2019 
Diddens, D., Baschnagel, J., & Johner, A. (2019). Microscopic Structure of Compacted Polyelectrolyte Complexes: Insights from Molecular Dynamics Simulations. Acs Macro Letters, 8(2), 123–127.
Abstract: We utilize atomistic molecular dynamics (MD) simulations to study local structural changes inside a polyelectrolyte complex consisting of poly(styrenesulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA) upon densification, in analogy to ultracentrifugation in experiments. In particular, we focus on the water content and on the reinforcement of the PSSPDADMA network for various external accelerations. We demonstrate that apart from the formation of mesoscopic pores observed experimentally also the microscopic structure and the local relaxation processes likely affect the unique rheological properties of compacted polyelectrolyte complexes, as densification increases both the number of PSSPDADMA coordinations and the intermixing of PSS and PDADMA. These processes slow down local rearrangements, thus further stabilizing the compacted state. We find that the concept of binary PSSPDADMA salt bondsrelevant for theoretical modelsis not strictly valid in the dense limit.


Klochko, L., Baschnagel, J., Wittmer, J. P., & Semenov, A. N. (2019). Relaxation dynamics in supercooled oligomer liquids: From shearstress fluctuations to shear modulus and structural correlations. Journal Of Chemical Physics, 151(5).
Abstract: Static and dynamical properties of a model glassforming oligomer liquid are analyzed using molecular dynamics simulations. The temperature and system size effects are assessed for the affine shear modulus mu(A), the quasistatic shear modulus mu(sf) (obtained using the stressfluctuation relation), and the shear relaxation modulus G(t). It is found that while both mu(A) and mu(sf) are nearly independent of the system size, their variances show significant system size dependence, in particular, below the glass transition temperature Tg. It is also shown that the standard deviation of the shear modulus, delta mu(sf)(T), exhibits a pronounced peak at T approximate to Tg whose position is nearly independent of the system volume V. Moreover, the whole function delta mu(sf)(T) is nearly the same for different system sizes above the glass transition. We propose a theory which quantitatively predicts delta mu(sf)(T) at T greater than or similar to Tg and explains both its independence of V and its peak near Tg. It is also established that below Tg the variance of the affine modulus follows the standard power law, delta mu A2 proportional to 1/V, while delta mu(sf) shows anomalously a slow decrease with V as >delta mu sf2 proportional to 1/V alpha with alpha < 1. On this basis, it is argued that the studied glassforming systems must show longrange structural correlations in the amorphous state.


2018 
George, G., Kriuchevskyi, I., Meyer, H., Baschnagel, J., & Wittmer, J. P. (2018). Shearstress relaxation in freestanding polymer films. Physical Review E, 98(6).
Abstract: Using molecular dynamics simulation of a polymer glass model we investigate freestanding polymer films focusing on the inplane shear modulus mu, defined by means of the stressfluctuation formula, as a function of temperature T, film thickness H (tuned by means of the lateral box size L), and sampling time Delta t. Various observables are seen to vary linearly with 1/H, demonstrating thus the (to leading order) linear superposition of bulk and surface properties. Confirming the timetranslational invariance of our systems, mu(Delta t) is shown to be numerically equivalent to a second integral over the shearstress relaxation modulus G(t). It is thus a natural smoothing function statistically better behaved as G(t). As shown from the standard deviations delta mu. and delta G, this is especially important for large times and for temperatures around the glass transition. mu and G are found to decrease continuously with T and a jumpsingularity is not observed. Using the EinsteinHelfand relation for mu(Delta t) and the successful timetemperature superposition scaling of mu(Delta t) and G(t), the shear viscosity eta(T) can be estimated for a broad range of temperatures.


Helfferich, J., Brisch, J., Meyer, H., Benzerara, O., Ziebert, F., Farago, J., et al. (2018). Continuoustime randomwalk approach to supercooled liquids: Selfpart of the van Hove function and related quantities. European Physical Journal E, 41(6).
Abstract: From equilibrium molecular dynamics (MD) simulations of a beadspring model for shortchain glassforming polymer melts we calculate several quantities characterizing the singlemonomer dynamics near the (extrapolated) critical temperature Tc of modecoupling theory: the meansquare displacement g(0)(t), the nonGaussian parameter alpha(2)(t) and the selfpart of the van Hove function G(s)(r, t) which measures the distribution of monomer displacements r in time t. We also determine these quantities from a continuoustime random walk (CTRW) approach. The CTRW is defined in terms of various probability distributions which we know from previous analysis. Utilizing these distributions the CTRW can be solved numerically and compared to the MD data with no adjustable parameter. The MD results reveal the heterogeneous and nonGaussian singleparticle dynamics of the supercooled melt near Tc. In the time window of the early a relaxation alpha(2)(t) is large and G(s)(r, t) is broad, reflecting the coexistence of monomer displacements that are much smaller (âslow particlesâ) and much larger (âfast particlesâ) than the average at time t, i.e. than r = g(0)(t)(1/2). For large r the tail of G(s)(r, t) is compatible with an exponential decay, as found for many glassy systems. The CTRW can reproduce the spatiotemporal dependence of G(s)(r, t) at a qualitative to semiquantitative level. However, it is not quantitatively accurate in the studied temperature regime, although the agreement with the MD data improves upon cooling. In the early a regime we also analyze the MD results for G(s)(r, t) via the spacetime factorization theorem predicted by ideal modecoupling theory. While we find the factorization to be well satisfied for small r, both above and below Tc, deviations occur for larger r comprising the tail of G(s)(r, t). The CTRW analysis suggests that singleparticle âhopsâ are a contributing factor for these deviations.


Klochko, L., Baschnagel, J., Wittmer, J. P., & Semenov, A. N. (2018). Longrange stress correlations in viscoelastic and glassforming fluids. Soft Matter, 14(33), 6835–6848.
Abstract: A simple and rigorous approach to obtain stress correlations in viscoelastic liquids (including supercooled liquid and equilibrium amorphous systems) is proposed. The longrange dynamical correlations of local shear stress are calculated and analyzed in 2dimensional space. It is established how the longrange character of the stress correlations gradually emerges as the relevant dynamical correlation length ? grows in time. The correlation range ? is defined by momentum propagation due to acoustic waves and vorticity diffusion which are the basic mechanisms for transmission of shear stress perturbations. We obtain the general expression defining the time and distancedependent stress correlation tensor in terms of material functions (generalized relaxation moduli). The effect of liquid compressibility is quantitatively analyzed; it is shown to be important at large distances and/or short times. The revealed longrange stress correlation effect is shown to be dynamical in nature and unconnected with static structural correlations in liquids (correlation length (s)). Our approach is based on the assumption that (s) is small enough as reflected in weak wavenumber dependencies of the generalized relaxation moduli. We provide a simple physical picture connecting the elucidated longrange fluctuation effect with anisotropic correlations of the (transient) inherent stress field, and discuss its implications.


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).


Ruscher, C., Baschnagel, J., & Farago, J. (2018). Voronoi glassforming liquids: A structural study. Physical Review E, 97(3).
Abstract: We introduce a 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.


2017 
Chapuis, P., Montgomery, P. C., Anstotz, F., LeongHoi, A., Gauthier, C., Baschnagel, J., et al. (2017). A novel interferometric method for the study of the viscoelastic properties of ultrathin polymer films determined from nanobubble inflation. Review Of Scientific Instruments, 88(9).
Abstract: Glass formation and glassy behavior remain as the important areas of investigation in soft matter physics with many aspects which are still not completely understood, especially at the nanometer sizescale. In the present work, we show an extension of the ânanobubble inflationâ method developed by OâConnell and McKenna [Rev. Sci. Instrum. 78, 013901 (2007)] which uses an interferometric method to measure the topography of a large array of 5 mu m sized nanometer thick films subjected to constant inflation pressures during which the bubbles grow or creep with time. The interferometric method offers the possibility of making measurements on multiple bubbles at once as well as having the advantage over the AFM methods of OâConnell and McKenna of being a true noncontact method. Here we demonstrate the method using ultrathin films of both poly(vinyl acetate) (PVAc) and polystyrene (PS) and discuss the capabilities of the method relative to the AFM method, its advantages and disadvantages. Furthermore we show that the results from experiments on PVAc are consistent with the prior work on PVAc, while high stress results with PS show signs of a new nonlinear response regime that may be related to the plasticity of the ultrathin film. Published by AIP Publishing.


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. Journal Of Chemical Physics, 146(5).
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 monomerâs 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. European Physical Journal E, 40(4).
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.


Ruscher, C., Semenov, A. N., Baschnagel, J., & Farago, J. (2017). Anomalous sound attenuation in Voronoi liquid. Journal Of Chemical Physics, 146(14).
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. Journal Of Chemical Physics, 146(20).
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 
Diddens, D., Lee, N.  K., Obukhov, S., Baschnagel, J., & Johner, A. (2016). Disentanglement of Two Single Polymer Chains: Contacts and Knots. Acs Macro Letters, 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. Physical Review E, 93(6).
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. Physical Review E, 93(1).
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. European Physical Journal E, 38(2).
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 Tc of modecoupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > Tc we provide evidence for the spacetime factorization property of the beta relaxation and for the timetemperature superposition principle (TTSP) of the a relaxation, and we also discuss deviations from these predictions for T approximate to Tc. 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 Tc, is the exponent parameter lambda. For the fully flexible polymer models studied we find that. 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 Tc(infinity). This increase can be described by Tc(infinity) – Tc(N) similar to 1/N and may be interpreted in terms of the N dependence of the monomer density., if we assume that the MCT glass transition is ruled by a softspherelike constant coupling parameter Gamma(c) = rho Tc(c)1/4, where rho(c) is the monomer density at Tc. In addition, we also estimate Tc from a HansenVerlet like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the HansenVerlet criterion and the MCT calculations suggest Tc 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

