Publications (138)283.94 Total impact
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ABSTRACT: The continuoustime random walk (CTRW) describes the singleparticle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jumplength distribution (JLD), the waitingtime distribution (WTD), and the persistencetime distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the meansquare displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early α process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivitydominated regime, but not in the early α regime where they systematically underestimate the MSD from the MD.Physical Review E 04/2014; 89(41):042604. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Singleparticle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuoustime random walk (CTRW). We perform molecular dynamics simulations of equilibrated shortchain polymer melts near the critical temperature of modecoupling theory Tc and extract "moves" from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forwardbackward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jumplength and waitingtime distributions as well as on characteristic time scales, such as the average waiting time ("exchange time") and the average time for the first move ("persistence time"). The refinement modifies the temperature (T) dependence of these time scales. For instance, the average waiting time changes from an Arrheniustype to a VogelFulchertype T dependence. We discuss this observation in the context of the bifurcation of the α process and (Johari) β process found in many glassforming materials to occur near Tc. Our analysis lays the foundation for a study of the jumplength and waitingtime distributions, their temperature and chainlength dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper [J. Helfferich et al., Phys. Rev. E 89, 042604 (2014)].Physical Review E 04/2014; 89(41):042603. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Singleparticle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuoustime random walk (CTRW). We perform molecular dynamics simulations of equilibrated shortchain polymer melts near the critical temperature of modecoupling theory Tc and extract "moves" from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forwardbackward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jumplength and waitingtime distributions as well as on characteristic time scales, such as the average waiting time ("exchange time") and the average time for the first move ("persistence time"). The refinement modifies the temperature (T) dependence of these time scales. For instance, the average waiting time changes from an Arrheniustype to a VogelFulchertype T dependence. We discuss this observation in the context of the bifurcation of the α process and (Johari) β process found in many glassforming materials to occur near Tc. Our analysis lays the foundation for a study of the jumplength and waitingtime distributions, their temperature and chainlength dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper [J. Helfferich et al., Phys. Rev. E 89, 042604 (2014), 10.1103/PhysRevE.89.042604].03/2014; 89(4).  [Show abstract] [Hide abstract]
ABSTRACT: The continuoustime random walk (CTRW) describes the singleparticle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014), 10.1103/PhysRevE.89.042603], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jumplength distribution (JLD), the waitingtime distribution (WTD), and the persistencetime distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the meansquare displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early α process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivitydominated regime, but not in the early α regime where they systematically underestimate the MSD from the MD.03/2014; 89(4).  [Show abstract] [Hide abstract]
ABSTRACT: Conformational properties of regular dendrimers and more general hyperbranched polymer stars with Gaussian statistics for the spacer chains between branching points are revisited numerically. We investigate the scaling for asymptotically long chains especially for fractal dimensions d f = 3 (marginally compact) and d f = 2.5 (diffusion limited aggregation). Powerlaw stars obtained by imposing the number of additional arms per generation are compared to truly selfsimilar stars. We discuss effects of weak excludedvolume interactions and sketch the regime where the Gaussian approximation should hold in dense solutions and melts for sufficiently large spacer chains.The European Physical Journal E 02/2014; 37(2):9968. · 2.18 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Melts of unconcatenated and unknotted polymer rings are a paradigm for soft matter ruled by topological interactions. We propose a description of a system of rings of length N as a collection of smaller polydisperse Gaussian loops, ranging from the entanglement length to the skeleton ring length \sim N^{2/3} , assembled in random trees. Individual rings in the melt are predicted to be marginally compact with a mean square radius of gyration R_g^2 \sim N^{2/3}(1\text{const} \cdot N^{1/3}) . As a rule, simple power laws for asymptotically long rings come with sluggish crossovers. Experiments and computer simulations merely deal with crossover regimes typically extending to N\sim 10^{3\text{}4} . The estimated crossover functions allow for a satisfactory fit of simulation data.01/2014; 105(4).  [Show abstract] [Hide abstract]
ABSTRACT: Recent computational studies on melts of nonconcatenated rings suggest compact configurations of fractal dimension df = 3. This begs the question of whether the irregular surfaces of these compact rings may be characterized by a fractal surface dimension ds < 3. We revisit the scaling analysis of the form factor by Halverson et al. [J. Chem. Phys. 134, 204904 (2011)] implying ds ≈ 2.8. Our analysis suggests that this conclusion might be due to the application of the Generalized Porod Law at large wavevectors where length scales other than the total chain size do matter. We present an alternative "decorated Gaussian loop" model which does not require ds < 3.The Journal of Chemical Physics 12/2013; 139(21):217101. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Presenting simple coarsegrained models of isotropic solids and fluids in d = 1 , 2 and 3 dimensions we investigate the correlations of the instantaneous pressure and its ideal and excess contributions at either imposed pressure (NPTensemble, λ = 0 or volume (NVTensemble, λ = 1 and for more general values of the dimensionless parameter λ characterizing the constantvolume constraint. The stress fluctuation representation [Formula: see text] of the compression modulus K in the NVTensemble is derived directly (without a microscopic displacement field) using the wellknown thermodynamic transformation rules between conjugated ensembles. The transform is made manifest by computing the Rowlinson functional [Formula: see text] also in the NPTensemble where [Formula: see text] with x = P id/K being a scaling variable, P id the ideal pressure and f 0(x) = x(2x) a universal function. By gradually increasing λ by means of an external spring potential, the crossover between both classical ensemble limits is monitored. This demonstrates, e.g., the lever rule [Formula: see text].The European Physical Journal E 11/2013; 36(11):9945. · 2.18 Impact Factor  [Show abstract] [Hide abstract]
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 Krow of the compression modulus for NPTensembles. It is shown theoretically and numerically that Krow∣P = Pid(2  Pid∕K) with Pid being the ideal pressure contribution.The Journal of Chemical Physics 05/2013; 138(19):191101. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The shear modulus G of two glassforming 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 twopoint correlation function. At variance, nonmonotonous 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. · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The density crossover scaling of thermodynamic and conformational properties of solutions and melts of selfavoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions (d = 2) is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse grained beadspring model. We focus on properties related to the contact exponent set by the intrachain subchain size distribution. With R ∼ N ν being the size of chains of length N and ρ the monomer density, the interaction energy e int between monomers from different chains and the corresponding number n int of interchain contacts per monomer are found to scale as with ν = 3/4 and θ2 = 19/12 for dilute solutions and ν = 1/d and θ2 = 3/4 for N≫ g(ρ) ≈ 1/ρ2. Irrespective of ρ, long chains thus become compact packings of blobs of contour length with d p = d − θ2 = 5/4 being the fractal line dimension. Due to the generalized Porod scattering of the compact chains, the Kratky representation of the intramolecular form factor F(q) reveals a nonmonotonous behavior approaching with increasing chain length and density a powerlaw slope $F(q)q^d /\rho \approx 1/(qR)^{\theta _2 } $ in the intermediate regime of the wavevector q. The specific intermolecular contact probability is argued to imply an enhanced compatibility for polymer blends confined to ultrathin films. We comment briefly on finite persistence length effects.Polymer Science Series C 01/2013; 55(1). · 0.63 Impact Factor  [Show abstract] [Hide abstract]
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 stressfluctuation 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 LennardJones 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(42):046705. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The density crossover scaling of various thermodynamic properties of solutions and melts of selfavoiding 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 coarsegrained beadspring 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 nonaffine 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. · 2.18 Impact Factor  [Show abstract] [Hide abstract]
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 centerofmass diffusion, first described in Farago et al (2011 Phys. Rev. Lett. 107 178301).Journal of Physics Condensed Matter 07/2012; 24(28):284105. · 2.22 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A modecoupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [ Farago, Meyer and Semenov Phys. Rev. Lett. 107 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the densitybased MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the centerofmass velocity autocorrelation function (c.m. VAF). We show that in most cases the VHI mechanism is dominant; for long chains and prediffusive times it yields a negative tail ∝−N−1/2t−3/2 for the c.m. VAF. The case of nonmomentumconserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first −N−1t−5/4 (as in the dMCT approach), then −N−1/2t−3/2. Both the amplitude and the duration of the first t−5/4 stage crucially depend on the Langevin friction parameter γ. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the c.m. VAF, thus account for the anomalous subdiffusive regime of the c.m. mean square displacement widely observed in numerical and experimental works.Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 05/2012; 85(5).  [Show abstract] [Hide abstract]
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 densitybased modecoupling theory (dMCT) using the MoriZwanzig approach and projecting the fluctuating force onto pairdensity fluctuation modes. The effect of dynamical density fluctuations on the centerofmass (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 nonmomentumconserving 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].Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 05/2012; 85(5).  Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 03/2012; 85(3).
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ABSTRACT: This paper studies the rheology of weakly entangled polymer melts and films in the glassy domain and near the rubbery domain using two different methods: molecular dynamics (MD) and finite element (FE) simulations. In a first step, the uniaxial mechanical behavior of a bulk polymer sample is studied by means of particlebased MD simulations. The results are in good agreement with experimental data, and mechanical properties may be computed from the simulations. This uniaxial mechanical behavior is then implemented in FE simulations using an elastoviscoelastoviscoplastic constitutive law in a continuum mechanics (CM) approach. In a second step, the mechanical response of a polymer film during an indentation test is modeled with the MD method and with the FE simulations using the same constitutive law. Good agreement is found between the MD and CM results. This work provides evidence in favor of using MD simulations to investigate the local physics of contact mechanics, since the volume elements studied are representative and thus contain enough information about the microstructure of the polymer model, while surface phenomena (adhesion and surface tension) are naturally included in the MD approach.Physical Review E 02/2012; 85(2 Pt 1):021808. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Using molecular dynamics simulation of a standard beadspring model we investigate the density crossover scaling of strictly twodimensional selfavoiding 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.Macromolecules. 12/2011; 45(3).  [Show abstract] [Hide abstract]
ABSTRACT: A melt of nonentangled polymer chains confined between two smooth and purely repulsive walls is studied for various film thicknesses D and temperatures. The dynamics of the supercooled films is qualitatively identical to that of the bulk, but the walls lead to faster relaxation. To quantify this observation we analyze the data by the modecoupling theory (MCT) of the glass transition. We find that the critical temperature of MCT, Tc(D), decreases with D and that T  Tc(D) is a relevant temperature scale. The static structure factor and dynamic correlation functions at intermediate times coincide with bulk behavior when compared to the same T  Tc(D).International Journal of Modern Physics C 11/2011; 13(06). · 0.62 Impact Factor
Publication Stats
2k  Citations  
283.94  Total Impact Points  
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Institutions

2010–2014

University of Strasbourg
 Institut Charles Sadron
Strasburg, Alsace, France


2012

University of Lorraine
Nancy, Lorraine, France


1991–2011

Johannes GutenbergUniversität Mainz
 Institute of Physics
Mainz, RhinelandPalatinate, Germany


2006

Institut de France
Lutetia Parisorum, ÎledeFrance, France
