Shear stress relaxation and ensemble transformation of shear stress autocorrelation functions revisited

We revisit the relation between the shear stress relaxation modulus $G(t)$, computed at finite shear strain $0 < \gamma \ll 1$, and the shear stress autocorrelation functions $C(t)|_{\gamma}$ and $C(t)|_{\tau}$ computed, respectively, at imposed strain $\gamma$ and mean stress $\tau$. Focusing on permanent isotropic spring networks it is shown theoretically and computationally that in general $G(t) = C(t)|_{\tau} = C(t)|_{\gamma} + G_{eq}$ for $t > 0$ with $G_{eq}$ being the static equilibrium shear modulus. $G(t)$ and $C(t)|_{\gamma}$ thus must become different for solids and it is impossible to obtain $G_{eq}$ alone from $C(t)|_{\gamma}$ 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 $G(t) = C(t)|_{\tau} = C(t)|_{\gamma}$ should reveal an intermediate plateau set by the shear modulus $G_{eq}(f=0)$ of the quenched network.Comment: 8 pages, 4 figure

Molecular-Dynamics Simulation of a Glassy Polymer Melt: Incoherent Scattering Function

We present simulation results for a model polymer melt, consisting of short, nonentangled chains, in the supercooled state. The analysis focuses on the monomer dynamics, which is monitored by the incoherent intermediate scattering function. The scattering function is recorded over six decades in time and for many different wave-vectors. The lowest temperatures studied are slightly above the critical temperature of mode-coupling theory (MCT), which was determined from a quantitative analysis of the beta- and alpha-relaxations. We find evidence for the space-time factorization theorem in the beta-relaxation regime, and for the time-temperature superposition principle in the alpha-regime, if the temperature is not too close to the critical temperature. The wave-vector dependence of the nonergodicity parameter, of the critical amplitude, and the alpha-relaxation time are in qualitative agreement with calculations for hard spheres. For wave-vectors larger than the maximum of the structure factor the alpha-relaxation time already agrees fairly well with the asymptotic MCT-prediction. The behavior of the relaxation time at small wave-vectors can be rationalized by the validity of the Gaussian approximation and the value of the Kohlrausch stretching exponent.Comment: 23 pages of REVTeX, 13 PostScript figures, submitted to Phys. Rev.

Monte Carlo Simulation of Long Chain Polymer Melts: Crossover from Rouse to Reptation Dynamics

We present data of Monte Carlo simulations for monodisperse linear polymer chains in dense melts with degrees of polymerization between N=16 and N=512. The aim of this study is to investigate the crossover from Rouse-like dynamics for short chains to reptation-like dynamics for long chains. To address this problem we calculate a variety of different quantities: standard mean-square displacements of inner monomers and of the chain's center of mass, the recently proposed cubic invariant, persistence of bond-vector orientation with time, and the auto-correlation functions of the bond vector, the end-to-end vector and the Rouse modes. This analysis reveals that the crossover from non- to entangled dynamics is very protracted. Only the largest chain length N=512, which is about 13 times larger than the entanglement length, shows evidence for reptation.Comment: 38 pages of REVTeX, 14 PostScript figure