A Mathematical Formulation of the Brittle/Ductile Transition of Impact Modified Polymers

Abstract

The subject of this paper is the impact modification of polymers with elastomers via melt blending. A mathematical model was developed to account for the shape of the Izod S-curves (Izod values versus impact modifier content). Wu introduced the critical ligament thickness concept to explain the Brittle/Ductile Transition of polymers modified with elastomers: only when the ligament thickness (surface to surface distance of two rubber particles) is smaller than a critical value can the rubber particles promote toughness. In an ideal model with rubber particles distributed in an ordered lattice this transition would be a 90-degree step, whereas in practice this transition curve is more or less rounded. The smoothness of this transition is attributed in the present paper to the random distribution of rubber particles inside the polymer matrix: from this concept, an equation for the B/D Transition part of the S-curve was developed. This equation introduces the concept of the critical number of rubber particles, that is the number of particles within the ligament thickness distance necessary to trigger the toughness. The polymers investigated were polypropylene (PP) of different viscosity, polyamide (PA), polystyrene (PS), and polycarbonate (PC).