Thermomechanical equation of state

This article reviews recent developments in polymer thermomechanics both in theory and experiment. The first section is concerned with theories of thermomechanics of polymers both in rubbery and solid (glassy and crystalline) states with special emphasis on relationships following from the thermomechanical equations of state. In the second section, some of the methods of thermomechanical measurements are briefly described. The third section deals with the thermomechanics of molecular networks and rubberlike materials including such technically important materials as filled rubbers and block and graft copolymers. Some recent data on thermomechanical behaviour of bioelastomers are also described. In the fourth section, thermomechanics of solid polymers both in undrawn and drawn states are discussed with a special focus on the molecular and structural interpretation of thermomechanical experiments. The concluding remarks stress the progress in the understanding of the thermomechanical properties of polymers. 

Thermomechanical Equations of State Based on Statistical Theories 40... 

The thermomechanical equation of state of such a solid body may be obtained by combining the Hook s law and the law of thermal expansion710. Hence, for uniform extension we have (as a first approximation)... 

The thermomechanical equation of state of an isotropic Hookean rod subjected to force f along the rod axis can be obtained analogously to that used for the uniform deformation 3 7 8)... 

In the above thermomechanical equations of state we neglect the variation of K, E, oc and P with temperature and strain (or stress). As we will see later, this is a good... 

There is in this Handbook a whole Chapter 7 by Robert Orwoll on equation-of-state P-V-T properties of polymers. Briefly, confining our attention to what is pertinent for PLCs, there are basically two experimental procedures for a determination. One can measure l in a thermomechanical analysis (TMA) apparatus and then calculate a fi om Eqs. (41.4) or (41.5) [57,58]. Or, one can use an apparatus which produces full P-V-T data, that is specific volume v as a function of temperature T, v(T), plus a(T) plus also isothermal compressibility fCj-(7), where... 

Third Level. At the third level of complexity, the unsteady character of the polymer linked to the fact that it is out of equilibrium in the glassy state must be taken into account. The behavior of the material depends not only on the mechanical stimuli and environmental conditions but also on its thermomechanical history since its processing. In other words, time must be added as a variable to the constitutive equations ... 

This equation is valid for a homogeneous state of equilibrium. For slow reactions, it is reasonable to assume that the chemical process is proceeding through states that are in thermomechanical equilibrium at all times, although chemical equilibrium is not established. This assumption is supported by the fact that, for example, for a gaseous mixture, collisions not causing reactions are far more frequent than collisions that cause reactions. At a specified... 

In macroscopic modeling, these functions are obtained from a certain amount of data including state equations, thermomechanical coefficients, heat capacities, variations in surface tensions. Young s modulus and all variables which are classed under thermodynamic coefBcients, themselves grouped into characteristic matrices. This will be the focus of Chapter 2, in which we introduce these concepts and study this method. 

---