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.


Duranty, E. R., Baschnagel, J., & Dadmun, M. (2017). Diffusion of copolymers composed of monomers with drastically different friction factors in copolymer/homopolymer blends. J. Chem. Phys., 146(5), 7 pp.
Abstract: Copolymers are commonly used as interface modifiers that allow for the compatibilization of polymer components in a blend. For copolymers to function as a compatibilizer, they must diffuse through the matrix of the blend to the interface between the two blend components. The diffusivity of a copolymer in a blend matrix therefore becomes important in determining good candidates for use as compatibilizers. In this work, coarsegrained Monte Carlo simulations using the bond fluctuation model modified with an overlap penalty have been developed to study the diffusive behavior of PS/PMMA random copolymers in a PMMA homopolymer blend. The simulations vary the connectivity between different monomers, the thermodynamic interactions between the monomers which manifest within a chain, and between copolymer and homopolymer matrix and define the monomer friction coefficient of each component independently, allowing for the determination of the combined effect of these parameters on copolymer chain diffusion. The results of this work indicate that PSrPMMA copolymer diffusion is not linearly dependent on the copolymer composition on a logarithmic scale, but its diffusion is a balance of the kinetics governed by the dominant motion of the faster styrene monomers and thermodynamics, which are governed by the concentration of styrene monomer within a given monomer's local volume. Published by AIP Publishing.


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.


Ruscher, C., Semenov, A. N., Baschnagel, J., & Farago, J. (2017). Anomalous sound attenuation in Voronoi liquid. J. Chem. Phys., 146(14), 15 pp.
Abstract: The physics of simple fluids in the hydrodynamic limit and notably the connection between the proper microscopic scales and the macroscopic hydrodynamical description are nowadays well understood. In particular, the three peak shape of the dynamical structure factor S(k, omega) is a universal feature, as well as the kdependence of the peak position (proportional to/k) and width proportional to k(2), the latter accounting for the sound attenuation rate. In this paper, we present a theoretical model of monodisperse fluid, whose interactions are defined via the Voronoi tessellations of the configurations [called the Voronoi liquid and first studied in Ruscher et al., Europhys. Lett. 112, 66003 (2015)], which displays at low temperatures a marked violation of the universal features of S(k,omega) with a sound attenuation rate only proportional to k. This anomalous behaviour, which apparently violates the basic symmetries of the liquid state, is traced back to the existence of a time scale which is both short enough for the viscoelastic features of the liquid to impact the relaxational dynamics and however long enough for the momentum diffusion to be substantially slower than the sound propagation on that characteristic time. Published by AIP Publishing.


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


Diddens, D., Lee, N. K., Obukhov, S., Baschnagel, J., & Johner, A. (2016). Disentanglement of Two Single Polymer Chains: Contacts and Knots. ACS Macro Lett., 5(6), 740–744.
Abstract: Understanding the consequences of the non crossing constraint is one of the remaining challenges in the physics of walks and polymers. To address this problem, we performed molecular simulations for the separation of only two initially connected, overlapping polymer chains with interactions tuned such that they are nearly random walks. The separation time for a configuration strongly correlates with the number of monomer contacts between both chains. We obtain a broad distribution of separation times with a slowly decaying tail. Knots only play a role for those configurations that contribute to the tail of the distribution. In contrast, when starting from the same initial configuration but allowing for chain crossings, separation is qualitatively faster and the time distribution narrow. The simulation results are rationalized by analytical theory. A theory of contacts based on polymer fractality and criticality is presented, along with the expected effects of knots.


Wittmer, J. P., Kriuchevskyi, I., Cavallo, A., Xu, H., & Baschnagel, J. (2016). Shearstress fluctuations in selfassembled transient elastic networks. Phys. Rev. E, 93(6), 11 pp.
Abstract: Focusing on shearstress fluctuations, we investigate numerically a simple generic model for selfassembled transient networks formed by repulsive beads reversibly bridged by ideal springs. With Lambda t being the sampling time and t(star)(f) similar to 1/f the Maxwell relaxation time (set by the spring recombination frequency f), the dimensionless parameter Delta x = Delta t/ t(star) (f) is systematically scanned from the liquid limit (Delta x >> 1) to the solid limit (Delta x << 1) where the network topology is quenched and an ensemble average over mindependent configurations is required. Generalizing previous work on permanent networks, it is shown that the shearstress relaxation modulus G(t) may be efficiently determined for all Delta x using the simpleaverage expression G(t) = mu(A) – h(t) with mu(A) = G(0) characterizing the canonicalaffine shear transformation of the system at t = 0 and h(t) the (rescaled) meansquare displacement of the instantaneous shear stress as a function of time t. This relation is compared to the standard expression G(t) = (c) over tilde (t) using the (rescaled) shearstress autocorrelation function (c) over tilde (t). Lower bounds for the m configurations required by both relations are given.


Wittmer, J. P., Xu, H., & Baschnagel, J. (2016). Simple average expression for shearstress relaxation modulus. Phys. Rev. E, 93(1), 5 pp.
Abstract: Focusing on isotropic elastic networks we propose a 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. 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 (tau) over cap (t) as a function of time t. We discuss sampling time and ensemble effects and emphasize possible pitfalls of alternative expressions using the shearstress autocorrelation function. We argue finally that our key relation may be readily adapted for more general linear response functions.


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


Ruscher, C., Baschnagel, J., & Farago, J. (2015). The Voronoi liquid. Epl, 112(6).
Abstract: We introduce a new theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and manybody. The resulting system is studied both theoretically and numerically. We show that the fluid, though sharing the global features of other models of fluids with soft interactions, has several unusual characteristics, which are investigated and discussed. Copyright (C) EPLA, 2015


Wittmer, J. P., Kriuchevskyi, I., Baschnagel, J., & Xu, H. (2015). Shearstrain and shearstress fluctuations in generalized Gaussian ensemble simulations of isotropic elastic networks. European Physical Journal B, 88(9).
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. characterizing the generalized Gaussian ensemble. It allows to tune the strain fluctuations mu(gamma gamma) beta V


Wittmer, J. P., Xu, H., & Baschnagel, J. (2015). Shearstress relaxation and ensemble transformation of shearstress autocorrelation functions. Physical Review E, 91(2).
Abstract: We revisit the relation between the shearstress relaxation modulus G(t), computed at finite shear strain 0


Wittmer, J. P., Xu, H., Benzerara, O., & Baschnagel, J. (2015). Fluctuationdissipation relation between shear stress relaxation modulus and shear stress autocorrelation function revisited. Molecular Physics, 113(1718), 2881–2893.
Abstract: The shear stress relaxation modulus G(t) may be determined from the shear stress (tau) over cap (t) after switching on a tiny step strain gamma or by inverse Fourier transformation of the storage modulus G'(omega) or the loss modulus G ''(omega) obtained in a standard oscillatory shear experiment at angular frequency.. It is widely assumed that G(t) is equivalent in general to the equilibrium stress autocorrelation function C(t) = beta V


2014 
Farago, J., Semenov, A., Frey, S., & Baschnagel, J. (2014). New conserved structural fields for supercooled liquids. European Physical Journal E, 37(6).
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.


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

