correlations of the instantaneous pressure and its ideal and excess contributions. Focusing on the compression modulus K it is emphasized that the stress fluctuation representation of the elastic moduli may be obtained directly (without a microscopic displacement field) by comparing the stress fluctuations in conjugated ensembles. This is made manifest by computing the Rowlinson stress fluctuation expression K_row of the compression modulus for NPT-ensembles. It is shown theoretically and numerically that K_row|P = P_id (2 - P_id/K) with P_id being the ideal pressure contribution.

cond-mat.soft↗

arXiv2012

Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time

The shear modulus G of two glass-forming colloidal model systems in d=3 and d=2 dimensions is investigated by means of, respectively, molecular dynamics and Monte Carlo simulations. Comparing ensembles where either the shear strain gamma or the conjugated (mean) shear stress tau are imposed, we compute G from the respective stress and strain fluctuations as a function of temperature T while keeping a constant normal pressure P. The choice of the ensemble is seen to be highly relevant for the shear stress fluctuations mu_F(T) which at constant tau decay monotonously with T following the affine shear elasticity mu_A(T), i.e. a simple two-point correlation function. At variance, non-monotonous behavior with a maximum at the glass transition temperature T_g is demonstrated for mu_F(T) at constant gamma. The increase of G below T_g is reasonably fitted for both models by a continuous cusp singularity, G(T) is proportional to (1-T/T_g)^(1/2), in qualitative agreement with some recent replica calculations. It is argued, however, that longer sampling times may lead to a sharper transition. The additive jump discontinuity predicted by mode-coupling theory and other replica calculations thus cannot ultimately be ruled out.

cond-mat.soft↗

arXiv2012

Strictly two-dimensional self-avoiding walks: Thermodynamic properties revisited

The density crossover scaling of various thermodynamic properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse-grained bead-spring model. In the semidilute regime we confirm over an order of magnitude of the monomer density rho the expected power-law scaling for the interaction energy between different chains e_inter\simρ^(21/8), the total pressure P\simρ^3 and the dimensionless compressibility gT=lim(q->0)(S(q)\sim1/ρ^2). Various elastic contributions associated to the affine and non-affine response to an infinitesimal strain are analyzed as functions of density and sampling time. We show how the size xi(rho) of the semidilute blob may be determined experimentally from the total monomer structure factor S(q) characterizing the compressibility of the solution at a given wavevector q. We comment briefly on finite persistence length effects.

cond-mat.soft↗

arXiv2012

Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential

The truncation of a pair potential at a distance r_cut is well-known to imply in general an impulsive correction to the pressure and other moments of the first derivatives of the potential. That depending on r_cut the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in d dimensions. Focusing on isotropic liquids for which the shear modulus G must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, d=3 and d=2 dimensions.

cond-mat.soft↗

arXiv2011

Interchain monomer contact probability in two-dimensional polymer solutions

Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the intrachain subchain size distribution. Irrespective of the density sufficiently long chains are found to consist of compact packings of blobs of fractal perimeter dimension dp = 5/4.

cond-mat.soft↗

arXiv2011

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.

cond-mat.soft↗

arXiv2011

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 $ξ$ 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 $r \gg ξ$. 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.

cond-mat.soft↗

arXiv2010

Static Properties of Polymer Melts in Two Dimensions

Self-avoiding polymers in strictly two-dimensional ($d=2$) melts are investigated by means of molecular dynamics simulation of a standard bead-spring model with chain lengths ranging up to N=2048. % The chains adopt compact configurations of typical size $R(N) \sim N^ν$ with $ν=1/d$. % The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents $Θ_0=3/8$, $Θ_1=1/2$ and $Θ_2=3/4$ predicted by Duplantier. % Due to the segregation of the chains the ratio of end-to-end distance $\Rend(N)$ and gyration radius $\Rgyr(N)$ becomes $\Rend^2(N)/\Rgyr^2(N) \approx 5.3 < 6$ for $N \gg 100$ and the chains are more spherical than Gaussian phantom chains. % The second Legendre polynomial $P_2(s)$ of the bond vectors decays as $P_2(s) \sim 1/s^{1+νΘ_2}$ measuring thus the return probability of the chain after $s$ steps. % The irregular chain contours are shown to be characterized by a perimeter length $L(N) \sim R(N)^{\dc}$ of fractal line dimension $\dc = d-Θ_2 =5/4$. % % In agreement with the generalized Porod scattering of compact objects with fractal contour the Kratky representation of the intramolecular structure factor $F(q)$ reveals a strong non-monotonous behavior with $q^dF(q) \sim 1/(q R(N))^{Θ_2}$ in the intermediate regime of the wave vector $q$. This may allow to confirm the predicted contour fractality in a real experiment.

cond-mat.soft↗

arXiv2009

Non-extensivity of the chemical potential of polymer melts

Following Flory's ideality hypothesis the chemical potential of a test chain of length $n$ immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in $n$. We argue that an additional contribution $δμ_c(n) \sim +1/ρ\sqrt{n}$ arises ($ρ$ being the monomer density) for all $¶(N)$ if $n \ll $ which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory distributed melts we obtain $δμ_c(n) \approx (1- 2 n/ ) / ρ\sqrt{n}$ for $n \ll ^2$, hence, $δμ_c(n) \approx - 1/ρ\sqrt{n}$ if $n$ is similar to the typical length of the bath $ $. Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond-fluctuation model. As predicted we find, e.g., the non-exponentiality parameter $K_p \equiv 1 - /p! ^p$ to decay as $K_p \approx 1 / \sqrt{ }$ for all moments $p$ of the distribution.

cond-mat.soft↗

arXiv2009

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 $ξ\ll r \ll \r^*$ with $ξ$ being the screening length of the density fluctuations and $r^* \sim N^{1/3}$ a novel length scale increasing slowly with (mean) chain length $N$.

cond-mat.soft↗

arXiv2009

A finite excluded volume bond-fluctuation model: Static properties of dense polymer melts revisited

The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty $\overlap$. This is done to vary systematically the dimensionless compressibility $g$ of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various s tatic properties at constant overall monomer density. The compressibility is obtained directly from the low-wavevector limit of the static structure fa ctor. We consider, e.g., the intrachain bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain. It is shown that the excluded volume interactions are never fully screened for very long chains. If distances smaller than the thermal blob size are probed ($s \ll g$) the chains are swollen acc ording to the classical Fixman expansion where, e.g., $P(s) \sim g^{-1}s^{-1/2}$. More importantly, the polymers behave on larger distances ($s \gg g$) like swollen chains of incompressible blobs with $P(s) \si m g^0s^{-3/2}$.

cond-mat.soft↗

arXiv2009

Perimeter Length and Form Factor of Two-Dimensional Polymer Melts

Self-avoiding polymers in two-dimensional ($d=2$) melts are known to adopt compact configurations of typical size $R(N) \sim N^{1/d}$ with $N$ being the chain length. Using molecular dynamics simulations we show that the irregular shapes of these chains are characterized by a perimeter length $L(N) \sim R(N)^{\dpm}$ of fractal dimension $\dpm = d-Θ_2 =5/4$ with $Θ_2=3/4$ being a well-known contact exponent. Due to the self-similar structure of the chains, compactness and perimeter fractality repeat for subchains of all arc-lengths $s$ down to a few monomers. The Kratky representation of the intramolecular form factor $F(q)$ reveals a strong non-monotonous behavior with $q^2F(q) \sim 1/(qN^{1/d})^{Θ_2}$ in the intermediate regime of the wavevector $q$. Measuring the scattering of labeled subchains %($s F(q) \sim L(s)$) the form factor may allow to test our predictions in real experiments.

cond-mat.soft↗

arXiv2007

Static Rouse Modes and Related Quantities: Corrections to Chain Ideality in Polymer Melts

Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (`hard monomers') to no excluded volume (`phantom chains'). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.

cond-mat.soft↗

arXiv2007

Soft particle model for block copolymers

A soft particle model for diblock (AB) copolymer melts is proposed. Each molecule is mapped onto two soft spheres built by Gaussian A- and B-monomer distributions. An approximate analytical expression for the joint distribution function for the distance between both spheres and their radii of gyration is derived, which determines the entropic contribution to the intramolecular free energy. Adding a mean-field expression for the intermolecular interactions, we obtain the total free energy of the system. Based on this free energy, Monte Carlo simulations are carried out to study the kinetics of microphase ordering in the bulk and its effect on molecular diffusion. This is followed by an analysis of thin films with emphasis on pattern transfer from walls with a periodic structure. It is shown that the level of coarse graining in the soft particle model is suitable to describe structural and kinetic properties of copolymers on mesoscopic scales.

cond-mat.mtrl-sci↗

arXiv2007

Intramolecular long-range correlations in polymer melts: The segmental size distribution and its moments

Presenting theoretical arguments and numerical results we demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion $u(s) \approx s/ρR^3(s) \approx ce/\sqrt{s}$ when connecting two segments together where $s$ denotes the curvilinear length of a segment, $R(s)$ its typical size, $ce \approx 1/ρbe^3$ the ``swelling coefficient", $be$ the effective bond length and $ρ$ the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to $u(s)$. The analysis of different moments of this distribution allows for a precise determination of the effective bond length $be$ and the swelling coefficient $ce$ of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's ideality hypothesis the bond-bond correlation function of two bonds separated by $s$ monomers along the chain is found to decay algebraically as $1/s^{3/2}$. Effects of finite chain length are considered briefly.

cond-mat.soft↗

arXiv2007

Bond formation and slow heterogeneous dynamics in adhesive spheres with long--ranged repulsion: Quantitative test of Mode Coupling Theory

A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semi-quantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).

cond-mat.soft↗

arXiv2007

Why polymer chains in a melt are not random walks

A cornerstone of modern polymer physics is the `Flory ideality hypothesis' which states that a chain in a polymer melt adopts `ideal' random-walk-like conformations. Here we revisit theoretically and numerically this pivotal assumption and demonstrate that there are noticeable deviations from ideality. The deviations come from the interplay of chain connectivity and the incompressibility of the melt, leading to an effective repulsion between chain segments of all sizes $s$. The amplitude of this repulsion increases with decreasing $s$ where chain segments become more and more swollen. We illustrate this swelling by an analysis of the form factor $F(q)$, i.e. the scattered intensity at wavevector $q$ resulting from intramolecular interferences of a chain. A `Kratky plot' of $q^2F(q)$ {\em vs.} $q$ does not exhibit the plateau for intermediate wavevectors characteristic of ideal chains. One rather finds a conspicuous depression of the plateau, $δ(F^{-1}(q)) = |q|^3/32ρ$, which increases with $q$ and only depends on the monomer density $ρ$.

cond-mat.soft↗

arXiv2006

On the Dynamics and Disentanglement in Thin and Two-Dimensional Polymer Films

We present results from molecular dynamics simulations of strictly two-dimensional (2D) polymer melts and thin polymer films in a slit geometry of thickness of the order of the radius of gyration. We find that the dynamics of the 2D melt is qualitatively different from that of the films. The 2D monomer mean-square displacement shows a $t^{8/15}$ power law at intermediate times instead of the $t^{1/2}$ law expected from Rouse theory for nonentangled chains. In films of finite thickness, chain entanglements may occur. The impact of confinement on the entanglement length $N_\mathrm{e}$ has been analyzed by a primitive path analysis. The analysis reveals that $N_\mathrm{e}$ increases strongly with decreasing film thickness.

cond-mat.soft↗