Modeling the Endothermic Decomposition of Hydrated Solids

Mineral fillers, particularly hydrated solids such as aluminum trihydroxide or magnesium hydroxide, have been used as flame retardant additives in polymers for many years. Their great advantage lies in providing a green method of imparting increased thermal stability to otherwise combustible solids and also lowering heat release rate (although they must be used in large quantities ∼50% by weight). An added benefit is lower smoke production, but ignition resistance is not significantly increased. Interest in these materials (particularly in conjunction with other additives such as nanocomposites) has undergone something of a resurgence in recent years due to the increasing environmental concerns over halogenated flame retardants. Although straightforward in principle, the endothermic liberation of water actually provides considerable technical challenges from the modeling perspective. For example, in many cases, as water is liberated, a microporous residue is created with highly complex thermal properties, which strongly affect heat transfer to the remaining material. This chapter deals with the issues involved in modeling the endothermic decomposition of fillers and intrinsically hydrated solids in the context of laboratory-scale tests such as the cone calorimeter, but also in larger scale fire resistance scenarios such as standard furnace tests. The central importance of how degradation kinetics are modeled is discussed and also how kinetic mechanisms are linked to heat transfer models via the principles of energy and mass conservation is clearly explained. The important topic of composite and total effective thermal conductivity of porous solids is also explored in detail. The culmination of the chapter is a mathematical model for endothermic decomposition of a solid. A stripped-down version of the model is then briefly explored, demonstrating its important qualitative behavior.