Amorphous solids viscoelastic properties

In the molten state polymers are viscoelastic that is they exhibit properties that are a combination of viscous and elastic components. The viscoelastic properties of molten polymers are non-Newtonian, i.e., their measured properties change as a function of the rate at which they are probed. (We discussed the non-Newtonian behavior of molten polymers in Chapter 6.) Thus, if we wait long enough, a lump of molten polyethylene will spread out under its own weight, i.e., it behaves as a viscous liquid under conditions of slow flow. However, if we take the same lump of molten polymer and throw it against a solid surface it will bounce, i.e., it behaves as an elastic solid under conditions of high speed deformation. As a molten polymer cools, the thermal agitation of its molecules decreases, which reduces its free volume. The net result is an increase in its viscosity, while the elastic component of its behavior becomes more prominent. At some temperature it ceases to behave primarily as a viscous liquid and takes on the properties of a rubbery amorphous solid. There is no well defined demarcation between a polymer in its molten and rubbery amorphous states. 

Since the viscoelastic properties of the solid undergo a significant change as the solid undergoes a transition from the amorphous to rubbery states (due to elevation of temperature at constant moisture content or to an increase in moisture content at constant temperature), one also expects marked changes in the processing properties of these solids as this transition occurs. Some properties that are likely to be affected include tablet compaction [76], gelatin capsule... 

Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time dependent strain. Whereas elasticity is usually the result of bond stretching along crystallographic planes in an ordered solid, viscoelasticity is the result of the diffusion of atoms or molecules inside of an amorphous material [3-6],... 

Our discussion of the viscoelastic properties of polymers is restricted to the linear viscoelastic behavior of solid polymers. The term linear refers to the mechanical response in whieh the ratio of the overall stress to strain is a function of time only and is independent of the magnitudes of the stress or strain (i.e., independent of stress or strain history). At the onset we concede that linear viscoelastie behavior is observed with polymers only under limited conditions involving homogeneous, isotropie, amorphous samples under small strains and at temperatures close to or above the Tg. In addition, test conditions must preclude those that ean result in specimen rupture. Nevertheless, the theory of linear viseoelastieity, in spite of its limited use in predicting service performance of polymeric articles, provides a useful reference point for many applications. 

More details about physical properties of amorphous polymers can be found in Ferry JD (1980) Viscoelastic Properties of Polymers, 3" edn. Wiley, New York Ward IM (1983) Mechanical Properties of Solid Polymers, 2 edn. Wiley, New York Matsuoka S (1992) Relaxation Phenomena in Polymers. Hanser, MUnchen. 

DMA methods are widely used by thermal analysts to determine the viscoelastic properties of pol5uners for a number of purposes (see Viscoelasticity). The primary application of these techniques to the study of polymeric solids and melts is well documented. Excellent general discussions covering the subject are provided in References 70-72. Linear Amorphous Polymers (qv) exist in a number of characteristic physical states depending on the time scale and temperature of measurement. These are illustrated in Figure 31 in terms of an arbitrary modulus fimction and are classified as glassy, leathery, rubbery, rubbery flow, and viscous (73). All linear amorphous polymers exhibit these five physical states when they... 

Molecular dynamics (MD) is an invaluable tool to study structural and dynamical details of polymer processes at the atomic or molecular level and to link these observations to experimentally accessible macroscopic properties of polymeric materials. For example, in their pioneering studies of MD simulations of polymers, Rigby and Roe in 1987 introduced detailed atomistic modeling of polymers and developed a fundamental understanding of the relationship between macroscopic mechanical properties and molecular dynamic events [183-186]. Over the past 15 years, molecular dynamics have been applied to a number of different polymers to study behavior and mechanical properties [187-193], polymer crystallization [194-196], diffusion of a small-molecule penetrant in an amorphous polymer [197-199], viscoelastic properties [200], blend [201,202] and polymer surface analysis[203-210]. In this article, we discuss MD studies on polyethylene (PE) with up to 120,000 atoms, polyethylproplyene (PEP), atactic polypropylene (aPP) and polyisobutylene (PIB) with up to 12,000 backbone atoms. The purpose of our work has been to interpret the structure and properties of a fine polymer particle stage distinguished from the bulk solid phase by the size and surface to volume ratio. 

Figure 1.1 describes the general regions of viscoelastic behavior for amorphous polymers where mechanochemistry may be conducted. The tensile and shear moduli for crystalline and amorphous polymers in the solid state are generally in the range of 10 dyn/cm. For the rubbery state, the value is about 10 dyn/cm, and it varies with the density of entanglements and chemical cross-links. The modulus can be calculated from the theory of rubber elasticity, and the short-time viscoelastic properties in the rubbery state are not unlike those of a common rubber band. 

Before examining the viscoelastic behavior of amorphous polymeric substances in more detail, some of the fundamental properties of polymer melts and elastic solids will be reviewed. 

Materials with molecular networks, such as cross-linked elastomers and crystalline polymers, do not flow and so are classified as viscoelastic solids. Shear stresses do not decay to zero with time, ie, equilibrium stresses can be supported. Above Tg, such amorphous materials are still classified as solids, but most of their physical properties such as thermal expansivity, thermal conductivity, and heat capacity are liquid-like. 

Some transitions that are only known for macromolecules, however, will not be mentioned at all since they are covered elsewhere in this Encyclopedia (see, eg. Gel Point). Also we shall not be concerned here with the transformations from the molten state to the solid state of polymeric materials, since this is the subject of separate treatments (see Crystallization Kinetics Glass Transition Viscoelasticity). Unlike other materials, polymers in the solid state rarely reach full thermal equilibrium. Of course, all amorphous materials can be considered as frozen fluids (see Glass Transition) Rather perfect crystals exist for metals, oxides, semiconductors etc, whereas polymers typically are semicrystalline, where amorphous regions alternate with crystalline lamellae, and the detailed structure and properties are history-dependent (see Semicrystalline Polymers). Such out-of-equilibrium aspects are out of the scope of the present article, which rather emphasizes general facts of the statistical thermodynamics (qv) of phase transitions and their applications to polymers in fluid phases. 

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