Publications (156)363.36 Total impact

Article: The Voronoi liquid
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ABSTRACT: Focusing on isotropic elastic networks we propose a novel simpleaverage expression $G(t) = \mu_A  h(t)$ for the computational determination of the shearstress relaxation modulus $G(t)$ of a classical elastic solid or fluid and its equilibrium modulus $\G_{eq} = \lim_{t \to \infty} G(t)$. Here, $\mu_A = G(0)$ characterizes the shear transformation of the system at $t=0$ and $h(t)$ the (rescaled) meansquare displacement of the instantaneous shear stress $\hat{\tau}(t)$ as a function of time $t$. While investigating sampling time effects we also discuss the related expressions in terms of shearstress autocorrelation functions. We argue finally that our key relation may be readily adapted for more general linear response functions.  [Show abstract] [Hide abstract]
ABSTRACT: Shearstrain and shearstress correlations in isotropic elastic bodies are investigated both theoretically and numerically at either imposed mean shearstress $\tau$ ($\lambda=0$) or shearstrain $\gamma$ ($\lambda=1$) and for more general values of a dimensionless parameter $\lambda$ characterizing the generalized Gaussian ensemble. It allows to tune the strain fluctuations $\mu_{\gamma\gamma} \equiv \beta V \la \delta \gamma^2 \ra = (1\lambda)/G_{eq}$ with $\beta$ being the inverse temperature, $V$ the volume, $\gamma$ the instantaneous strain and $G_{eq}$ the equilibrium shear modulus. Focusing on spring networks in two dimensions we show, e.g., for the stress fluctuations $\mu_{\tau\tau} \equiv \beta V \la \delta\tau^2 \ra$ ($\tau$ being the instantaneous stress) that $\mu_{\tau\tau} = \mu_{A}  \lambda G_{eq}$ with $\mu_{A} = \mu_{\tau\tau}_{\lambda=0}$ being the affine shearelasticity. For the stress autocorrelation function $c_{\tau\tau}(t) \equiv \beta V \la \delta \tau(t) \delta \tau(0) \ra$ this result is then seen (assuming a sufficiently slow shearstress barostat) to generalize to $c_{\tau\tau}(t) = G(t)  \lambda \Geq$ with $G(t)$ being the shearstress relaxation modulus.  [Show abstract] [Hide abstract]
ABSTRACT: The shear stress relaxation modulus G(t) may be determined from the shear stress after switching on a tiny step strain γ or by inverse Fourier transformation of the storage modulus G′(ω) or the loss modulus G′′(ω) obtained in a standard oscillatory shear experiment at angular frequency ω. It is widely assumed that G(t) is equivalent in general to the equilibrium stress autocorrelation function which may be readily computed in computer simulations (β being the inverse temperature and V the volume). Focusing on isotropic solids formed by permanent spring networks we show theoretically by means of the fluctuationdissipation theorem and computationally by molecular dynamics simulation that in general G(t) = Geq + C(t) for t > 0 with Geq being the static equilibrium shear modulus. A similar relation holds for G′(ω). G(t) and C(t) must thus become different for a solid body and it is impossible to obtain Geq directly from C(t). 
Article: Shearstress relaxation and ensemble transformation of shearstress autocorrelation functions
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ABSTRACT: We revisit the relation between the shearstress relaxation modulus G(t), computed at finite shear strain 0<γ≪1, and the shearstress autocorrelation functions C(t)_{γ} and C(t)_{τ} computed, respectively, at imposed strain γ and mean stress τ. Focusing on permanent isotropic spring networks it is shown theoretically and computationally that in general G(t)=C(t)_{τ}=C(t)_{γ}+G_{eq} for t>0 with G_{eq} being the static equilibrium shear modulus. G(t) and C(t)_{γ} thus must become different for solids and it is impossible to obtain G_{eq} alone from C(t)_{γ} as often assumed. We comment briefly on selfassembled transient networks where G_{eq}(f) must vanish for a finite scissionrecombination frequency f. We argue that G(t)=C(t)_{τ}=C(t)_{γ} should reveal an intermediate plateau set by the shear modulus G_{eq}(f=0) of the quenched network. 
Article: Glass formers display universal nonequilibrium dynamics on the level of singleparticle jumps
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ABSTRACT: Glasses are inherently outofequilibrium systems evolving slowly toward their equilibrium state in a process called physical aging. During aging, dynamic observables depend on the history of the system, hampering comparative studies of dynamics in different glass formers. Here, we demonstrate how glass formers can be directly compared on the level of singleparticle jumps, i.e. the structural relaxation events underlying the αprocess. Describing the dynamics in terms of a continuoustime random walk, an analytic prediction for the jump rate is derived. The result is subsequently compared to moleculardynamics simulations of amorphous silica and a polymer melt as two generic representatives of strong and fragile glass formers, and good agreement is found.  [Show abstract] [Hide abstract]
ABSTRACT: We present moleculardynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T c of modecoupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T c we provide evidence for the spacetime factorization property of the β relaxation and for the timetemperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ T c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late β regime. Within MCT a key quantity, in addition to T c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 0.735 ) typical of simple glassforming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T c (∞) . This increase can be described by T c (∞)  T c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a softspherelike constant coupling parameter Γ c = ρ c T c (1/4), where ρ c is the monomer density at T c. In addition, we also estimate T c from a HansenVerletlike criterion and MCT calculations based on structural input from the simulation. For our polymer model both the HansenVerlet criterion and the MCT calculations suggest T c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.  [Show abstract] [Hide abstract]
ABSTRACT: We discuss systems for which two carefully derived, yet conflicting, theories coexisted. Dense polymers in two dimensions and starshaped polymers in the ?regime are considered. In both cases the two proposed theories are in a sense exact, but turn out to satisfy different crossing rules (for the 2d polymer) or to correspond to different orders of limits. Finally, both theories prove very useful, albeit for different subclasses of physical systems.  [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)].  [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)], 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.  [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.  [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].  [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 excluded volume interactions and sketch the regime where the Gaussian approximation should hold in dense solutions and melts for sufficiently large spacer chains.  [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.  [Show abstract] [Hide abstract]
ABSTRACT: By considering Voronoi tessellations of the configurations of a fluid, we propose two new conserved fields, which provide structural information not fully accounted for by the usual 2point density correlation functions. One of these fields is scalar and associated with the volume of the Voronoi cell, whereas the other one, termed the “geometric polarisation”, is vectorial and related to the local anisotropy of the configurations. We study the static and dynamical properties of these fields in the supercooled regime of a model glassforming liquid. We show that the geometric polarisation is statically correlated to the force field, but contrary to it develops a plateau regime when the temperature is lowered. This different relaxation is related to the cage effect in glassforming liquids, which prevents a complete relaxation of the shape of the cage around particle on intermediate time scales. Graphical abstract  [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.  [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 \(\left. {\mathcal{F}_{Row} } \right_{\lambda = 0} = Kf_0 (x)\) 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 \(\mathcal{F}_{Row}\) also in the NPTensemble where \(\left. {\mathcal{F}_{Row} } \right_{\lambda = 0} = Kf_0 (x)\) with x = P id/K being a scaling variable, P id the ideal pressure and f 0(x) = x(2−x) 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 \(\left. {\mathcal{F}_{Row} } \right_\lambda = K\left[ {\lambda + (1  \lambda )f_0 (x)} \right]\). Graphical abstract  [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.  [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.  [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.
Publication Stats
4k  Citations  
363.36  Total Impact Points  
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Institutions

20082015

University of Strasbourg
 Institut Charles Sadron
Strasburg, Alsace, France


20032011

French National Centre for Scientific Research
Lutetia Parisorum, ÎledeFrance, France


19912007

Johannes GutenbergUniversität Mainz
 Institute of Physics
Mainz, RhinelandPalatinate, Germany


2006

Institut de France
Lutetia Parisorum, ÎledeFrance, France
