Kinetic crystallinity

In the entire chapter, a strong emphasis has been put on sparingly soluble, rapid kinetics crystalline materials because the authors felt that this domain of the reactive crystallization spectrum is the most representative for precipitation as well as distinct from other crystallization processes. 

Bonartsev, A. R et al. Hydrolytic degradation of poly(3-hydroxybutyrate),polylactide and their derivatives kinetics, crystallinity, and surface morphology. Mole. Cryst. Liquid Cryst 2012, 556(1), 288-300. 

Figure 7.9 Crystallization kinetics (crystallinity vs. time) for HNA/0.73PHB at 232°C, wt% PLC is shown. (Permission granted for reproduction of D. Melot and W.J. MacKnight (1992) Polymer Adv. Technol, 3, 382. Copyright John Wiley and Sons Ltd.)...

The latter is also called the kinetic crystallinity that can be measured by tracing the crystallization process with dilatometer, depolarized light intensity, dynamic X-ray diffraction and DSC. Polymer crystallization is a volume-contraction process. When the dilatometer is used to measure the change of the sample volume with time evolution at a constant crystallization temperature, one obtains the relative crystallinity as... 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

Many different approaches have been suggested as possible approaches to this problem, from the 1960s onwards [Verwer and Leusen 1998]. What is obvious from all of these ellorts is that this is an extremely difficult problem. Both thermodynamics and kinetics can be important in determining which crystalline form is obtained under a certain se1 of experimental conditions. Kinetic effects are particularly difficult to take into accouni and so are usually ignored. A proper treatment of the thermodynamic factors would lequire one to deal with the relative free energies of the different possible polymorphs... 

Some of the distinctions that we shall have to examine in more detail before proceeding much further are the considerations of order versus disorder, solid versus liquid, and thermodynamics versus kinetics. These dualities are taken up in the next section. With those distinctions as background, we shall examine both the glassy and crystalline states from both the experimental and modelistic viewpoint. 

In order to carry out an experimental study of the kinetics of crystallization, it is first necessary to be able to measure the fraction d of polymer crystallized. While this is necessary, it is not sufficient we must also be able to follow changes in the fraction of crystallinity with time. So far in this chapter we have said nothing about the experimental aspects of determining 6. We shall now briefly rectify this situation by citing some of the methods for determining 6. It must be remembered that not all of these techniques will be suitable for kinetic studies. 

A wide variety of guest molecules may be trapped by the Wemer-type crystalline host lattice, ranging, eg, from noble gases to condensed aromatic hydrocarbons. These clathrates may be formed from solution or by sorption. Kinetics of sorption—desorption have been studied (83). 

More recently, Raman spectroscopy has been used to investigate the vibrational spectroscopy of polymer Hquid crystals (46) (see Liquid crystalline materials), the kinetics of polymerization (47) (see Kinetic measurements), synthetic polymers and mbbers (48), and stress and strain in fibers and composites (49) (see Composite materials). The relationship between Raman spectra and the stmcture of conjugated and conducting polymers has been reviewed (50,51). In addition, a general review of ft-Raman studies of polymers has been pubUshed (52). 

Under equiUbrium vapor pressure of water, the crystalline tfihydroxides, Al(OH)2 convert to oxide—hydroxides at above 100°C (9,10). Below 280°—300°C, boehmite is the prevailing phase, unless diaspore seed is present. Although spontaneous nucleation of diaspore requires temperatures in excess of 300 °C and 20 MPa (200 bar) pressure, growth on seed crystals occurs at temperatures as low as 180 °C. For this reason it has been suggested that boehmite is the metastable phase although its formation is kinetically favored at lower temperatures and pressures. The ultimate conversion of the hydroxides to comndum [1302-74-5] AI2O2, the final oxide form, occurs above 360°C and 20 MPa. 

A crystalline or semicrystalline state in polymers can be induced by thermal changes from a melt or from a glass, by strain, by organic vapors, or by Hquid solvents (40). Polymer crystallization can also be induced by compressed (or supercritical) gases, such as CO2 (41). The plasticization of a polymer by CO2 can increase the polymer segmental motions so that crystallization is kinetically possible. Because the amount of gas (or fluid) sorbed into the polymer is a dkect function of the pressure, the rate and extent of crystallization may be controUed by controlling the supercritical fluid pressure. As a result of this abiHty to induce crystallization, a history effect may be introduced into polymers. This can be an important consideration for polymer processing and gas permeation membranes. 

The a-form, which crystallines as the kinetic product, is the commercial form of ammonium pentaborate tetrahydrate and the P-form is the thermodynamic product but is slow to crystalline. Its heat capacity has been measured over a broad temperature range (85). Solubihty data are given ia Table 9 and pH data ia Table 10. 

Another matrix diffusional implant consists of an outer layer of micronized, crystalline 17P-estradiol dispersed in siUcone mbber over a nonmedicated, cylindrical siUcone mbber core. The system, implanted subcutaneously in the ears of cattie, releases estradiol for up to 400 days with kinetics to improve growth rate and feed efficiency (83). 

Effects of Impurities nd Solvent. The presence of impurities usually decreases the growth rates of crystalline materials, and problems associated with the production of crystals smaller than desired are commonly attributed to contamination of feed solutions. Strict protocols should be followed in operating units upstream from a crystallizer to minimize the possibiUty of such occurrences. Equally important is monitoring the composition of recycle streams so as to detect possible accumulation of impurities. Furthermore, crystalliza tion kinetics used in scaleup should be obtained from experiments on solutions as similar as possible to those expected in the full-scale process. 

The use of water as a co-catalyst in Ziegler-type polymerizations was first introduced in 1962 (47). The reaction kinetics and crystallinity of the resulting polymers measured by x-ray scattering has been studied (48—51). 

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

In chemicals like salol the molecules are elongated (non-spherical) and a lot of energy is needed to rotate the randomly arranged liquid molecules into the specific orientations that they take up in the crystalline solid. Then q is large, is small, and the interface is very sluggish. There is plenty of time for latent heat to flow away from the interface, and its temperature is hardly affected. The solidification of salol is therefore interface controlled the process is governed almost entirely by the kinetics of molecular diffusion at the interface. 

A well-known example of this time-temperature equivalence is the steady-state creep of a crystalline metal or ceramic, where it follows immediately from the kinetics of thermal activation (Chapter 6). At a constant stress o the creep rate varies with temperature as... 

It is one of the wonders of the history of physics that a rigorous theory of the behaviour of a chaotic assembly of molecules - a gas - preceded by several decades the experimental uncovering of the structure of regular, crystalline solids. Attempts to create a kinetic theory of gases go all the way back to the Swiss mathematician, Daniel Bernouilli, in 1738, followed by John Herapath in 1820 and John James Waterston in 1845. But it fell to the great James Clerk Maxwell in the 1860s to take... 

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