Thermodynamics of Polymer Crystallization

The phase transition from disordered states of polymer melt or solutions to ordered crystals is called crystallization-, while the opposite process is called melting. Nowadays, more than two thirds of the global product volumes of synthetic polymer materials are crystallizable, mainly constituted by those large species, such as high density polyethylene (HOPE), isotactic polypropylene (iPP), linear low density polyethylene (LLDPE), PET and Nylon. Natural polymers such as cellulose, starch, silks and chitins are also semi-crystalUne materials. The crystalline state of polymers provides the necessary mechanical strength to the materials, and thus in nature it not only props up the towering trees, but also protects fragile lives. Therefore, polymer crystallization is a physical process of phase transition with important practical relevance. It controls the assembly of ordered crystalline structures from polymer chains, which determines the basic physical properties of crystalline polymer materials. 

The crystallization and melting behaviors of polymers are conventionally measured by the method of differential scanning calorimetry (DSC). One can obtain the heat flow or compensation power dQ/dt as a function of temperature, which is in principle proportional to the heat capacity of materials Cp and the scanning rate q, as given by 

As illustrated by the crossover point of the curves in Fig. 10. lb, the isobaric free energy change of the polymer bulk system at the melting point appears as 

One can see that, as illustrated in Fig. 10.1a, the practical Tc is always lower than The volume-temperature curves for crystallization/melting are roughly the same results. Such a hysteresis loop is an important feature of first-order phase transitions. If we make a reference to the melting point of infinitely large crystals, we can define the 

Liquid crystalline polymers exhibit mesophases with various degrees of ordering between the amorphous state and the crystalline state, i.e. the liquid crystalline 

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Simha, R., Jain, R. K., Statistical thermodynamics of polymer crystal and melt. Journal of Polymer Science, Polymer Physics Edition, 16(8), pp. 1471-1489 (1978). 

L. Jarecki Effects of molecular orientation on thermodynamics of polymer crystallization. PhD Thesis, Institute of Fundamental Technological Research, Warsaw (1974)... 

With the appearance of new experimental results about the kinetics and thermodynamics of polymer crystallization, the... 

Before concluding this section, there is one additional thermodynamic factor to be mentioned which also has the effect of lowering. Since we shall not describe the thermodynamics of polymer solutions until Chap. 8, a quantitative treatment is inappropriate at this point. However, some relationships familiar from the behavior of low molecular weight compounds may be borrowed for qualitative discussion. The specific effect we consider is that of chain ends. The position we take is that they are foreign species from the viewpoint of crystallization. 

Figure 3 illustrates the thermodynamic interplay of polymer crystallization and liquid-liquid demixing in polymer solutions. The liquid-liquid binodal curve is primarily determined by the B value. With the increase of Ep values, the liquid-liquid binodal curves shift slightly upward. On the other hand, the... 

The fascinating issues relating to polymer structures preceding crystallization are still largely open to investigation. More specific and articulated models of such states may provide a better understanding of polymer crystallization, both from the thermodynamic and the kinetic viewpoint. Furthermore, the different mechanisms that lead polymers to crystallize may eventually be understood in a coherent, more unified picture. 

Before addressing these fundamental questions, we present a brief review on phenomenology, classical thermodynamics, and kinetic models of polymer crystallization. Advances made recently (as of 2003) using molecular modeling are reviewed next. 

Polymers don t behave like the atoms or compounds that have been described in the previous sections. We saw in Chapter 1 that their crystalline structure is different from that of metals and ceramics, and we know that they can, in many cases, form amorphous structures just as easily as they crystallize. In addition, unlike metals and ceramics, whose thermodynamics can be adequately described in most cases with theories of mixing and compound formation, the thermodynamics of polymers involves solution thermodynamics—that is, the behavior of the polymer molecules in a liquid solvent. These factors contribute to a thermodynamic approach to describing polymer systems that is necessarily different from that for simple mixtures of metals and compounds. Rest assured that free energy will play an important role in these discussions, just as it has in previous sections, but we are now dealing with highly inhomogeneous systems that will require some new parameters. 

Figure 1 also shows that plasticized polyvinyl chloride begins to flow at a lower temperature. This is to be expected in view of the fact that equilibrium melting temperature of polymer crystals is depressed by monomeric diluents. A statistical thermodynamic treatment by Flory (13), showed that this effect depends on the nature of the polymer, concentration of the diluent, and the degree of polymer-diluent interaction in the following manner ... 

We have shown that mesoscopic non-equilibrium thermodynamics satisfactorily describes the dynamics of activated processes in general and that of polymer crystallization in particular. Identification of the different mesoscopic configurations of the system, when it irreversibly proceeds from the initial to the final phases, through a set of internal coordinates, and application of the scheme of non-equilibrium thermodynamics enable us to derive the non-linear kinetic laws governing the behavior of the system. 

This seemingly simple entropy-separation process has been widely adopted in the thermodynamic studies of polymer crystallization. Nevertheless, the hypothetical principle underlying Eqs. (7.13) and (7.14), in conjunction with the physical meaning of the y value at the transition point, has been controversial in the literature [Karasz etal., 1977 Wunderlich and Czornyj, 1977 Naoki and Tomomatsu, 1980 Wiirflinger,... 

Hu WB, Mathot VBF, Frenkel D (2003a) Lattice model study of the thermodynamic interplay of polymer crystallization and liquid-liquid demixing. J Chem Phys 118 10343-10348 Hu WB, Frenkel D, Mathot VBF (2003b) Sectorization of a lamellar polymer crystal studied by dynamic Monte Carlo simulations. Macromolecules 36 549-552 Hu WB, Frenkel D, Mathot VBF (2003c) Intramolecular nucleation model for polymer crystallization. Macromolecules 36 8178-8183... 

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