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ABSTRACT: 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.
05/2013;
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ABSTRACT: 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 γ or the conjugated (mean) shear stress τ 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 μF(T) which at constant τ decay monotonously with T following the affine shear elasticity μA(T), i.e., a simple two-point correlation function. At variance, non-monotonous behavior with a maximum at the glass transition temperature Tg is demonstrated for μF(T) at constant γ. The increase of G below Tg is reasonably fitted for both models by a continuous cusp singularity, G(T)∝(1 - T∕Tg)(1∕2), in qualitative agreement with recent theoretical predictions. It is argued, however, that longer sampling times may lead to a sharper transition.
The Journal of chemical physics 03/2013; 138(12):12A533. · 3.09 Impact Factor
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ABSTRACT: The truncation of a pair potential at a distance r_{c} 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_{c}, 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 2 dimensions. Both models being glass formers, we comment briefly on the temperature (T) dependence of the (corrected) shear modulus G(T) around the glass transition temperature T_{g}.
Physical Review E 10/2012; 86(4-2):046705. · 2.26 Impact Factor
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ABSTRACT: 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 ρ the expected power law scaling for the interaction energy between different chains e ( int ) ∼ ρ (21/8), the total pressure P ∼ ρ (3) and the dimensionless compressibility gT = lim( q→0) S(q) ∼ 1/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 ξ(ρ) 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 wave vector q . We comment briefly on finite persistence length effects.
The European Physical Journal E 09/2012; 35(9):9771. · 1.94 Impact Factor
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ABSTRACT: We develop a fluctuating hydrodynamics approach to study the impact of the hydrodynamic and viscoelastic interactions on the motion of the center of mass of a polymer as well as on the relaxation of Rouse modes, either in a Θ solvent or in a melt of identical unentangled chains. We show that this method allows us to describe the effect of hydrodynamic interactions beyond the Zimm (for a single chain in a Θ solvent) or the Rouse models (for an unentangled melt). In the latter case, we recover the same important effect of the viscoelastic hydrodynamic interactions on the center-of-mass diffusion, first described in Farago et al (2011 Phys. Rev. Lett. 107 178301).
Journal of Physics Condensed Matter 07/2012; 24(28):284105. · 2.55 Impact Factor
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ABSTRACT: We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c.m. velocity autocorrelation function (c.m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t1 and the Rouse relaxation time tN. We obtain an analytical expression for the c.m. VAF in terms of molecular parameters. In particular, the c.m. VAF scales as −N−1t−5/4 (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted −t−5/4 dependence of the c.m. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [ Farago et al. Phys. Rev. E 85 051807 (2012), the following paper].
Phys. Rev. E. 05/2012; 85(5).
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J. P. Wittmer,
A. Cavallo,
H. Xu,
J. E. Zabel,
P. Polińska,
N. Schulmann,
H. Meyer,
J. Farago,
A. Johner,
S. P. Obukhov, J. Baschnagel
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ABSTRACT: 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≫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.
KeywordsPolymer melts–Monte Carlo simulations–Time-dependent properties
Journal of Statistical Physics 04/2012; 145(4):1017-1126. · 1.40 Impact Factor
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ABSTRACT: 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.
12/2011;
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ABSTRACT: 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) ∼ -1/(N t) 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.
The Journal of chemical physics 11/2011; 135(18):186101. · 3.09 Impact Factor
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ABSTRACT: By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature T(g) and for the elastic properties of the glassy state are presented. We find that T(g) increases with chain length N and is for all N larger for the semiflexible model. The N dependence of T(g) is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below T(g) via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching T(g) from below, the shear modulus μ displays a much stronger decrease near T(g). From the present simulation data it is not possible to decide whether μ takes a finite value at T(g), as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.
The European Physical Journal E 09/2011; 34(9):97. · 1.94 Impact Factor
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J. P. Wittmer,
A. Cavallo,
H. Xu,
J. E. Zabel,
P. Polińska,
N. Schulmann,
H Meyer,
J Farago,
A. Johner,
S. P. Obukhov, J. Baschnagel
[show abstract]
[hide abstract]
ABSTRACT: 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.
07/2011;
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ABSTRACT: By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints, we examine the center-of-mass (COM) dynamics of polymer melts in d = 3 dimensions. Our analysis focuses on the COM displacement correlation function C(N)(t)≈∂(t) (2)h(N)(t)/2, measuring the curvature of the COM mean-square displacement h(N)(t). We demonstrate that C(N)(t) ≈ -(R(N)∕T(N))(2)(ρ∗/ρ) f(x = t/T(N)) with N being the chain length (16 ≤ N ≤ 8192), R(N) ∼ N(1/2) is the typical chain size, T(N) ∼ N(2) is the longest chain relaxation time, ρ is the monomer density, ρ(*)≈N/R(N) (d) is the self-density, and f(x) is a universal function decaying asymptotically as f(x) ∼ x(-ω) with ω = (d + 2) × α, where α = 1/4 for x ≪ 1 and α = 1/2 for x ≫ 1. We argue that the algebraic decay NC(N)(t) ∼ -t(-5/4) for t ≪ T(N) results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.
The Journal of chemical physics 06/2011; 134(23):234901. · 3.09 Impact Factor
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ABSTRACT: We characterize the response of compressed, sheared polymer-brush bilayers with colloidal inclusions to highly nonstationary inversion processes by means of molecular dynamics simulations and scaling theory. Bilayers with a simple (dimeric) solvent reveal an overshoot for the shear stress, while simulations of dry brushes without explicit solvent molecules fail to display this effect. We demonstrate that mechanical instabilities can be controlled by the inclusion of macromolecular structures, such as colloids of varying softness. Based on a recently developed theory, we suggest a scaling approach to determine a characteristic time for conformational and collective responses.
Physical Review Letters 04/2011; 106(16):168301. · 7.37 Impact Factor
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ABSTRACT: Corrections to chain ideality have been demonstrated recently for polymer melts in the bulk and in ultrathin films. It has been shown that the effect of incomplete screening is stronger in the latter. We show here that the deviation from ideality is even stronger in thin capillaries. Describing the crossover from the free bulk to the confined regime as the radius of the capillary decreases below the typical coil radius we make connection to the so far disconnected work by Brochard and de Gennes (J. Phys. (Paris), Lett., 40 (1979) 399) predicting chain segregation in very thin capillaries. Due to the generalized Porod scattering of the segregated chains, the Kratky representation of the intrachain structure factor reveals a plateau for all regimes although the chains become swollen with increasing confinement.
EPL (Europhysics Letters) 02/2011; 93(4):48002. · 2.17 Impact Factor
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ABSTRACT: Cited By (since 1996): 1, Export Date: 12 October 2012, Source: Scopus, CODEN: WEARA, doi: 10.1016/j.wear.2011.05.026, Language of Original Document: English, Correspondence Address: Solar, M.; Institut Charles Sadron UPR 0022, Campus CNRS de Cronenbourg, 23 rue du Loess BP 84047, 67034 Strasbourg Cedex 2, France; email: mathieu.solar@ics-cnrs.unistra.fr, References: Lemaitre, J., Chaboche, J.L., (1988) Mechanics of Solid Materials, , Dunod, Paris;
Wear. 01/2011; 271(11-12):2751-2758.
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ABSTRACT: By means of molecular dynamics simulations we demonstrate power laws for macroscopic transport properties of strongly compressed polymer-brush bilayers to stationary shear motion beyond the Newtonian response. The corresponding exponents are derived from a recently developed scaling theory, where the interpenetration between the brushes is taken as the relevant length scale. This allows to predict the dependence of the critical shear rate, which separates linear and non-linear behavior, on compression and molecular parameters of the bilayer. We present scaling plots for chain extension (R), viscosity (η) , and shear force (F over a wide range of Weissenberg numbers, W . In agreement with our theory, the simulation reveals simple power laws, R ∼ W (0.53), η ∼ W (-0.46), and F ∼ W (0.54), for the non-Newtonian regime.
The European Physical Journal E 12/2010; 33(4):307-11. · 1.94 Impact Factor
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ABSTRACT: In this work, a mechanical analysis of normal contact using molecular dynamics (MD) simulations is presented. Conical indentation on amorphous polymer surfaces was simulated at various temperatures and indentation rates under displacement or load control. The results are qualitatively compared with experimental data from tests on epoxy materials with different glass transition temperatures (Tg), and show good agreement with experiments. Moreover, MD simulations of nano-indentation tests allow us to estimate the mechanical properties of the polymer films studied as in experimental nano-indentation tests, which demonstrates the relevance of this approach.
Journal of Physics D Applied Physics 10/2010; 43(45):455406. · 2.54 Impact Factor
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ABSTRACT: Dense self-avoiding polymer chains in strictly two dimensions are compact objects with fractal contours. Using scaling arguments and molecular dynamics simulations (with negligible momentum conservation) it is shown that correlated amoebalike fluctuations of the (sub)chain contours dominate the relaxation dynamics on all scales. The incompressibility of the melt and the compactness of (sub)chains impose a scale-free constraint on the contour fluctuations. This leads to strong long range spatiotemporal correlations of the displacement field as shown, e.g., by the (negative) algebraic decay of the center-of-mass velocity correlation function C(t)∼-1/t(6/5) with time t.
Physical Review Letters 07/2010; 105(3):037802. · 7.37 Impact Factor
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ABSTRACT: The apparent analogy between the self-diffusion of linear oligomers in monodisperse systems, 2 up to 32 monomers, and their tracer diffusion in an entangled polymer matrix of length 256 is investigated by molecular dynamics simulations at constant pressure. Oligomers and polymers are represented by the same coarse-grained (bead-spring) model. An analysis based on the Rouse model is presented. The scaling relationship of the self-diffusion coefficient D with the chain length N written as D proportional, variantN(-alpha) is analyzed for a wide range of temperatures down to the glass transition temperature T(g). Near T(g), the heterogeneous dynamics is explored by the self-part of the van Hove distribution function and various non-Gaussian parameters. For the self-diffusion in a monodisperse system a scaling exponent alpha(T)>1 depending on temperature is found, whereas for the tracer diffusion in an entangled matrix alpha=1 is obtained at all temperatures, regardless of the oligomer length. The different scaling behavior between both systems is explained by a different monomer mobility, which depends on chain length for monodisperse systems, but is constant for all tracers in the polymer matrix.
The Journal of chemical physics 05/2010; 132(19):194902. · 3.09 Impact Factor
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ABSTRACT: By means of molecular dynamics simulations and scaling theory we study the response of opposing polymer brushes to constant shear motion under good solvent conditions. Model systems that contain explicit solvent molecules (Lennard-Jones dimers) are compared to solvent-free systems while varying of the distance between the grafted layers and their molecular parameters, chain length and grafting density. Our study reveals a power-law dependence of macroscopic transport properties on the Weissenberg number, W, beyond linear response. For instance, we find that the kinetic friction constant scales as mu approximately W(0.57) for large values of W. We develop a scaling theory that describes our data and previous numerical data including recent experiments.
Langmuir 05/2010; 26(9):6418-29. · 4.19 Impact Factor
