Nucleation constant

There are two hmiting cases for Eq. (7.3) for the initial stages of nucleation (low t value). Eirst, for large nucleation constant A, Eq. (7.3) reduces to... 

It should be noted here that this system is not completely homogeneous but involves some element of a heterogenous system, since high concentrations of cations and anions are directly reacted with each other at an extremely high supersaturation so that nucleation constantly occurs throughout the whole process. If the dissolu-... 

The secondary nucleation constant was very low (10-3) suggesting that no secondary nucleation exists, and that all particles were of the same size and grow at the same rate. Therefore, Skovborg and Rasmussen suggested that the crystallization population balance could be removed from the model. 

Let us start with the nucleated assembly that is not self-catalyzed. It turns out useful to distinguish between the mean aggregation number of all the material in the solution, N, from that in which only the activated species is considered and that we denote by Na. If we define the equilibrium constant K = exp [—.%] with g as the binding free energy, and introduce the nucleation constant Ka = exp[—/3ya], then under conditions of thermodynamic equilibrium, mass action gives (Aggeli, 2001 Ciferri, 2005 Nyrkova et al., 2000 Tobolsky and Eisenberg, 1960)... 

Figure 12. Quantitative comparison of the reduction (a = fraction reduced) of bulk and silica-supported NiO at 538 K in a flow of pure H2 [78]. The parameter A characterizes the relative rates of nucleation (constant k ) and interface progress (constant k,). Assuming spherical particles, A corresponds to the average number of nuclei being formed on each NiO particle in the time necessary for the interface to travel a distance equal to the radius a of the particle [7] A = 4nk x k iai.

JJ = activation energy for diffusion T0c = temperature where flow stops Tm 0 = equilibrium melting temperature Kg = nucleation constant. 

The first term represents the diffusion of chains to the growth front while the second is related to the secondary nucleation barrier. Go represents a preexponential factor, U is the activation energy for chain mobility, R is the gas constant, Tc is the isothermal crystallization temperature and Ar=T — TV is the supercooling (T is the equilibrium melting temperature). Too is the temperature where viscous flow ceases (AT —30A) and/is a temperature correction factor defined as 2TV / (T -)- TV), while Kg is the nucleation constant (which is proportional to the energy barrier for secondary nucleation) given by ... 

Nucleation activity and nucleation constant ate numerical expressions usefiil in comparison of the effects of different nucleating agents. The nucleation activity expression, developed by Dobreva and Gutzow, - is as follows ... 

The nucleation constant, Kg is related to the product of lateral and folding surface free energy and it represents the free energy which is needed in order to form a nucleirs of a critical size." For neat PP, nucleation constant was 1.95x10 and 0.433x10 for P-nucleated polymer with proprietary nucleating agent." ... 

Figure 6.3 shows how different concentrations of radiation vulcanized polybutadiene rubber influences nucleation constant of polypropylene. The use of polybutadiene rubber promoted the crystals to become perfect and resulted in a larger crystallite size, which caused nucleation constant to decrease in value. This is compatible with Hoffman theory which predicts lower value of nucleation constant for neat PP because of heterogeneous nucleation effect of addition of vulcanized polybutadiene robber. Figure 6.4 shows the effect of exfoliated graphite on nucleation constant of PP com-... 

Figure 6.3. Nucleation constant, Kg, of PP containing variable amounts of radiation vulcanized polybutadiene rubber. [Data, from Abadcbi, M R Jalali-Arani, A,...

Figure 6.4. Effect of exfoliated graphite on nucleation constant of polypropylene. [Data from Ferreira, C I Dal Castel, C Oviedo, MAS Mauler, R S, Thermochim. Acta, SS3, 40-48, 2013.1...

Crystallization of poly(P-hydroxybutyrate) was enhanced by cellulose crystals. Nucleation constant for pure PHB was 4.99x10 and 4.88x10 for PHB containing 2 wt%... 

Nucleation constant increased with addition of acetaminophen to poly(ethylene oxide) because the chain folding in PEO was hindered by the presence of acetaminophen... 

The fundamental parameters, namely a, the helix nucleation constant, AHq, the enthalpy change on helix formation, and s (0°C), the average helix propagation parameter at 0°C, were all determined by Scholtz et al. by fitting the theoretical transition curve to the experimental ones [72],... 

This expression, which does not depend on the reactivity of growth, makes it possible to recognize such a law, and thus, the calculation of the nucleation constant g. deduction of growth reactivity while substituting into [A9.19] or [A9.20],... 

We notice that expressions [A.9.25] and [A.9.26] do not depend on the nucleation constant and should thus allow calculating growth reactivity directly. It will be noted, however, that this is realizable only if the approximation applies for short times (large under the terms of Remark 2 of section A.9.1.2. 

We thus obtain power in time laws with powers on the rate different from 3. It will be noted that these laws do not make it possible to separately calculate the growth reactivity and the nucleation constant starting from the experiment. On the other hand, we can determine q, which gives indications on the structure of the mechanism of nucleatioa... 

We used the nucleation constant speed law to cany out calculation of course, other laws can be obtained using equations [A.9.9] and [A.9.10] and other expressions derived from the models of Avrami and Erofeev can be obtained. 

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