2017 
Dolgushev, M., Hauber, A. L., Pelagejcev, P., & Wittmer, J. P. (2017). Marginally compact fractal trees with semiflexibility. Phys. Rev. E, 96(1), 15 pp.
Abstract: We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bondbond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the tree' behavior and to consider larger structures. Due to the local stiffness, the selfcontact density gets drastically reduced.


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.


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


Li, D., Xu, H., & Wittmer, J. P. (2016). Glass transition of twodimensional 8020 KobAndersen model at constant pressure. J. PhysicsCondensed Matter, 28(4), 045101.
Abstract: We reconsider numerically the twodimensional version of the KobAndersen model (KA2d) with a fraction of 80% of large spheres. A constant moderate pressure is imposed while the temperature T is systematically quenched from the liquid limit through the glass transition at Tg approximate to 0.3 down to very low temperatures. Monodisperse LennardJones (mdLJ) bead systems, forming a crystal phase at low temperatures, are used to highlight several features of the KA2d model. As can be seen, e.g. from the elastic shear modulus G(T), determined using the stressfluctuation formalism, our KA2d model is a good glassformer. A continuous cuspsingularity, G(T) proportional to (1 – T/Tg)(alpha) with alpha approximate to 0.6, is observed in qualitative agreement with other recent numerical and theoretical work, however in striking conflict with the additive jump discontinuity predicted by modecoupling theory.
Keywords: computersimulation,dynamics,elastic moduli,elasticconstants,glass transition,order,simulation,solids,stress fluctuations


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 
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 
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


Polinska, P., Gillig, C., Wittmer, J. P., & Baschnagel, J. (2014). Hyperbranched polymer stars with Gaussian chain statistics revisited. European Physical Journal E, 37(2).
Abstract: Conformational properties of regular dendrimers and more general hyperbranched polymer stars with Gaussian statistics for the spacer chains between branching points are revisited numerically. We investigate the scaling for asymptotically long chains especially for fractal dimensions d(f) = 3 (marginally compact) and d(f) = 2.5 (diffusion limited aggregation). Powerlaw stars obtained by imposing the number of additional arms per generation are compared to truly selfsimilar stars. We discuss effects of weak excludedvolume interactions and sketch the regime where the Gaussian approximation should hold in dense solutions and melts for sufficiently large spacer chains.


2013 
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


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).


Wittmer, J. P., Xu, H., Polinska, P., Gillig, C., Helfferich, J., Weysser, F., et al. (2013). Compressibility and pressure correlations in isotropic solids and fluids. European Physical Journal E, 36(11), 1–17.
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, lambda = 0 or volume (NVTensemble, lambda = 1 and for more general values of the dimensionless parameter lambda characterizing the constantvolume constraint. The stress fluctuation representation 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 also in the NPTensemble where with x = P (id)/K being a scaling variable, P (id) the ideal pressure and f (0)(x) = x(2x) a universal function. By gradually increasing lambda by means of an external spring potential, the crossover between both classical ensemble limits is monitored. This demonstrates, e.g., the lever rule FRow vertical bar(lambda) – K[lambda + (1 – lambda)f(0)(x)].


Wittmer, J. P., Xu, H., Polinska, P., Weysser, F., & Baschnagel, J. (2013). Communication: Pressure fluctuations in isotropic solids and fluids. Journal of Chemical Physics, 138(19).
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 vertical bar P = Pid(2 – Pid/K) with Pid being the ideal pressure contribution. (C) 2013 AIP Publishing LLC.


Wittmer, J. P., Xu, H., Polinska, P., Weysser, F., & Baschnagel, J. (2013). Shear modulus of simulated glassforming model systems: Effects of boundary condition, temperature, and sampling time. Journal of Chemical Physics, 138(12).
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 gamma or the conjugated (mean) shear stress tau 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 mu(F)(T) which at constant tau decay monotonously with T following the affine shear elasticity mu(A)(T), i.e., a simple twopoint correlation function. At variance, nonmonotonous behavior with a maximum at the glass transition temperature Tg is demonstrated for mu(F)(T) at constant gamma. The increase of G below Tg is reasonably fitted for both models by a continuous cusp singularity, G(T) proportional to (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. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790137]


2012 
Farago, J., Semenov, A. N., Meyer, H., Wittmer, J. P., Johner, A., & Baschnagel, J. (2012). Modecoupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations. Physical Review E, 85(5), 051806.
Abstract: We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a densitybased modecoupling theory (dMCT) using the MoriZwanzig approach and projecting the fluctuating force onto pairdensity fluctuation modes. The effect of dynamical density fluctuations on the centerofmass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c. m. velocity autocorrelation function (c. m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t(1) and the Rouse relaxation time t(N). We obtain an analytical expression for the c. m. VAF in terms of molecular parameters. In particular, the c. m. VAF scales as N(1)t(5/4) (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted t(5/4) dependence of the c. m. VAF is supported by data of nonmomentumconserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper].

