Simple generic picture of toughness in solid polymer blends

Toughness $\mathcal{T}$ of a brittle polymeric solid can be enhanced by blending another compatible and ductile polymer. While this common wisdom is generally valid, a generic picture is lacking that connects the atomistic details to the macroscopic non-linear mechanics. Using all-atom and complementary generic simulations we show how a delicate balance between the side group contact density of the brittle polymers ${\rho }_{\mathrm{c}}$ and its dilution upon adding a second component controls $\mathcal{T}$. A broad range of systems follows a universal trend in $\mathcal{T}$ with $\mathrm{d}{\rho }_{\mathrm{c}}\mathrm{/}\mathrm{d}\epsilon$, where $\epsilon$ is the tensile strain. The simulation data is consistent with a simple model based on the parallel spring analogy.