Temperature dependence, polymer crystal

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 The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...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 ... 

The crystalline phase typically grows as spherical aggregates called spherulites. However, other geometries such as disks or rods may be found with, as shown below, a consequent modification of the rate equation. M. Avrami [26] first derived these rate equations in the form used for polymer kinetics for the solidification of metals. The weight of the crystalline phase is calculated as a function of time at constant temperature. As will be described below, the temperature dependence of crystallization can be derived from classical nucleation theory. 

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)... 

Other crystallization parameters have been determined for some of the polymers. The dependence of the melting temperature on the crystallization temperature for the orthorhombic form of POX (T = 323K) and both monoclinic (T = 348K) and orthorhombic (T = 329K) modifications of PDMOX has been determined (284). The enthalpy of fusion, Aff, for the same polymers has been determined by the polymer diluent method and by calorimetry at different levels of crystallinity (284). for POX was found to be 150.9 J/g (36.1 cal/g) for the dimethyl derivative, it ranged from 85.6 to 107.0 J/g (20.5—25.6 cal/g). Numerous crystal stmcture studies have been made (285—292). Isothermal crystallization rates of POX from the melt have been determined from 19 to —50 C (293,294). Similar studies have been made for PDMOX from 22 to 44°C (295,296). 

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... 

The polymer crystallization depends sensitively on the temperature Tc at which it occurs, more precisely on the degree of undercooling A T=Tm-Tc below the melting temperature Tm. Since we have to estimate Tm, at least roughly, of our lamellar crystal model, we first study the melting process of a lamella during the temperature increase at a constant rate. 

The second consideration, anticipated in Sect. 3.1, is that whereas Sm and Sc increase little with temperature (see Fig. 8) so that in the literature the temperature dependence of Gc and Gm is often approximated by straight lines, Sl varies moderately up to the glass transition temperature Tg but will increase substantially between Tg and the isotropization temperature. The behavior of Sl is due to the fact that, as the temperature increases, polymer chains are progressively more likely to bend sharply in the melt, whereas they are forced to remain straight in the mesophase and in crystals. The downward curvature of Gl in Fig. 8 shifts to lower temperatures with inherently more flexible chains. With very flexible polymers Tml becomes therefore smaller than the crystal-melting temperature Tcl and a stable mesophase cannot form. 

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