Correlation between rearrangements and soft modes in polymer glasses during deformation and recovery

We explore the link between soft vibrational modes and local relaxation events in polymer glasses during physical aging, active deformation at constant strain rate, and subsequent recovery. A softness field is constructed out of the superposition of the amplitudes of the lowest energy normal modes, and found to predict up to 70% of the rearrangements. Overlap between softness and rearrangements increases logarithmically during aging and recovery phases as energy barriers rise due to physical aging, while yielding rapidly rejuvenates the overlap to that of a freshly prepared glass. In the strain hardening regime, correlations rise for uniaxial tensile deformation but not for simple shear. These trends can be explained by considering the differing degrees of localization of the soft modes in the two deformation protocols.

Figure 1

(a)–(c) Three exemplary lowest energy vibrational modes, visualized by their polarization vector fields (coloring indicates depth). The participation ratios as defined in Eq. (4) are 0.12 (a), 0.29 (b), and 0.62 (c). (d) Exemplary simulation snapshot with particle softness indicated by color (blue to red is small to large $\varphi$). The right side shows only the 10% softest particles.

Figure 2

(a) Fraction of hops in soft spots as function of coverage fraction of soft spots measured in three deformation regimes for uniaxial tension: elastic $\left(\epsilon =0.0\right)$, strain softening $\left(\epsilon =0.1\right)$, and strain hardening $\left(\epsilon =4.0\right)$. The dotted line indicates no correlation. (b) Stress-strain curves for uniaxial tensile (solid line) and simple shear (dashed line). Vertical colored lines indicate the investigated deformations at strains $\epsilon =0.0,0.04,0.1,0.5,1.0,2.0,3.0,4.0$ and the inset shows the region of the yield point in more detail. (c) Stress recovery from uniaxial tensile deformation. The evolution of the predictive success rate reached at $f=0.3$ is shown during aging (d), deformation (e), and in the recovery regime (f).

Figure 3

(a) Mean participation ratio as function of eigenfrequency at three values of strain for uniaxial tensile $(\circ )$ and simple shear $(▿)$ deformations. (b) Mean participation ration of all $N_m$ modes used for the softness field calculation as function of total strain.

Figure 4

Comparison of spatial correlation, participation ratio (top row), and potential energy stored in the LJ interaction and in the covalent bonds (bottom row) during aging, deformation, and recovery. The relative change is defined as $(Q-Q_0)/(Q_{\mathrm{ext}}-Q_0)$, where $Q$ is a placeholder for one of the measured quantities (see legend), and $Q_{\mathrm{ext}}$ is an extremal value observed during the simulation run [maximum for $\mathrm{\Theta }(30\%),U_{\text{IS}}^{\mathrm{bond}}$ and minimum for $\langle P\left(\omega \right)\rangle ,U_{\text{IS}}^{\text{LJ}}]$.