Thermodynamics of polymer blends

A necessary condition for two polymers to form a miscible blend is that the free energy of mixing, should be less than zero, where AG i is given by the following equation  

Simply having a negative free energy of mixing does not guarantee phase stability. The necessary condition for phase stability in a blend composition x at a fixed temperature and pressure is that the second derivative of the free energy with respect to composition is greater than zero, i.e., 

Without satisfaction of this condition, the miscible system is thermodynamically unstable and phase separation will occur. 

One of the most common models for treating the free energy of mixing in polymer blends is the Flory-Huggins treatment. That model assumes that 

Based on the rigid conformation of many high temperature polymers, it is expected that the criteria for miscibility of such polymers will be even stricter than for random coil polymers. However, several high temperature miscible polymer blends have been discovered and reported in the litera-ture2-6. 2-i6 Yvhich are based on poly(2,2 (m-phenylene)-5-5 bibenzimidazole) (FBI), the chemical structure of which is shown in Fig. 1.1. Chapter 7 

National Research Council Canada, Industrial Materials Institute, Boucherville, QC, Canada 

Performance of polymer blends depends on the properties of polymeric components, as well as how they are arranged in space. The spatial arrangement is controlled by the thermodynamics and flow-imposed morphology. The word thermodynamics invariably brings to mind miscibility. However, thermodynamics has a broader use for the practitioners of polymer science and technology than predicting miscibility. The aim of this chapter is to describe how to measure, interpret, and predict the thermodynamic properties of polymer blends, as well as where to find the required information and/or the numerical values. 

For these reasons, there is a tendency to use low molecular homologues or solutions. Furthermore, it is an accepted practice to purify the polymers before measuring their thermodynamic properties. However, the industrial polymers have high molecular weights, and are modified by incorporating low molecular weight additives. Furthermore they are processed under high flow rates and stresses that preclude the possibility of thermodynamic equilibrium. For these and other reasons, a direct application of the laboratory data to industrial systems may not always be advisable. 

For convenience, the thermodynamic systems are assumed closed, isolated from the surroundings. The laws that govern such systems are written in terms of two types of variables the intensive 

Combinatorial entropy Comb That part that originates from the number of possible 

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Balsara NP (1996) Thermodynamics of polymer blends. In Mark JE (ed) Physical properties of polymers handbook. AIP Press, New York, p 257... 

Y.S. Lipatov, A.E. Nesterov, Thermodynamics of polymer blends, Lancaster-Basel, Technomic, 1997. 

Balsara, N. P. Thermodynamics of polymer blends In Physical Properties of Polymers Handbook, ed. J. E. Mark (AIP Press, 1996). 

Three theoretical approaches to the thermodynamics of polymer blends were briefly discussed (1) the lattice theories, including the newer equation of state theories, (2) of-lattice theories, and... 

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