Free volume polymer blends

PAL has been used to study both miscible and immiscible polymer blends [41, 61, 67-70], PAL results have shown both positive and negative deviations from additivity of free volume with blend composition. In the case of multi phase systems, PAL data analysis is complicated by the fact that Ps may diffuse between the different blend phases. 

Dlubek, G., Alam, M. A., Stolp, M., and Radusch, H.-J., The local free volume in blends of acrylonitrile-butadiene-styrene copolymer and polyamide 6 a positron lifetime study, J. Polym. Sci. B, 37,1749-1752 (1999). 

Before providing such an explanation it should first be noted that progressive addition of a plasticiser causes a reduction in the glass transition temperature of the polymer-plasticiser blend which eventually will be rubbery at room temperature. This suggests that plasticiser molecules insert themselves between polymer molecules, reducing but not eliminating polymer-polymer contacts and generating additional free volume. With traditional hydrocarbon softeners as used in diene rubbers this is probably almost all that happens. However, in the... 

Lohse et al. have summarized the results of recent work in this area [21]. The focus of the work is obtaining the interaction parameter x of the Hory-Huggins-Stavermann equation for the free energy of mixing per unit volume for a polymer blend. For two polymers to be miscible, the interaction parameter has to be very small, of the order of 0.01. The interaction density coefficient X = ( y/y)R7 , a more relevant term, is directly measured by SANS using random phase approximation study. It may be related to the square of the Hildebrand solubility parameter (d) difference which is an established criterion for polymer-polymer miscibility ... 

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]. 

From the point of view of the applicability of the iso-free-volume concept, it is of great interest to test it for some systems more complicated than simple polymeric liquids, despite the fact that, as we have already shown, this concept has failed in many cases even for simple polymers. The more complicated cases considered are compositions and polymeric blends and alloys. 

The activation energy of isothermal contraction in polymer blends calculated in 9 is considerably lower than for pure components, this pointing to the appearance of the free-volume as well, which facilitates the relaxation processes and diminishes the activation energy. 

The relationship between glass temperature and composition for different types of polymer blends may be established on the basis of Eq. (110). According to Hirai-Eiring theory20, the partial free-volume is... 

To discuss the phase stability of polymer blends in more detail one has to specify the free-energy parameter X. This can be done in terms of an equation-of-state theory [8]. Theories that take into account the compressible nature of the pure components as well as that of the mixture are called equation-of-state theories. As basic quantities characterizing the thermodynamic state of a system the reduced temperature (T), volume (V) and pressure (P) are employed and defined by... 

For a fixed strain rate, a comparison of Eq. (74) and experimental data [51, 52] of miscible blends is shown in Fig. 32. Curves 1 and 2 represent, respectively, the PPO/PS blends in compression, and the PPO/PS-pCIS blends in tension.Table 2 lists the three parameters fjf2, CK, and A/f2 used in curves 1 and 2. The unique feature here is the presence of a maximum yield (or strength) for 0 <

nonequilibrium interaction (A < 0). Such phenomenon does not occur in incompatible blends or composite systems. Table 2 also reveals that the frozen-in free volume fractions which are equal to 0.0243 and 0.0211 for polystyrene and for PPO, respectively. These are reasonable values for polymers in the glassy state. In the search for strong blends, we prefer to have —A/f2 > 1, and a larger difference between the yield stresses of blending polymers. 

Liu, J., Jean, Y.C., Yang, H. (1995) Free volume properties of polymer blends by positron annihilation spectroscopy Miscibility . Macromolecules. 28, 5774. 

The lattice fluid equation-of-state theory for polymers, polymer solutions, and polymer mixtures is a useful tool which can provide information on equa-tion-of-state properties, and also allows prediction of surface tension of polymers, phase stability of polymer blends, etc. [17-20]. The theory uses empty lattice sites to account for free volume, and therefore one may treat volume changes upon mixing, which are not possible in the Flory-Huggins theory. As a result, lower critical solution temperature (LCST) behaviors can, in principle, be described in polymer systems which interact chiefly through dispersion forces [17]. The equation-of-state theory involves characteristic parameters, p, v, and T, which have to be determined from experimental data. The least-squares fitting of density data as a function of temperature and pressure yields a set of parameters which best represent the data over the temperature and pressure ranges considered [21]. The method,however,requires tedious experiments to deter-... 

Despite the fact that the mixing entropy is small for polymer blends, it is always positive and hence promotes mixing. Mixtures with no difference in interaction energy between components are called ideal mixtures. Let us denote the volume fraction of component A by — and the corresponding volume fraction of component B becomes = 1 — The free energy of mixing per site for ideal mixtures is purely entropic ... 

Many properties of pure polymers (and of polymer solutions) can be estimated with group contributions (GC). Examples of properties for which (GC) methods have been developed are the density, the solubility parameter, the melting and glass transition temperatures, as well as the surface tension. Phase equilibria for polymer solutions and blends can also be estimated with GC methods, as we discuss in Section 16.4 and 16.5. Here we review the GC principle, and in the following sections we discuss estimation methods for the density and the solubility parameter. These two properties are relevant for many thermodynamic models used for polymers, e.g., the Hansen and Flory-Hug-gins models discussed in Section 16.3 and the free-volume activity coefficient models discussed in Section 16.4. 

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