Crystallization rate determination

The overall crystallization rate, determined after self-nucleation, decreases with decreasing PA6 droplet size (20-1 pm), indicating the disturbing effect of the small dimensions of the micrometer-sized PA6 particles. 

Avrami exponent Crystal geometry Nucleation mode Rate determination Equation ... 

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). 

In this reaction sequence, equation 47, the formation of the complex ion, Zn(OH)3, is the rate determining step. Once the solubiUty of 2incate, Zn(OH), is exceeded, 2inc hydroxide [20427-58-17, Zn(OH)2, precipitates. The crystal form that falls out of solution depends on the concentration of the alkah. 

In addition to induction time measurements, several other methods have been proposed for determination of bulk crystallization kinetics since they are often considered appropriate for design purposes, either growth and nucleation separately or simultaneously, from both batch and continuous crystallization. Additionally, Mullin (2001) also describes methods for single crystal growth rate determination. 

The nucleation rate onto a crystal is determined by the flux onto an ensemble of substrates. As the nuclei should be widely separated for the nucleation approach to be valid, this does not appear to be unreasonable. However, the subsequent way in which this flux is used to determine the thickness and growth rate seems somewhat inconsistent as explained below. However, a modification of the derivations would satisfy this query, and it is not likely that this will greatly affect the results. 

Thirdly, the multicomponent model was applied to the case of crystallization of a random A-B copolymer by Helfand and Lauritzen [127]. Their main result is that the composition of, 4 s and B s in the crystal is determined by kinetic, rather than equilibrium considerations the inclusion of excess B increases with growth rate. 

Pai Vemeker and Kannan [1273] observe that data for the decomposition of BaN6 single crystals fit the Avrami—Erofe ev equation [eqn. (6), n = 3] for 0.05 < a < 0.90. Arrhenius plots (393—463 K) showed a discontinuous rise in E value from 96 to 154 kJ mole-1 at a temperature that varied with type and concentration of dopant present Na+ and CO2-impurities increased the transition temperature and sensitized the rate, whereas Al3+ caused the opposite effects. It is concluded, on the basis of these and other observations, that the rate-determining step in BaN6 decomposition is diffusion of Ba2+ interstitial ions rather than a process involving electron transfer. 

It is important to realize that the assumption of a rate-determining step limits the scope of our description. As with the steady state approximation, it is not possible to describe transients in the quasi-equilibrium model. In addition, the rate-determining step in the mechanism might shift to a different step if the reaction conditions change, e.g. if the partial pressure of a gas changes markedly. For a surface science study of the reaction A -i- B in an ultrahigh vacuum chamber with a single crystal as the catalyst, the partial pressures of A and B may be so small that the rates of adsorption become smaller than the rate of the surface reaction. 

The rate-determinating step in reaction (45) is second order, illustrating that Lewis acid-base interactions are involved in this process. Eqs. (43)-(45) are similar to reactions (36) and (37) since the tin(II) compounds formed are highly associated (tin(II) chloride and tin(II) sulfide can be isolated as pure and large crystals), the equilibrium is shifted to the right side. 

In fact, by fractional precipitation we found that the fractions with the highest molecular weights are sterically very uniform and contain more than 97 % of cis-1,4 double bonds (Table IV). Lower molecular weight fractions, on the other hand, have relatively high trans-1,4 contents. We therefore take the view that the rate of crystallization is determined mainly by the high molecular weight fractions. 

Dislocation motion in covalent crystals is thermally activated at temperatures above the Einstein (Debye) temperature. The activation energies are well-defined, and the velocities are approximately proportional to the applied stresses (Sumino, 1989). These facts indicate that the rate determining process is localized to atomic dimensions. Dislocation lines do not move concertedly. Instead, sharp kinks form along their lengths, and as these kinks move so do the lines. The kinks are localized at individual chemical bonds that cross the glide plane (Figure 5.8). 

Rate and equilibrium constant data, including substituent and isotope effects, for the reaction of [Pt(bpy)2]2+ with hydroxide, are all consistent with, and interpreted in terms of, reversible addition of the hydroxide to the coordinated 2,2 -bipyridyl (397). Equilibrium constants for addition of hydroxide to a series of platinum(II)-diimine cations [Pt(diimine)2]2+, the diimines being 2,2 -bipyridyl, 2,2 -bipyrazine, 3,3 -bipyridazine, and 2,2 -bipyrimidine, suggest that hydroxide adds at the 6 position of the coordinated ligand (398). Support for this covalent hydration mechanism for hydroxide attack at coordinated diimines comes from crystal structure determinations of binuclear mixed valence copper(I)/copper(II) complexes of 2-hydroxylated 1,10-phenanthroline and 2,2 -bipyridyl (399). 

The rate of an electrode reaction is a function of three principle types of species charge carriers on the surface, active surface atoms and reactant species in the solution as illustrated in Figure 23. That is, r cc [h] [Siactive] [A]. Carrier concentration and reactant concentration do not, in general, depend on surface orientation while active surface atoms may be a function of surface orientation. Anisotropic effect occurs when the rate determining step depends on the active surface atoms that vary with crystal orientation of the surface. On the other hand, reactions are isotropic when the concentration of active surface atoms is not a function of surface orientation or when the rate determining step does not involve active surface atoms. 

It is of course important to note that the overall rate of crystallization is not only determined by the growth rate of the spherulites, but also by the amount of nuclei being present in the system. This possibility is used as an effective method to influence the total crystallization rate of commercial polymeric materials in a controlled manner and to influence the size of spherulites and thus the physical properties of finished articles made from semicrystalline polymers. 

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