Temperature of Polymer Crystals

Recalling that the free energy of a crystal lamella is given by Equation 10-44 (we told you we d get back to this)  

FIGURE 10-41 Schematic diagram showing the effect of crystallization temperature on the melting point. 

This also explains why polymers melt over a broad range of temperatures. Samples 

FIGURE 10-42 Schematic graph of fold period versus temperature. 

---

Fig. 17 B/E-p dependence of the critical temperatures of liquid-liquid demixing (dashed line) and the equilibrium melting temperatures of polymer crystals (solid line) for 512-mers at the critical concentrations, predicted by the mean-field lattice theory of polymer solutions. The triangles denote Tcol and the circles denote T cry both are obtained from the onset of phase transitions in the simulations of the dynamic cooling processes of a single 512-mer. The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

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 ... 

Determination of the equilibrium melting temperature of polymer crystals linear and nonlinear Hofiman-Weeks extrapolations. Macromolecules, 31, 8219-8229. 

F igiire 6.1. Temperature dependence of Apicr nd Api, (o), concentration dependence of AGm for solution (the single-phase state) (6), and the dependence of the melting temperature of polymer crystals on polymer concentration in solution (the liquidus curve) (c) (Schematic)... 

Thermodynamic Equilibrium Melting Temperature of Polymer Crystals... 

Lovell R, Mitchell GR, Windle A (1979) Wide-angle X-ray scattering study of structural parameters in non-crystalline polymers. Faraday Discuss Chcm Soc 68 46-57 Maraud H, Xu JN, Srinivas S (1998) Determination of the equilibrium melting temperature of polymer crystals Linear and nonlinear Hoffinan-Weeks extrapolatimis. Macromolecules... 

Ivanov, D.A. and Magonov, S.N., Atomic Force Microscopy Studies of Semicrystalline Polymers at Variable Temperature, in Polymer Crystallization Observations, Concepts and Interpretations, Sommer, J.-U. and Reiter, G., Eds., Springer, Heidelberg, Germany, 2003, chap. 7. 

Abstract In this review, we consider a variety of aspects of polymer crystallization using a very simple lattice model. This model has three ingredients that give it the necessary flexibility to account for many features of polymer crystallization that have been observed experimentally. These ingredients are (1) a difference in attraction between neighboring (nonbonded) components, (2) attraction between parallel bonds, and (3) temperature-dependent flexibility due to the energy cost associated with kinks in the... 

Fig. 1 Melting temperatures of polymers k%Tm/Ec) with variable Ev/Ec values. The line is calculated from Eq. 10 and the circles are the simulation results obtained from the onset of crystallization on the cooling curves of disorder parameters, in a short-chain (r = 32) system (occupation density is 0.9375 in a 32-sized cubic box) with a template substrate (Hu and Frenkel, unpublished results)...

In the classical Lauritzen-Hoffman theory for the mechanism of polymer crystal growth [106], it is assumed that the observed lamellar thickness corresponds to those crystallites that happen to have the largest growth velocity. However, this picture is hard to reconcile with the experimental observation that the thickness of polyethylene single crystals can be modulated by varying the temperature at which they are grown [117,118]. In fact, simulations by Doye et al. [119,120] suggest that the observed lamellar thickness does... 

Finally, we were led to the last stage of research where we treated the crystallization from the melt in multiple chain systems [22-24]. In most cases, we considered relatively short chains made of 100 beads they were designed to be mobile and slightly stiff to accelerate crystallization. We could then observe the steady-state growth of chain-folded lamellae, and we discussed the growth rate vs. crystallization temperature. We also examined the molecular trajectories at the growth front. In addition, we also studied the spontaneous formation of fiber structures from an oriented amorphous state [25]. In this chapter of the book, we review our researches, which have been performed over the last seven years. We want to emphasize the potential power of the molecular simulation in the studies of polymer crystallization. 

With decreasing temperature, the density oscillation becomes very pronounced and grows into a deeper melt region. At 300 K, for example, we can see at least 5 layers after 1.28 ns. Within the layers, as will be shown later, definite order in chain orientation and chain packing is observed suggesting the growth of polymer crystals. 

On the basis of the concept described above, we propose a model for the homogeneous crystallization mechanism of one component polymers, which is schematically shown in Fig. 31. When the crystallization temperature is in the coexistence region above the binodal temperature Tb, crystal nucleation occurs directly from the melt, which is the well-known mechanism of polymer crystal nucleation. However, the rate of crystallization from the coexistence region is considered to be extremely slow, resulting in single crystals in the melt matrix. Crystallization at a greater rate always involves phase separation the quench below Tb causes phase separations. The most popular case... 

Fig. 31 Structural formation model for the initial stage of polymer crystallization [19], N G nucleation and growth of oriented domains, SD spinodal decomposition into oriented and unoriented domains, Tb, Ts, and Tx bimodal, spinodal, and crystallization temperatures, respectively I isotropic, N smectic, and C crystalline...

Crystallization of PCT is relatively rapid, but because of its higher Tg (90 °C) the maximum rate of crystallization occurs at a higher temperature than is typical of other crystalline polymers such as PET (Tg at about 70 °C) or PBT (Tg at about 35 °C). Figure 7.2 compares the crystallization half-times of PET and PCT from both the glass and the melt (data were obtained via DSC measurements). The effect of the higher Tg on the temperature of maximum crystallization rate (i.e. minimum half-time) is most clearly seen in the data from the melt. The basic rapid crystallization rate of PCT allows it to be used as a high-performance injection molding material. 

The results (Table I) show that at a given temperature the polymers crystallize faster with increasing amounts of plasticizer. 

---