Nonmonotonic dependence of polymer-glass mechanical response on chain bending stiffness

We investigate the mechanical properties of amorphous polymers by means of coarse-grained simulations and nonaffine lattice dynamics theory. A small increase of polymer chain bending stiffness leads first to softening of the material, while hardening happens only upon further strengthening of the backbones. This nonmonotonic variation of the storage modulus $G^{\prime }$ with bending stiffness is caused by a competition between additional resistance to deformation offered by stiffer backbones and decreased density of the material due to a necessary decrease in monomer-monomer coordination. This counterintuitive finding suggests that the strength of polymer glasses may in some circumstances be enhanced by softening the bending of constituent chains.

Figure 1

Entry into the glassy state and its structural properties for ${\theta }_0=109.5^{\circ }$. (a) Sketch of polymer chain illustrating the angle $\theta$ and rest positions for LJ ($2^{1/6}\sigma$) and FENE ($0.96\sigma$) interactions. (b) Snapshot of glassy polymer in periodic box [14]. (c) The decrease of volume associated with decreasing $T^{*}$ at fixed pressure, for several values of ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$. We approximate the low- and high-temperature dependences as linear, and take their intersection to occur at $T^{*}=T_g^{*}$. (d) Variation of glass transition temperature $T_g^{*}$ with ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$. (e) Variation of $N_p{\sigma }^3/V_g$, the density at $T_g^{*}$, with ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$. (f) Variation of $Z_g$, the coordination number at $T_g^{*}$, with ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$. Dashed line in (d)–(f) indicates ${\varepsilon }_{\mathrm{bend}}=0$.

Figure 2

Nonmonotonic mechanical response of a polymer glass as a function of chain bending stiffness. (a) Elastic modulus $G^{\prime }$ as a function of ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$ for three values of ${\varepsilon }_{\mathrm{LJ}}$. We used five realizations and found the variation between realizations to be smaller than the marker size. (b) Elastic modulus $G^{\prime }$ as a function of ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$ for three values of ${\theta }_0$. Inset: decreasing density with increasing ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$. (c) Elastic modulus contributions from LJ, FENE, and angular potentials for ${\varepsilon }_{\mathrm{LJ}}=\epsilon$ and ${\theta }_0=109.5^{\circ }$. (d) Lissajous-Bowditch plots showing linear elastic stress contributions [i] the total $\mathrm{\Sigma }$, [ii] ${\mathrm{\Sigma }}^{\mathrm{LJ}}$, [iii] ${\mathrm{\Sigma }}^{\mathrm{FENE}}$, and [iv] ${\mathrm{\Sigma }}^{\mathrm{bend}}$, each rescaled by their maximal values. Strains are rescaled by the amplitude ${\gamma }_0$. (e) Temperature dependence of $G^{\prime }$ across a range of bending stiffnesses ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$. (f) Contour plot showing $G^{\prime }$ as a function of rescaled temperature $T^{*}/T_g^{*}$ and ${\varepsilon }_{\mathrm{bend}}/{\varepsilon }_{\mathrm{LJ}}$. Dashed black arrows indicate decreasing $G^{\prime }$; dotted white lines show region of minimal $G^{\prime }$.