Separation, thermodynamics of phase

When the phase separation occurs, the curve of Af versus 02 exhibits a common tangent line at two points of A and B, as illustrated in Fig. 9.1b. This implies that at A and B states, 

The common tangent rule above is the thermodynamic condition for the equilibrium between A and B phases. The temperature dependence of the concentrations at A and B states outlines the phase coexistence curve, which is called the binodal line. 

When temperature is high enough, A and B points will merge at the critical point of phase separation. The thermodynamic condition for the critical point is that partial derivatives of both the first and the second orders for the free energy with respect to the concentration are equal to zero. From 

Solve the above three simultaneous equations, we can obtain 

For a symmetric polymer blend, two components share the same molecular weights, i.e., r =V2 = r, and the critical point becomes 

This section will present the theoretical framework and understanding about the thermodynamics of phase separation in block copolymers. Most theories consider four factors that influence the phase separation of block copoly- 

The interfacial thickness (r) was predicted to be approximately equal to the following  

Numerous studies were completed on block copolymers in the SSL long before a theory of the detail inherent in the Helfand and Wasserman approach 

Leibler s theory outlined an experimental method for testing its conclusions. The structure factor for scattering of radiation by the disordered phase was given by  

FIGURE 15 Comparison of 1/SANS peak intensity vs. inverse temperature for PEP-PEE diblock copolymer and comparison to theory. 

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In this chapter, synthesis of segmented copolymers and the thermodynamics of phase separation will be discussed briefly. The main focus, however, summarizes recent research activities in the study of structure-property relationships of these segmented copolymers. 

PNDB occurs for blends that are miscible only within a small range of concentration. To understand these systems, the interaction between the flow and the phase separation must be considered. This has become an area of considerable scientific activity. One needs to consider both how the phase separation influences the rheological behavior and how the flow (or stress) affects the thermodynamics of phase separation. 

Cartoons that illustrate the two principal tjfpes of IPN are given in Figure 1.38. The properties of the IPN and the morphology that results are governed by the kinetics and thermodynamics of phase separation. 

Many aspects of the formation of symmetric or asymmetric membranes can be rationalized by applying the basic thermodynamic and kinetic relations of phase separation. There are, however, other parameters-such as surface tension, polymer relaxation, sol and gel structures-which are not directly related to the thermodynamics of phase separation but which will have a strong effect on membrane structures and properties. A mathematical treatment of the formation of porous structures is difficult. But many aspects of membrane structures and the effect of various preparation parameters Can be qualitatively interpreted. 

With moderate compatibility, intermediate and complex phase behavior results. Thus IPNs with dispersed phase domains have been reported ranging from a few micrometers (the largest) to a few hundred nanometers (intermediate) to those without a resolvable domain structure (complete mixing). With highly incompatible polymers, on the other hand, the thermodynamics of phase separation is so powerful that it occurs before it can be prevented by cross-linking. 

However, understanding the thermodynamics of phase separation in liquid crystalline block copolymers is in its infancy. The morphology of such block copolymers will be influenced by the competition between... 

This chapter summarizes the thermodynamics of multicomponent polymer systems, with special emphasis on polymer blends and mixtures. After a brief introduction of the relevant thermodynamic principles - laws of thermodynamics, definitions, and interrelations of thermodynamic variables and potentials - selected theories of liquid and polymer mixtures are provided Specifically, both lattice theories (such as the Hory-Huggins model. Equation of State theories, and the gas-lattice models) and ojf-lattice theories (such as the strong interaction model, heat of mixing approaches, and solubility parameter models) are discussed and compared. Model parameters are also tabulated for the each theory for common or representative polymer blends. In the second half of this chapter, the thermodynamics of phase separation are discussed, and experimental methods - for determining phase diagrams or for quantifying the theoretical model parameters - are mentioned. 

Using thermal analytical techniques, the range over which a polymer melts can readily be defined for various thermal histories, i.e. the rate of heating, the crystallization temperature, etc. Thermal history has an important ect since the melting point is determined by kinetic parameters and the thermodynamics of phase separation, and is not a unique parameter of the crystalline polymer. 

CAB Cabezas, H., Kabiri-Badr, M., and Szlag, F.C., Statistical thermodynamics of phase separation and ion partitioning in aqueous two-phase systems. Bioseparation, 1, 227, 1990. 

Ronca G, Russell TP (1985) Thermodynamics of phase separation in polymer mixtures. 

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