Shear-stress fluctuations and relaxation in polymer glasses

Abstract

We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasistatic and dynamical) shear-stress fluctuations as a function of temperature T and sampling time Δt. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time averaged for each shear plane) to the stress-fluctuation relation μ_{sf} for the shear modulus and the shear-stress relaxation modulus G(t). Using 100 independent configurations, we pay attention to the respective standard deviations. While the ensemble-averaged modulus μ_{sf}(T) decreases continuously with increasing T for all Δt sampled, its standard deviation δμ_{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 time-translational invariance of our systems, the Δt dependence of μ_{sf} and related quantities can be understood using a weighted integral over G(t).

Shear-stress relaxation in free-standing polymer films

“…5. As stressed elsewhere [14], µ A = µ 0 for an equilibrium liquid since both µ = (µ A − µ 0 ) + µ 1 and µ 1 must vanish. Frozen-in out-of-equilibrium stresses are observed upon cooling below T g as made manifest by the dramatic increase of the dimensionless ratio µ 0 /µ A − 1.…”

“…(2) holds for films. Using the Einstein-Helfand relation [14,23] Sec. III D the shear viscosity η for our highest temperatures.…”

“…As in our earlier work [6,13,14] our results are obtained by means of MD simulation of a coarse-grained bead-spring model of Kremer-Grest type [25]. Details concerning the model Hamiltonian may be found in Appendix B 1.…”

“…(See Ref. [14] for bulk systems.) The values are given in Table I. As expected from a wealth of literature [27-29, 31, 32, 52-54, 56-58, 62], T g increases with H. More precisely, as seen in the left inset of Fig.…”

“…The indicated ∆t-dependences naturally arise since the averages for µ A and µ F are commonly and most conveniently done by first "timeaveraging" over time windows of length ∆t of the stored * Electronic address: joachim.wittmer@ics-cnrs.unistra.fr data entries of a given configuration and only in a second step by "ensemble-averaging" over completely independent configurations (Appendix B 2). Assuming the time-translational invariance of the time series it can be demonstrated (Appendix C) that the ∆t-dependence can be traced back to the stationarity relation [9,11,14] µ(∆t) = 2 ∆t 2 ∆t 0 dt t 0 dt G(t ).…”