Statistical Thermodynamics of Polymer Solutions
Polymer chains spontaneously assemble together via phase separation or crystallization from the multi-component miscible systems. The mixing free energy of polymer-based miscible systems has been derived by the Flory-Huggins lattice statistical thermodyna
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Statistical Thermodynamics of Polymer Solutions
8.1
Polymer-Based Multi-Component Systems
Polymer-based multi-component systems can be classified into two categories: one is a miscible system, in which polymers are homogeneously mixed with other molecules; the other one is a composite system, in which polymers are not mixed with other molecules, except at interfaces. Polymer-based composite systems normally consist of a continuous matrix and a dispersed phase like particles. Polymers are the great candidates as matrix materials. In the case where the matrix is an inorganic material and the particles are polymeric materials, such a composite system is commonly regarded as an organic/inorganic hybrid. In the composite system, the dispersed particles may have a wide range of shapes and sizes, and play a dominant role in the functional enhancement of the matrix, although never mixed with the matrix in their thermal history, such as carbon black, liquid crystal droplets, high-strength fibers and their textiles, inorganic fillers, carbon nanotubes and graphines. The interface properties of composites are one of central issues in the investigation of high performance polymer composites. However, we hereby focus our attention mainly on the polymer-based miscible systems. The polymer-based miscible systems can be either intermolecular mixtures, for instance polymer solutions and blends, or intramolecular mixtures, such as block copolymers, star-shape multi-arm copolymers, grafted copolymers, random copolymers, and gradient copolymers with a composition gradient from one chain end to the other. Polymer-based miscible systems can phase separate into segregated phases with stable interfaces, or crystallize into crystalline ordered phases. In other words, there are two types of phase transitions, phase separation and crystallization. Under proper thermodynamic conditions, two phase transitions may occur simultaneously. The interplay of these two transitions will dictate the final morphology of the system. In the following, we will choose polymer solutions as typical examples to introduce the polymer-based miscible systems.
W. Hu, Polymer Physics, DOI 10.1007/978-3-7091-0670-9_8, # Springer-Verlag Wien 2013
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8 Statistical Thermodynamics of Polymer Solutions
Fig. 8.1 Illustration of typical phase diagrams of polymer solutions for (a) UCST phase separation, (b) crystallization, and (c) monotectic triple point formed by the interception of two phase diagrams
Polymer solutions display a typical phase diagram as illustrated in Fig. 8.1a, which exhibits a highest critical phase separation temperature, called upper critical solution temperature (UCST). Within the same temperature window, polymer solutions may also crystallize below the solution-crystal coexistence line, as illustrated in Fig. 8.1b. Two kinds of phase transitions will interplay with each other, so that an interception point is observed in the corresponding phase diagrams. The interception point is a three-phase-coexisting point, as illustrated in Fig. 8
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