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 $\rho_{\rm c}$ and its dilution upon adding a second component controls $\mathcal{T}$. A broad range of systems follows a universal trend in $\mathcal{T}$ with ${\rm d}\rho_{\rm c}/{\rm d}\varepsilon$, where $\varepsilon$ is the tensile strain. The simulation data is consistent with a simple model based on the parallel spring analogy.