Unexpected Ductility in Semiflexible Polymer Glasses with Entanglement Length Equal to Their Kuhn Length

Semiflexible polymer glasses (SPGs), including those formed by the recently synthesized semiflexible conjugated polymers, are expected to be brittle because classical formulas for their craze extension ratio ${\lambda }_{\text{craze}}$ and fracture stretch ${\lambda }_{\mathrm{frac}}$ predict that systems with $N_e=C_{\infty }$ have ${\lambda }_{\text{craze}}={\lambda }_{\mathrm{frac}}=1$ and hence cannot be deformed to large strains. Using molecular dynamics simulations, we show that in fact such glasses can form stable crazes with ${\lambda }_{\text{craze}}\simeq N_e^{1/4}\simeq C_{\infty }^{1/4}$, and that they fracture at ${\lambda }_{\mathrm{frac}}=(3N_e^{1/2}-2{)}^{1/2}\simeq (3C_{\infty }^{1/2}-2{)}^{1/2}$. We argue that the classical formulas for ${\lambda }_{\text{craze}}$ and ${\lambda }_{\mathrm{frac}}$ fail to describe SPGs’ mechanical response because they do not account for Kuhn segments’ ability to stretch during deformation.

Figure 1

Stress-strain curves for our model SPG at $T=0$ [panel (a)] and $T\simeq 3T_g/4$ [panel (b)]. Vertical dashed lines from left to right respectively correspond to $\lambda ={\lambda }_{\text{yield}}$, $\lambda ={\lambda }_{\text{craze}}$, and $\lambda ={\lambda }_{\mathrm{frac}}$, and the horizontal dashed lines illustrate the coexistence of unyielded and crazed regions at equal ${\sigma }_{zz}$.

Figure 2

Density profiles vs. strain for our model SPG at $T=0$ [panel (a)] and $T\simeq 3T_g/4$ [panel (b)]. The dashed black line in panel (a) indicates ${\rho }_{\mathrm{fd}}$. Here, the $L_z=\lambda L_z^0$ are the lengths of the periodic simulation cells along their $z$ axes.

Figure 3

Cross sections of thickness $5\sigma$ illustrate the structure of our SPG at $\lambda ={\lambda }_{\text{craze}}$, for $T=0$ [panel (a)] and $T=3T_g/4$ [panel (b)].

Figure 4

Number of topologically distinct voids $N_{dv}$ [panel (a)] and average void volumes $⟨V_v⟩$ [panel (b)] in model SPGs and in model FPGs with $\kappa =0$ and $\kappa =2ϵ$ [29]. Solid and dotted curves, respectively, show results for $T=0$ and $T=3T_g/4$.