Nucleation: induction period

There has long been an interest in the potential effects on the nucleation process of externally applied electrostatic or magnetic fields. There is evidence that both homogeneous nucleation and the duration of the nucleation induction period (section 5.5) can be influenced. However, the relevance of experimental data, obtained from small-scale investigations under controlled laboratory conditions, to bulk solutions in flow or agitated conditions normally encountered in industrial practice (section 9.5) is still the subject of considerable controversy (Sohnel and Mullin, 1988c). A detailed account of recent theor-... 

Gypsum Nucleation Induction Period and the Surface Free Energy... 

As discussed in section 2.3, the surface free energy of a crystal can be obtained by measuring the nucleation induction period at various supersaturation conditions. He et al. (1994a) investigated gypsum nucleation with NaCl concentration vaiying from 0 to 6 mol/kg... 

Experimental results are in general conformity with the Avrami equation, but the interpretation of various observations is still complicated in many instances. One intriguing observation is that the induction period for nucleation is inversely proportional to the length of time the liquid is held in the liquid state after previous melting. This dependence on prior history may be qualitatively understood... 

Characteristic features of a—time curves for reactions of solids are discussed with reference to Fig. 1, a generalized reduced-time plot in which time values have been scaled to t0.s = 1.00 when a = 0.5. A is an initial reaction, sometimes associated with the decomposition of impurities or unstable superficial material. B is the induction period, usually regarded as being terminated by the development of stable nuclei (often completed at a low value of a). C is the acceleratory period of growth of such nuclei, perhaps accompanied by further nucleation, and which extends to the... 

The Avrami—Erofe ev equation, eqn. (6), has been successfully used in kinetic analyses of many solid phase decomposition reactions examples are given in Chaps. 4 and 5. For no substance, however, has this expression been more comprehensively applied than in the decomposition of ammonium perchlorate. The value of n for the low temperature reaction of large crystals [268] is reduced at a 0.2 from 4 to 3, corresponding to the completion of nucleation. More recently, the same rate process has been the subject of a particularly detailed and rigorous re-analysis by Jacobs and Ng [452] who used a computer to optimize curve fitting. The main reaction (0.01 < a < 1.0) was well described by the exact Avrami equation, eqn. (4), and kinetic interpretation also included an examination of the rates of development and of multiplication of nuclei during the induction period (a < 0.01). The complete kinetic expressions required to describe quantitatively the overall reaction required a total of ten parameters. 

Reactions of the general type A + B -> AB may proceed by a nucleation and diffusion-controlled growth process. Welch [111] discusses one possible mechanism whereby A is accepted as solid solution into crystalline B and reacts to precipitate AB product preferentially in the vicinity of the interface with A, since the concentration is expected to be greatest here. There may be an initial induction period during solid solution formation prior to the onset of product phase precipitation. Nuclei of AB are subsequently produced at surfaces of particles of B and growth may occur with or without maintained nucleation. 

It is seen from these examples that, in appropriate systems, it is possible to introduce product into the reactant in such a manner that an effective reaction interface is established before the reactant has been heated to the decomposition temperature. Accordingly, the induction period is removed and the acceleratory process may be less pronounced or eliminated altogether. Artificial nucleation results in changes in reaction geometry with consequent variation in the a—time curve shape and the maximum value of da/dt but does not enhance the rate of interface advance. We have found no studies in which increases in reaction rates were quantitatively correlated with the increased interfacial area and/or density of nucleation which resulted from the reactant pretreatment. 

Direct Evidence of Nucleation During the Induction Period. 148... 

Extended chain crystal (ECC) Folded chain crystal (FCC) Growth Growth rate Induction period Melt relaxation Molecular weight Nucleation Nucleation rate Nucleus Optical microscope (OM) Polyethylene Polymer Power law ... 

The purpose of this review is to solve these two unresolved problems by confirming the nucleation during the induction period of nucleation and the important role of the topological nature with experimental facts regarding the molecular weight (M)- or number density of the entanglement (independence of nucleation and growth rates. 

The primary nucleation process is divided into two periods in CNT one is the so called induction period and the other is the steady (or stationary) nucleation period (Fig. 2) [16,17]. It has been proposed by CNT that small (nanometer scale) nuclei will be formed spontaneously by thermal fluctuation after quenching into the supercooled melt, some of the nuclei could grow into a critical nucleus , and some of the critical nuclei will finally survive into macroscopic crystals. The induction period is defined as the period where the nucleation rate (I) increases with time f, whereas the steady period is that where I nearly saturates to a constant rate (fst). It should be noted that I is a function of N and t,I = I(N, t). In Fig. 2, N and N mean the size of a nucleus and that of the critical nucleus, respectively. The size N is defined... 

Fig. 2 Illustration of the induction and the steady (stationary) periods during the nucleation process. Small clusters exist in the supercooled melt at t = 0. During the induction period (t < r,), isolated nuclei of size N, smaller than the critical nuclei (named nanonuclei or embryo), are formed. The nuclei grow larger and larger with increase of time and some of them attain a much larger size than the critical size, N ...

Direct evidence of nucleation during the induction period will also solve a recent argument within the field of polymer science as to whether the mechanism of the induction of polymers is related to the nucleation process or to the phase separation process (including spinodal decomposition). The latter was proposed by Imai et al. based on SAXS observation of so-called cold crystallization from the quenched glass (amorphous state) of polyethylene terephthalate) (PET) [19]. They supposed that the latter mechanism could be expanded to the usual melt crystallization, but there is no experimental support for the supposition. Our results will confirm that the nucleation mechanism is correct, in the case of melt crystallization. 

The purpose of this section is to present direct evidence of nucleation during the induction period by means of synchrotron small angle X-ray scattering (SAXS). In the classical nucleation theory (CNT), the number density distribution function of nuclei of size N at time t, f(N, t), is expected to increase with an increase of t during the induction period and saturates to a steady f(N, t),fst(N) in the steady period. The change off(N, t) should correspond to that of the scattering intensity of SAXS. 

As Ix(Nucleus) increases with an increase of the number density of nuclei, this clearly confirmed that the number density of nuclei increases during the induction period. Thus, it is concluded that the nucleation during the induction period is directly confirmed experimentally for the first time. 

This means that the lamellae start stacking after ri(SAXS). Therefore, nucleation can be observed without any disturbance of the stacked lamellae during the induction period. 

Fig. 12 Comparison of time evolution of 7x(Nucleus) for PE with NA and that of 7X(L1) for PE without NA. Nucleation during induction period was clearly confirmed. Nucleation was observed only when NA was mixed. Without mixing NA, only formation of stacked lamellae was observed... 

Lamellae start stacking much later than nuclei start developing. The onset time of stacked lamellae was similar to the induction time. Therefore, nucleation during the induction period can be observed without being affected by the stacked lamellae. 

Keywords Induction period Melt and glass crystallization Nucleation and growth Optical microscopy Scattering techniques Spinodal decomposition... 

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