Glassy polymers, thermodynamic

Petrie, S. E. B. The effect of excess thermodynamic properties versus structure formation on the physical properties of glassy polymers. J. Macromol. Sci., Phys. 12, 225 (1976)... 

Of the thermodynamic quantities just mentioned, only the determination of the expansion coefficient or other quantities reflecting its change have assumed practical importance for the identification of secondary transitions in glassy polymers. The most efficient methods for the investigation of the dynamics and intensity of molecular motions have so far been those based on the interference between molecular motion and the oscillating magnetic, electric or mechanical force field. In recent years, methods which employ various probes or labels in the study of molecular mobility have increasingly been used. 

In this section, the composite system with the properties given by Eq. (58) will be used. Since glassy polymers are not in thermodynamic equilibrium, the change in the nonequilibrium glassy state and its relaxation define the viscoelastic response. The relaxation modulus is given by Eq. (40). 

Thermodynamically stable mixtures will of course form stable blends. This implies miscibility on a molecular level. It is desirable for some applications but not for others, like rubber modification of glassy polymers. 

For ideal systems (usually as in elastomers), the solubility wiU be independent of concentration and the sorption curve will follow Henry s law (Equation 4.6), i.e., gas concentration within the polymer is proportional to the applied pressure. For nonideal systems (usually as in glassy polymers), the sorption isotherm is generally curved and highly nonlinear. Such behavior can be described by free-volume models and Flory-Huggins thermodynamics—comprehensive discussions on this may be found elsewhere [1,25,26]. 

Molecular modeling techniques have been used to predict and interpret mechanical properties of polymers [88-95]. Theodorou and Suter [88, 89] found that the internal energy contribution to the elastic response is much more important than the entropic contribution for glassy polymers by a thermodynamic... 

The solubility factor in Equation 5 is thermodynamic in nature and is determined by polymer-penetrant interactions and the amount of excess interchain gaps existing in the glassy polymer (17). 

Thus, one could conclude that the molecular structure of glassy polymers has only a small effect on the relaxation processes associated with the nonequilibrium thermodynamic state of the glasses. 

Considerable effort has been made during the last two decades to develop a "microscopic" description of gas diffusion in polymers, which is more detailed than the simplified continuum viewpoint of Fick s laws. It has been known for a long time that the mechanism of diffusion is very different in "rubbery" and "glassy" polymers, i.e., at temperatures above and below the glass-transition temperature, Tg, of the polymers, respectively. This is due to the fact that glassy polymers are not in a true state of thermodynamic equilibrium, cf. refs. (1,3,5,7-11). Some of the models and theories that have been proposed to describe gas diffusion in rubbery and glassy polymers are discussed below. The models selected for presentation in this review reflect only the authors present interests. 

The differences in the transport and solution behavior of gases in rubbery and glassy polymers are due to the fact that, as mentioned previously, the latter are not in a state of true thermodynamic equilibrium (1,3-8). Rubbery polymers have very short relaxation times and respond very rapidly to stresses that tend to change their physical conditions. Thus, a change in a temperature causes an immediate adjustment to a new equilibrium state (e.g., a new volume). A similar adjustment occurs when small penetrant molecules are absorbed by a rubbery polymer at constant temperature and pressure absorption (solution) equilibrium is very rapidly established. Furthermore, there appears to exist a unique mode of penetrant absorption and diffusion in rubbery polymers (2) ... 

In rubbery polymers, such relationships can be obtained in a rather straightforward way, since true thermodynamic equilibrium is reached locally immediately. In such cases, one simply has to choose the proper equilibrium thermodynamic constitutive equation to represent the penetrant chemical potential in the polymeric phase, selecting between the activity coefficient approacht or equation-of-state (EoS) method ", using the most appropriate expression for the case under consideration. On the other hand, the case of glassy polymers is quite different insofar as the matrix is under non-equilibrium conditions and the usual thermodynamic results do not hold. For this case, a suitable non-equilibrium thermodynamic treatment must be used. 

The thermodynamic derivation of the NELF model has been reported in several publicationsP° " l From a more general point of view, such a model represents a special application of the non-equilibrium thermodynamics of glassy polymers (NET-GP) which indicates the relationships existing in general between the thermodynamic properties above and below the glass transition temperature the NET-GP results hold for any thermodynamic model and are not limited to any particular EoS. 

In the NET-GP analysis, the glassy polymer-penetrant phases are considered homogeneous, isotropic, and amorphous, and their state is characterized by the classical thermodynamic variables (i.e. composition, temperature, and pressure) with the addition of a single-order parameter, accounting for the departure from equilibrium. The specific volume of the polymer network, or, equivalently, the polymer density Pp, is chosen as the proper order parameter. In other words, the hindered mobility of the glassy polymer chains freezes the material into a non-equilibrium state that can be labeled by the... 

It has been noted previously that the structures and properties of polymers are studied using the principles of synergetics and methods of fractal analysis. This is based on several prerequisites. Firstly, amorphous glassy polymers have thermodynamically nonequilibrimn structure [32]. Schaefer and Keefer [33] showed that fractal structures are formed in nonequilibrium processes. Therefore, there is good reason to believe that there are fractal structures in glassy polymers and that they can be described using the methods of synergetics. These assumptions have been repeatedly confirmed by experiments [32, 34-40]. 

Drozdov, A. D., Volume and enthalpy relaxation in glassy polymers, J. Non-Equilibrium Thermodynam., 24, 203-2X1 (1999). 

Adolf, D. B., Chambers, R. S., and Caruthers, J. M., Extensive validation of a thermodynamically consistent, nonlinear viscoelastic model for glassy polymers, Polymer, 45, 4599-4621 (2004). 

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