Nucleation parameters

Unfortunately, both primary nucleation parameters cannot be predicted a priori as yet and in practice the nucleation rate must be measured and correlated empirically for each system. 

Engel et al.92) have estimated the nucleation parameter for H(Pro-Pro-Gly) OH by computing AG° and AS° with Eq. (5) and reported melting temperatures Tm and AH0 values determined calorimetrically. Utilizing the chain length dependence, they obtained the following parameters (in diluted acetic acid at 25 °C n = 5, 10, 14.15) ... 

The nucleation parameters have to be determined with the help of the chain length dependence of Tm, since no calorimetric data are available. Using Eqs. (2, 7, 8) we obtain... 

Figure 56. Plot of (a) 1 -1) N/tf% vs. t)c and (b) tjN vs. tjc for polypyrrole films submitted to potential sweeps, from which the nucleation parameters (z and / ) can be obtained. (Reprinted from T. F. Otero, H.-J. Grande, andJ. Rodriguez, J. Phys. Chem. 101,8525,1997, Figs. 3-11, 13. Copyright 1997. Reproduced with permission from the American Chemical Society.)...

Several investigators have offered various techniques for estimating crystallization growth and nucleation parameters. Parameters such as kg, 6, and ki are the ones usually estimated. Often different results are presented for identical systems. These discrepancies are discussed by several authors (13,14). One weakness of most of these schemes is that the validity of the parameter estimates, i.e., the confidence in the estimates, is not assessed. This section discusses two of the more popular routines to evaluate kinetic parameters and introduces a method that attempts to improve the parameter inference and provide a measure of the reliability of the estimates. 

An alternative scheme, proposed by Garside et al. (16,17), uses the dynamic desupersaturation data from a batch crystallization experiment. After formulating a solute mass balance, where mass deposition due to nucleation was negligible, expressions are derived to calculate g and kg in Equation 3 explicitly. Estimates of the first and second derivatives of the transient desupersaturation curve at time zero are required. The disadvantages of this scheme are that numerical differentiation of experimental data is quite inaccurate due to measurement noise, the nucleation parameters are not estimated, and the analysis is invalid if nucleation rates are significant. Other drawbacks of both methods are that they are limited to specific model formulations, i.e., growth and nucleation rate forms and crystallizer configurations. 

First, for the case in which only solute concentration measurements are available, pseudo-experimental data are simulated and used in the parameter estimation scheme. Even with noise-free data, the recovered parameters differ greatly from the true parameters and the uncertainties of the nucleation parameters are large. This indicates that there exists a large set of quite different b and ki, pairs that would lead to very similar solute concentration profiles. The insensitivity of the objective function to the nucleation parameters can be attributed to the fact that the mass of a nucleated particle is almost negligible and the change in the solute concentration is primarily due to seed growth. 

It is shown that while solute concentration data can be used to estimate the kinetic growth parameters, information about the CSD is necessary to evaluate the nucleation parameters. The fraction of light obscured by an illuminated sample of crystals provides a measure of the second moment of the CSD. Numerical and experimental studies demonstrate that all of the kinetic parameters can be identified by using the obscuration measurement along with the concentration measurement. It is also shown that characterization of the crystal shape is very important when evaluating CSD information from light scattering instruments. 

This removal function gives rise to a discontinuity in the population density at the cutsize of the fines. The nucleation parameters are given in equation 19 In Figure 3 the responses are shown of the population density at 120 pm and of the growth rate after a step in the heat input to the crystallizer from 120 to I70 kW for three simulation edgorithms. The cut-size of the fines was 100 pm, a size dependent growth rate was used as described by Equation 4 with a= -250 and the number of grid points was kOO. When the simulation was performed with the method of lines, severe oscillations are present in the response of the population density at 120 pm, which dampen out rather slowly. Also the response of the Lax-Wendroff method shows these oscillations to a lesser extend. 

Helix initiation (represented by the helix nucleation parameter a) in a random coil conformation is the slowest and energetically least favored step, whereas subsequent growth of the helix nucleus (represented by the helix propagation factor, s) is rapid and relatively favored. 83 ... 

After the stochastic nature of hydrate crystal nucleation, the quantification of the hydrate growth rate provides some relief for modeling hydrate formation. However, only a limited amount of accurate data exist for the crystal growth rate after nucleation. Most of the nucleation parameters (displacement from equilibrium conditions, surface area, agitation, water history, and gas composition) continue to be important in hydrate growth. 

ECR-1 is a new 12-ring zeolite which crystallizes as a boundary phase between the crystallization fields of mazzite and mordenite when bis(2-hydroxyethyl) dimethyl- ammonium or bis(2-hydroxypropyl) dimethyl ammonium cations are present in the synthesis gels. Synthesis studies show that cocrystallization of these latter zeolites is rare and that nucleation parameters may dominate compositional stability. 

Two GaN layers are grown on the CMP porous SiC substrates with different nucleation parameters, as listed in Table 6.5. Before growth, the CMP porous SiC substrates are cleaned with standard RCA procedure followed by HF-dip to remove the surface oxide. For CVD1456, a 100 nm thick GaN nucleation layer is deposited at 930 °C and 30 Torr, followed by a 3 pm thick GaN epilayer grown at 76 Torr and 1030 °C. For CVD1489, a 600 nm thick GaN nucleation layer is deposited at 960 °C and 200 Torr, followed by a 3 pm thick GaN epilayer grown with the same parameters as those of CVD1456. 

The partition function for the zipper model is derived from the basic relationships of the noncooperative model. The only difference is the statistical weight for the first step Wi that must include a nucleation parameter, a to represent the probability (lower probability therefore a < 1) for initiating the transition. Therefore the statistical weight for the state / = 1 is w, = as. Two possibilities exist for the next step of the transition. In one case,... 

In applying the zipper model, the transitions are characterized by the nucleation parameter o and propagation parameter s. 

Kishore, K. and Vasanthakumari, R. (1988) Nucleation parameters for polymer crystallization from non-isothermal thermal analysis. Colloid Polym. ScL, 266 (11), 999-1002. 

Analysis of ln(7) versus l/ r] relationships from experimental data allows to determine the nucleation parameters n and AG for the critical nucleus, through the relation [52]... 

Figure 1.12 plots z, 0, v, and the mean helix length f = 6/v as functions of the temperature. Temperature is measured in terms of in s (T). The CH transition takes place at around Ins = 0. The transition becomes sharper for a smaller nucleation parameter a (stronger cooperativity). The transition also becomes sharper with molecular weight, and becomes a real phase transition with discontinuous 6 in the limit of infinite chain length. 

Note that in this oversimplified model, all the details of the mixing are lumped into the nucleation parameter c, while the chemistry is summed up by the polymerization addition rate B. 

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