Configurational entropy free volume

In polymer electrolytes (even prevailingly crystalline), most of ions are transported via the mobile amorphous regions. The ion conduction should therefore be related to viscoelastic properties of the polymeric host and described by models analogous to that for ion transport in liquids. These include either the free volume model or the configurational entropy model . The former is based on the assumption that thermal fluctuations of the polymer skeleton open occasionally free volumes into which the ionic (or other) species can migrate. For classical liquid electrolytes, the free volume per molecule, vf, is defined as ... 

The common disadvantage of both the free volume and configuration entropy models is their quasi-thermodynamic approach. The ion transport is better described on a microscopic level in terms of ion size, charge, and interactions with other ions and the host matrix. This makes a basis of the percolation theory, which describes formally the ion conductor as a random mixture of conductive islands (concentration c) interconnected by an essentially non-conductive matrix. (The mentioned formalism is applicable not only for ion conductors, but also for any insulator/conductor mixtures.)... 

The configurational entropy model describes transport properties which are in agreement with VTF and WLF equations. It can, however, predict correctly the pressure dependences, for example, where the free volume models cannot. The advantages of this model over free volume interpretations of the VTF equation are numerous but it lacks the simplicity of the latter, and, bearing in mind that neither takes account of microscopic motion mechanisms, there are many arguments for using the simpler approach. 

Free Volume Versus Configurational Entropy Descriptions of Glass Formation Isothermal Compressibility, Specific Volume, Shear Modulus, and Jamming Influence of Side Group Size on Glass Formation Temperature Dependence of Structural Relaxation Times Influence of Pressure on Glass Formation... 

VI. FREE VOLUME VERSUS CONFIGURATIONAL ENTROPY DESCRIPTIONS OF GLASS FORMATION... 

Endless discussion exists regarding whether a theory based on the configurational entropy or the excess free volume 8v provides the more correct description of glass formation. Thus, this section briefly analyzes the relation... 

Figure 15. The LCT configurational entropy s T (normalized as in Fig. 11) as a function of the reduced specific volume 8v = [v T) — v(T = To)]/v(T), which is a measure of the excess free volume in the polymer system. Different curves refer to the F-F and F-S polymer fluids and to low and high molar mass polymer chains.

This was the first suggestion that the concept of free-volume somehow reflects changes in configurational entropy, which may be estimated by the parameter Zg. 

It is now generally accepted that the viscous flow of polymeric liquids is connected with chain segment rotation, i.e. with configurational entropy. From this point of view Miller concluded that the Simha-Boyer equation was not correct since the relative free-volume in SB theory equals zero at 0 K, not at T = T0. If the latter... 

Free volume Configurational entropy Coupling model Conventional thermodynamics Statistical thermodynamics Molecular dynamics Fox et al. (1955) Di Marzio (1964) Ngai et al. (1986)... 

T 1 oo = temperature at which the free volume fraction or configurational entropy become zero, K... 

The Kauzmann temperature plays an important role in the most widely applied phenomenological theories, namely the configurational entropy [100] and the free-volume theories [101,102]. In the entropy theory, the excess entropy ASex obtained from thermodynamic studies is related to the temperature dependence of the structural relaxation time xa. A similar relation is derived in the free-volume theory, connecting xa with the excess free volume AVex. In both cases, the excess quantity becomes zero at a distinguished temperature where, as a consequence, xa(T) diverges. Although consistent data analyses are sometimes possible, the predictive power of these phenomenological theories is limited. In particular, no predictions about the evolution of relaxation spectra are made. Essentially, they are theories for the temperature dependence of x.-jT) and r (T). 

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

Figure 2.2. In (a) and (b), the same number of spheres of the same size are packed into the same space. The disordered sphere packing in (a) can create more free volume by ordering into a regular packing in (b), thereby creating volume entropy while losing configurational entropy (after Lekkerkerker, unpublished). (From Poon and Pusey, fig. 4, with kind permission of Kluwer Academic Publishers, Copyright 1995.)...

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