Entropic free volume model

In the entropic-free volume model, the activity coefficient of the solvent is given by Eqs. (44)-(48) with p = 1 [52]. The residual contribution is represented by the residual contribution of the UNIFAC model with temperature-dependent interaction parameters [53]. The liquid molar volumes needed for the calculation of the free volume of a component can be taken from experiment or calculated from the Tait equation [4] or by the group contribution method of Elbro et al. [56]. This model is relatively easy to use. 

The solubility of a gas is an integral part for the prediction of the permeation properties. Various models for the prediction of the solubility of gases in elastomeric polymers have been evaluated (57). Only a few models have been found to be suitable for predictive calculations. For this reason, a new model has been developed. This model is based on the entropic free volume activity coefficient model in combination with Hildebrand solubility parameters, which is commonly used for the theory of regular solutions. It has been demonstrated that mostly good results are obtained. An exception... 

Since 1980 polymer thermodynamics has been developed considerably and, to date, models are available that are suitable for at least satisfactory calculations of VLE and, qualitatively, also for LLE. Some of these methods are models for the activity coefficient, which are modifications of the FH equation. These modifications use a similar to FH but better combinatorial/free-volume expression and a local-composition-type energetic term such as those found in the UNIQUAC and UNIFAC models. Models like the UNIFAC-FV and the Entropic-FV are discussed in Section 16.4. 

A common feature of UNIEAC-EV, Entropic-FV, and other similar models is that they require the volumes of solvents and polymers (at the different temperatures where application is required). This can be a problem in those cases where the densities are not available experimentally and have to be estimated using one of the methods discussed in Section 16.2. Figure 16.3 shows that both UNlFAC-FV and Entropic-FV are rather sensitive to the density values used for the calculation of solvent activities. The UNIFAC-FV model, in particular, can be extremely sensitive if the free volume percentage of the polymer is very low. 

Enthalpic and Entropic Contributions to the Excess Free Energy Molecular Picture of the Dissolution Process Model for Description of the Aqueous Activity Coefficient Box 5.1 Estimating Molar Volumes from Structure Illustrative Example 5.2 Evaluating the Factors that Govern the Aqueous Activity Coefficient of a Given Compound... 

In Chapters 2-4, the mathematical models described, such as the binary interaction model, group solubility parameter approach, and entropic difference model, can be used to obtain an expression for free energy of mixing of the blend. The molar volume in the entropic term can be expressed in terms of temperature and pressure using the different EOS discussed in Chapter 2. Then Eqnations (5.12) and (5.13) can be used to obtain the phase bonndaries in the phase diagrams. Several cases are possible. Six cases are discussed below. 

Despite the numerical support, the above model is quite unrealistic in regard to real systems. Actually, most hydrogels used in chemomechanics experiments are polyacids or polybases that sweU/shrink as a function of the pH of the aqueous solution. In this case, the volume dependence cannot be accounted for on the same principles. The volume changes are associated with energetic effects due to the electrostatic interactions between ions attached to the polymer and with entropic effects due to an excess of free ions that exerts an additional osmotic pressure between the gel contents and the surroundings. Although the electrostatic... 

The affine network model assumes that the network consists of phantom Gaussian chains, that all network changes are entropical, that deformation is affine and that the volume remains constant during deformation, and yields the following expression for the free energy change accompanying the deformation Ui, A2,... 

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