A generalized criterion for rubber toughening: The critical matrix ligament thickness

TLDR: In this article, the thickness of the matrix ligament is defined as the surface-to-surface interparticle distance between two neighboring rubber particles, and the ligament thickness is the single parameter determining whether a polymer/rubber blend will be tough or brittle.

Abstract: The thickness of matrix ligament is shown to be the single parameter determining whether a polymer/rubber blend will be tough or brittle. The matrix ligament is defined as the region of the matrix between two neighboring rubber particles. Specifically, the ligament thickness is the surface-to-surface interparticle distance. When the average ligament thickness is smaller than a critical value, a blend will be tough; when greater, it will be brittle. In other words, a sharp brittle–tough transition occurs at the critical ligament thickness. This critical parameter is independent of rubber volume fraction and particle size, and is characteristic of the matrix for a given mode, temperature and rate of deformation. What is important is the matrix ligament, not rubber particles. The single matrix parameter explains the effects of phase morphology, rubber volume fraction, particle size, particle-size polydispersity, and particle flocculation on toughness.