Equilibrium crystals, first-order transitions

As with liquid crystals (Sect. 5.1.2), only the equilibrium transition to the fully ordered crystal and the transition to the isotropic melt have been studied extensively16c 102). Both transitions are of the first order transition type, similar to that shown in Fig. 1. A series of transition data are collected in Table 7. Plastic crystals with motifs as small as... 

A simple analysis of an irreversible first-order transition is the cold crystallization, defined in Sect 3.5.5. For polymers, crystallization on heating from the glassy state may be so far from equilibrium that the temperature modulation will have little effect on its rate, as seen in Fig. 4.122. The modeling of the measurement of heat capacity in the presence of large, irreversible heat flows in Fig. 4.102, and irreversible melting in Figs. 3.89 and 4.123, document this capability of TMDSC to separate irreversible and reversible effects. Little needs to be added to this important application. 

Crystallization, one of the two first-order transitions encountered in the thermal analysis of polymers, is a process in which a material from the amorphous state is transformed into the crystalline state from either solution or the melt. Crystallization of macromolecules is different from the crystallization of low-molecular-mass materials. First, similar to the melting process, it takes place at conditions far from equilibrium. When compared to low-molecular-mass substances, the crystallization process of polymers is much slower because of the lower mobility of the polymer chain segments therefore in nonisother-mal conditions this process takes place over much wider temperature ranges. Crystallization of low-molecular-mass materials is mentioned here very briefly, and only for the purpose of comparison with macromolecules. 

For liquid crystals of small molecules only the equilibrium transitions have received attention (left side of Fig. 3). In addition to the basic transitions indicated in Fig. 2, the polymorphic transitions have to be added which normally are also first order... 

Figure 4. Schematic showing a hysteresis loop for the CdSe nanociystals with the smearing of the thermodynamic transition pressure caused by the finite nature of the nanocrystal particle. The thermodynamic transition pressure is offset from the hysteresis center to emphasize that in first-order solid-solid transformations, this pressure is unlikely to be precisely centered. The lower plot shows the estimated smearing for CdSe nanocrystals as inversely proportional to the number of atoms in the crystal, at two temperatures, as discussed in the text. Note that nanocrystals are not ordinarily synAesized or studied in sizes smaller than 20 A in diameter. This figure shows that this thermal smearing is insignificant compared to the large hysteresis width in the CdSe nanociystals studied (25-130 A in diameter), such that the transition is bulk-like from this perspective. This means that observed transformations occur at pressures far from equilibrium, where there is little probability of back reaction to the metastable state once a nanociystal has transformed. In much smaller crystals or with larger temperatures, the smearing could become on the order of the hysteresis width, and the crystals would transform from one stmcture to the other at thermal equilibrium.

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