Dynamical heterogeneity in periodically deformed polymer glasses

The dynamics of structural relaxation in a model polymer glass subject to spatially homogeneous, time-periodic shear deformation is investigated using molecular dynamics simulations. We study a coarse-grained bead-spring model of short polymer chains below the glass transition temperature. It is found that at small strain amplitudes, the segmental dynamics is nearly reversible over about ${10}^4$ cycles, while at strain amplitudes above a few percent, polymer chains become fully relaxed after a hundred cycles. At the critical strain amplitude, the transition from slow to fast relaxation dynamics is associated with the largest number of dynamically correlated monomers as indicated by the peak value of the dynamical susceptibility. The analysis of individual monomer trajectories showed that mobile monomers tend to assist their neighbors to become mobile and aggregate into relatively compact transient clusters.

Figure 1

A snapshot of the polymer glass during homogeneous time-periodic shear deformation with the strain amplitude ${\gamma }_0=0.02$ and frequency $\omega \tau =0.05$. Four chains of $N=10$ monomers are marked by solid lines and filled circles (not drawn to scale). The black arrows indicate the direction of the applied shear strain. The Lees-Edwards periodic boundary conditions are imposed in the $xz$ plane.

Figure 2

The averaged mean-square displacement of monomers as a function of time for the oscillation frequency $\omega \tau =0.05$ and period $T=2\pi /\omega =125.66\tau$. The strain amplitudes from bottom to top are ${\gamma }_0=0.02,0.03,0.04,0.05,0.06,0.07,0.08,\text{and}0.09$. The straight black line with the slope $0.87$ is shown for reference.

Figure 3

The autocorrelation function of (a) $p=1$ and (b) $p=9$ normal modes defined by Eq. (5) for the oscillation frequency $\omega \tau =0.05$ and period $T=2\pi /\omega =125.66\tau$. The strain amplitudes from top to bottom are ${\gamma }_0=0.02,0.03,0.04,0.05,0.06,0.07,0.08,\text{and}0.09$.

Figure 4

The contour plots of the correlation functions $Q_s(a,t)$ (top) and ${\chi }_4(a,t)$ (bottom) for the strain amplitude ${\gamma }_0=0.06$ and oscillation frequency $\omega \tau =0.05$. The oscillation period is $T=125.66\tau$.

Figure 5

The time dependence of the self-correlation function $Q_s(a,t)$ computed at $a=0.12\sigma$ for the oscillation frequency $\omega \tau =0.05$ and period $T=2\pi /\omega =125.66\tau$. The strain amplitudes from top to bottom are ${\gamma }_0=0.02,0.03,0.04,0.05,0.06,0.07,0.08,\text{and}0.09$.

Figure 6

The dynamic susceptibility ${\chi }_4(a,t)$ defined by Eq. (7) for the oscillation frequency $\omega \tau =0.05$ and period $T=2\pi /\omega =125.66\tau$. The strain amplitudes from bottom to top are ${\gamma }_0=0.02\text{at}a=0.06\sigma$, ${\gamma }_0=0.03\text{at}a=0.06\sigma$, ${\gamma }_0=0.04\text{at}a=0.07\sigma$, ${\gamma }_0=0.05\text{at}a=0.08\sigma$, ${\gamma }_0=0.06\text{at}a=0.21\sigma$. The other curves correspond to ${\gamma }_0=0.07\text{at}a=0.20\sigma$ (dashed curve), ${\gamma }_0=0.08\text{at}a=0.17\sigma$ (dash-dotted curve), and ${\gamma }_0=0.09\text{at}a=0.19\sigma$ (dash-double-dotted curve). The inset shows the dynamic correlation length ${\xi }_4={\left[{\chi }_4^{\text{max}}(a,t)\right]}^{1/3}$ as a function of the strain amplitude ${\gamma }_0$.

Figure 7

The total number of mobile monomers during cyclic deformation with frequency $\omega \tau =0.05$, period $T=2\pi /\omega =125.66\tau$, and strain amplitudes (a) ${\gamma }_0=0.02$, (b) ${\gamma }_0=0.04$, and (c) ${\gamma }_0=0.06$.

Figure 8

Snapshots of mobile monomer configurations at strain amplitudes (a) ${\gamma }_0=0.03$, (b) ${\gamma }_0=0.04$, (c) ${\gamma }_0=0.05$, and (d) ${\gamma }_0=0.06$.

Figure 9

The ratio of dynamically facilitated mobile monomers and the total number of mobile monomers as a function of the time interval preceding cage jumps. The oscillation frequency is $\omega \tau =0.05$ and strain amplitudes are ${\gamma }_0=0.02,0.03,0.04,0.05,\text{and}0.06$ (from bottom to top).