Free volume equation

Plots of D versus water volume fraction " show that the concentration dependence of D is in fact described well by the Fujita free volume equation. " This was surprising considering that the underpinning of this equation simply involves available free volume for molecular hopping. The interpretation is that water molecules plasticize the perfluoroalkyl ether side chain domains and this increases D with increasing water content. D for water varied from... 

In many production routes, and also during processing, polymer systems have to undergo pressure. Changes in the volume of a system by compression or expansion, however, cannot be dealt with in rigid-lattice-type models. Thus, non-combinatorial free volume ( equation of state ) contributions to AG have been advanced [23 - 29]. Detailed interaction functions have been suggested (but all of them are based on adjustable parameters, for blends, e.g., Mean-field lattice gas [30], SAFT [31], specific interactions [32]), and have been succesfully applied, for example, by Kennis et al. [33]. 

A central theme of the modern theory of liquids is a reappreciation of the van der Waals equation of state. The traditional presentations of the van der Waals equation of state feature discussion of two concepts (Widom, 2002, see Section 7.2) (/) 2ifree volume modification of the ideal gas equation of state based on the fact that molecules can t overlap much, and (ii) modification of that free volume equation of state to reflect attractive interactions between molecules. The result is... 

The complex shape of the viscosity-pressure behaviour gives way to simple universal scaling when volume replaces pressure (Fig. 3.53). The physics underlying this scaling can be expressed through the free volume equation. The normalized form of this equation is... 

The numerical results obtained for the equation of state of the three-dimensional hard sphere system in the low density region are shown in Fig. 1. A comparison is made with the equation of state obtained by numerical integration of Eq. (13) subject to Eq. (15), the superposition theory [cf. Eq. (11)], the free-volume equation of state (23), and the five-term virial expansion (32). The last... 

Semi-empirical approaches are often used to model lct,TD as a function of system viscosity (Equation 3.54), conversion (Equation 3.55) or system free-volume (Equation 3.56) ... 

While the Flory-Orwoll theory for the equation of state of bulk polymers can be employed, a simpler free-volume equation of state is often used in practice. The details of this theory and its application to the description of the viscosity of low-molecular-weight polymer liquids is presented... 

Clarifies the Flory-Orwell theory of polymer solutions and free volume equation of state... 

The presence of additional penetrants in the feed stream can be accounted for by the addition of a term in the free-volume equation to accoimt for the presence of each penetrant and the applied hydrostatic pressure above Ps = 101.3 kPa (1 atm) as follows ... 

Figure 5.41 The relation between the dimensions of fluctuation free volume (Equation 5.72) and extra energy localisation regions Z)y (Equation 5.65) for epoxy polymers EP-1 (1), EP-2 (2) and EP-3 (3) [155]...

---