Migration Prediction

Reynier A., Dole R, Feigenbaum A., (2002), Integrated approach of migration prediction using numerical modelling associated to determination of key parameters. Food Additives and Contaminants, 19, pp 42-55. 

Migration predictions usually assume that radioactivity would be transferred from the geosphere to the biosphere without change 1n physical or chemical properties. Such assumptions may be valid, but verification would help assure validation of the migration predictions. Evaluations should be made on a site-specific basis for the anticipated time and place of transfer of... 

The surface diffusion of crystallites is more complicated than the diffusion of ad-atoms due to the dependence of surface diffusivity on crystallite size. A review on this subject can be found in the article by Kashchiev (1979). Theoretical models available for crystallite migration predict power or exponential dependence of the diffusivity on the size r (or the number of atoms fte making up the crystallite). The activation energy for the diffusion can be either size-dependent or size-indepen-... 

For migration predictions based upon the FDA model , the Equations described by Limm and Hollifield [10] and Begley [23] were used. Equation 14.6 contains empirical constants derived from Irganox 1010 experimental migration measurements. 

Figure 14.6 compares observed migration, predicted using the migration model for the migration of octadecyl-3-(3,5, di-ter -butyl-4-hydroxyphenyl) propionate from HDPE into olive oil and the results obtained from this investigation. Here, the data set labelled measured , the experimentally obtained data, are compared with the data set labelled Model , which have been derived using Equation 14.10. 

The one-step vinyl migration mechanism makes the same regiochemical prediction. The less substituted vinyl group should migrate, because the substituent(s) will stabilize the residual radical. 

Thermo-diffusion calculations analyze the migration of hazardous material from compartment to compartment to release in containment. These calculations use physico-chemical parameters to predict the retention of hazardous materials by filtration, deposition on cold surfaces and other retention processes in the operation. Containment event trees aid in determining the amount, duration and types of hazardous material that leaves the containment. 

In the well-known Brook rearrangment, silyl groups migrate from oxygen to carbon, but the following example is less obvious and not necessarily predictable ... 

It is of interest that the reversible migration of hydrogen between positions 1 and 2 of thi.s sj stem corre.spond to a 1,5-sigmatropie shift, a proee.s.s predicted to be favorable on theoretical grounds [R. R. Woodward and R. Hoffmann, J. Am. Ghem. Soc. 87, 2511 (1965)] and known to occur with exceptional facility (R. B. Woodward in Aromaticity, Spec. Publ. No. 21, p. 217. The Chemical Society, London, 1967). 

The stereochemical course of the Beckmann rearrangement often allows for the prediction of the reaction product to be obtained in general the substituent R anti to either the hydroxy or the leaving group will migrate ... 

Natural colloid particles in aqueous systems, such as clay particles, silica, etc. may serve as carriers of ionic species that are being sorbed on the particulates (pseudocolloids). It seems evident that the formation and transport properties of plutonium pseudocolloids can not yet be described in quantitative terms or be well predicted. This is an important area for further studies, since the pseudocolloidal transport might be the dominating plutonium migration mechanism in many environmental waters. 

If the reaction is carried out with ketone labeled in the C=0 group with the first pathway predicts that the product will contain all the " C in the C=0 carbon, while in the second pathway the label will be in the a carbon (demonstrating migration of oxygen). The results of such experiments have shown that in some cases only the C=0 carbon was labeled, in other cases only the a carbon, while in still others both carbons bore the label, indicating that in these cases both pathways were in operation. With a-hydroxy aldehydes and ketones, the process may stop after only one migration (this is called the a-ketol rearrangement). 

As expected, the Mobius-Hiickel method leads to the same predictions. Here we look at the basis set of orbitals shown in G and H for [1,3] and [1,5] rearrangements, respectively, A [1,3] shift involves four electrons, so an allowed thermal pericyclic reaction must be a Mobius system (p. 1070) with one or an odd number of sign inversions. As can be seen in G, only an antarafacial migration can achieve this. A [1,5] shift, with six electrons, is allowed thermally only when it is a Hiickel system with zero or an even number of sign inversions hence it requires a suprafacial migration. 

Note that the first example bears out the stereochemical prediction made earlier. Only the two isomers shown were formed. In the second example, migration can > continue around the ring. Migrations of this kind are called circumambulatory rearrangements. Such migrations are known for cyclopentadiene, pyrrole, and phosphole derivatives.[1,5] Hydrogen shifts are also known with vinyl aziridines." ... 

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