J. P. Wittmer

Simulated glass-forming polymer melts: glass transition temperature and elastic constants of the glassy state.

By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature Tg and for the elastic properties of the glassy state are presented. We find that Tg increases with chain length N and is for all N larger for the semiflexible model. The N dependence of Tg is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below Tg via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching Tg from below, the shear modulus μ displays a much stronger decrease near Tg. From the present simulation data it is not possible to decide whether μ takes a finite value at Tg, as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.

Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length ξ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances r≫ξ. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.

Scale-free center-of-mass displacement correlations in polymer melts without topological constraints and momentum conservation: A bond-fluctuation model study

By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints, we examine the center-of-mass (COM) dynamics of polymer melts in d = 3 dimensions. Our analysis focuses on the COM displacement correlation function C(N)(t)≈∂(t) (2)h(N)(t)/2, measuring the curvature of the COM mean-square displacement h(N)(t). We demonstrate that C(N)(t) ≈ -(R(N)∕T(N))(2)(ρ∗/ρ)u2009f(x = t/T(N)) with N being the chain length (16 ≤ N ≤ 8192), R(N) ∼ N(1/2) is the typical chain size, T(N) ∼ N(2) is the longest chain relaxation time, ρ is the monomer density, ρ(*)≈N/R(N) (d) is the self-density, and f(x) is a universal function decaying asymptotically as f(x) ∼ x(-ω) with ω = (d + 2) × α, where α = 1/4 for x ≪ 1 and α = 1/2 for x ≫ 1. We argue that the algebraic decay NC(N)(t) ∼ -t(-5/4) for t ≪ T(N) results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.

Shear-stress relaxation and ensemble transformation of shear-stress autocorrelation functions.

We revisit the relation between the shear-stress relaxation modulus G(t), computed at finite shear strain 0<γ≪1, and the shear-stress 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 self-assembled transient networks where G(eq)(f) must vanish for a finite scission-recombination 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.

Compressibility and pressure correlations in isotropic solids and fluids

Presenting simple coarse-grained 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 (NPT-ensemble, λ = 0 or volume (NVT-ensemble, λ = 1 and for more general values of the dimensionless parameter λ characterizing the constant-volume constraint. The stress fluctuation representation

Strictly two-dimensional self-avoiding walks: Density crossover scaling

left. {mathcal{F}_{Row} } right|_{lambda = 0} = Kf_0 (x)

Fluctuation-dissipation relation between shear stress relaxation modulus and shear stress autocorrelation function revisited

of the compression modulus K in the NVT-ensemble is derived directly (without a microscopic displacement field) using the well-known thermodynamic transformation rules between conjugated ensembles. The transform is made manifest by computing the Rowlinson functional