Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State

TL;DR

This paper reviews the theoretical understanding of the vulcanisation transition in macromolecular systems, where a liquid transforms into an amorphous solid with randomly localized molecules, akin to a spin glass state.

Contribution

It provides a detailed theoretical analysis of the equilibrium properties of randomly crosslinked macromolecular systems at the vulcanisation transition, highlighting their amorphous solid state.

Findings

Identification of the amorphous solid as an equilibrium state with random localization.

Analysis of the subtle order parameter characterizing the transition.

Comparison of the vulcanised solid state to spin glass systems.

Abstract

As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equi- librium phase transition, the liquid state, in which all macromolecules are delocalised, is transformed into a solid state, in which a nonzero fraction of macromolecules have spontaneously become localised. This solid state is a most unusual one: localisation occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanisation transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter. In this review we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanisation transition.