The Molten State

Abstract

A fluid phase is a liquid if the kinetic energy of the molecules and the potential energy of its interactions are comparable, so that the molecules can move 'viscously' relatively to each other. A fluid phase is a gas if the kinetic energy greatly exceeds the potential energy of the interactions. In fact, the internal energy (U) of an ideal gas is exclusively kinetic energy, i.e. U is only a function of T. The translative kinetic energy of molecules in crystals is negligible. Conventional liquids possess only short-range order, and long-range order is absent. Rheology, which is the first topic of this chapter, is the mathematical discipline within which relationships between stress and strain in liquids are expressed. This discipline is essential for several applications, including polymer processing (cf. Gedde et al. 2020a). The molten state of polymers is more dependent on the molar mass than any of their other physical states. Flexible-chain polymer molecules possess essentially random conformations in the molten state. The coiled molecules entangle in high-molar-mass polymers. These chain entanglements are important for the rheological properties of the melt. The second part of this chapter deals with the rheology of flexible-chain polymer melts. A discussion of the deformation mechanisms, including the theoretical aspects, is also presented. A special class of polymers, the liquid-crystalline polymers, exhibits orientational order, i.e. alignment of molecules along a common director in the molten state. Liquid-crystalline polymers are after solidification, used as strong and stiff engineering plastics and fibres. 'Functional' liquid-crystalline polymers with unique electrical and optical properties have been developed. The fundamental physical and rheological aspects of liquid-crystalline polymers are the third subject of this chapter. Finally, the rheology of a few native polymers is dealt with. 6.2 Fundamental Concepts in Rheology Rheology is the discipline that deals with the deformation of fluids. Stresses acting on a liquid lead to deformation. The stress-strain relationships are referred to as constitutive equations. Such relationships are based on balance equations, which are statements of universal laws of the conservation of mass, momentum and energy. They can be expressed as follows: