Nucleation control

A larger number of smaller spherulites are produced at larger undercoolings, a situation suggesting nucleation control. Various details of the Maltese cross pattern, such as the presence or absence of banding, may also depend on the temperature of crystallization. 

Fig. 3.3. Growth rate versus supercooling for two different face orientations. T is above its roughening temperature and is approximately linear. 2 is below its roughening temperature and is nucleation controlled at low supercooling but the growth rapidly increases after kinetic roughening...

The growth rate of a nucleation-controlled face can be expressed, within certain limits, in terms of i and g without their explicit evaluation. The first limit we shall consider is that of large g so that a nucleus, having formed, spreads rapidly to cover the substrate before another nucleation event occurs, see Fig. 3.5 a. If the substrate has a width L, then the rate of nucleation is iL and the growth rate is given by ... 

Although specific calculations for i and g are not made until Sect. 3.5 onwards, the mere postulate of nucleation controlled growth predicts certain qualitative features of behaviour, which we now investigate further. First the effect of the concentration of the polymer in solution is addressed - apparently the theory above fails to predict the observed concentration dependence. Several modifications of the model allow agreement to be reached. There should also be some effect of the crystal size on the observed growth rates because of the factor L in Eq. (3.17). This size dependence is not seen and we discuss the validity of the explanations to account for this defect. Next we look at twin crystals and any implications that their behaviour contain for the applicability of nucleation theories. Finally we briefly discuss the role of fluctuations in the spreading process which, as mentioned above, are neglected by the present treatment. 

Bishop MF, Ferrone FA. Kinetics of nucleation-controlled polymerization. A perturbation treatment for use with a secondary pathway. Biophys J 1984 46 631-644. 

These newer PET formulations utilize not only a nucleating agent, but also a plasticizing agent [3-9], The crystallization rate of polymeric materials can be broken down into two different regions, i.e. nucleation-controlled and diffusion-controlled (Figure 15.3). In the injection molding process, hot polymer is injected... 

The values of n for LiBr and Ii2S04 he between 1 and 2, implying a two-dimensional diffusion-controlled mechanism with deceleratory nucleation. However, the liNOs process has n = 0.5, indicating that this process is completely nucleation controlled. liOH has n = 2.2, consistent with a phase boundary controlled process in two dimensions, with deceleratory nucleation again. 

The activation energies for these reactions were found to lie in the range 25 to 55 kj mol , consistent with a nucleation controlled process (diffusion con-... 

Aspartame is relatively unstable in solution, undergoing cyclisation by intramolecular self-aminolysis at pH values in excess of 2.0 [91]. This follows nucleophilic attack of the free base N-terminal amino group on the phenylalanine carboxyl group resulting in the formation of 3-methylenecarboxyl-6-benzyl-2, 5-diketopiperazine (DKP). The DKP further hydrolyses to L-aspartyl-L-phenyl-alanine and to L-phenylalanine-L-aspartate [92]. Grant and co-workers [93] have extensively investigated the solid-state stability of aspartame. At elevated temperatures, dehydration followed by loss of methanol and the resultant cyclisation to DKP were observed. The solid-state reaction mechanism was described as Prout-Tompkins kinetics (via nucleation control mechanism). 

A nucleation approach was also applied to predicting the extension of solid solubility obtained in Al-alloys by rapid solidification. In this case the competition for forming either the supersaturated A1 solid solution or the equilibrium compound was taken to be nucleation controlled (Saunders and Tsakiropoulos 1988). The model was first applied to high-pressure gas-atomised (HPGA) Al-Cr and Al—Zr alloys and was innnediately able to predict a number of important general effects, all of which are consistent with experimental observation. 

Video microscopy with crossed polarizers permits the direct and non-invasive observahon of the nucleahon and growth process for many substances, and thus the study of the hme evoluhon of the spherulite radius R t). When the growth is controlled by diffusion the radius of the spherulites increases as R t) a while when the growth is determined by a nucleation-controlled process (incorporahon of atoms or molecules to the surface of the crystalline part) the radius increases linearly with hme, R t) a t. 

Chi EY, Weickmann J, Carpenter JF, Manning MC, Randolph TW. Heterogeneous nucleation-controlled particulate formation of recombinant human platelet-activating factor acetylhydrolase in pharmaceutical formulation. J Pharm Sci 2005 94(2) 256-274. 

Price and Wendorff31 > and Jabarin and Stein 32) analyzed the solidification of cholesteryl myristate. Under equilibrium conditions it changes at 357.2 K from the isotropic to the cholesteric mesophase and at 352.9 K to the smectic mesophase (see Sect. 5.1.1). At 346.8 K the smectic liquid crystal crystallized to the fully ordered crystal. Dilatometry resulted in Avrami exponents of 2, 2, and 4 for the respective transitions. The cholesteric liquid crystal has a second transition right after the relatively quick formation of a turbid homeotropic state from the isotropic melt. It aggregates without volume change to a spherulitic texture. This process was studied by microscopy32) between 343 and 355.2 K and revealed another nucleation controlled process with an Avrami exponent of 3. 

Figure 8.8 Very large crystals such as this sample of KDP (KH2PO4) used for laser frequency doubling are produced by careful nucleation control at the metastable boundary between an unsaturated and supersaturated solution (image courtesy of the Lawrence Livermore National Laboratory).

Thermal studies of bis(2-amino-5-phenyl-l,3,4-thiadiazole)copper(II) sulfate indicate that decomposition is a nucleation-controlled process and starts at the site of defects (78MI42702). 

Figure 1. Nucleation-controlled interface reaction (NCI) and interface-controlled reaction (ICI) at various times to-tj.

IC reactions can be of two types. The nucleation of the new phase (e.g. Ni produced by the reduction of NiO) may be rate determining. In that case, separate nuclei of the new phase can be detected (Fig. 1(a)). These are called nucleation-controlled interface or NCI reactions. In other cases, all the surface of the initial solid reacts, and a continuous interface entirely covers the solid reactant. With respect to kinetics, the interfacial process entirely controls the reaction in this last case. This is an ICI reaction (Fig. 1(b)). 

Where crystalline materials are involved, a supersaturated solution is set up prior to the onset of crystallization, followed by controlled crystal nucleation, controlled crystal growth and finally controlled cessation of growth. 

Overall Crystallization Behavior. If instead of plotting the crystallization half times vs. blend composition we plot the crystallization rates for each component in the blends vs. temperature of crystallization, we obtain a series of curves which show a maximum. The right side of these curves is nucleation controlled while the left side is diffusion controlled (Figures 18 and 19). 

Alternatively, supersaturation and nucleation can be triggered by a slow ramping of the reaction temperature. Precursors are mixed at low temperature and slowly brought to the temperature at which precursor reaction and decomposition occur sufficiently quickly to result in supersaturation." Supersaturation is again relieved by a nucleation burst , after which temperature is controlled to avoid additional nucleation events, allowing monomer addition to existing nuclei to occur more rapidly than new nuclei formation. Thus, nucleation does not need to be instantaneous, but it should be a single, temporally discreet event to provide for the desired nucleation-controlled narrow size dispersions. ... 

Davey, R. Blagden, N. Righini, S. Ahson, H. Ferrari, E. Nucleation control in solution mediated polymorphic phase transformations the case of 2,6-dihydroxybenzoic acid. J. Phys. Chem. B 2002, 106, 1954-1959. 

The sweetener aspartame exists as a hemihydrate (C14H18N2O5 O.5H2O ASH), under ambient conditions. When heated, ASH converted to aspartame anhydrate (ASA), which on further heating decomposed to form a diketopiperazine (DKP) derivative. The XRD patterns of ASH, ASA, and DKP showed pronounced differences (Fig. 12). XRD was used to simultaneously quantify the (i) disappearance of ASH and appearance of ASA in the first reaction and (ii) disappearance of ASA and appearance of DKP in the second reaction. For studying the kinetics of the first reaction, the peaks unique to ASH at 15.9 and 16.4° 20 and the 17.1° 20 peak of ASA were used. For the second reaction, the sum of the integrated intensities of the peaks at 10.2, 11.0, and 11.8° 20 of ASA and the 13.0° 20 peak of DKP were used. While the dehydration of ASH appeared to follow first-order kinetics, the cyclization of ASA was a nucleation-controlled process. Figs. 13 and 14 contain the dehydration and cyclization data at 118 and 180°C respectively. Since the concentrations of the crystalline reactant as well as the product were simultaneously monitored, mass balance calculations of the crystalline phases were possible at each time point. The reaction... 

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