2018 
Kriuchevskyi, I., Wittmer, J. P., Meyer, H., Benzerara, O., & Baschnagel, J. (2018). Shearstress fluctuations and relaxation in polymer glasses. Physical Review E, 97(1).
Abstract: We investigate by means of molecular dynamics simulation a coarsegrained polymer glass model focusing on (quasistatic and dynamical) shearstress fluctuations as a function of temperature T and sampling time Delta t. The linear response is characterized using (ensembleaveraged) expectation values of the contributions (time averaged for each shear plane) to the stressfluctuation relation mu(sf) for the shear modulus and the shearstress relaxation modulus G(t). Using 100 independent configurations, we pay attention to the respective standard deviations. While the ensembleaveraged modulus mu(sf) (T) decreases continuously with increasing T for all Delta t sampled, its standard deviation delta mu(sf) (T) is nonmonotonic with a striking peak at the glass transition. The question of whether the shear modulus is continuous or has a jump singularity at the glass transition is thus ill posed. Confirming the effective timetranslational invariance of our systems, the Delta t dependence of mu(sf) and related quantities can be understood using a weighted integral over G(t).


2017 
Dolgushev, M., Wittmer, J. P., Johner, A., Benzerara, O., Meyer, H., & Baschnagel, J. (2017). Marginally compact hyperbranched polymer trees. Soft Matter, 13(13), 2499–2512.
Abstract: Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution rho(pair)(r) or the shearstress relaxation modulus G(t), are investigated theoretically and by means of computer simulations. We emphasize that albeit the selfcontact density rho(c) = rho(pair)(r approximate to 0) similar to log(N/S)/root S diverges logarithmically with the total mass N, this effect becomes rapidly irrelevant with increasing spacer length S. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time tau p of mode p must scale as tau(p) similar to (N/p)(5/3) rather than the usual square power law for linear chains.


Kriuchevskyi, I., Wittmer, J. P., Benzerara, O., Meyer, H., & Baschnagel, J. (2017). Numerical determination of shear stress relaxation modulus of polymer glasses. Eur. Phys. J. E, 40(4), 6 pp.
Abstract: Focusing on simulated polymer glasses well below the glass transition, we confirm the validity and the efficiency of the recently proposed simpleaverage expression G(t) = mu(A)h(t) for the computational determination of the shear stress relaxation modulus G(t). Here, mu(A) = G(0) characterizes the affine shear transformation of the system at t = 0 and h(t) the meansquare displacement of the instantaneous shear stress as a function of time t. This relation is seen to be particulary useful for systems with quenched or sluggish transient shear stresses which necessarily arise below the glass transition. The commonly accepted relation G(t) = c(t) using the shear stress autocorrelation function c(t) becomes incorrect in this limit.


Kriuchevskyi, I., Wittmer, J. P., Meyer, H., & Baschnagel, J. (2017). Shear Modulus and ShearStress Fluctuations in Polymer Glasses. Physical Review Letters, 119(14).
Abstract: Using molecular dynamics simulation of a standard coarsegrained polymer glass model, we investigate by means of the stressfluctuation formalism the shear modulus mu as a function of temperature T and sampling time Delta t. While the ensembleaveraged modulus mu(T) is found to decrease continuously for all Delta t sampled, its standard deviation delta mu(T) is nonmonotonic, with a striking peak at the glass transition. Confirming the effective timetranslational invariance of our systems, mu(Delta t) can be understood using a weighted integral over the shearstress relaxation modulus G(t). While the crossover of mu(T) gets sharper with an increasing Delta t, the peak of delta mu(T) becomes more singular. It is thus elusive to predict the modulus of a single configuration at the glass transition.


Lee, N. K., Diddens, D., Meyer, H., & Johner, A. (2017). Local Chain Segregation and Entanglements in a Confined Polymer Melt. Phys. Rev. Lett., 118(6), 5 pp.
Abstract: The reptation mechanism, introduced by de Gennes and Edwards, where a polymer diffuses along a fluffy tube, defined by the constraints imposed by its surroundings, convincingly describes the relaxation of long polymers in concentrated solutions and melts. We propose that the scale for the tube diameter is set by local chain segregation, which we study analytically. We show that the concept of local segregation is especially operational for confined geometries, where segregation extends overmesoscopic domains, drastically reducing binary contacts, and provide an estimate of the entanglement length. Our predictions are quantitatively supported by extensive molecular dynamics simulations on systems consisting of long, entangled chains.


Tanis, I., Meyer, H., Salez, T., Raphael, E., Maggs, A. C., & Baschnagel, J. (2017). Molecular dynamics simulation of the capillary leveling of viscoelastic polymer films. J. Chem. Phys., 146(20), 8 pp.
Abstract: Surface tensiondriven flow techniques have recently emerged as an efficient means of shedding light into the rheology of thin polymer films. Motivated by experimental and theoretical approaches in films bearing a varying surface topography, we present results on the capillary relaxation of a square pattern at the free surface of a viscoelastic polymer film, using molecular dynamics simulations of a coarsegrained polymer model. Height profiles are monitored as a function of time after heating the system above its glasstransition temperature and their time dependence is fitted to the theory of capillary leveling. Results show that the viscosity is not constant, but time dependent. In addition to providing a complementary insight about the local inner mechanisms, our simulations of the capillaryleveling process therefore probe the viscoelasticity of the polymer and not only its viscosity, in contrast to most experimental approaches. Published by AIP Publishing.


2016 
Baschnagel, J., Meyer, H., Wittmer, J., Kulic, I., Mohrbach, H., Ziebert, F., et al. (2016). Semiflexible Chains at Surfaces: WormLike Chains and beyond. Polymers, 8(8), 35 pp.
Abstract: We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict twodimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the wellknown wormlikechain (WLC) model. There is mounting evidence that biofilaments (except stable dDNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.
Keywords: semiflexible polymers; polymers at interfaces; biopolymers


2015 
Frey, S., Weysser, F., Meyer, H., Farago, J., Fuchs, M., & Baschnagel, J. (2015). Simulated glassforming polymer melts: dynamic scattering functions, chain length effects, and modecoupling theory analysis. The European physical journal. E, Soft matter, 38(2), 97.
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 beta relaxation and for the timetemperature superposition principle (TTSP) of the alpha 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 beta regime. Within MCT a key quantity, in addition to T c, is the exponent parameter lambda. For the fully flexible polymer models studied we find that lambda is independent of N and has a value (lambda = 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 rho, if we assume that the MCT glass transition is ruled by a softspherelike constant coupling parameter Gamma c = rho c T c (1/4), where rho 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.


Helfferich, J., VollmayrLee, K., Ziebert, F., Meyer, H., & Baschnagel, J. (2015). Glass formers display universal nonequilibrium dynamics on the level of singleparticle jumps. Epl, 109(3).
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 aprocess. 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. Copyright (C) EPLA, 2015


2014 
Helfferich, J., Ziebert, F., Frey, S., Meyer, H., Farago, J., Blumen, A., et al. (2014). Continuoustime randomwalk approach to supercooled liquids. I. Different definitions of particle jumps and their consequences. Physical Review E, 89(4).
Abstract: Singleparticle trajectories in supercooled liquids display long periods of localization interrupted by “fast moves.” This observation suggests a modeling by a continuoustime randomwalk (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 a process and (Johari) beta 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.


Helfferich, J., Ziebert, F., Frey, S., Meyer, H., Farago, J., Blumen, A., et al. (2014). Continuoustime randomwalk approach to supercooled liquids. II. Meansquare displacements in polymer melts. Physical Review E, 89(4).
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 a 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 a regime where they systematically underestimate the MSD from the MD.


Johner, A., Thalmann, F., Baschnagel, J., Meyer, H., Obukhov, S., & Wittmer, J. P. (2014). Twodimensional polymeric liquids and polymer stars: learning from conflicting theories. Journal of Statistical MechanicsTheory and Experiment, 2014.
Abstract: We discuss systems for which two carefully derived, yet conflicting, theories coexisted. Dense polymers in two dimensions and starshaped polymers in the thetaregime 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.


Obukhov, S., Johner, A., Baschnagel, J., Meyer, H., & Wittmer, J. P. (2014). Melt of polymer rings: The decorated loop model. Epl, 105(4).
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 similar to N2/3, assembled in random trees. Individual rings in the melt are predicted to be marginally compact with a mean square radius of gyration Rg(2) similar to N2/3 (1const center dot N1/3). 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 similar to 10(34). The estimated crossover functions allow for a satisfactory fit of simulation data. Copyright (C) EPLA, 2014


2013 
Morhenn, H., Busch, S., Meyer, H., Richter, D., Petry, W., & Unruh, T. (2013). Collective Intermolecular Motions Dominate the Picosecond Dynamics of Short Polymer Chains. Physical Review Letters, 111(17).
Abstract: Neutron scattering and extensive molecular dynamics simulations of an all atom C100H202 system were performed to address the shorttime dynamics leading to centerofmass selfdiffusion. The simulated dynamics are in excellent agreement with resolution resolved timeofflight quasielastic neutron scattering. The anomalous subdiffusive centerofmass motion could be modeled by explicitly accounting for viscoelastic hydrodynamic interactions. A modelfree analysis of the local reorientations of the molecular backbone revealed three relaxation processes: While two relaxations characterize local bond rotation and global molecular reorientation, the third component on intermediate times could be attributed to transient flowlike motions of atoms on different molecules. The existence of these collective motions, which are clearly visualized in this Letter, strongly contribute to the chain relaxations in molecular liquids.


Mortazavi, B., Benzerara, O., Meyer, H., Bardon, J., & Ahzi, S. (2013). Combined molecular dynamicsfinite element multiscale modeling of thermal conduction in graphene epoxy nanocomposites. Carbon, 60, 356–365.
Abstract: We developed a multiscale scheme using molecular dynamics (MD) and finite element (FE) methods for evaluating the effective thermal conductivity of graphene epoxy nanocomposites. The proposed hierarchical multiscale approach includes three different scales. First, we used MD simulations for the investigation of thermal conduction in graphene epoxy assembly at atomic scale. Our results suggest that thermal conductivity of single layer graphene decline by around 30% in epoxy matrix for two different hardener chemicals. Using MD, we also calculated thermal boundary conductance (TBC) between crosslinked epoxy and graphene sheet. In the next step, using the results obtained by the MD method, we developed FE based representative volume elements (RVE) of the nanocomposite in order to evaluate the thermal conductivity at the microscale. Finally,,nanocomposite effective thermal conductivity was obtained using FE homogenization of an ensemble of microscale RVEs. The validity of the proposed approach was confirmed by comparing predicted results with experimental results in the literature. (C) 2013 Elsevier Ltd. All rights reserved.


Schulmann, N., Meyer, H., Kreer, T., Cavallo, A., Johner, A., Baschnagel, J., et al. (2013). Strictly TwoDimensional SelfAvoiding Walks: Density Crossover Scaling. Polymer Science Series C, 55(1), 181–211.
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 theta(2) set by the intrachain subchain size distribution. With R – Nnu being the size of chains of length N and rho 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 e(int) similar to n(int) similar to 1/Nnu theta 2 with nu = 3/4 and theta(2) = 19/12 for dilute solutions and nu = 1/d and theta(2) = 3/4 for N >> g(rho) approximate to 1/rho(2). Irrespective of rho, long chains thus become compact packings of blobs of contour length L similar to Nn(int) similar to Rdp with d(p) = d – theta(2) = 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 approximate to 1/(qR)(theta 2) in the intermediate regime of the wavevector. 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.


Schulmann, N., Meyer, H., Kreer, T., Cavallo, A., Johner, A., Baschnagel, J., et al. (2013). Strictly TwoDimensional SelfAvoiding Walks: Density Crossover Scaling. Polymer Science Series A, 55(7), 990.
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 coarsegrained beadspring model. We focus on properties related to the contact exponent


Semenov, A. N., & Meyer, H. (2013). Anomalous diffusion in polymer monolayers. Soft Matter, 9(16), 4249–4272.
Abstract: The tagged chain dynamics in strictly twodimensional (2D) polymer melts (where the chains are collapsed to dense spots) is considered both theoretically and by computer simulations. It is shown that the chain relaxation time in such systems scales as t(m) proportional to Nalpha with alpha approximate to 1.73 (N is the number of monomer units per chain). An extended transient regime of anomalous subdiffusion is identified at t less than or similar to t(m) where the chain centreofmass (CM) velocity autocorrelation function (VAF) scales as C(t) proportional to N(0)t(1.42). This anomalous dynamics is accounted for by the effect of the viscoelastic hydrodynamic interactions (VHI). The developed quantitative theory of the VHIcontrolled chain dynamics is in good agreement, with no parameter adjustment, with the extensive simulation data. The dynamics of polymer monolayers with frictional contact to the supporting surface is considered as well. It is shown that an external (Langevin) friction gamma leads to the asymptotic regime C(t) f proportional to (N gamma)(1.37)t(0.84) that crosses over to N(0)t(1.42) at longer t. We also present a detailed analysis of other important factors controlling the 2D chain diffusion: finite boxsize, inertial and finite compressibility effects.


Solar, M., Meyer, H., & Gauthier, C. (2013). Analysis of local properties during a scratch test on a polymeric surface using molecular dynamics simulations. European Physical Journal E, 36(3).
Abstract: This work demonstrates a possible route to connect a particle (chain) based understanding with continuum mechanical questions about contact mechanics. The bond orientation, chain conformation and stress field of a polymer film were analyzed during scratch tests (tangential contact) using a molecular dynamics (MD) simulation approach. Scratch tests with a conical tip at constant scratching velocity were simulated on linear amorphous polymer surfaces at various temperatures and roughnesses of the tip and for various interactions between the tip and the particles of the polymer chains. The second Legendre polynomial (computed for small domains around the tip) gave the bond orientation inside the polymer film during sliding of the tip. The gyration tensor (layerresolved in the direction of the polymer film thickness) provided information about the conformation of the polymer chains. These results allowed us to argue in favor of Briscoe's hypothesis (thin film sheared vs. “bulk” compressive behavior) concerning the friction properties of the polymer surfaces. Finally, the first stress measurements of the virial stress tensor (in subboxes placed in the MD cell) revealed a complex combination between compressive hydrostatic pressure and shear stress, which may be interpreted as a complex sheared domain at the interface.


Wittmer, J. P., Meyer, H., Johner, A., Obukhov, S., & Baschnagel, J. (2013). Comment on “Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics” J. Chem. Phys. 134, 204904 (2011). Journal of Chemical Physics, 139(21).

