Semicrystalline polymers thermodynamics

The crystallization process of flexible long-chain molecules is rarely if ever complete. The transition from the entangled liquid-like state where individual chains adopt the random coil conformation, to the crystalline or ordered state, is mainly driven by kinetic rather than thermodynamic factors. During the course of this transition the molecules are unable to fully disentangle, and in the final state liquid-like regions coexist with well-ordered crystalline ones. The fact that solid- (crystalline) and liquid-like (amorphous) regions coexist at temperatures below equilibrium is a violation of Gibb s phase rule. Consequently, a metastable polycrystalline, partially ordered system is the one that actually develops. Semicrystalline polymers are crystalline systems well removed from equilibrium. 

PVDF is among the few semicrystalline polymers that exhibit thermodynamic compatibility with other polymers,80 in particular with acrylic or methacrylic resins.81 The morphology, properties, and performance of these blends depend on the structure and composition of the additive polymer, as well as on the particular PVDF resin. These aspects have been studied and are reported in some detail in Reference 82. For example, polyethyl acrylate is miscible with polyvinylidene fluoride, but polyisopropyl acrylate and homologues are not. Strong dipolar interactions are important to achieve miscibility with PVDF, as suggested by the observation that polyvinyl fluoride is incompatible with polyvinylidene fluoride.83... 

Brockmeier, N. F. McCoy, R. W. Meyer, J. A., "Gas Chromatographic Determination of Thermodynamic Properties of Polymer Solutions. II. Semicrystalline Polymer Systems," Macromolecules, 6, 176 (1973). 

SPECIFIC HEAT AND RELATED THERMODYNAMIC PROPERTIES OF SEMICRYSTALLINE POLYMERS. 

The crystallization of blends tends to depend on the level of mutual miscibility of the components. In miscible blends, the general result is that suppression or otherwise of crystallization with miscibility is dependent on the relative glass transition temperatures of both phases [33, 34]. For example, in a blend of an amorphous and semicrystalline polymer, if the amorphous material has the higher Tg, the miscible blend will also have a higher Tg than that of the semicrystalline homopolymer and, at a given temperature, the mobility and thus the efficacy of the semicrystalline phase molecules to crystallize is reduced. The converse is often true if the amorphous phase has a lower glass transition. Effects such as chemical interactions and other thermodynamic considerations also play a role and the depression of the melting point in a miscible blend can be used to determine the Flory interaction parameter x [40]. 

Some transitions that are only known for macromolecules, however, will not be mentioned at all since they are covered elsewhere in this Encyclopedia (see, eg. Gel Point). Also we shall not be concerned here with the transformations from the molten state to the solid state of polymeric materials, since this is the subject of separate treatments (see Crystallization Kinetics Glass Transition Viscoelasticity). Unlike other materials, polymers in the solid state rarely reach full thermal equilibrium. Of course, all amorphous materials can be considered as frozen fluids (see Glass Transition) Rather perfect crystals exist for metals, oxides, semiconductors etc, whereas polymers typically are semicrystalline, where amorphous regions alternate with crystalline lamellae, and the detailed structure and properties are history-dependent (see Semicrystalline Polymers). Such out-of-equilibrium aspects are out of the scope of the present article, which rather emphasizes general facts of the statistical thermodynamics (qv) of phase transitions and their applications to polymers in fluid phases. 

To determine crystallinity in a semicrystalline polymer, diffraction, thermodynamic, and spectroscopic methods can be used. Diffraction method is mainly used with waxd methods. Thermodynamic methods include dilatometiy, differential scanning calorimetry (dsc), etc, while ir and nuclear magnetic resonance (nmr), and other spectroscopic methods can also be used. 

Thermodynamic approaches provide powerfiil tools to characterize the properties in identifying these metastable states to imderstand the effects of phase size, dimensionality, and composition on the materials properties. One well-known example is the density gradient column method to determine densities of semicrystalline polymers. Based on known equilibrium crystalhne and amorphous densities, the crystallinity of a semicrystalline sample can be calculated by using equations 4 and 5. However, it should be noted that the determination of these equilibrium density data is not trivial. Proper extrapolations are necessary to ensure the equilibrium nature of the results. Detailed issues discussed can be foimd in Reference 146. Another commonly used method is to measure the heat of crystallization or fusion by using dsc. By knowing the equilibrium heat of fusion, the crystallinity of a sample can be easily calculated. 

For many years, the thermodynamic description of macromolecules lagged behind other materials because of the unique tendency of pol5nneric systems to assume nonequilibrium states. Most standard sources of thermodynamic data are, thus, almost devoid of polymer information (1-7). Much of the aversion to include polymer data in standard reference sources can be traced to their nonequilibrium nature. In the meantime, polymer scientists have learned to recognize equilibrium states and utilize nonequilibrium states to explore the history of samples. For a nonequilibrium sample it is possible, for example, to thermally establish how it was transferred into the solid state (determination of the thermal and mechanical history). More recently, it was discovered with the use of temperature-modulated differential scanning calorimetry (TMDSC) that within the global, nonequilibrium structure of semicrystalline polymers, locally reversible melting and crystallization processes are possible on a nanophase level (8). 

Amorphous polymers (transparent in the solid state to be precise, it is not a solid but rather a supercooled liquid) are usually easy to dissolve in the good solvent. In contrast, crystalline and semicrystalline polymers (opaque in the solid state) are sometimes not easy to dissolve. Within a crystallite, polymer chains are folded into a regular, thermodynamically stable arrangement. It is not easy to unfold the chain from the self-locked state into a disordered state in solution even if the latter state is thermodynamically more stable. Heating may help the dissolution because it facilitates the unfolding. Once dissolved, polymer chains take a random-coil conformation unless the chain is rigid. 

The basic thermodynamic, kinetic, and structural principles which govern the crystallization behavior of polymers have been developed so far. These principles can now be applied to give an understanding of the properties of semicrystalline polymers. There is a continuing interest in understanding the properties of crystalline polymers in terms of structure. Because of the non-equilibrium character of the... 

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